Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 73.6% → 82.2%

Time: 42.5s

Alternatives: 32

Speedup: 0.5×

• 57.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\\ t_2 := b \cdot \left(t \cdot i - c \cdot z\right)\\ t_3 := j \cdot \left(a \cdot c - i \cdot y\right) - \left(x \cdot \left(a \cdot t - z \cdot y\right) - t_2\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* j i))) (* a (- (* x t) (* j c)))))
        (t_2 (* b (- (* t i) (* c z))))
        (t_3 (- (* j (- (* a c) (* i y))) (- (* x (- (* a t) (* z y))) t_2))))
   (if (<= t_3 (- INFINITY)) (+ t_1 t_2) (if (<= t_3 INFINITY) t_3 t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)));
	double t_2 = b * ((t * i) - (c * z));
	double t_3 = (j * ((a * c) - (i * y))) - ((x * ((a * t) - (z * y))) - t_2);
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_1 + t_2;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)));
	double t_2 = b * ((t * i) - (c * z));
	double t_3 = (j * ((a * c) - (i * y))) - ((x * ((a * t) - (z * y))) - t_2);
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1 + t_2;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)))
	t_2 = b * ((t * i) - (c * z))
	t_3 = (j * ((a * c) - (i * y))) - ((x * ((a * t) - (z * y))) - t_2)
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_1 + t_2
	elif t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(j * i))) - Float64(a * Float64(Float64(x * t) - Float64(j * c))))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(c * z)))
	t_3 = Float64(Float64(j * Float64(Float64(a * c) - Float64(i * y))) - Float64(Float64(x * Float64(Float64(a * t) - Float64(z * y))) - t_2))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(t_1 + t_2);
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)));
	t_2 = b * ((t * i) - (c * z));
	t_3 = (j * ((a * c) - (i * y))) - ((x * ((a * t) - (z * y))) - t_2);
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_1 + t_2;
	elseif (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(j * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(N[(a * t), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$3, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < -inf.0

   1. Initial program 83.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 83.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 83.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 83.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 83.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 92.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 92.3%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   if -inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 95.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 18.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 29.7%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in b around 0 51.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) + a \cdot \left(c \cdot j - t \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(a \cdot c - i \cdot y\right) - \left(x \cdot \left(a \cdot t - z \cdot y\right) - b \cdot \left(t \cdot i - c \cdot z\right)\right) \leq -\infty:\\ \;\;\;\;\left(y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{elif}\;j \cdot \left(a \cdot c - i \cdot y\right) - \left(x \cdot \left(a \cdot t - z \cdot y\right) - b \cdot \left(t \cdot i - c \cdot z\right)\right) \leq \infty:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) - \left(x \cdot \left(a \cdot t - z \cdot y\right) - b \cdot \left(t \cdot i - c \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\\ \end{array} \]

Alternative 2: 75.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq 3 \cdot 10^{+55}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - i \cdot y, x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j 3e+55)
   (+
    (- (* y (- (* x z) (* j i))) (* a (- (* x t) (* j c))))
    (* b (- (* t i) (* c z))))
   (fma
    j
    (- (* a c) (* i y))
    (- (* x (- (* z y) (* a t))) (* b (fma z c (* t (- i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= 3e+55) {
		tmp = ((y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)))) + (b * ((t * i) - (c * z)));
	} else {
		tmp = fma(j, ((a * c) - (i * y)), ((x * ((z * y) - (a * t))) - (b * fma(z, c, (t * -i)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= 3e+55)
		tmp = Float64(Float64(Float64(y * Float64(Float64(x * z) - Float64(j * i))) - Float64(a * Float64(Float64(x * t) - Float64(j * c)))) + Float64(b * Float64(Float64(t * i) - Float64(c * z))));
	else
		tmp = fma(j, Float64(Float64(a * c) - Float64(i * y)), Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(b * fma(z, c, Float64(t * Float64(-i))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, 3e+55], N[(N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(j * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c + N[(t * (-i)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < 3.00000000000000017e55

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 84.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 86.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   if 3.00000000000000017e55 < j

   1. Initial program 79.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 89.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

      5. fma-neg 91.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\mathsf{fma}\left(z, c, -t \cdot i\right)}\right) \]

      6. distribute-lft-neg-out 91.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{\left(-t\right) \cdot i}\right)\right) \]

      7. *-commutative 91.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \mathsf{fma}\left(z, c, \color{blue}{i \cdot \left(-t\right)}\right)\right) \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \mathsf{fma}\left(z, c, i \cdot \left(-t\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq 3 \cdot 10^{+55}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - i \cdot y, x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \mathsf{fma}\left(z, c, t \cdot \left(-i\right)\right)\right)\\ \end{array} \]

Alternative 3: 75.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{if}\;j \leq 5 \cdot 10^{+55}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - i \cdot y, x \cdot \left(z \cdot y - a \cdot t\right) + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* c z)))))
   (if (<= j 5e+55)
     (+ (- (* y (- (* x z) (* j i))) (* a (- (* x t) (* j c)))) t_1)
     (fma j (- (* a c) (* i y)) (+ (* x (- (* z y) (* a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (c * z));
	double tmp;
	if (j <= 5e+55) {
		tmp = ((y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)))) + t_1;
	} else {
		tmp = fma(j, ((a * c) - (i * y)), ((x * ((z * y) - (a * t))) + t_1));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(c * z)))
	tmp = 0.0
	if (j <= 5e+55)
		tmp = Float64(Float64(Float64(y * Float64(Float64(x * z) - Float64(j * i))) - Float64(a * Float64(Float64(x * t) - Float64(j * c)))) + t_1);
	else
		tmp = fma(j, Float64(Float64(a * c) - Float64(i * y)), Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) + t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, 5e+55], N[(N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(j * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if j < 5.00000000000000046e55

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 79.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 84.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 86.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   if 5.00000000000000046e55 < j

   1. Initial program 79.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 89.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \]

      5. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) \]

      6. *-commutative 89.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq 5 \cdot 10^{+55}:\\ \;\;\;\;\left(y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\right) + b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - i \cdot y, x \cdot \left(z \cdot y - a \cdot t\right) + b \cdot \left(t \cdot i - c \cdot z\right)\right)\\ \end{array} \]

Alternative 4: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - i \cdot y\right) - \left(x \cdot \left(a \cdot t - z \cdot y\right) - b \cdot \left(t \cdot i - c \cdot z\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (-
          (* j (- (* a c) (* i y)))
          (- (* x (- (* a t) (* z y))) (* b (- (* t i) (* c z)))))))
   (if (<= t_1 INFINITY)
     t_1
     (- (* y (- (* x z) (* j i))) (* a (- (* x t) (* j c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (i * y))) - ((x * ((a * t) - (z * y))) - (b * ((t * i) - (c * z))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (i * y))) - ((x * ((a * t) - (z * y))) - (b * ((t * i) - (c * z))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (i * y))) - ((x * ((a * t) - (z * y))) - (b * ((t * i) - (c * z))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(i * y))) - Float64(Float64(x * Float64(Float64(a * t) - Float64(z * y))) - Float64(b * Float64(Float64(t * i) - Float64(c * z)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(j * i))) - Float64(a * Float64(Float64(x * t) - Float64(j * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (i * y))) - ((x * ((a * t) - (z * y))) - (b * ((t * i) - (c * z))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(N[(a * t), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(j * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 92.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 18.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 29.7%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in b around 0 51.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) + a \cdot \left(c \cdot j - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(a \cdot c - i \cdot y\right) - \left(x \cdot \left(a \cdot t - z \cdot y\right) - b \cdot \left(t \cdot i - c \cdot z\right)\right) \leq \infty:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) - \left(x \cdot \left(a \cdot t - z \cdot y\right) - b \cdot \left(t \cdot i - c \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\\ \end{array} \]

Alternative 5: 69.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right)\\ t_3 := t_2 + b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-181}:\\ \;\;\;\;t_2 + j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* j i))) (* a (- (* x t) (* j c)))))
        (t_2 (* x (- (* z y) (* a t))))
        (t_3 (+ t_2 (* b (- (* t i) (* c z))))))
   (if (<= b -2.5e+29)
     t_3
     (if (<= b -4.3e-281)
       t_1
       (if (<= b 1.2e-181)
         (+ t_2 (* j (- (* a c) (* i y))))
         (if (<= b 1.65e-52) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)));
	double t_2 = x * ((z * y) - (a * t));
	double t_3 = t_2 + (b * ((t * i) - (c * z)));
	double tmp;
	if (b <= -2.5e+29) {
		tmp = t_3;
	} else if (b <= -4.3e-281) {
		tmp = t_1;
	} else if (b <= 1.2e-181) {
		tmp = t_2 + (j * ((a * c) - (i * y)));
	} else if (b <= 1.65e-52) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)))
    t_2 = x * ((z * y) - (a * t))
    t_3 = t_2 + (b * ((t * i) - (c * z)))
    if (b <= (-2.5d+29)) then
        tmp = t_3
    else if (b <= (-4.3d-281)) then
        tmp = t_1
    else if (b <= 1.2d-181) then
        tmp = t_2 + (j * ((a * c) - (i * y)))
    else if (b <= 1.65d-52) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)));
	double t_2 = x * ((z * y) - (a * t));
	double t_3 = t_2 + (b * ((t * i) - (c * z)));
	double tmp;
	if (b <= -2.5e+29) {
		tmp = t_3;
	} else if (b <= -4.3e-281) {
		tmp = t_1;
	} else if (b <= 1.2e-181) {
		tmp = t_2 + (j * ((a * c) - (i * y)));
	} else if (b <= 1.65e-52) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)))
	t_2 = x * ((z * y) - (a * t))
	t_3 = t_2 + (b * ((t * i) - (c * z)))
	tmp = 0
	if b <= -2.5e+29:
		tmp = t_3
	elif b <= -4.3e-281:
		tmp = t_1
	elif b <= 1.2e-181:
		tmp = t_2 + (j * ((a * c) - (i * y)))
	elif b <= 1.65e-52:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(j * i))) - Float64(a * Float64(Float64(x * t) - Float64(j * c))))
	t_2 = Float64(x * Float64(Float64(z * y) - Float64(a * t)))
	t_3 = Float64(t_2 + Float64(b * Float64(Float64(t * i) - Float64(c * z))))
	tmp = 0.0
	if (b <= -2.5e+29)
		tmp = t_3;
	elseif (b <= -4.3e-281)
		tmp = t_1;
	elseif (b <= 1.2e-181)
		tmp = Float64(t_2 + Float64(j * Float64(Float64(a * c) - Float64(i * y))));
	elseif (b <= 1.65e-52)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)));
	t_2 = x * ((z * y) - (a * t));
	t_3 = t_2 + (b * ((t * i) - (c * z)));
	tmp = 0.0;
	if (b <= -2.5e+29)
		tmp = t_3;
	elseif (b <= -4.3e-281)
		tmp = t_1;
	elseif (b <= 1.2e-181)
		tmp = t_2 + (j * ((a * c) - (i * y)));
	elseif (b <= 1.65e-52)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(j * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e+29], t$95$3, If[LessEqual[b, -4.3e-281], t$95$1, If[LessEqual[b, 1.2e-181], N[(t$95$2 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e-52], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.5e29 or 1.64999999999999998e-52 < b

   1. Initial program 80.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 80.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 80.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 80.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 80.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 75.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   if -2.5e29 < b < -4.30000000000000023e-281 or 1.2000000000000001e-181 < b < 1.64999999999999998e-52

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 83.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 86.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in b around 0 86.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) + a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -4.30000000000000023e-281 < b < 1.2000000000000001e-181

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 74.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 74.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 74.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 74.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 80.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) + b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-281}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) + j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-52}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) + b \cdot \left(t \cdot i - c \cdot z\right)\\ \end{array} \]

Alternative 6: 69.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) + b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-182}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + \left(x \cdot \left(z \cdot y\right) - x \cdot \left(a \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* j i))) (* a (- (* x t) (* j c)))))
        (t_2 (+ (* x (- (* z y) (* a t))) (* b (- (* t i) (* c z))))))
   (if (<= b -3.2e+29)
     t_2
     (if (<= b -4e-281)
       t_1
       (if (<= b 8.5e-182)
         (+ (* j (- (* a c) (* i y))) (- (* x (* z y)) (* x (* a t))))
         (if (<= b 9e-53) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)));
	double t_2 = (x * ((z * y) - (a * t))) + (b * ((t * i) - (c * z)));
	double tmp;
	if (b <= -3.2e+29) {
		tmp = t_2;
	} else if (b <= -4e-281) {
		tmp = t_1;
	} else if (b <= 8.5e-182) {
		tmp = (j * ((a * c) - (i * y))) + ((x * (z * y)) - (x * (a * t)));
	} else if (b <= 9e-53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)))
    t_2 = (x * ((z * y) - (a * t))) + (b * ((t * i) - (c * z)))
    if (b <= (-3.2d+29)) then
        tmp = t_2
    else if (b <= (-4d-281)) then
        tmp = t_1
    else if (b <= 8.5d-182) then
        tmp = (j * ((a * c) - (i * y))) + ((x * (z * y)) - (x * (a * t)))
    else if (b <= 9d-53) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)));
	double t_2 = (x * ((z * y) - (a * t))) + (b * ((t * i) - (c * z)));
	double tmp;
	if (b <= -3.2e+29) {
		tmp = t_2;
	} else if (b <= -4e-281) {
		tmp = t_1;
	} else if (b <= 8.5e-182) {
		tmp = (j * ((a * c) - (i * y))) + ((x * (z * y)) - (x * (a * t)));
	} else if (b <= 9e-53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)))
	t_2 = (x * ((z * y) - (a * t))) + (b * ((t * i) - (c * z)))
	tmp = 0
	if b <= -3.2e+29:
		tmp = t_2
	elif b <= -4e-281:
		tmp = t_1
	elif b <= 8.5e-182:
		tmp = (j * ((a * c) - (i * y))) + ((x * (z * y)) - (x * (a * t)))
	elif b <= 9e-53:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(j * i))) - Float64(a * Float64(Float64(x * t) - Float64(j * c))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) + Float64(b * Float64(Float64(t * i) - Float64(c * z))))
	tmp = 0.0
	if (b <= -3.2e+29)
		tmp = t_2;
	elseif (b <= -4e-281)
		tmp = t_1;
	elseif (b <= 8.5e-182)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(i * y))) + Float64(Float64(x * Float64(z * y)) - Float64(x * Float64(a * t))));
	elseif (b <= 9e-53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (j * i))) - (a * ((x * t) - (j * c)));
	t_2 = (x * ((z * y) - (a * t))) + (b * ((t * i) - (c * z)));
	tmp = 0.0;
	if (b <= -3.2e+29)
		tmp = t_2;
	elseif (b <= -4e-281)
		tmp = t_1;
	elseif (b <= 8.5e-182)
		tmp = (j * ((a * c) - (i * y))) + ((x * (z * y)) - (x * (a * t)));
	elseif (b <= 9e-53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(j * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.2e+29], t$95$2, If[LessEqual[b, -4e-281], t$95$1, If[LessEqual[b, 8.5e-182], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision] - N[(x * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-53], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.19999999999999987e29 or 8.9999999999999997e-53 < b

