Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.6% → 78.9%

Time: 38.2s

Alternatives: 30

Speedup: 0.4×

• 58.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 72.6% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 78.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := \left(t_2 + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{-91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2 + \left(t_1 + y \cdot \left(x \cdot z - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (+ (+ t_2 (* x (- (* y z) (* t a)))) (* j (- (* t c) (* y i))))))
   (if (<= t_3 -5e-91)
     t_3
     (if (<= t_3 INFINITY) (+ t_2 (+ t_1 (* y (- (* x z) (* i j))))) 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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = (t_2 + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_3 <= -5e-91) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2 + (t_1 + (y * ((x * z) - (i * j))));
	} 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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = (t_2 + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_3 <= -5e-91) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2 + (t_1 + (y * ((x * z) - (i * j))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = b * ((a * i) - (z * c))
	t_3 = (t_2 + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_3 <= -5e-91:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_2 + (t_1 + (y * ((x * z) - (i * j))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(Float64(t_2 + Float64(x * Float64(Float64(y * z) - Float64(t * a)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_3 <= -5e-91)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = Float64(t_2 + Float64(t_1 + Float64(y * Float64(Float64(x * z) - Float64(i * j)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = b * ((a * i) - (z * c));
	t_3 = (t_2 + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_3 <= -5e-91)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2 + (t_1 + (y * ((x * z) - (i * j))));
	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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e-91], t$95$3, If[LessEqual[t$95$3, Infinity], N[(t$95$2 + N[(t$95$1 + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < -4.99999999999999997e-91

   1. Initial program 93.7%

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

   if -4.99999999999999997e-91 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 80.6%

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

   2. Taylor expanded in y around -inf 81.1%

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

   4. Simplified 89.1%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around inf 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

      4. *-commutative 53.1%

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

      5. *-commutative 53.1%

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

   4. Simplified 53.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq -5 \cdot 10^{-91}:\\ \;\;\;\;\left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;\left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + \left(t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 2: 76.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := \left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_2 \leq 5 \cdot 10^{+283}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_1 + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2
         (+
          (+ (* b (- (* a i) (* z c))) (* x (- (* y z) (* t a))))
          (* j (- (* t c) (* y i))))))
   (if (<= t_2 5e+283)
     t_2
     (if (<= t_2 INFINITY) (+ t_1 (* y (- (* x z) (* i j)))) 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 = t * ((c * j) - (x * a));
	double t_2 = ((b * ((a * i) - (z * c))) + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= 5e+283) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1 + (y * ((x * z) - (i * j)));
	} 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 = t * ((c * j) - (x * a));
	double t_2 = ((b * ((a * i) - (z * c))) + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= 5e+283) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + (y * ((x * z) - (i * j)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = ((b * ((a * i) - (z * c))) + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_2 <= 5e+283:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_1 + (y * ((x * z) - (i * j)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + Float64(x * Float64(Float64(y * z) - Float64(t * a)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= 5e+283)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(t_1 + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = ((b * ((a * i) - (z * c))) + (x * ((y * z) - (t * a)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_2 <= 5e+283)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_1 + (y * ((x * z) - (i * j)));
	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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 5e+283], t$95$2, If[LessEqual[t$95$2, Infinity], N[(t$95$1 + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < 5.0000000000000004e283

   1. Initial program 94.1%

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

   if 5.0000000000000004e283 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 70.4%