   1. Initial program 80.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 80.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 80.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 80.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 80.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 75.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   if -3.19999999999999987e29 < b < -4.0000000000000001e-281 or 8.5000000000000001e-182 < b < 8.9999999999999997e-53

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 83.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 86.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in b around 0 86.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) + a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -4.0000000000000001e-281 < b < 8.5000000000000001e-182

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 74.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 74.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 74.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 74.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 80.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
   5. Step-by-step derivation

      1. cancel-sign-sub-inv 80.5%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \color{blue}{\left(y \cdot z + \left(-a\right) \cdot t\right)} \]

      2. distribute-rgt-in 80.5%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(\left(-a\right) \cdot t\right) \cdot x\right)} \]

      3. *-commutative 80.5%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(\color{blue}{\left(z \cdot y\right)} \cdot x + \left(\left(-a\right) \cdot t\right) \cdot x\right) \]

      4. distribute-lft-neg-in 80.5%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(z \cdot y\right) \cdot x + \color{blue}{\left(-a \cdot t\right)} \cdot x\right) \]

      5. distribute-rgt-neg-in 80.5%

         \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \left(\left(z \cdot y\right) \cdot x + \color{blue}{\left(a \cdot \left(-t\right)\right)} \cdot x\right) \]

   6. Applied egg-rr 80.5%

      \[\leadsto j \cdot \left(a \cdot c - i \cdot y\right) + \color{blue}{\left(\left(z \cdot y\right) \cdot x + \left(a \cdot \left(-t\right)\right) \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+29}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) + b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-281}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-182}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + \left(x \cdot \left(z \cdot y\right) - x \cdot \left(a \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-53}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right) - a \cdot \left(x \cdot t - j \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) + b \cdot \left(t \cdot i - c \cdot z\right)\\ \end{array} \]

Alternative 7: 61.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z\right)\\ t_2 := j \cdot \left(a \cdot c - i \cdot y\right)\\ t_3 := t_2 + t \cdot \left(i \cdot b\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-21}:\\ \;\;\;\;t_2 + x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-228}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-306}:\\ \;\;\;\;t_2 - z \cdot \left(c \cdot b\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x (- (* z y) (* a t))) (* b (* c z))))
        (t_2 (* j (- (* a c) (* i y))))
        (t_3 (+ t_2 (* t (* i b)))))
   (if (<= x -4e+85)
     t_1
     (if (<= x -1e-21)
       (+ t_2 (* x (* z y)))
       (if (<= x -3.6e-228)
         t_3
         (if (<= x 6.6e-306)
           (- t_2 (* z (* c b)))
           (if (<= x 2.5e-83) t_3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((z * y) - (a * t))) - (b * (c * z));
	double t_2 = j * ((a * c) - (i * y));
	double t_3 = t_2 + (t * (i * b));
	double tmp;
	if (x <= -4e+85) {
		tmp = t_1;
	} else if (x <= -1e-21) {
		tmp = t_2 + (x * (z * y));
	} else if (x <= -3.6e-228) {
		tmp = t_3;
	} else if (x <= 6.6e-306) {
		tmp = t_2 - (z * (c * b));
	} else if (x <= 2.5e-83) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * ((z * y) - (a * t))) - (b * (c * z))
    t_2 = j * ((a * c) - (i * y))
    t_3 = t_2 + (t * (i * b))
    if (x <= (-4d+85)) then
        tmp = t_1
    else if (x <= (-1d-21)) then
        tmp = t_2 + (x * (z * y))
    else if (x <= (-3.6d-228)) then
        tmp = t_3
    else if (x <= 6.6d-306) then
        tmp = t_2 - (z * (c * b))
    else if (x <= 2.5d-83) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((z * y) - (a * t))) - (b * (c * z));
	double t_2 = j * ((a * c) - (i * y));
	double t_3 = t_2 + (t * (i * b));
	double tmp;
	if (x <= -4e+85) {
		tmp = t_1;
	} else if (x <= -1e-21) {
		tmp = t_2 + (x * (z * y));
	} else if (x <= -3.6e-228) {
		tmp = t_3;
	} else if (x <= 6.6e-306) {
		tmp = t_2 - (z * (c * b));
	} else if (x <= 2.5e-83) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((z * y) - (a * t))) - (b * (c * z))
	t_2 = j * ((a * c) - (i * y))
	t_3 = t_2 + (t * (i * b))
	tmp = 0
	if x <= -4e+85:
		tmp = t_1
	elif x <= -1e-21:
		tmp = t_2 + (x * (z * y))
	elif x <= -3.6e-228:
		tmp = t_3
	elif x <= 6.6e-306:
		tmp = t_2 - (z * (c * b))
	elif x <= 2.5e-83:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(b * Float64(c * z)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(i * y)))
	t_3 = Float64(t_2 + Float64(t * Float64(i * b)))
	tmp = 0.0
	if (x <= -4e+85)
		tmp = t_1;
	elseif (x <= -1e-21)
		tmp = Float64(t_2 + Float64(x * Float64(z * y)));
	elseif (x <= -3.6e-228)
		tmp = t_3;
	elseif (x <= 6.6e-306)
		tmp = Float64(t_2 - Float64(z * Float64(c * b)));
	elseif (x <= 2.5e-83)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((z * y) - (a * t))) - (b * (c * z));
	t_2 = j * ((a * c) - (i * y));
	t_3 = t_2 + (t * (i * b));
	tmp = 0.0;
	if (x <= -4e+85)
		tmp = t_1;
	elseif (x <= -1e-21)
		tmp = t_2 + (x * (z * y));
	elseif (x <= -3.6e-228)
		tmp = t_3;
	elseif (x <= 6.6e-306)
		tmp = t_2 - (z * (c * b));
	elseif (x <= 2.5e-83)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+85], t$95$1, If[LessEqual[x, -1e-21], N[(t$95$2 + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.6e-228], t$95$3, If[LessEqual[x, 6.6e-306], N[(t$95$2 - N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-83], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.0000000000000001e85 or 2.5e-83 < x

   1. Initial program 85.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 77.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in c around inf 74.3%

      \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]

   if -4.0000000000000001e85 < x < -9.99999999999999908e-22

   1. Initial program 86.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 84.4%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in t around 0 73.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)} \]

   if -9.99999999999999908e-22 < x < -3.6000000000000002e-228 or 6.6000000000000002e-306 < x < 2.5e-83

   1. Initial program 71.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 71.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 71.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 71.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 71.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 71.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 69.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 69.9%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 69.9%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*l* 71.3%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 71.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   if -3.6000000000000002e-228 < x < 6.6000000000000002e-306

   1. Initial program 57.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 57.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 57.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 57.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 57.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 57.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 64.0%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. associate-*r* 69.9%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(b \cdot c\right) \cdot z\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 69.9%

         \[\leadsto -1 \cdot \color{blue}{\left(z \cdot \left(b \cdot c\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*r* 69.9%

         \[\leadsto \color{blue}{\left(-1 \cdot z\right) \cdot \left(b \cdot c\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      4. mul-1-neg 69.9%

         \[\leadsto \color{blue}{\left(-z\right)} \cdot \left(b \cdot c\right) + j \cdot \left(a \cdot c - y \cdot i\right) \]

      5. *-commutative 69.9%

         \[\leadsto \left(-z\right) \cdot \color{blue}{\left(c \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 69.9%

      \[\leadsto \color{blue}{\left(-z\right) \cdot \left(c \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-228}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-306}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) - z \cdot \left(c \cdot b\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-83}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + t \cdot \left(i \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z\right)\\ \end{array} \]

Alternative 8: 50.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b - a \cdot x\right)\\ t_2 := c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.8 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.9 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-92}:\\ \;\;\;\;i \cdot \left(t \cdot b - j \cdot y\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* i b) (* a x)))) (t_2 (* c (- (* j a) (* z b)))))
   (if (<= c -2.8e-9)
     t_2
     (if (<= c -5.3e-107)
       t_1
       (if (<= c -3.9e-237)
         (* y (- (* x z) (* j i)))
         (if (<= c 1.6e-260)
           t_1
           (if (<= c 1.8e-92)
             (* i (- (* t b) (* j y)))
             (if (<= c 9.2e-57)
               (* z (- (* x y) (* c b)))
               (if (<= c 3.2e+118) (* x (- (* z y) (* a t))) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((i * b) - (a * x));
	double t_2 = c * ((j * a) - (z * b));
	double tmp;
	if (c <= -2.8e-9) {
		tmp = t_2;
	} else if (c <= -5.3e-107) {
		tmp = t_1;
	} else if (c <= -3.9e-237) {
		tmp = y * ((x * z) - (j * i));
	} else if (c <= 1.6e-260) {
		tmp = t_1;
	} else if (c <= 1.8e-92) {
		tmp = i * ((t * b) - (j * y));
	} else if (c <= 9.2e-57) {
		tmp = z * ((x * y) - (c * b));
	} else if (c <= 3.2e+118) {
		tmp = x * ((z * y) - (a * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((i * b) - (a * x))
    t_2 = c * ((j * a) - (z * b))
    if (c <= (-2.8d-9)) then
        tmp = t_2
    else if (c <= (-5.3d-107)) then
        tmp = t_1
    else if (c <= (-3.9d-237)) then
        tmp = y * ((x * z) - (j * i))
    else if (c <= 1.6d-260) then
        tmp = t_1
    else if (c <= 1.8d-92) then
        tmp = i * ((t * b) - (j * y))
    else if (c <= 9.2d-57) then
        tmp = z * ((x * y) - (c * b))
    else if (c <= 3.2d+118) then
        tmp = x * ((z * y) - (a * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((i * b) - (a * x));
	double t_2 = c * ((j * a) - (z * b));
	double tmp;
	if (c <= -2.8e-9) {
		tmp = t_2;
	} else if (c <= -5.3e-107) {
		tmp = t_1;
	} else if (c <= -3.9e-237) {
		tmp = y * ((x * z) - (j * i));
	} else if (c <= 1.6e-260) {
		tmp = t_1;
	} else if (c <= 1.8e-92) {
		tmp = i * ((t * b) - (j * y));
	} else if (c <= 9.2e-57) {
		tmp = z * ((x * y) - (c * b));
	} else if (c <= 3.2e+118) {
		tmp = x * ((z * y) - (a * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((i * b) - (a * x))
	t_2 = c * ((j * a) - (z * b))
	tmp = 0
	if c <= -2.8e-9:
		tmp = t_2
	elif c <= -5.3e-107:
		tmp = t_1
	elif c <= -3.9e-237:
		tmp = y * ((x * z) - (j * i))
	elif c <= 1.6e-260:
		tmp = t_1
	elif c <= 1.8e-92:
		tmp = i * ((t * b) - (j * y))
	elif c <= 9.2e-57:
		tmp = z * ((x * y) - (c * b))
	elif c <= 3.2e+118:
		tmp = x * ((z * y) - (a * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(i * b) - Float64(a * x)))
	t_2 = Float64(c * Float64(Float64(j * a) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.8e-9)
		tmp = t_2;
	elseif (c <= -5.3e-107)
		tmp = t_1;
	elseif (c <= -3.9e-237)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(j * i)));
	elseif (c <= 1.6e-260)
		tmp = t_1;
	elseif (c <= 1.8e-92)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(j * y)));
	elseif (c <= 9.2e-57)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(c * b)));
	elseif (c <= 3.2e+118)
		tmp = Float64(x * Float64(Float64(z * y) - Float64(a * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((i * b) - (a * x));
	t_2 = c * ((j * a) - (z * b));
	tmp = 0.0;
	if (c <= -2.8e-9)
		tmp = t_2;
	elseif (c <= -5.3e-107)
		tmp = t_1;
	elseif (c <= -3.9e-237)
		tmp = y * ((x * z) - (j * i));
	elseif (c <= 1.6e-260)
		tmp = t_1;
	elseif (c <= 1.8e-92)
		tmp = i * ((t * b) - (j * y));
	elseif (c <= 9.2e-57)
		tmp = z * ((x * y) - (c * b));
	elseif (c <= 3.2e+118)
		tmp = x * ((z * y) - (a * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(i * b), $MachinePrecision] - N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(j * a), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.8e-9], t$95$2, If[LessEqual[c, -5.3e-107], t$95$1, If[LessEqual[c, -3.9e-237], N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.6e-260], t$95$1, If[LessEqual[c, 1.8e-92], N[(i * N[(N[(t * b), $MachinePrecision] - N[(j * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.2e-57], N[(z * N[(N[(x * y), $MachinePrecision] - N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e+118], N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -2.79999999999999984e-9 or 3.20000000000000016e118 < c

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 78.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 78.0%

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{z \cdot b}\right) \]

   6. Simplified 78.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -2.79999999999999984e-9 < c < -5.3e-107 or -3.8999999999999998e-237 < c < 1.59999999999999997e-260

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 59.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 59.8%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 59.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(\color{blue}{x \cdot a} - b \cdot i\right)\right) \]

      3. *-commutative 59.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(x \cdot a - \color{blue}{i \cdot b}\right)\right) \]

   6. Simplified 59.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(x \cdot a - i \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 59.8%

         \[\leadsto t \cdot \color{blue}{\left(-\left(x \cdot a - i \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 59.8%

         \[\leadsto \color{blue}{-t \cdot \left(x \cdot a - i \cdot b\right)} \]

      3. *-commutative 59.8%

         \[\leadsto -t \cdot \left(\color{blue}{a \cdot x} - i \cdot b\right) \]

   8. Applied egg-rr 59.8%

      \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - i \cdot b\right)} \]

   if -5.3e-107 < c < -3.8999999999999998e-237

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 74.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 74.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 74.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 74.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 65.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 65.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)} \]

      2. neg-mul-1 65.6%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \]

      3. *-commutative 65.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot \left(-y\right)} \]

      4. +-commutative 65.6%

         \[\leadsto \color{blue}{\left(i \cdot j + -1 \cdot \left(x \cdot z\right)\right)} \cdot \left(-y\right) \]

      5. mul-1-neg 65.6%

         \[\leadsto \left(i \cdot j + \color{blue}{\left(-x \cdot z\right)}\right) \cdot \left(-y\right) \]

      6. unsub-neg 65.6%

         \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right)} \cdot \left(-y\right) \]

      7. *-commutative 65.6%

         \[\leadsto \left(\color{blue}{j \cdot i} - x \cdot z\right) \cdot \left(-y\right) \]

   6. Simplified 65.6%

      \[\leadsto \color{blue}{\left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)} \]

   if 1.59999999999999997e-260 < c < 1.80000000000000008e-92

   1. Initial program 83.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 83.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 83.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 83.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 83.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 56.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 56.1%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

      2. *-commutative 56.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(\color{blue}{y \cdot j} - b \cdot t\right)\right) \]

      3. *-commutative 56.1%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j - \color{blue}{t \cdot b}\right)\right) \]

   6. Simplified 56.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - t \cdot b\right)\right)} \]

   if 1.80000000000000008e-92 < c < 9.2000000000000001e-57

   1. Initial program 83.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 83.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 83.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 83.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 83.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 65.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 65.1%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 65.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   if 9.2000000000000001e-57 < c < 3.20000000000000016e118

   1. Initial program 89.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 89.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 89.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 89.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 89.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 86.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 89.6%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in x around inf 52.3%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   8. Step-by-step derivation

      1. +-commutative 52.3%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} \]

      2. mul-1-neg 52.3%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) \]

      3. sub-neg 52.3%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

   9. Simplified 52.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.8 \cdot 10^{-9}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \left(i \cdot b - a \cdot x\right)\\ \mathbf{elif}\;c \leq -3.9 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(i \cdot b - a \cdot x\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-92}:\\ \;\;\;\;i \cdot \left(t \cdot b - j \cdot y\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \left(x \cdot y - c \cdot b\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \end{array} \]

Alternative 9: 65.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+29} \lor \neg \left(b \leq 3.3 \cdot 10^{-88}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) + j \cdot \left(a \cdot c - i \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -8.2e+29) (not (<= b 3.3e-88)))
   (- (* b (- (* t i) (* c z))) (* a (* x t)))
   (+ (* x (- (* z y) (* a t))) (* j (- (* a c) (* i y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -8.2e+29) || !(b <= 3.3e-88)) {
		tmp = (b * ((t * i) - (c * z))) - (a * (x * t));
	} else {
		tmp = (x * ((z * y) - (a * t))) + (j * ((a * c) - (i * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-8.2d+29)) .or. (.not. (b <= 3.3d-88))) then
        tmp = (b * ((t * i) - (c * z))) - (a * (x * t))
    else
        tmp = (x * ((z * y) - (a * t))) + (j * ((a * c) - (i * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -8.2e+29) || !(b <= 3.3e-88)) {
		tmp = (b * ((t * i) - (c * z))) - (a * (x * t));
	} else {
		tmp = (x * ((z * y) - (a * t))) + (j * ((a * c) - (i * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -8.2e+29) or not (b <= 3.3e-88):
		tmp = (b * ((t * i) - (c * z))) - (a * (x * t))
	else:
		tmp = (x * ((z * y) - (a * t))) + (j * ((a * c) - (i * y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -8.2e+29) || !(b <= 3.3e-88))
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(c * z))) - Float64(a * Float64(x * t)));
	else
		tmp = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) + Float64(j * Float64(Float64(a * c) - Float64(i * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -8.2e+29) || ~((b <= 3.3e-88)))
		tmp = (b * ((t * i) - (c * z))) - (a * (x * t));
	else
		tmp = (x * ((z * y) - (a * t))) + (j * ((a * c) - (i * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -8.2e+29], N[Not[LessEqual[b, 3.3e-88]], $MachinePrecision]], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.2000000000000007e29 or 3.29999999999999994e-88 < b

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 75.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in y around 0 70.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 70.7%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. distribute-rgt-neg-in 70.7%

         \[\leadsto \color{blue}{a \cdot \left(-t \cdot x\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

   7. Simplified 70.7%

      \[\leadsto \color{blue}{a \cdot \left(-t \cdot x\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   if -8.2000000000000007e29 < b < 3.29999999999999994e-88

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 78.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+29} \lor \neg \left(b \leq 3.3 \cdot 10^{-88}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) + j \cdot \left(a \cdot c - i \cdot y\right)\\ \end{array} \]

Alternative 10: 68.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+30} \lor \neg \left(b \leq 9.5 \cdot 10^{-90}\right):\\ \;\;\;\;t_1 + b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + j \cdot \left(a \cdot c - i \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* z y) (* a t)))))
   (if (or (<= b -6.4e+30) (not (<= b 9.5e-90)))
     (+ t_1 (* b (- (* t i) (* c z))))
     (+ t_1 (* j (- (* a c) (* i y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((z * y) - (a * t));
	double tmp;
	if ((b <= -6.4e+30) || !(b <= 9.5e-90)) {
		tmp = t_1 + (b * ((t * i) - (c * z)));
	} else {
		tmp = t_1 + (j * ((a * c) - (i * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z * y) - (a * t))
    if ((b <= (-6.4d+30)) .or. (.not. (b <= 9.5d-90))) then
        tmp = t_1 + (b * ((t * i) - (c * z)))
    else
        tmp = t_1 + (j * ((a * c) - (i * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((z * y) - (a * t));
	double tmp;
	if ((b <= -6.4e+30) || !(b <= 9.5e-90)) {
		tmp = t_1 + (b * ((t * i) - (c * z)));
	} else {
		tmp = t_1 + (j * ((a * c) - (i * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((z * y) - (a * t))
	tmp = 0
	if (b <= -6.4e+30) or not (b <= 9.5e-90):
		tmp = t_1 + (b * ((t * i) - (c * z)))
	else:
		tmp = t_1 + (j * ((a * c) - (i * y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(z * y) - Float64(a * t)))
	tmp = 0.0
	if ((b <= -6.4e+30) || !(b <= 9.5e-90))
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(c * z))));
	else
		tmp = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(i * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((z * y) - (a * t));
	tmp = 0.0;
	if ((b <= -6.4e+30) || ~((b <= 9.5e-90)))
		tmp = t_1 + (b * ((t * i) - (c * z)));
	else
		tmp = t_1 + (j * ((a * c) - (i * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -6.4e+30], N[Not[LessEqual[b, 9.5e-90]], $MachinePrecision]], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.39999999999999945e30 or 9.5000000000000003e-90 < b

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 80.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 75.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   if -6.39999999999999945e30 < b < 9.5000000000000003e-90

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 77.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 78.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+30} \lor \neg \left(b \leq 9.5 \cdot 10^{-90}\right):\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) + b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) + j \cdot \left(a \cdot c - i \cdot y\right)\\ \end{array} \]

Alternative 11: 59.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - i \cdot y\right)\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-30}:\\ \;\;\;\;t_1 + x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;x \leq 170000000000:\\ \;\;\;\;t_1 + t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* i y)))) (t_2 (* x (- (* z y) (* a t)))))
   (if (<= x -2.5e+85)
     t_2
     (if (<= x -5.6e-30)
       (+ t_1 (* x (* z y)))
       (if (<= x 170000000000.0)
         (+ t_1 (* t (* i b)))
         (if (<= x 4.6e+109) (* b (- (* t i) (* c z))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (i * y));
	double t_2 = x * ((z * y) - (a * t));
	double tmp;
	if (x <= -2.5e+85) {
		tmp = t_2;
	} else if (x <= -5.6e-30) {
		tmp = t_1 + (x * (z * y));
	} else if (x <= 170000000000.0) {
		tmp = t_1 + (t * (i * b));
	} else if (x <= 4.6e+109) {
		tmp = b * ((t * i) - (c * z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (i * y))
    t_2 = x * ((z * y) - (a * t))
    if (x <= (-2.5d+85)) then
        tmp = t_2
    else if (x <= (-5.6d-30)) then
        tmp = t_1 + (x * (z * y))
    else if (x <= 170000000000.0d0) then
        tmp = t_1 + (t * (i * b))
    else if (x <= 4.6d+109) then
        tmp = b * ((t * i) - (c * z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (i * y));
	double t_2 = x * ((z * y) - (a * t));
	double tmp;
	if (x <= -2.5e+85) {
		tmp = t_2;
	} else if (x <= -5.6e-30) {
		tmp = t_1 + (x * (z * y));
	} else if (x <= 170000000000.0) {
		tmp = t_1 + (t * (i * b));
	} else if (x <= 4.6e+109) {
		tmp = b * ((t * i) - (c * z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (i * y))
	t_2 = x * ((z * y) - (a * t))
	tmp = 0
	if x <= -2.5e+85:
		tmp = t_2
	elif x <= -5.6e-30:
		tmp = t_1 + (x * (z * y))
	elif x <= 170000000000.0:
		tmp = t_1 + (t * (i * b))
	elif x <= 4.6e+109:
		tmp = b * ((t * i) - (c * z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(i * y)))
	t_2 = Float64(x * Float64(Float64(z * y) - Float64(a * t)))
	tmp = 0.0
	if (x <= -2.5e+85)
		tmp = t_2;
	elseif (x <= -5.6e-30)
		tmp = Float64(t_1 + Float64(x * Float64(z * y)));
	elseif (x <= 170000000000.0)
		tmp = Float64(t_1 + Float64(t * Float64(i * b)));
	elseif (x <= 4.6e+109)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(c * z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (i * y));
	t_2 = x * ((z * y) - (a * t));
	tmp = 0.0;
	if (x <= -2.5e+85)
		tmp = t_2;
	elseif (x <= -5.6e-30)
		tmp = t_1 + (x * (z * y));
	elseif (x <= 170000000000.0)
		tmp = t_1 + (t * (i * b));
	elseif (x <= 4.6e+109)
		tmp = b * ((t * i) - (c * z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+85], t$95$2, If[LessEqual[x, -5.6e-30], N[(t$95$1 + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 170000000000.0], N[(t$95$1 + N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+109], N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.5e85 or 4.60000000000000021e109 < x

   1. Initial program 86.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 77.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 79.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in x around inf 74.1%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   8. Step-by-step derivation

      1. +-commutative 74.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} \]

      2. mul-1-neg 74.1%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) \]

      3. sub-neg 74.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

   9. Simplified 74.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]

   if -2.5e85 < x < -5.59999999999999977e-30

   1. Initial program 86.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 84.4%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in t around 0 73.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)} \]

   if -5.59999999999999977e-30 < x < 1.7e11

   1. Initial program 71.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 71.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 64.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 64.2%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 64.2%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*l* 64.8%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 64.8%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   if 1.7e11 < x < 4.60000000000000021e109

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 80.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 80.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 80.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 80.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 69.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 69.6%

         \[\leadsto b \cdot \left(\color{blue}{t \cdot i} - c \cdot z\right) \]

      2. *-commutative 69.6%

         \[\leadsto b \cdot \left(t \cdot i - \color{blue}{z \cdot c}\right) \]

   6. Simplified 69.6%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i - z \cdot c\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-30}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;x \leq 170000000000:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right)\\ \end{array} \]

Alternative 12: 61.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z\right)\\ t_2 := j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{if}\;x \leq -2.06 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-21}:\\ \;\;\;\;t_2 + x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-83}:\\ \;\;\;\;t_2 + t \cdot \left(i \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x (- (* z y) (* a t))) (* b (* c z))))
        (t_2 (* j (- (* a c) (* i y)))))
   (if (<= x -2.06e+86)
     t_1
     (if (<= x -1.25e-21)
       (+ t_2 (* x (* z y)))
       (if (<= x 4.8e-83) (+ t_2 (* t (* i b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((z * y) - (a * t))) - (b * (c * z));
	double t_2 = j * ((a * c) - (i * y));
	double tmp;
	if (x <= -2.06e+86) {
		tmp = t_1;
	} else if (x <= -1.25e-21) {
		tmp = t_2 + (x * (z * y));
	} else if (x <= 4.8e-83) {
		tmp = t_2 + (t * (i * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((z * y) - (a * t))) - (b * (c * z))
    t_2 = j * ((a * c) - (i * y))
    if (x <= (-2.06d+86)) then
        tmp = t_1
    else if (x <= (-1.25d-21)) then
        tmp = t_2 + (x * (z * y))
    else if (x <= 4.8d-83) then
        tmp = t_2 + (t * (i * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((z * y) - (a * t))) - (b * (c * z));
	double t_2 = j * ((a * c) - (i * y));
	double tmp;
	if (x <= -2.06e+86) {
		tmp = t_1;
	} else if (x <= -1.25e-21) {
		tmp = t_2 + (x * (z * y));
	} else if (x <= 4.8e-83) {
		tmp = t_2 + (t * (i * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((z * y) - (a * t))) - (b * (c * z))
	t_2 = j * ((a * c) - (i * y))
	tmp = 0
	if x <= -2.06e+86:
		tmp = t_1
	elif x <= -1.25e-21:
		tmp = t_2 + (x * (z * y))
	elif x <= 4.8e-83:
		tmp = t_2 + (t * (i * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(b * Float64(c * z)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(i * y)))
	tmp = 0.0
	if (x <= -2.06e+86)
		tmp = t_1;
	elseif (x <= -1.25e-21)
		tmp = Float64(t_2 + Float64(x * Float64(z * y)));
	elseif (x <= 4.8e-83)
		tmp = Float64(t_2 + Float64(t * Float64(i * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((z * y) - (a * t))) - (b * (c * z));
	t_2 = j * ((a * c) - (i * y));
	tmp = 0.0;
	if (x <= -2.06e+86)
		tmp = t_1;
	elseif (x <= -1.25e-21)
		tmp = t_2 + (x * (z * y));
	elseif (x <= 4.8e-83)
		tmp = t_2 + (t * (i * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.06e+86], t$95$1, If[LessEqual[x, -1.25e-21], N[(t$95$2 + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e-83], N[(t$95$2 + N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.06e86 or 4.8000000000000002e-83 < x

   1. Initial program 85.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 77.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in c around inf 74.3%

      \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]

   if -2.06e86 < x < -1.24999999999999993e-21

   1. Initial program 86.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 86.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 84.4%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in t around 0 73.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)} \]

   if -1.24999999999999993e-21 < x < 4.8000000000000002e-83

   1. Initial program 69.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 69.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 69.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 65.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 65.2%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 65.2%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*l* 66.9%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 66.9%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.06 \cdot 10^{+86}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-83}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + t \cdot \left(i \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - b \cdot \left(c \cdot z\right)\\ \end{array} \]