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

   2. Taylor expanded in y around -inf 76.8%

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

   4. Simplified 84.5%

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

   5. Taylor expanded in b around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. *-commutative 77.9%

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

      3. *-commutative 77.9%

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

      4. mul-1-neg 77.9%

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

      5. unsub-neg 77.9%

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

   7. Simplified 77.9%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around inf 53.1%

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

      1. +-commutative 53.1%

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

      2. mul-1-neg 53.1%

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

      3. unsub-neg 53.1%

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

      4. *-commutative 53.1%

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

      5. *-commutative 53.1%

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

   4. Simplified 53.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq 5 \cdot 10^{+283}:\\ \;\;\;\;\left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;\left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 3: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-14}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{+94}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.46e+128)
   (* a (- (* b i) (* x t)))
   (if (<= a -9.4e-14)
     (+ (* t (- (* c j) (* x a))) (* b (- (* a i) (* z c))))
     (if (<= a 7e-139)
       (+ (* y (- (* x z) (* i j))) (* c (- (* t j) (* z b))))
       (if (<= a 6.3e+94)
         (+
          (* j (- (* t c) (* y i)))
          (- (* x (- (* y z) (* t a))) (* z (* b c))))
         (- (* i (* a b)) (* t (- (* x a) (* c j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.46e+128) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -9.4e-14) {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	} else if (a <= 7e-139) {
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	} else if (a <= 6.3e+94) {
		tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (z * (b * c)));
	} else {
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)));
	}
	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 (a <= (-1.46d+128)) then
        tmp = a * ((b * i) - (x * t))
    else if (a <= (-9.4d-14)) then
        tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
    else if (a <= 7d-139) then
        tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)))
    else if (a <= 6.3d+94) then
        tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (z * (b * c)))
    else
        tmp = (i * (a * b)) - (t * ((x * a) - (c * j)))
    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 (a <= -1.46e+128) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -9.4e-14) {
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	} else if (a <= 7e-139) {
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	} else if (a <= 6.3e+94) {
		tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (z * (b * c)));
	} else {
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.46e+128:
		tmp = a * ((b * i) - (x * t))
	elif a <= -9.4e-14:
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
	elif a <= 7e-139:
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)))
	elif a <= 6.3e+94:
		tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (z * (b * c)))
	else:
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.46e+128)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (a <= -9.4e-14)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (a <= 7e-139)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(c * Float64(Float64(t * j) - Float64(z * b))));
	elseif (a <= 6.3e+94)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c))));
	else
		tmp = Float64(Float64(i * Float64(a * b)) - Float64(t * Float64(Float64(x * a) - Float64(c * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.46e+128)
		tmp = a * ((b * i) - (x * t));
	elseif (a <= -9.4e-14)
		tmp = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	elseif (a <= 7e-139)
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	elseif (a <= 6.3e+94)
		tmp = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) - (z * (b * c)));
	else
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.46e+128], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -9.4e-14], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e-139], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.3e+94], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(x * a), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.4599999999999999e128

   1. Initial program 56.6%

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

   2. Taylor expanded in y around -inf 64.0%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in a around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

   7. Simplified 75.4%

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

   if -1.4599999999999999e128 < a < -9.4000000000000003e-14

   1. Initial program 72.5%

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

   2. Taylor expanded in y around 0 72.4%

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

   4. Simplified 72.4%

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

   if -9.4000000000000003e-14 < a < 7.00000000000000002e-139

   1. Initial program 75.1%

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

   2. Taylor expanded in y around -inf 83.0%

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

   4. Simplified 87.0%

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

   5. Taylor expanded in a around 0 82.2%

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

      1. +-commutative 82.2%

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

      2. associate-+l+ 82.2%

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

      3. +-commutative 82.2%

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

      4. associate-*r* 82.2%

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

      5. *-commutative 82.2%

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

      6. associate-*r* 83.2%

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

      7. associate-*r* 83.2%

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

      8. *-commutative 83.2%

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

      9. distribute-rgt-in 84.2%

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

   7. Simplified 84.2%

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

   if 7.00000000000000002e-139 < a < 6.3000000000000001e94

   1. Initial program 67.9%

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

   2. Taylor expanded in c around inf 70.3%

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

      1. *-commutative 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*l* 74.7%

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

   4. Simplified 74.7%

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

   if 6.3000000000000001e94 < a

   1. Initial program 53.1%

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

   2. Taylor expanded in y around 0 50.2%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in i around inf 71.3%

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

      1. associate-*r* 31.2%

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

      2. *-commutative 31.2%

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

   7. Simplified 69.8%

      \[\leadsto t \cdot \left(j \cdot c - x \cdot a\right) + \color{blue}{\left(b \cdot a\right) \cdot i} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -9.4 \cdot 10^{-14}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-139}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{+94}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \end{array} \]