Alternative 13: 29.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+161}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-260}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-175}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 280000000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -4.8e+161)
   (* i (* t b))
   (if (<= b -5.2e-12)
     (* b (* c (- z)))
     (if (<= b -3.3e-130)
       (* y (* j (- i)))
       (if (<= b -6.8e-236)
         (* z (* x y))
         (if (<= b -2.5e-260)
           (* i (* y (- j)))
           (if (<= b 3.9e-175)
             (* j (* a c))
             (if (<= b 280000000000.0)
               (* a (* x (- t)))
               (* (- z) (* c b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4.8e+161) {
		tmp = i * (t * b);
	} else if (b <= -5.2e-12) {
		tmp = b * (c * -z);
	} else if (b <= -3.3e-130) {
		tmp = y * (j * -i);
	} else if (b <= -6.8e-236) {
		tmp = z * (x * y);
	} else if (b <= -2.5e-260) {
		tmp = i * (y * -j);
	} else if (b <= 3.9e-175) {
		tmp = j * (a * c);
	} else if (b <= 280000000000.0) {
		tmp = a * (x * -t);
	} else {
		tmp = -z * (c * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-4.8d+161)) then
        tmp = i * (t * b)
    else if (b <= (-5.2d-12)) then
        tmp = b * (c * -z)
    else if (b <= (-3.3d-130)) then
        tmp = y * (j * -i)
    else if (b <= (-6.8d-236)) then
        tmp = z * (x * y)
    else if (b <= (-2.5d-260)) then
        tmp = i * (y * -j)
    else if (b <= 3.9d-175) then
        tmp = j * (a * c)
    else if (b <= 280000000000.0d0) then
        tmp = a * (x * -t)
    else
        tmp = -z * (c * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4.8e+161) {
		tmp = i * (t * b);
	} else if (b <= -5.2e-12) {
		tmp = b * (c * -z);
	} else if (b <= -3.3e-130) {
		tmp = y * (j * -i);
	} else if (b <= -6.8e-236) {
		tmp = z * (x * y);
	} else if (b <= -2.5e-260) {
		tmp = i * (y * -j);
	} else if (b <= 3.9e-175) {
		tmp = j * (a * c);
	} else if (b <= 280000000000.0) {
		tmp = a * (x * -t);
	} else {
		tmp = -z * (c * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -4.8e+161:
		tmp = i * (t * b)
	elif b <= -5.2e-12:
		tmp = b * (c * -z)
	elif b <= -3.3e-130:
		tmp = y * (j * -i)
	elif b <= -6.8e-236:
		tmp = z * (x * y)
	elif b <= -2.5e-260:
		tmp = i * (y * -j)
	elif b <= 3.9e-175:
		tmp = j * (a * c)
	elif b <= 280000000000.0:
		tmp = a * (x * -t)
	else:
		tmp = -z * (c * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -4.8e+161)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= -5.2e-12)
		tmp = Float64(b * Float64(c * Float64(-z)));
	elseif (b <= -3.3e-130)
		tmp = Float64(y * Float64(j * Float64(-i)));
	elseif (b <= -6.8e-236)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= -2.5e-260)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (b <= 3.9e-175)
		tmp = Float64(j * Float64(a * c));
	elseif (b <= 280000000000.0)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = Float64(Float64(-z) * Float64(c * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -4.8e+161)
		tmp = i * (t * b);
	elseif (b <= -5.2e-12)
		tmp = b * (c * -z);
	elseif (b <= -3.3e-130)
		tmp = y * (j * -i);
	elseif (b <= -6.8e-236)
		tmp = z * (x * y);
	elseif (b <= -2.5e-260)
		tmp = i * (y * -j);
	elseif (b <= 3.9e-175)
		tmp = j * (a * c);
	elseif (b <= 280000000000.0)
		tmp = a * (x * -t);
	else
		tmp = -z * (c * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -4.8e+161], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.2e-12], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.3e-130], N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.8e-236], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.5e-260], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.9e-175], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 280000000000.0], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], N[((-z) * N[(c * b), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -4.7999999999999998e161

   1. Initial program 86.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 76.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in i around inf 40.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.1%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. associate-*l* 43.6%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   7. Simplified 43.6%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if -4.7999999999999998e161 < b < -5.19999999999999965e-12

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 69.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in c around inf 40.9%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.9%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 40.9%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

   7. Simplified 40.9%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} \]

   if -5.19999999999999965e-12 < b < -3.2999999999999998e-130

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 82.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 82.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 82.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 82.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 63.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 63.4%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 63.4%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*l* 60.3%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 60.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 44.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]

   9. Simplified 44.1%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   10. Taylor expanded in i around 0 44.1%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 47.4%

          \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} \]

       2. mul-1-neg 47.4%

          \[\leadsto \color{blue}{-\left(i \cdot j\right) \cdot y} \]

       3. distribute-rgt-neg-in 47.4%

          \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

   12. Simplified 47.4%

       \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

   if -3.2999999999999998e-130 < b < -6.79999999999999961e-236

   1. Initial program 89.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 89.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 89.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 89.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 89.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 89.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 43.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 43.7%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 43.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   7. Taylor expanded in x around inf 44.0%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -6.79999999999999961e-236 < b < -2.5000000000000002e-260

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 57.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 57.7%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 57.7%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*l* 57.7%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 57.7%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 67.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]

   9. Simplified 67.6%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if -2.5000000000000002e-260 < b < 3.89999999999999998e-175

   1. Initial program 70.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 68.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 70.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in j around inf 56.7%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + a \cdot c\right)} \]
   8. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + -1 \cdot \left(i \cdot y\right)\right)} \]

      2. mul-1-neg 56.7%

         \[\leadsto j \cdot \left(a \cdot c + \color{blue}{\left(-i \cdot y\right)}\right) \]

      3. sub-neg 56.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      4. *-commutative 56.7%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   9. Simplified 56.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   10. Taylor expanded in a around inf 38.3%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 43.9%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 43.9%

          \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   12. Simplified 43.9%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   if 3.89999999999999998e-175 < b < 2.8e11

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 66.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 66.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 66.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 66.5%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 66.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around 0 58.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 58.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot t\right) \cdot x\right)} \]

      2. neg-mul-1 58.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(-t\right)} \cdot x\right) \]

      3. *-commutative 58.5%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 58.5%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if 2.8e11 < b

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 52.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 52.0%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 52.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   7. Taylor expanded in x around 0 46.8%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 46.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot c\right)} \]

      2. neg-mul-1 46.8%

         \[\leadsto z \cdot \left(\color{blue}{\left(-b\right)} \cdot c\right) \]

      3. *-commutative 46.8%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   9. Simplified 46.8%

      \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+161}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-130}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-260}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-175}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 280000000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(c \cdot b\right)\\ \end{array} \]

Alternative 14: 29.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-129}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-235}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -6.1 \cdot 10^{-260}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-173}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 28500000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -6.8e+163)
   (* t (* i b))
   (if (<= b -5.2e-10)
     (* b (* c (- z)))
     (if (<= b -1.7e-129)
       (* y (* j (- i)))
       (if (<= b -5.2e-235)
         (* z (* x y))
         (if (<= b -6.1e-260)
           (* i (* y (- j)))
           (if (<= b 2.9e-173)
             (* j (* a c))
             (if (<= b 28500000.0) (* a (* x (- t))) (* (- z) (* c b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -6.8e+163) {
		tmp = t * (i * b);
	} else if (b <= -5.2e-10) {
		tmp = b * (c * -z);
	} else if (b <= -1.7e-129) {
		tmp = y * (j * -i);
	} else if (b <= -5.2e-235) {
		tmp = z * (x * y);
	} else if (b <= -6.1e-260) {
		tmp = i * (y * -j);
	} else if (b <= 2.9e-173) {
		tmp = j * (a * c);
	} else if (b <= 28500000.0) {
		tmp = a * (x * -t);
	} else {
		tmp = -z * (c * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-6.8d+163)) then
        tmp = t * (i * b)
    else if (b <= (-5.2d-10)) then
        tmp = b * (c * -z)
    else if (b <= (-1.7d-129)) then
        tmp = y * (j * -i)
    else if (b <= (-5.2d-235)) then
        tmp = z * (x * y)
    else if (b <= (-6.1d-260)) then
        tmp = i * (y * -j)
    else if (b <= 2.9d-173) then
        tmp = j * (a * c)
    else if (b <= 28500000.0d0) then
        tmp = a * (x * -t)
    else
        tmp = -z * (c * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -6.8e+163) {
		tmp = t * (i * b);
	} else if (b <= -5.2e-10) {
		tmp = b * (c * -z);
	} else if (b <= -1.7e-129) {
		tmp = y * (j * -i);
	} else if (b <= -5.2e-235) {
		tmp = z * (x * y);
	} else if (b <= -6.1e-260) {
		tmp = i * (y * -j);
	} else if (b <= 2.9e-173) {
		tmp = j * (a * c);
	} else if (b <= 28500000.0) {
		tmp = a * (x * -t);
	} else {
		tmp = -z * (c * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -6.8e+163:
		tmp = t * (i * b)
	elif b <= -5.2e-10:
		tmp = b * (c * -z)
	elif b <= -1.7e-129:
		tmp = y * (j * -i)
	elif b <= -5.2e-235:
		tmp = z * (x * y)
	elif b <= -6.1e-260:
		tmp = i * (y * -j)
	elif b <= 2.9e-173:
		tmp = j * (a * c)
	elif b <= 28500000.0:
		tmp = a * (x * -t)
	else:
		tmp = -z * (c * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -6.8e+163)
		tmp = Float64(t * Float64(i * b));
	elseif (b <= -5.2e-10)
		tmp = Float64(b * Float64(c * Float64(-z)));
	elseif (b <= -1.7e-129)
		tmp = Float64(y * Float64(j * Float64(-i)));
	elseif (b <= -5.2e-235)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= -6.1e-260)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (b <= 2.9e-173)
		tmp = Float64(j * Float64(a * c));
	elseif (b <= 28500000.0)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = Float64(Float64(-z) * Float64(c * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -6.8e+163)
		tmp = t * (i * b);
	elseif (b <= -5.2e-10)
		tmp = b * (c * -z);
	elseif (b <= -1.7e-129)
		tmp = y * (j * -i);
	elseif (b <= -5.2e-235)
		tmp = z * (x * y);
	elseif (b <= -6.1e-260)
		tmp = i * (y * -j);
	elseif (b <= 2.9e-173)
		tmp = j * (a * c);
	elseif (b <= 28500000.0)
		tmp = a * (x * -t);
	else
		tmp = -z * (c * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -6.8e+163], N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.2e-10], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e-129], N[(y * N[(j * (-i)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.2e-235], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.1e-260], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e-173], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 28500000.0], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], N[((-z) * N[(c * b), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -6.8000000000000002e163

   1. Initial program 86.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 61.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 61.3%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 61.3%

         \[\leadsto t \cdot \left(-1 \cdot \left(\color{blue}{x \cdot a} - b \cdot i\right)\right) \]

      3. *-commutative 61.3%

         \[\leadsto t \cdot \left(-1 \cdot \left(x \cdot a - \color{blue}{i \cdot b}\right)\right) \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(x \cdot a - i \cdot b\right)\right)} \]

   7. Taylor expanded in x around 0 46.5%

      \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot i\right)\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*r* 46.5%

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot i\right)}\right) \]

      2. neg-mul-1 46.5%

         \[\leadsto t \cdot \left(-1 \cdot \left(\color{blue}{\left(-b\right)} \cdot i\right)\right) \]

      3. *-commutative 46.5%

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) \]

   9. Simplified 46.5%

      \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) \]

   if -6.8000000000000002e163 < b < -5.19999999999999962e-10

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 69.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in c around inf 40.9%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.9%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 40.9%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

   7. Simplified 40.9%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} \]

   if -5.19999999999999962e-10 < b < -1.70000000000000007e-129

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 82.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 82.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 82.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 82.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 63.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 63.4%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 63.4%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*l* 60.3%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 60.3%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 44.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]

   9. Simplified 44.1%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   10. Taylor expanded in i around 0 44.1%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 47.4%

          \[\leadsto -1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} \]

       2. mul-1-neg 47.4%

          \[\leadsto \color{blue}{-\left(i \cdot j\right) \cdot y} \]

       3. distribute-rgt-neg-in 47.4%

          \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

   12. Simplified 47.4%

       \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

   if -1.70000000000000007e-129 < b < -5.2000000000000001e-235

   1. Initial program 88.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 88.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 88.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 88.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 88.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 45.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 45.6%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 45.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   7. Taylor expanded in x around inf 46.0%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -5.2000000000000001e-235 < b < -6.1000000000000003e-260

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 80.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 80.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 80.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 80.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 61.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 61.9%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 61.9%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*l* 61.9%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 61.9%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 61.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]

   9. Simplified 61.7%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if -6.1000000000000003e-260 < b < 2.8999999999999998e-173

   1. Initial program 70.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 68.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 70.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in j around inf 56.7%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + a \cdot c\right)} \]
   8. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + -1 \cdot \left(i \cdot y\right)\right)} \]

      2. mul-1-neg 56.7%

         \[\leadsto j \cdot \left(a \cdot c + \color{blue}{\left(-i \cdot y\right)}\right) \]

      3. sub-neg 56.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      4. *-commutative 56.7%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   9. Simplified 56.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   10. Taylor expanded in a around inf 38.3%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 43.9%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 43.9%

          \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   12. Simplified 43.9%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   if 2.8999999999999998e-173 < b < 2.85e7

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 66.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 66.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 66.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 66.5%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 66.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around 0 58.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 58.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot t\right) \cdot x\right)} \]

      2. neg-mul-1 58.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(-t\right)} \cdot x\right) \]

      3. *-commutative 58.5%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 58.5%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if 2.85e7 < b

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 52.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 52.0%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 52.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   7. Taylor expanded in x around 0 46.8%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 46.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot c\right)} \]

      2. neg-mul-1 46.8%

         \[\leadsto z \cdot \left(\color{blue}{\left(-b\right)} \cdot c\right) \]

      3. *-commutative 46.8%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   9. Simplified 46.8%

      \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-129}:\\ \;\;\;\;y \cdot \left(j \cdot \left(-i\right)\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-235}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -6.1 \cdot 10^{-260}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-173}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 28500000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(c \cdot b\right)\\ \end{array} \]

Alternative 15: 51.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(i \cdot b - a \cdot x\right)\\ t_2 := c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* i b) (* a x)))) (t_2 (* c (- (* j a) (* z b)))))
   (if (<= c -7.5e-8)
     t_2
     (if (<= c -1.35e-108)
       t_1
       (if (<= c -1.15e-236)
         (* y (- (* x z) (* j i)))
         (if (<= c 2.1e-236)
           t_1
           (if (<= c 3.5e+118) (* x (- (* z y) (* a t))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((i * b) - (a * x));
	double t_2 = c * ((j * a) - (z * b));
	double tmp;
	if (c <= -7.5e-8) {
		tmp = t_2;
	} else if (c <= -1.35e-108) {
		tmp = t_1;
	} else if (c <= -1.15e-236) {
		tmp = y * ((x * z) - (j * i));
	} else if (c <= 2.1e-236) {
		tmp = t_1;
	} else if (c <= 3.5e+118) {
		tmp = x * ((z * y) - (a * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((i * b) - (a * x))
    t_2 = c * ((j * a) - (z * b))
    if (c <= (-7.5d-8)) then
        tmp = t_2
    else if (c <= (-1.35d-108)) then
        tmp = t_1
    else if (c <= (-1.15d-236)) then
        tmp = y * ((x * z) - (j * i))
    else if (c <= 2.1d-236) then
        tmp = t_1
    else if (c <= 3.5d+118) then
        tmp = x * ((z * y) - (a * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((i * b) - (a * x));
	double t_2 = c * ((j * a) - (z * b));
	double tmp;
	if (c <= -7.5e-8) {
		tmp = t_2;
	} else if (c <= -1.35e-108) {
		tmp = t_1;
	} else if (c <= -1.15e-236) {
		tmp = y * ((x * z) - (j * i));
	} else if (c <= 2.1e-236) {
		tmp = t_1;
	} else if (c <= 3.5e+118) {
		tmp = x * ((z * y) - (a * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((i * b) - (a * x))
	t_2 = c * ((j * a) - (z * b))
	tmp = 0
	if c <= -7.5e-8:
		tmp = t_2
	elif c <= -1.35e-108:
		tmp = t_1
	elif c <= -1.15e-236:
		tmp = y * ((x * z) - (j * i))
	elif c <= 2.1e-236:
		tmp = t_1
	elif c <= 3.5e+118:
		tmp = x * ((z * y) - (a * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(i * b) - Float64(a * x)))
	t_2 = Float64(c * Float64(Float64(j * a) - Float64(z * b)))
	tmp = 0.0
	if (c <= -7.5e-8)
		tmp = t_2;
	elseif (c <= -1.35e-108)
		tmp = t_1;
	elseif (c <= -1.15e-236)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(j * i)));
	elseif (c <= 2.1e-236)
		tmp = t_1;
	elseif (c <= 3.5e+118)
		tmp = Float64(x * Float64(Float64(z * y) - Float64(a * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((i * b) - (a * x));
	t_2 = c * ((j * a) - (z * b));
	tmp = 0.0;
	if (c <= -7.5e-8)
		tmp = t_2;
	elseif (c <= -1.35e-108)
		tmp = t_1;
	elseif (c <= -1.15e-236)
		tmp = y * ((x * z) - (j * i));
	elseif (c <= 2.1e-236)
		tmp = t_1;
	elseif (c <= 3.5e+118)
		tmp = x * ((z * y) - (a * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(i * b), $MachinePrecision] - N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(j * a), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.5e-8], t$95$2, If[LessEqual[c, -1.35e-108], t$95$1, If[LessEqual[c, -1.15e-236], N[(y * N[(N[(x * z), $MachinePrecision] - N[(j * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e-236], t$95$1, If[LessEqual[c, 3.5e+118], N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -7.4999999999999997e-8 or 3.50000000000000016e118 < c

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 78.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 78.0%

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{z \cdot b}\right) \]

   6. Simplified 78.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -7.4999999999999997e-8 < c < -1.35000000000000002e-108 or -1.15000000000000003e-236 < c < 2.09999999999999979e-236

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 78.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 78.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 78.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 57.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 57.8%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 57.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(\color{blue}{x \cdot a} - b \cdot i\right)\right) \]

      3. *-commutative 57.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(x \cdot a - \color{blue}{i \cdot b}\right)\right) \]

   6. Simplified 57.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(x \cdot a - i \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 57.8%

         \[\leadsto t \cdot \color{blue}{\left(-\left(x \cdot a - i \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 57.8%

         \[\leadsto \color{blue}{-t \cdot \left(x \cdot a - i \cdot b\right)} \]

      3. *-commutative 57.8%

         \[\leadsto -t \cdot \left(\color{blue}{a \cdot x} - i \cdot b\right) \]

   8. Applied egg-rr 57.8%

      \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - i \cdot b\right)} \]

   if -1.35000000000000002e-108 < c < -1.15000000000000003e-236

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 74.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 74.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 74.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 74.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 65.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 65.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)} \]

      2. neg-mul-1 65.6%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \]

      3. *-commutative 65.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot \left(-y\right)} \]

      4. +-commutative 65.6%

         \[\leadsto \color{blue}{\left(i \cdot j + -1 \cdot \left(x \cdot z\right)\right)} \cdot \left(-y\right) \]

      5. mul-1-neg 65.6%

         \[\leadsto \left(i \cdot j + \color{blue}{\left(-x \cdot z\right)}\right) \cdot \left(-y\right) \]

      6. unsub-neg 65.6%

         \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right)} \cdot \left(-y\right) \]

      7. *-commutative 65.6%

         \[\leadsto \left(\color{blue}{j \cdot i} - x \cdot z\right) \cdot \left(-y\right) \]

   6. Simplified 65.6%

      \[\leadsto \color{blue}{\left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)} \]

   if 2.09999999999999979e-236 < c < 3.50000000000000016e118

   1. Initial program 84.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 84.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 84.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 84.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 84.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 84.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 88.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 89.9%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in x around inf 50.9%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   8. Step-by-step derivation

      1. +-commutative 50.9%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} \]

      2. mul-1-neg 50.9%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) \]

      3. sub-neg 50.9%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

   9. Simplified 50.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{-8}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.35 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \left(i \cdot b - a \cdot x\right)\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \left(x \cdot z - j \cdot i\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \left(i \cdot b - a \cdot x\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \end{array} \]

Alternative 16: 58.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+30} \lor \neg \left(b \leq 9 \cdot 10^{-180}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.15e+30) (not (<= b 9e-180)))
   (- (* b (- (* t i) (* c z))) (* a (* x t)))
   (+ (* j (- (* a c) (* i y))) (* x (* z y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.15e+30) || !(b <= 9e-180)) {
		tmp = (b * ((t * i) - (c * z))) - (a * (x * t));
	} else {
		tmp = (j * ((a * c) - (i * y))) + (x * (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.15d+30)) .or. (.not. (b <= 9d-180))) then
        tmp = (b * ((t * i) - (c * z))) - (a * (x * t))
    else
        tmp = (j * ((a * c) - (i * y))) + (x * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.15e+30) || !(b <= 9e-180)) {
		tmp = (b * ((t * i) - (c * z))) - (a * (x * t));
	} else {
		tmp = (j * ((a * c) - (i * y))) + (x * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.15e+30) or not (b <= 9e-180):
		tmp = (b * ((t * i) - (c * z))) - (a * (x * t))
	else:
		tmp = (j * ((a * c) - (i * y))) + (x * (z * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.15e+30) || !(b <= 9e-180))
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(c * z))) - Float64(a * Float64(x * t)));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(i * y))) + Float64(x * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.15e+30) || ~((b <= 9e-180)))
		tmp = (b * ((t * i) - (c * z))) - (a * (x * t));
	else
		tmp = (j * ((a * c) - (i * y))) + (x * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.15e+30], N[Not[LessEqual[b, 9e-180]], $MachinePrecision]], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.15e30 or 9.00000000000000019e-180 < b

   1. Initial program 79.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 79.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 79.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 79.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 73.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in y around 0 69.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 69.7%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

      2. distribute-rgt-neg-in 69.7%

         \[\leadsto \color{blue}{a \cdot \left(-t \cdot x\right)} - b \cdot \left(c \cdot z - i \cdot t\right) \]

   7. Simplified 69.7%

      \[\leadsto \color{blue}{a \cdot \left(-t \cdot x\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   if -1.15e30 < b < 9.00000000000000019e-180

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 79.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in t around 0 67.8%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+30} \lor \neg \left(b \leq 9 \cdot 10^{-180}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 17: 57.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-166}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;b \leq 900000000000:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* c z)))))
   (if (<= b -2.8e+30)
     t_1
     (if (<= b 7.5e-166)
       (+ (* j (- (* a c) (* i y))) (* x (* z y)))
       (if (<= b 900000000000.0) (* a (- (* j c) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (c * z));
	double tmp;
	if (b <= -2.8e+30) {
		tmp = t_1;
	} else if (b <= 7.5e-166) {
		tmp = (j * ((a * c) - (i * y))) + (x * (z * y));
	} else if (b <= 900000000000.0) {
		tmp = a * ((j * c) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (c * z))
    if (b <= (-2.8d+30)) then
        tmp = t_1
    else if (b <= 7.5d-166) then
        tmp = (j * ((a * c) - (i * y))) + (x * (z * y))
    else if (b <= 900000000000.0d0) then
        tmp = a * ((j * c) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (c * z));
	double tmp;
	if (b <= -2.8e+30) {
		tmp = t_1;
	} else if (b <= 7.5e-166) {
		tmp = (j * ((a * c) - (i * y))) + (x * (z * y));
	} else if (b <= 900000000000.0) {
		tmp = a * ((j * c) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (c * z))
	tmp = 0
	if b <= -2.8e+30:
		tmp = t_1
	elif b <= 7.5e-166:
		tmp = (j * ((a * c) - (i * y))) + (x * (z * y))
	elif b <= 900000000000.0:
		tmp = a * ((j * c) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(c * z)))
	tmp = 0.0
	if (b <= -2.8e+30)
		tmp = t_1;
	elseif (b <= 7.5e-166)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(i * y))) + Float64(x * Float64(z * y)));
	elseif (b <= 900000000000.0)
		tmp = Float64(a * Float64(Float64(j * c) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (c * z));
	tmp = 0.0;
	if (b <= -2.8e+30)
		tmp = t_1;
	elseif (b <= 7.5e-166)
		tmp = (j * ((a * c) - (i * y))) + (x * (z * y));
	elseif (b <= 900000000000.0)
		tmp = a * ((j * c) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+30], t$95$1, If[LessEqual[b, 7.5e-166], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 900000000000.0], N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.79999999999999983e30 or 9e11 < b

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 61.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 61.3%

         \[\leadsto b \cdot \left(\color{blue}{t \cdot i} - c \cdot z\right) \]

      2. *-commutative 61.3%

         \[\leadsto b \cdot \left(t \cdot i - \color{blue}{z \cdot c}\right) \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i - z \cdot c\right)} \]

   if -2.79999999999999983e30 < b < 7.49999999999999947e-166

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around 0 78.9%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   5. Taylor expanded in t around 0 66.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)} \]

   if 7.49999999999999947e-166 < b < 9e11

   1. Initial program 71.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 71.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 71.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 67.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 67.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 67.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 67.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 67.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 67.8%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 67.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-166}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;b \leq 900000000000:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \end{array} \]

Alternative 18: 29.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ t_3 := x \cdot \left(a \cdot \left(-t\right)\right)\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+204}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))) (t_2 (* b (* t i))) (t_3 (* x (* a (- t)))))
   (if (<= x -2.8e+85)
     t_3
     (if (<= x 2.4e-201)
       t_1
       (if (<= x 1.7e-105)
         t_2
         (if (<= x 1.1e+33)
           t_1
           (if (<= x 1.55e+105)
             t_2
             (if (<= x 2.9e+204) t_3 (* z (* x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double t_2 = b * (t * i);
	double t_3 = x * (a * -t);
	double tmp;
	if (x <= -2.8e+85) {
		tmp = t_3;
	} else if (x <= 2.4e-201) {
		tmp = t_1;
	} else if (x <= 1.7e-105) {
		tmp = t_2;
	} else if (x <= 1.1e+33) {
		tmp = t_1;
	} else if (x <= 1.55e+105) {
		tmp = t_2;
	} else if (x <= 2.9e+204) {
		tmp = t_3;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * (a * c)
    t_2 = b * (t * i)
    t_3 = x * (a * -t)
    if (x <= (-2.8d+85)) then
        tmp = t_3
    else if (x <= 2.4d-201) then
        tmp = t_1
    else if (x <= 1.7d-105) then
        tmp = t_2
    else if (x <= 1.1d+33) then
        tmp = t_1
    else if (x <= 1.55d+105) then
        tmp = t_2
    else if (x <= 2.9d+204) then
        tmp = t_3
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double t_2 = b * (t * i);
	double t_3 = x * (a * -t);
	double tmp;
	if (x <= -2.8e+85) {
		tmp = t_3;
	} else if (x <= 2.4e-201) {
		tmp = t_1;
	} else if (x <= 1.7e-105) {
		tmp = t_2;
	} else if (x <= 1.1e+33) {
		tmp = t_1;
	} else if (x <= 1.55e+105) {
		tmp = t_2;
	} else if (x <= 2.9e+204) {
		tmp = t_3;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	t_2 = b * (t * i)
	t_3 = x * (a * -t)
	tmp = 0
	if x <= -2.8e+85:
		tmp = t_3
	elif x <= 2.4e-201:
		tmp = t_1
	elif x <= 1.7e-105:
		tmp = t_2
	elif x <= 1.1e+33:
		tmp = t_1
	elif x <= 1.55e+105:
		tmp = t_2
	elif x <= 2.9e+204:
		tmp = t_3
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	t_2 = Float64(b * Float64(t * i))
	t_3 = Float64(x * Float64(a * Float64(-t)))
	tmp = 0.0
	if (x <= -2.8e+85)
		tmp = t_3;
	elseif (x <= 2.4e-201)
		tmp = t_1;
	elseif (x <= 1.7e-105)
		tmp = t_2;
	elseif (x <= 1.1e+33)
		tmp = t_1;
	elseif (x <= 1.55e+105)
		tmp = t_2;
	elseif (x <= 2.9e+204)
		tmp = t_3;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	t_2 = b * (t * i);
	t_3 = x * (a * -t);
	tmp = 0.0;
	if (x <= -2.8e+85)
		tmp = t_3;
	elseif (x <= 2.4e-201)
		tmp = t_1;
	elseif (x <= 1.7e-105)
		tmp = t_2;
	elseif (x <= 1.1e+33)
		tmp = t_1;
	elseif (x <= 1.55e+105)
		tmp = t_2;
	elseif (x <= 2.9e+204)
		tmp = t_3;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(a * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+85], t$95$3, If[LessEqual[x, 2.4e-201], t$95$1, If[LessEqual[x, 1.7e-105], t$95$2, If[LessEqual[x, 1.1e+33], t$95$1, If[LessEqual[x, 1.55e+105], t$95$2, If[LessEqual[x, 2.9e+204], t$95$3, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.7999999999999999e85 or 1.55000000000000002e105 < x < 2.90000000000000004e204

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 82.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 82.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 82.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 82.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 58.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 58.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 58.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 58.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 58.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 58.4%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 58.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around 0 51.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 51.7%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. associate-*r* 51.8%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot x} \]

   9. Simplified 51.8%

      \[\leadsto \color{blue}{-\left(a \cdot t\right) \cdot x} \]

   if -2.7999999999999999e85 < x < 2.40000000000000009e-201 or 1.69999999999999996e-105 < x < 1.09999999999999997e33

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 80.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 82.4%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in j around inf 51.3%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + a \cdot c\right)} \]
   8. Step-by-step derivation

      1. +-commutative 51.3%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + -1 \cdot \left(i \cdot y\right)\right)} \]

      2. mul-1-neg 51.3%

         \[\leadsto j \cdot \left(a \cdot c + \color{blue}{\left(-i \cdot y\right)}\right) \]

      3. sub-neg 51.3%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      4. *-commutative 51.3%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   9. Simplified 51.3%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   10. Taylor expanded in a around inf 29.2%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 34.9%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 34.9%