Alternative 4: 69.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;a \leq -2.7 \cdot 10^{+146}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-71}:\\ \;\;\;\;\left(b \cdot \left(a \cdot i - z \cdot c\right) + t_1\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+94}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(t_1 - z \cdot \left(b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= a -2.7e+146)
     (* a (- (* b i) (* x t)))
     (if (<= a -6.6e-71)
       (- (+ (* b (- (* a i) (* z c))) t_1) (* y (* i j)))
       (if (<= a 1.4e-136)
         (+ (* y (- (* x z) (* i j))) (* c (- (* t j) (* z b))))
         (if (<= a 5.6e+94)
           (+ (* j (- (* t c) (* y i))) (- t_1 (* z (* b c))))
           (- (* i (* a b)) (* t (- (* x a) (* c j))))))))))

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 * ((y * z) - (t * a));
	double tmp;
	if (a <= -2.7e+146) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -6.6e-71) {
		tmp = ((b * ((a * i) - (z * c))) + t_1) - (y * (i * j));
	} else if (a <= 1.4e-136) {
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	} else if (a <= 5.6e+94) {
		tmp = (j * ((t * c) - (y * i))) + (t_1 - (z * (b * c)));
	} else {
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)));
	}
	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 * ((y * z) - (t * a))
    if (a <= (-2.7d+146)) then
        tmp = a * ((b * i) - (x * t))
    else if (a <= (-6.6d-71)) then
        tmp = ((b * ((a * i) - (z * c))) + t_1) - (y * (i * j))
    else if (a <= 1.4d-136) then
        tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)))
    else if (a <= 5.6d+94) then
        tmp = (j * ((t * c) - (y * i))) + (t_1 - (z * (b * c)))
    else
        tmp = (i * (a * b)) - (t * ((x * a) - (c * j)))
    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 * ((y * z) - (t * a));
	double tmp;
	if (a <= -2.7e+146) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -6.6e-71) {
		tmp = ((b * ((a * i) - (z * c))) + t_1) - (y * (i * j));
	} else if (a <= 1.4e-136) {
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	} else if (a <= 5.6e+94) {
		tmp = (j * ((t * c) - (y * i))) + (t_1 - (z * (b * c)));
	} else {
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if a <= -2.7e+146:
		tmp = a * ((b * i) - (x * t))
	elif a <= -6.6e-71:
		tmp = ((b * ((a * i) - (z * c))) + t_1) - (y * (i * j))
	elif a <= 1.4e-136:
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)))
	elif a <= 5.6e+94:
		tmp = (j * ((t * c) - (y * i))) + (t_1 - (z * (b * c)))
	else:
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (a <= -2.7e+146)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (a <= -6.6e-71)
		tmp = Float64(Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + t_1) - Float64(y * Float64(i * j)));
	elseif (a <= 1.4e-136)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(c * Float64(Float64(t * j) - Float64(z * b))));
	elseif (a <= 5.6e+94)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(t_1 - Float64(z * Float64(b * c))));
	else
		tmp = Float64(Float64(i * Float64(a * b)) - Float64(t * Float64(Float64(x * a) - Float64(c * j))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (a <= -2.7e+146)
		tmp = a * ((b * i) - (x * t));
	elseif (a <= -6.6e-71)
		tmp = ((b * ((a * i) - (z * c))) + t_1) - (y * (i * j));
	elseif (a <= 1.4e-136)
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	elseif (a <= 5.6e+94)
		tmp = (j * ((t * c) - (y * i))) + (t_1 - (z * (b * c)));
	else
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.7e+146], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6.6e-71], N[(N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e-136], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.6e+94], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(x * a), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.69999999999999989e146