          \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   12. Simplified 34.9%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   if 2.40000000000000009e-201 < x < 1.69999999999999996e-105 or 1.09999999999999997e33 < x < 1.55000000000000002e105

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 65.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in i around inf 42.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if 2.90000000000000004e204 < x

   1. Initial program 94.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 94.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 94.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 94.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 94.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 56.1%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 56.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   7. Taylor expanded in x around inf 56.1%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-201}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-105}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+33}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+105}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+204}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 19: 29.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+85}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+205}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))) (t_2 (* b (* t i))))
   (if (<= x -2.6e+85)
     (* a (* x (- t)))
     (if (<= x 7.8e-197)
       t_1
       (if (<= x 6.2e-107)
         t_2
         (if (<= x 5.5e+32)
           t_1
           (if (<= x 4.6e+104)
             t_2
             (if (<= x 1.45e+205) (* x (* a (- t))) (* z (* x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double t_2 = b * (t * i);
	double tmp;
	if (x <= -2.6e+85) {
		tmp = a * (x * -t);
	} else if (x <= 7.8e-197) {
		tmp = t_1;
	} else if (x <= 6.2e-107) {
		tmp = t_2;
	} else if (x <= 5.5e+32) {
		tmp = t_1;
	} else if (x <= 4.6e+104) {
		tmp = t_2;
	} else if (x <= 1.45e+205) {
		tmp = x * (a * -t);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (a * c)
    t_2 = b * (t * i)
    if (x <= (-2.6d+85)) then
        tmp = a * (x * -t)
    else if (x <= 7.8d-197) then
        tmp = t_1
    else if (x <= 6.2d-107) then
        tmp = t_2
    else if (x <= 5.5d+32) then
        tmp = t_1
    else if (x <= 4.6d+104) then
        tmp = t_2
    else if (x <= 1.45d+205) then
        tmp = x * (a * -t)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double t_2 = b * (t * i);
	double tmp;
	if (x <= -2.6e+85) {
		tmp = a * (x * -t);
	} else if (x <= 7.8e-197) {
		tmp = t_1;
	} else if (x <= 6.2e-107) {
		tmp = t_2;
	} else if (x <= 5.5e+32) {
		tmp = t_1;
	} else if (x <= 4.6e+104) {
		tmp = t_2;
	} else if (x <= 1.45e+205) {
		tmp = x * (a * -t);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	t_2 = b * (t * i)
	tmp = 0
	if x <= -2.6e+85:
		tmp = a * (x * -t)
	elif x <= 7.8e-197:
		tmp = t_1
	elif x <= 6.2e-107:
		tmp = t_2
	elif x <= 5.5e+32:
		tmp = t_1
	elif x <= 4.6e+104:
		tmp = t_2
	elif x <= 1.45e+205:
		tmp = x * (a * -t)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	t_2 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (x <= -2.6e+85)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (x <= 7.8e-197)
		tmp = t_1;
	elseif (x <= 6.2e-107)
		tmp = t_2;
	elseif (x <= 5.5e+32)
		tmp = t_1;
	elseif (x <= 4.6e+104)
		tmp = t_2;
	elseif (x <= 1.45e+205)
		tmp = Float64(x * Float64(a * Float64(-t)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	t_2 = b * (t * i);
	tmp = 0.0;
	if (x <= -2.6e+85)
		tmp = a * (x * -t);
	elseif (x <= 7.8e-197)
		tmp = t_1;
	elseif (x <= 6.2e-107)
		tmp = t_2;
	elseif (x <= 5.5e+32)
		tmp = t_1;
	elseif (x <= 4.6e+104)
		tmp = t_2;
	elseif (x <= 1.45e+205)
		tmp = x * (a * -t);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+85], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e-197], t$95$1, If[LessEqual[x, 6.2e-107], t$95$2, If[LessEqual[x, 5.5e+32], t$95$1, If[LessEqual[x, 4.6e+104], t$95$2, If[LessEqual[x, 1.45e+205], N[(x * N[(a * (-t)), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.60000000000000011e85

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 54.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 54.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 54.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 54.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 54.9%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 54.9%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 54.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around 0 47.3%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 47.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot t\right) \cdot x\right)} \]

      2. neg-mul-1 47.3%

         \[\leadsto a \cdot \left(\color{blue}{\left(-t\right)} \cdot x\right) \]

      3. *-commutative 47.3%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 47.3%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -2.60000000000000011e85 < x < 7.7999999999999998e-197 or 6.20000000000000043e-107 < x < 5.49999999999999984e32

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 80.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 82.4%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in j around inf 51.3%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + a \cdot c\right)} \]
   8. Step-by-step derivation

      1. +-commutative 51.3%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + -1 \cdot \left(i \cdot y\right)\right)} \]

      2. mul-1-neg 51.3%

         \[\leadsto j \cdot \left(a \cdot c + \color{blue}{\left(-i \cdot y\right)}\right) \]

      3. sub-neg 51.3%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      4. *-commutative 51.3%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   9. Simplified 51.3%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   10. Taylor expanded in a around inf 29.2%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 34.9%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 34.9%

          \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   12. Simplified 34.9%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   if 7.7999999999999998e-197 < x < 6.20000000000000043e-107 or 5.49999999999999984e32 < x < 4.59999999999999969e104

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 65.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in i around inf 42.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if 4.59999999999999969e104 < x < 1.4500000000000001e205

   1. Initial program 91.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 91.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 91.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 91.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 91.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 66.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 66.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 66.3%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 66.3%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 66.3%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 66.3%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 66.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around 0 61.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 61.8%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. associate-*r* 65.9%

         \[\leadsto -\color{blue}{\left(a \cdot t\right) \cdot x} \]

   9. Simplified 65.9%

      \[\leadsto \color{blue}{-\left(a \cdot t\right) \cdot x} \]

   if 1.4500000000000001e205 < x

   1. Initial program 94.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 94.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 94.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 94.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 94.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 56.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 56.1%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 56.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   7. Taylor expanded in x around inf 56.1%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+85}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-197}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-107}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+32}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+104}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+205}:\\ \;\;\;\;x \cdot \left(a \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 20: 29.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;b \leq -1.48 \cdot 10^{+168}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-42}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq -3.15 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-174}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 48000000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))))
   (if (<= b -1.48e+168)
     (* i (* t b))
     (if (<= b -5.1e-42)
       (* b (* c (- z)))
       (if (<= b -3.15e-254)
         t_1
         (if (<= b 2.2e-174)
           (* j (* a c))
           (if (<= b 48000000000000.0) t_1 (* (- z) (* c b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double tmp;
	if (b <= -1.48e+168) {
		tmp = i * (t * b);
	} else if (b <= -5.1e-42) {
		tmp = b * (c * -z);
	} else if (b <= -3.15e-254) {
		tmp = t_1;
	} else if (b <= 2.2e-174) {
		tmp = j * (a * c);
	} else if (b <= 48000000000000.0) {
		tmp = t_1;
	} else {
		tmp = -z * (c * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (x * -t)
    if (b <= (-1.48d+168)) then
        tmp = i * (t * b)
    else if (b <= (-5.1d-42)) then
        tmp = b * (c * -z)
    else if (b <= (-3.15d-254)) then
        tmp = t_1
    else if (b <= 2.2d-174) then
        tmp = j * (a * c)
    else if (b <= 48000000000000.0d0) then
        tmp = t_1
    else
        tmp = -z * (c * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double tmp;
	if (b <= -1.48e+168) {
		tmp = i * (t * b);
	} else if (b <= -5.1e-42) {
		tmp = b * (c * -z);
	} else if (b <= -3.15e-254) {
		tmp = t_1;
	} else if (b <= 2.2e-174) {
		tmp = j * (a * c);
	} else if (b <= 48000000000000.0) {
		tmp = t_1;
	} else {
		tmp = -z * (c * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	tmp = 0
	if b <= -1.48e+168:
		tmp = i * (t * b)
	elif b <= -5.1e-42:
		tmp = b * (c * -z)
	elif b <= -3.15e-254:
		tmp = t_1
	elif b <= 2.2e-174:
		tmp = j * (a * c)
	elif b <= 48000000000000.0:
		tmp = t_1
	else:
		tmp = -z * (c * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (b <= -1.48e+168)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= -5.1e-42)
		tmp = Float64(b * Float64(c * Float64(-z)));
	elseif (b <= -3.15e-254)
		tmp = t_1;
	elseif (b <= 2.2e-174)
		tmp = Float64(j * Float64(a * c));
	elseif (b <= 48000000000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(-z) * Float64(c * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * -t);
	tmp = 0.0;
	if (b <= -1.48e+168)
		tmp = i * (t * b);
	elseif (b <= -5.1e-42)
		tmp = b * (c * -z);
	elseif (b <= -3.15e-254)
		tmp = t_1;
	elseif (b <= 2.2e-174)
		tmp = j * (a * c);
	elseif (b <= 48000000000000.0)
		tmp = t_1;
	else
		tmp = -z * (c * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.48e+168], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.1e-42], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.15e-254], t$95$1, If[LessEqual[b, 2.2e-174], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 48000000000000.0], t$95$1, N[((-z) * N[(c * b), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.48e168

   1. Initial program 86.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 76.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in i around inf 40.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.1%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. associate-*l* 43.6%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   7. Simplified 43.6%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if -1.48e168 < b < -5.1e-42

   1. Initial program 79.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 79.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 79.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 79.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 63.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in c around inf 34.6%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.6%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 34.6%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

   7. Simplified 34.6%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} \]

   if -5.1e-42 < b < -3.1500000000000001e-254 or 2.20000000000000022e-174 < b < 4.8e13

   1. Initial program 81.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 81.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 81.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 81.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 81.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 81.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 57.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 57.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 57.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 57.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 57.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 57.5%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 57.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around 0 47.0%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 47.0%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot t\right) \cdot x\right)} \]

      2. neg-mul-1 47.0%

         \[\leadsto a \cdot \left(\color{blue}{\left(-t\right)} \cdot x\right) \]

      3. *-commutative 47.0%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 47.0%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if -3.1500000000000001e-254 < b < 2.20000000000000022e-174

   1. Initial program 68.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 68.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 66.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 69.0%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in j around inf 55.6%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + a \cdot c\right)} \]
   8. Step-by-step derivation

      1. +-commutative 55.6%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + -1 \cdot \left(i \cdot y\right)\right)} \]

      2. mul-1-neg 55.6%

         \[\leadsto j \cdot \left(a \cdot c + \color{blue}{\left(-i \cdot y\right)}\right) \]

      3. sub-neg 55.6%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      4. *-commutative 55.6%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   9. Simplified 55.6%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   10. Taylor expanded in a around inf 37.5%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 43.0%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 43.0%

          \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   12. Simplified 43.0%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   if 4.8e13 < b

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 52.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 52.0%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 52.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   7. Taylor expanded in x around 0 46.8%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 46.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot c\right)} \]

      2. neg-mul-1 46.8%

         \[\leadsto z \cdot \left(\color{blue}{\left(-b\right)} \cdot c\right) \]

      3. *-commutative 46.8%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   9. Simplified 46.8%

      \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.48 \cdot 10^{+168}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-42}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq -3.15 \cdot 10^{-254}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-174}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 48000000000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(c \cdot b\right)\\ \end{array} \]

Alternative 21: 29.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+166}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-256}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-175}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 28000000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -7.5e+166)
   (* i (* t b))
   (if (<= b -1.6e-12)
     (* b (* c (- z)))
     (if (<= b -4.6e-256)
       (* i (* y (- j)))
       (if (<= b 2.2e-175)
         (* j (* a c))
         (if (<= b 28000000000.0) (* a (* x (- t))) (* (- z) (* c b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -7.5e+166) {
		tmp = i * (t * b);
	} else if (b <= -1.6e-12) {
		tmp = b * (c * -z);
	} else if (b <= -4.6e-256) {
		tmp = i * (y * -j);
	} else if (b <= 2.2e-175) {
		tmp = j * (a * c);
	} else if (b <= 28000000000.0) {
		tmp = a * (x * -t);
	} else {
		tmp = -z * (c * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-7.5d+166)) then
        tmp = i * (t * b)
    else if (b <= (-1.6d-12)) then
        tmp = b * (c * -z)
    else if (b <= (-4.6d-256)) then
        tmp = i * (y * -j)
    else if (b <= 2.2d-175) then
        tmp = j * (a * c)
    else if (b <= 28000000000.0d0) then
        tmp = a * (x * -t)
    else
        tmp = -z * (c * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -7.5e+166) {
		tmp = i * (t * b);
	} else if (b <= -1.6e-12) {
		tmp = b * (c * -z);
	} else if (b <= -4.6e-256) {
		tmp = i * (y * -j);
	} else if (b <= 2.2e-175) {
		tmp = j * (a * c);
	} else if (b <= 28000000000.0) {
		tmp = a * (x * -t);
	} else {
		tmp = -z * (c * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -7.5e+166:
		tmp = i * (t * b)
	elif b <= -1.6e-12:
		tmp = b * (c * -z)
	elif b <= -4.6e-256:
		tmp = i * (y * -j)
	elif b <= 2.2e-175:
		tmp = j * (a * c)
	elif b <= 28000000000.0:
		tmp = a * (x * -t)
	else:
		tmp = -z * (c * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -7.5e+166)
		tmp = Float64(i * Float64(t * b));
	elseif (b <= -1.6e-12)
		tmp = Float64(b * Float64(c * Float64(-z)));
	elseif (b <= -4.6e-256)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (b <= 2.2e-175)
		tmp = Float64(j * Float64(a * c));
	elseif (b <= 28000000000.0)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = Float64(Float64(-z) * Float64(c * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -7.5e+166)
		tmp = i * (t * b);
	elseif (b <= -1.6e-12)
		tmp = b * (c * -z);
	elseif (b <= -4.6e-256)
		tmp = i * (y * -j);
	elseif (b <= 2.2e-175)
		tmp = j * (a * c);
	elseif (b <= 28000000000.0)
		tmp = a * (x * -t);
	else
		tmp = -z * (c * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -7.5e+166], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.6e-12], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.6e-256], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e-175], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 28000000000.0], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], N[((-z) * N[(c * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -7.50000000000000029e166

   1. Initial program 86.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 76.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in i around inf 40.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.1%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} \]

      2. associate-*l* 43.6%

         \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   7. Simplified 43.6%

      \[\leadsto \color{blue}{i \cdot \left(t \cdot b\right)} \]

   if -7.50000000000000029e166 < b < -1.6e-12

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 69.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in c around inf 40.9%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.9%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 40.9%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

   7. Simplified 40.9%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} \]

   if -1.6e-12 < b < -4.6e-256

   1. Initial program 84.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 84.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 84.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 84.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 84.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 84.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 57.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 57.4%

         \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} + j \cdot \left(a \cdot c - y \cdot i\right) \]

      2. *-commutative 57.4%

         \[\leadsto \color{blue}{\left(t \cdot i\right)} \cdot b + j \cdot \left(a \cdot c - y \cdot i\right) \]