   1. Initial program 55.7%

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

   2. Taylor expanded in y around -inf 63.8%

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

   4. Simplified 54.7%

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

   5. Taylor expanded in a around inf 78.9%

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

      1. +-commutative 78.9%

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

      2. mul-1-neg 78.9%

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

      3. unsub-neg 78.9%

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

      4. *-commutative 78.9%

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

      5. *-commutative 78.9%

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

   7. Simplified 78.9%

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

   if -2.69999999999999989e146 < a < -6.6000000000000003e-71

   1. Initial program 73.4%

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

   2. Taylor expanded in c around 0 75.4%

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

      1. associate-*r* 77.3%

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

      2. associate-*r* 77.3%

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

      3. *-commutative 77.3%

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

      4. mul-1-neg 77.3%

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

      5. distribute-rgt-neg-in 77.3%

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

   4. Simplified 77.3%

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

   if -6.6000000000000003e-71 < a < 1.4e-136

   1. Initial program 74.7%

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

   2. Taylor expanded in y around -inf 84.2%

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

   4. Simplified 88.8%

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

   5. Taylor expanded in a around 0 85.6%

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

      1. +-commutative 85.6%

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

      2. associate-+l+ 85.6%

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

      3. +-commutative 85.6%

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

      4. associate-*r* 85.6%

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

      5. *-commutative 85.6%

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

      6. associate-*r* 86.6%

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

      7. associate-*r* 86.6%

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

      8. *-commutative 86.6%

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

      9. distribute-rgt-in 87.7%

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

   7. Simplified 87.7%

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

   if 1.4e-136 < a < 5.59999999999999997e94

   1. Initial program 67.9%

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

   2. Taylor expanded in c around inf 70.3%

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

      1. *-commutative 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*l* 74.7%

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

   4. Simplified 74.7%

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

   if 5.59999999999999997e94 < a

   1. Initial program 53.1%

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

   2. Taylor expanded in y around 0 50.2%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in i around inf 71.3%

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

      1. associate-*r* 31.2%

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

      2. *-commutative 31.2%

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

   7. Simplified 69.8%

      \[\leadsto t \cdot \left(j \cdot c - x \cdot a\right) + \color{blue}{\left(b \cdot a\right) \cdot i} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+146}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-71}:\\ \;\;\;\;\left(b \cdot \left(a \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+94}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \end{array} \]

Alternative 5: 63.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;a \leq -1.68 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-285}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* t (- (* c j) (* x a))) (* b (- (* a i) (* z c))))))
   (if (<= a -1.68e+128)
     (* a (- (* b i) (* x t)))
     (if (<= a -4.8e-19)
       t_1
       (if (<= a -4.9e-73)
         (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))
         (if (<= a -1.42e-115)
           t_1
           (if (<= a 3.3e-285)
             (- (* y (- (* x z) (* i j))) (* c (* z b)))
             (if (<= a 4.5e-113)
               (- (* c (- (* t j) (* z b))) (* i (* y j)))
               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 = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	double tmp;
	if (a <= -1.68e+128) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -4.8e-19) {
		tmp = t_1;
	} else if (a <= -4.9e-73) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (a <= -1.42e-115) {
		tmp = t_1;
	} else if (a <= 3.3e-285) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else if (a <= 4.5e-113) {
		tmp = (c * ((t * j) - (z * b))) - (i * (y * j));
	} 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 = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
    if (a <= (-1.68d+128)) then
        tmp = a * ((b * i) - (x * t))
    else if (a <= (-4.8d-19)) then
        tmp = t_1
    else if (a <= (-4.9d-73)) then
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else if (a <= (-1.42d-115)) then
        tmp = t_1
    else if (a <= 3.3d-285) then
        tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
    else if (a <= 4.5d-113) then
        tmp = (c * ((t * j) - (z * b))) - (i * (y * j))
    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 = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	double tmp;
	if (a <= -1.68e+128) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -4.8e-19) {
		tmp = t_1;
	} else if (a <= -4.9e-73) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if (a <= -1.42e-115) {
		tmp = t_1;
	} else if (a <= 3.3e-285) {
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	} else if (a <= 4.5e-113) {
		tmp = (c * ((t * j) - (z * b))) - (i * (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
	tmp = 0
	if a <= -1.68e+128:
		tmp = a * ((b * i) - (x * t))
	elif a <= -4.8e-19:
		tmp = t_1
	elif a <= -4.9e-73:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	elif a <= -1.42e-115:
		tmp = t_1
	elif a <= 3.3e-285:
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b))
	elif a <= 4.5e-113:
		tmp = (c * ((t * j) - (z * b))) - (i * (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (a <= -1.68e+128)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (a <= -4.8e-19)
		tmp = t_1;
	elseif (a <= -4.9e-73)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (a <= -1.42e-115)
		tmp = t_1;
	elseif (a <= 3.3e-285)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(c * Float64(z * b)));
	elseif (a <= 4.5e-113)
		tmp = Float64(Float64(c * Float64(Float64(t * j) - Float64(z * b))) - Float64(i * Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (a <= -1.68e+128)
		tmp = a * ((b * i) - (x * t));
	elseif (a <= -4.8e-19)
		tmp = t_1;
	elseif (a <= -4.9e-73)
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	elseif (a <= -1.42e-115)
		tmp = t_1;
	elseif (a <= 3.3e-285)
		tmp = (y * ((x * z) - (i * j))) - (c * (z * b));
	elseif (a <= 4.5e-113)
		tmp = (c * ((t * j) - (z * b))) - (i * (y * j));
	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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.68e+128], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.8e-19], t$95$1, If[LessEqual[a, -4.9e-73], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.42e-115], t$95$1, If[LessEqual[a, 3.3e-285], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e-113], N[(N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.67999999999999993e128