      3. associate-*l* 54.1%

         \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   6. Simplified 54.1%

      \[\leadsto \color{blue}{t \cdot \left(i \cdot b\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]

   7. Taylor expanded in y around inf 41.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]

   9. Simplified 41.6%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if -4.6e-256 < b < 2.2e-175

   1. Initial program 70.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 68.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 70.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in j around inf 56.7%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + a \cdot c\right)} \]
   8. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + -1 \cdot \left(i \cdot y\right)\right)} \]

      2. mul-1-neg 56.7%

         \[\leadsto j \cdot \left(a \cdot c + \color{blue}{\left(-i \cdot y\right)}\right) \]

      3. sub-neg 56.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      4. *-commutative 56.7%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   9. Simplified 56.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   10. Taylor expanded in a around inf 38.3%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 43.9%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 43.9%

          \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   12. Simplified 43.9%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   if 2.2e-175 < b < 2.8e10

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 66.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 66.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 66.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 66.5%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 66.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around 0 58.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 58.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot t\right) \cdot x\right)} \]

      2. neg-mul-1 58.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(-t\right)} \cdot x\right) \]

      3. *-commutative 58.5%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 58.5%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if 2.8e10 < b

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 52.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 52.0%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 52.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   7. Taylor expanded in x around 0 46.8%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 46.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot c\right)} \]

      2. neg-mul-1 46.8%

         \[\leadsto z \cdot \left(\color{blue}{\left(-b\right)} \cdot c\right) \]

      3. *-commutative 46.8%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   9. Simplified 46.8%

      \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+166}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-12}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-256}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-175}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 28000000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(c \cdot b\right)\\ \end{array} \]

Alternative 22: 40.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+168}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(c \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -4.1e+168)
   (* t (* i b))
   (if (<= b -1.3e+19)
     (* b (* c (- z)))
     (if (<= b 5e+16) (* a (- (* j c) (* x t))) (* (- z) (* c b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4.1e+168) {
		tmp = t * (i * b);
	} else if (b <= -1.3e+19) {
		tmp = b * (c * -z);
	} else if (b <= 5e+16) {
		tmp = a * ((j * c) - (x * t));
	} else {
		tmp = -z * (c * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-4.1d+168)) then
        tmp = t * (i * b)
    else if (b <= (-1.3d+19)) then
        tmp = b * (c * -z)
    else if (b <= 5d+16) then
        tmp = a * ((j * c) - (x * t))
    else
        tmp = -z * (c * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4.1e+168) {
		tmp = t * (i * b);
	} else if (b <= -1.3e+19) {
		tmp = b * (c * -z);
	} else if (b <= 5e+16) {
		tmp = a * ((j * c) - (x * t));
	} else {
		tmp = -z * (c * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -4.1e+168:
		tmp = t * (i * b)
	elif b <= -1.3e+19:
		tmp = b * (c * -z)
	elif b <= 5e+16:
		tmp = a * ((j * c) - (x * t))
	else:
		tmp = -z * (c * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -4.1e+168)
		tmp = Float64(t * Float64(i * b));
	elseif (b <= -1.3e+19)
		tmp = Float64(b * Float64(c * Float64(-z)));
	elseif (b <= 5e+16)
		tmp = Float64(a * Float64(Float64(j * c) - Float64(x * t)));
	else
		tmp = Float64(Float64(-z) * Float64(c * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -4.1e+168)
		tmp = t * (i * b);
	elseif (b <= -1.3e+19)
		tmp = b * (c * -z);
	elseif (b <= 5e+16)
		tmp = a * ((j * c) - (x * t));
	else
		tmp = -z * (c * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -4.1e+168], N[(t * N[(i * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.3e+19], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e+16], N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-z) * N[(c * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.1000000000000003e168

   1. Initial program 86.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 86.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 61.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 61.3%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 61.3%

         \[\leadsto t \cdot \left(-1 \cdot \left(\color{blue}{x \cdot a} - b \cdot i\right)\right) \]

      3. *-commutative 61.3%

         \[\leadsto t \cdot \left(-1 \cdot \left(x \cdot a - \color{blue}{i \cdot b}\right)\right) \]

   6. Simplified 61.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(x \cdot a - i \cdot b\right)\right)} \]

   7. Taylor expanded in x around 0 46.5%

      \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot i\right)\right)}\right) \]
   8. Step-by-step derivation

      1. associate-*r* 46.5%

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot i\right)}\right) \]

      2. neg-mul-1 46.5%

         \[\leadsto t \cdot \left(-1 \cdot \left(\color{blue}{\left(-b\right)} \cdot i\right)\right) \]

      3. *-commutative 46.5%

         \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) \]

   9. Simplified 46.5%

      \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) \]

   if -4.1000000000000003e168 < b < -1.3e19

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 73.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in c around inf 44.5%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 44.5%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 44.5%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

   7. Simplified 44.5%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} \]

   if -1.3e19 < b < 5e16

   1. Initial program 77.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 77.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 50.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 50.4%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 50.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   if 5e16 < b

   1. Initial program 80.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 80.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 80.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 80.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 80.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 52.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 52.8%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 52.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   7. Taylor expanded in x around 0 47.5%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 47.5%

         \[\leadsto z \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot c\right)} \]

      2. neg-mul-1 47.5%

         \[\leadsto z \cdot \left(\color{blue}{\left(-b\right)} \cdot c\right) \]

      3. *-commutative 47.5%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   9. Simplified 47.5%

      \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+168}:\\ \;\;\;\;t \cdot \left(i \cdot b\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(c \cdot b\right)\\ \end{array} \]

Alternative 23: 52.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-172}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{elif}\;b \leq 8400000000000:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* c z)))))
   (if (<= b -2.5e+29)
     t_1
     (if (<= b 1.6e-172)
       (* j (- (* a c) (* i y)))
       (if (<= b 8400000000000.0) (* a (- (* j c) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (c * z));
	double tmp;
	if (b <= -2.5e+29) {
		tmp = t_1;
	} else if (b <= 1.6e-172) {
		tmp = j * ((a * c) - (i * y));
	} else if (b <= 8400000000000.0) {
		tmp = a * ((j * c) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((t * i) - (c * z))
    if (b <= (-2.5d+29)) then
        tmp = t_1
    else if (b <= 1.6d-172) then
        tmp = j * ((a * c) - (i * y))
    else if (b <= 8400000000000.0d0) then
        tmp = a * ((j * c) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (c * z));
	double tmp;
	if (b <= -2.5e+29) {
		tmp = t_1;
	} else if (b <= 1.6e-172) {
		tmp = j * ((a * c) - (i * y));
	} else if (b <= 8400000000000.0) {
		tmp = a * ((j * c) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (c * z))
	tmp = 0
	if b <= -2.5e+29:
		tmp = t_1
	elif b <= 1.6e-172:
		tmp = j * ((a * c) - (i * y))
	elif b <= 8400000000000.0:
		tmp = a * ((j * c) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(c * z)))
	tmp = 0.0
	if (b <= -2.5e+29)
		tmp = t_1;
	elseif (b <= 1.6e-172)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(i * y)));
	elseif (b <= 8400000000000.0)
		tmp = Float64(a * Float64(Float64(j * c) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (c * z));
	tmp = 0.0;
	if (b <= -2.5e+29)
		tmp = t_1;
	elseif (b <= 1.6e-172)
		tmp = j * ((a * c) - (i * y));
	elseif (b <= 8400000000000.0)
		tmp = a * ((j * c) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e+29], t$95$1, If[LessEqual[b, 1.6e-172], N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8400000000000.0], N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.5e29 or 8.4e12 < b

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 81.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 81.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 81.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 81.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 60.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 60.9%

         \[\leadsto b \cdot \left(\color{blue}{t \cdot i} - c \cdot z\right) \]

      2. *-commutative 60.9%

         \[\leadsto b \cdot \left(t \cdot i - \color{blue}{z \cdot c}\right) \]

   6. Simplified 60.9%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i - z \cdot c\right)} \]

   if -2.5e29 < b < 1.6000000000000001e-172

   1. Initial program 77.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 77.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 77.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 77.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 77.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 77.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 78.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 79.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in j around inf 53.4%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + a \cdot c\right)} \]
   8. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + -1 \cdot \left(i \cdot y\right)\right)} \]

      2. mul-1-neg 53.4%

         \[\leadsto j \cdot \left(a \cdot c + \color{blue}{\left(-i \cdot y\right)}\right) \]

      3. sub-neg 53.4%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      4. *-commutative 53.4%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   9. Simplified 53.4%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   if 1.6000000000000001e-172 < b < 8.4e12

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 66.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 66.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 66.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 66.5%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 66.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+29}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-172}:\\ \;\;\;\;j \cdot \left(a \cdot c - i \cdot y\right)\\ \mathbf{elif}\;b \leq 8400000000000:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \end{array} \]

Alternative 24: 51.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.95 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-243}:\\ \;\;\;\;t \cdot \left(i \cdot b - a \cdot x\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* j a) (* z b)))))
   (if (<= c -1.95e-7)
     t_1
     (if (<= c 1.3e-243)
       (* t (- (* i b) (* a x)))
       (if (<= c 6.8e+118) (* x (- (* z y) (* a t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((j * a) - (z * b));
	double tmp;
	if (c <= -1.95e-7) {
		tmp = t_1;
	} else if (c <= 1.3e-243) {
		tmp = t * ((i * b) - (a * x));
	} else if (c <= 6.8e+118) {
		tmp = x * ((z * y) - (a * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((j * a) - (z * b))
    if (c <= (-1.95d-7)) then
        tmp = t_1
    else if (c <= 1.3d-243) then
        tmp = t * ((i * b) - (a * x))
    else if (c <= 6.8d+118) then
        tmp = x * ((z * y) - (a * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((j * a) - (z * b));
	double tmp;
	if (c <= -1.95e-7) {
		tmp = t_1;
	} else if (c <= 1.3e-243) {
		tmp = t * ((i * b) - (a * x));
	} else if (c <= 6.8e+118) {
		tmp = x * ((z * y) - (a * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((j * a) - (z * b))
	tmp = 0
	if c <= -1.95e-7:
		tmp = t_1
	elif c <= 1.3e-243:
		tmp = t * ((i * b) - (a * x))
	elif c <= 6.8e+118:
		tmp = x * ((z * y) - (a * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(j * a) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.95e-7)
		tmp = t_1;
	elseif (c <= 1.3e-243)
		tmp = Float64(t * Float64(Float64(i * b) - Float64(a * x)));
	elseif (c <= 6.8e+118)
		tmp = Float64(x * Float64(Float64(z * y) - Float64(a * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((j * a) - (z * b));
	tmp = 0.0;
	if (c <= -1.95e-7)
		tmp = t_1;
	elseif (c <= 1.3e-243)
		tmp = t * ((i * b) - (a * x));
	elseif (c <= 6.8e+118)
		tmp = x * ((z * y) - (a * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(j * a), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.95e-7], t$95$1, If[LessEqual[c, 1.3e-243], N[(t * N[(N[(i * b), $MachinePrecision] - N[(a * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e+118], N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.95000000000000012e-7 or 6.79999999999999973e118 < c

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 78.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 78.0%

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{z \cdot b}\right) \]

   6. Simplified 78.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -1.95000000000000012e-7 < c < 1.2999999999999999e-243

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 77.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 51.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 51.4%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 51.4%

         \[\leadsto t \cdot \left(-1 \cdot \left(\color{blue}{x \cdot a} - b \cdot i\right)\right) \]

      3. *-commutative 51.4%

         \[\leadsto t \cdot \left(-1 \cdot \left(x \cdot a - \color{blue}{i \cdot b}\right)\right) \]

   6. Simplified 51.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(x \cdot a - i \cdot b\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 51.4%

         \[\leadsto t \cdot \color{blue}{\left(-\left(x \cdot a - i \cdot b\right)\right)} \]

      2. distribute-rgt-neg-out 51.4%

         \[\leadsto \color{blue}{-t \cdot \left(x \cdot a - i \cdot b\right)} \]

      3. *-commutative 51.4%

         \[\leadsto -t \cdot \left(\color{blue}{a \cdot x} - i \cdot b\right) \]

   8. Applied egg-rr 51.4%

      \[\leadsto \color{blue}{-t \cdot \left(a \cdot x - i \cdot b\right)} \]

   if 1.2999999999999999e-243 < c < 6.79999999999999973e118

   1. Initial program 84.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 84.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 84.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 84.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 84.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 84.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 88.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 89.9%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in x around inf 50.9%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   8. Step-by-step derivation

      1. +-commutative 50.9%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} \]

      2. mul-1-neg 50.9%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) \]

      3. sub-neg 50.9%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

   9. Simplified 50.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{-7}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{-243}:\\ \;\;\;\;t \cdot \left(i \cdot b - a \cdot x\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \end{array} \]

Alternative 25: 30.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot \left(c \cdot b\right)\\ \mathbf{if}\;b \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-255}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-175}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 7400000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- z) (* c b))))
   (if (<= b -8.2e+30)
     t_1
     (if (<= b -3.3e-255)
       (* z (* x y))
       (if (<= b 2.8e-175)
         (* j (* a c))
         (if (<= b 7400000000.0) (* a (* x (- t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -z * (c * b);
	double tmp;
	if (b <= -8.2e+30) {
		tmp = t_1;
	} else if (b <= -3.3e-255) {
		tmp = z * (x * y);
	} else if (b <= 2.8e-175) {
		tmp = j * (a * c);
	} else if (b <= 7400000000.0) {
		tmp = a * (x * -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -z * (c * b)
    if (b <= (-8.2d+30)) then
        tmp = t_1
    else if (b <= (-3.3d-255)) then
        tmp = z * (x * y)
    else if (b <= 2.8d-175) then
        tmp = j * (a * c)
    else if (b <= 7400000000.0d0) then
        tmp = a * (x * -t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -z * (c * b);
	double tmp;
	if (b <= -8.2e+30) {
		tmp = t_1;
	} else if (b <= -3.3e-255) {
		tmp = z * (x * y);
	} else if (b <= 2.8e-175) {
		tmp = j * (a * c);
	} else if (b <= 7400000000.0) {
		tmp = a * (x * -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -z * (c * b)
	tmp = 0
	if b <= -8.2e+30:
		tmp = t_1
	elif b <= -3.3e-255:
		tmp = z * (x * y)
	elif b <= 2.8e-175:
		tmp = j * (a * c)
	elif b <= 7400000000.0:
		tmp = a * (x * -t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-z) * Float64(c * b))
	tmp = 0.0
	if (b <= -8.2e+30)
		tmp = t_1;
	elseif (b <= -3.3e-255)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 2.8e-175)
		tmp = Float64(j * Float64(a * c));
	elseif (b <= 7400000000.0)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -z * (c * b);
	tmp = 0.0;
	if (b <= -8.2e+30)
		tmp = t_1;
	elseif (b <= -3.3e-255)
		tmp = z * (x * y);
	elseif (b <= 2.8e-175)
		tmp = j * (a * c);
	elseif (b <= 7400000000.0)
		tmp = a * (x * -t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-z) * N[(c * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.2e+30], t$95$1, If[LessEqual[b, -3.3e-255], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e-175], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7400000000.0], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.20000000000000011e30 or 7.4e9 < b

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 51.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 51.9%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 51.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   7. Taylor expanded in x around 0 42.8%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 42.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(-1 \cdot b\right) \cdot c\right)} \]

      2. neg-mul-1 42.8%

         \[\leadsto z \cdot \left(\color{blue}{\left(-b\right)} \cdot c\right) \]

      3. *-commutative 42.8%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   9. Simplified 42.8%

      \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   if -8.20000000000000011e30 < b < -3.29999999999999988e-255

   1. Initial program 83.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 83.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 83.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 83.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 83.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 83.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 38.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 38.0%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 38.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   7. Taylor expanded in x around inf 32.8%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -3.29999999999999988e-255 < b < 2.8e-175

   1. Initial program 70.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 70.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 68.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 70.5%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in j around inf 56.7%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + a \cdot c\right)} \]
   8. Step-by-step derivation

      1. +-commutative 56.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + -1 \cdot \left(i \cdot y\right)\right)} \]

      2. mul-1-neg 56.7%

         \[\leadsto j \cdot \left(a \cdot c + \color{blue}{\left(-i \cdot y\right)}\right) \]

      3. sub-neg 56.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      4. *-commutative 56.7%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   9. Simplified 56.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   10. Taylor expanded in a around inf 38.3%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 43.9%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 43.9%

          \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   12. Simplified 43.9%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   if 2.8e-175 < b < 7.4e9

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 74.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 66.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 66.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 66.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 66.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 66.5%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 66.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around 0 58.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 58.5%

         \[\leadsto a \cdot \color{blue}{\left(\left(-1 \cdot t\right) \cdot x\right)} \]

      2. neg-mul-1 58.5%

         \[\leadsto a \cdot \left(\color{blue}{\left(-t\right)} \cdot x\right) \]

      3. *-commutative 58.5%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 58.5%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;\left(-z\right) \cdot \left(c \cdot b\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-255}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-175}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 7400000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(c \cdot b\right)\\ \end{array} \]

Alternative 26: 52.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+19} \lor \neg \left(b \leq 2900000000000\right):\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -3.4e+19) (not (<= b 2900000000000.0)))
   (* b (- (* t i) (* c z)))
   (* a (- (* j c) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.4e+19) || !(b <= 2900000000000.0)) {
		tmp = b * ((t * i) - (c * z));
	} else {
		tmp = a * ((j * c) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-3.4d+19)) .or. (.not. (b <= 2900000000000.0d0))) then
        tmp = b * ((t * i) - (c * z))
    else
        tmp = a * ((j * c) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -3.4e+19) || !(b <= 2900000000000.0)) {
		tmp = b * ((t * i) - (c * z));
	} else {
		tmp = a * ((j * c) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -3.4e+19) or not (b <= 2900000000000.0):
		tmp = b * ((t * i) - (c * z))
	else:
		tmp = a * ((j * c) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -3.4e+19) || !(b <= 2900000000000.0))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(c * z)));
	else
		tmp = Float64(a * Float64(Float64(j * c) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -3.4e+19) || ~((b <= 2900000000000.0)))
		tmp = b * ((t * i) - (c * z));
	else
		tmp = a * ((j * c) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -3.4e+19], N[Not[LessEqual[b, 2900000000000.0]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(j * c), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.4e19 or 2.9e12 < b

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 59.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 59.7%

         \[\leadsto b \cdot \left(\color{blue}{t \cdot i} - c \cdot z\right) \]

      2. *-commutative 59.7%

         \[\leadsto b \cdot \left(t \cdot i - \color{blue}{z \cdot c}\right) \]

   6. Simplified 59.7%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i - z \cdot c\right)} \]

   if -3.4e19 < b < 2.9e12

   1. Initial program 78.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 50.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 50.7%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 50.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+19} \lor \neg \left(b \leq 2900000000000\right):\\ \;\;\;\;b \cdot \left(t \cdot i - c \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(j \cdot c - x \cdot t\right)\\ \end{array} \]

Alternative 27: 51.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{-23} \lor \neg \left(c \leq 3.2 \cdot 10^{+118}\right):\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -2.5e-23) (not (<= c 3.2e+118)))
   (* c (- (* j a) (* z b)))
   (* x (- (* z y) (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.5e-23) || !(c <= 3.2e+118)) {
		tmp = c * ((j * a) - (z * b));
	} else {
		tmp = x * ((z * y) - (a * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-2.5d-23)) .or. (.not. (c <= 3.2d+118))) then
        tmp = c * ((j * a) - (z * b))
    else
        tmp = x * ((z * y) - (a * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.5e-23) || !(c <= 3.2e+118)) {
		tmp = c * ((j * a) - (z * b));
	} else {
		tmp = x * ((z * y) - (a * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -2.5e-23) or not (c <= 3.2e+118):
		tmp = c * ((j * a) - (z * b))
	else:
		tmp = x * ((z * y) - (a * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -2.5e-23) || !(c <= 3.2e+118))
		tmp = Float64(c * Float64(Float64(j * a) - Float64(z * b)));
	else
		tmp = Float64(x * Float64(Float64(z * y) - Float64(a * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -2.5e-23) || ~((c <= 3.2e+118)))
		tmp = c * ((j * a) - (z * b));
	else
		tmp = x * ((z * y) - (a * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -2.5e-23], N[Not[LessEqual[c, 3.2e+118]], $MachinePrecision]], N[(c * N[(N[(j * a), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.5000000000000001e-23 or 3.20000000000000016e118 < c

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 76.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 76.6%

         \[\leadsto c \cdot \left(a \cdot j - \color{blue}{z \cdot b}\right) \]

   6. Simplified 76.6%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - z \cdot b\right)} \]

   if -2.5000000000000001e-23 < c < 3.20000000000000016e118

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 87.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 88.3%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in x around inf 46.0%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   8. Step-by-step derivation

      1. +-commutative 46.0%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} \]

      2. mul-1-neg 46.0%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) \]

      3. sub-neg 46.0%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

   9. Simplified 46.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{-23} \lor \neg \left(c \leq 3.2 \cdot 10^{+118}\right):\\ \;\;\;\;c \cdot \left(j \cdot a - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right)\\ \end{array} \]

Alternative 28: 29.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{-76} \lor \neg \left(c \leq 6 \cdot 10^{-101}\right):\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -7.2e-76) (not (<= c 6e-101))) (* a (* j c)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -7.2e-76) || !(c <= 6e-101)) {
		tmp = a * (j * c);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-7.2d-76)) .or. (.not. (c <= 6d-101))) then
        tmp = a * (j * c)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -7.2e-76) || !(c <= 6e-101)) {
		tmp = a * (j * c);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -7.2e-76) or not (c <= 6e-101):
		tmp = a * (j * c)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -7.2e-76) || !(c <= 6e-101))
		tmp = Float64(a * Float64(j * c));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -7.2e-76) || ~((c <= 6e-101)))
		tmp = a * (j * c);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -7.2e-76], N[Not[LessEqual[c, 6e-101]], $MachinePrecision]], N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -7.2000000000000001e-76 or 6.0000000000000006e-101 < c

   1. Initial program 78.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 78.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 43.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 43.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 43.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 43.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 43.6%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 43.6%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 43.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around inf 32.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -7.2000000000000001e-76 < c < 6.0000000000000006e-101

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 65.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in i around inf 28.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{-76} \lor \neg \left(c \leq 6 \cdot 10^{-101}\right):\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 29: 30.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+32} \lor \neg \left(y \leq 1.45 \cdot 10^{+62}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -9e+32) (not (<= y 1.45e+62))) (* z (* x y)) (* j (* a c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -9e+32) || !(y <= 1.45e+62)) {
		tmp = z * (x * y);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-9d+32)) .or. (.not. (y <= 1.45d+62))) then
        tmp = z * (x * y)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -9e+32) || !(y <= 1.45e+62)) {
		tmp = z * (x * y);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -9e+32) or not (y <= 1.45e+62):
		tmp = z * (x * y)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -9e+32) || !(y <= 1.45e+62))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -9e+32) || ~((y <= 1.45e+62)))
		tmp = z * (x * y);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -9e+32], N[Not[LessEqual[y, 1.45e+62]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.0000000000000007e32 or 1.44999999999999992e62 < y

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 67.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 67.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 67.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 67.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 47.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.6%

         \[\leadsto z \cdot \left(x \cdot y - \color{blue}{c \cdot b}\right) \]

   6. Simplified 47.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - c \cdot b\right)} \]

   7. Taylor expanded in x around inf 42.3%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -9.0000000000000007e32 < y < 1.44999999999999992e62

   1. Initial program 85.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 85.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 79.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 81.9%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in j around inf 41.5%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + a \cdot c\right)} \]
   8. Step-by-step derivation

      1. +-commutative 41.5%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + -1 \cdot \left(i \cdot y\right)\right)} \]

      2. mul-1-neg 41.5%

         \[\leadsto j \cdot \left(a \cdot c + \color{blue}{\left(-i \cdot y\right)}\right) \]

      3. sub-neg 41.5%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      4. *-commutative 41.5%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   9. Simplified 41.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   10. Taylor expanded in a around inf 26.9%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 30.1%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 30.1%

          \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   12. Simplified 30.1%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+32} \lor \neg \left(y \leq 1.45 \cdot 10^{+62}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]

Alternative 30: 29.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.9e-75)
   (* a (* j c))
   (if (<= c 3.8e-101) (* b (* t i)) (* c (* j a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.9e-75) {
		tmp = a * (j * c);
	} else if (c <= 3.8e-101) {
		tmp = b * (t * i);
	} else {
		tmp = c * (j * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.9d-75)) then
        tmp = a * (j * c)
    else if (c <= 3.8d-101) then
        tmp = b * (t * i)
    else
        tmp = c * (j * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.9e-75) {
		tmp = a * (j * c);
	} else if (c <= 3.8e-101) {
		tmp = b * (t * i);
	} else {
		tmp = c * (j * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.9e-75:
		tmp = a * (j * c)
	elif c <= 3.8e-101:
		tmp = b * (t * i)
	else:
		tmp = c * (j * a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.9e-75)
		tmp = Float64(a * Float64(j * c));
	elseif (c <= 3.8e-101)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(c * Float64(j * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.9e-75)
		tmp = a * (j * c);
	elseif (c <= 3.8e-101)
		tmp = b * (t * i);
	else
		tmp = c * (j * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.9e-75], N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.8e-101], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(j * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.89999999999999997e-75

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 51.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 51.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 51.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 51.5%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 51.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around inf 41.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -1.89999999999999997e-75 < c < 3.8000000000000001e-101

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 65.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in i around inf 28.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if 3.8000000000000001e-101 < c

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 82.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 82.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 82.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 82.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 76.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 79.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in j around inf 45.7%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + a \cdot c\right)} \]
   8. Step-by-step derivation

      1. +-commutative 45.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + -1 \cdot \left(i \cdot y\right)\right)} \]

      2. mul-1-neg 45.7%

         \[\leadsto j \cdot \left(a \cdot c + \color{blue}{\left(-i \cdot y\right)}\right) \]

      3. sub-neg 45.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      4. *-commutative 45.7%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   9. Simplified 45.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   10. Taylor expanded in a around inf 24.1%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   11. Step-by-step derivation

       1. *-commutative 24.1%

          \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

       2. associate-*r* 29.2%

          \[\leadsto \color{blue}{\left(a \cdot j\right) \cdot c} \]

       3. *-commutative 29.2%

          \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   12. Simplified 29.2%

       \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(j \cdot a\right)\\ \end{array} \]

Alternative 31: 29.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.8e-75)
   (* a (* j c))
   (if (<= c 6.6e-101) (* b (* t i)) (* j (* a c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.8e-75) {
		tmp = a * (j * c);
	} else if (c <= 6.6e-101) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.8d-75)) then
        tmp = a * (j * c)
    else if (c <= 6.6d-101) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.8e-75) {
		tmp = a * (j * c);
	} else if (c <= 6.6e-101) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.8e-75:
		tmp = a * (j * c)
	elif c <= 6.6e-101:
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.8e-75)
		tmp = Float64(a * Float64(j * c));
	elseif (c <= 6.6e-101)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.8e-75)
		tmp = a * (j * c);
	elseif (c <= 6.6e-101)
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.8e-75], N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.6e-101], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.8e-75

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 51.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 51.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 51.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 51.5%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   6. Simplified 51.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   7. Taylor expanded in j around inf 41.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -1.8e-75 < c < 6.59999999999999968e-101

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around 0 65.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   5. Taylor expanded in i around inf 28.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if 6.59999999999999968e-101 < c

   1. Initial program 82.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. *-commutative 82.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. *-commutative 82.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 82.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 82.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around -inf 76.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + a \cdot \left(c \cdot j\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   6. Simplified 79.8%

      \[\leadsto \color{blue}{\left(a \cdot \left(j \cdot c - x \cdot t\right) + \left(j \cdot i - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(t \cdot i - z \cdot c\right)} \]

   7. Taylor expanded in j around inf 45.7%

      \[\leadsto \color{blue}{j \cdot \left(-1 \cdot \left(i \cdot y\right) + a \cdot c\right)} \]
   8. Step-by-step derivation

      1. +-commutative 45.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + -1 \cdot \left(i \cdot y\right)\right)} \]

      2. mul-1-neg 45.7%

         \[\leadsto j \cdot \left(a \cdot c + \color{blue}{\left(-i \cdot y\right)}\right) \]

      3. sub-neg 45.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - i \cdot y\right)} \]

      4. *-commutative 45.7%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   9. Simplified 45.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   10. Taylor expanded in a around inf 24.1%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 32.7%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 32.7%

          \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]

   12. Simplified 32.7%

       \[\leadsto \color{blue}{j \cdot \left(a \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(j \cdot c\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-101}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]

Alternative 32: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(j \cdot c\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* j c)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (j * c);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (j * c)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (j * c);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (j * c)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(j * c))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (j * c);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(j * c), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.0%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. *-commutative 79.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. *-commutative 79.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. *-commutative 79.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. *-commutative 79.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right) \]

3. Simplified 79.0%

   \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)} \]

4. Taylor expanded in a around inf 40.4%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
5. Step-by-step derivation

   1. +-commutative 40.4%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 40.4%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 40.4%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 40.4%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. *-commutative 40.4%

      \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

6. Simplified 40.4%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

7. Taylor expanded in j around inf 22.7%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

8. Final simplification 22.7%

   \[\leadsto a \cdot \left(j \cdot c\right) \]

Developer target: 59.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023301 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))