   1. Initial program 56.6%

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

   2. Taylor expanded in y around -inf 64.0%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in a around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

   7. Simplified 75.4%

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

   if -1.67999999999999993e128 < a < -4.80000000000000046e-19 or -4.90000000000000028e-73 < a < -1.41999999999999992e-115 or 4.5000000000000001e-113 < a

   1. Initial program 64.1%

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

   2. Taylor expanded in y around 0 61.1%

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

   4. Simplified 69.4%

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

   if -4.80000000000000046e-19 < a < -4.90000000000000028e-73

   1. Initial program 81.7%

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

   2. Taylor expanded in b around 0 81.9%

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

   if -1.41999999999999992e-115 < a < 3.29999999999999985e-285

   1. Initial program 74.6%

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

   2. Taylor expanded in y around -inf 86.8%

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

   4. Simplified 93.4%

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

   5. Taylor expanded in a around 0 91.6%

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

      1. +-commutative 91.6%

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

      2. associate-+l+ 91.6%

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

      3. +-commutative 91.6%

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

      4. associate-*r* 91.6%

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

      5. *-commutative 91.6%

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

      6. associate-*r* 91.4%

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

      7. associate-*r* 91.4%

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

      8. *-commutative 91.4%

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

      9. distribute-rgt-in 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in j around 0 84.8%

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

      1. mul-1-neg 84.8%

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

      2. *-commutative 84.8%

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

      3. distribute-rgt-neg-in 84.8%

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

   10. Simplified 84.8%

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

   if 3.29999999999999985e-285 < a < 4.5000000000000001e-113

   1. Initial program 73.1%

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

   2. Taylor expanded in y around -inf 73.1%

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

   4. Simplified 77.8%

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

   5. Taylor expanded in a around 0 71.1%

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

      1. +-commutative 71.1%

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

      2. associate-+l+ 71.1%

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

      3. +-commutative 71.1%

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

      4. associate-*r* 71.1%

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

      5. *-commutative 71.1%

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

      6. associate-*r* 77.8%

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

      7. associate-*r* 77.8%

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

      8. *-commutative 77.8%

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

      9. distribute-rgt-in 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in i around inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. *-commutative 69.4%

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

   10. Simplified 69.4%

       \[\leadsto \color{blue}{\left(-i \cdot \left(y \cdot j\right)\right)} + c \cdot \left(j \cdot t - z \cdot b\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.68 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-19}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -4.9 \cdot 10^{-73}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.42 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-285}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-113}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 6: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;a \leq -7.1 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-75}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-115} \lor \neg \left(a \leq 2.4 \cdot 10^{-109}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* t (- (* c j) (* x a))) (* b (- (* a i) (* z c))))))
   (if (<= a -7.1e+127)
     (* a (- (* b i) (* x t)))
     (if (<= a -8.5e-19)
       t_1
       (if (<= a -3.8e-75)
         (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))
         (if (or (<= a -3e-115) (not (<= a 2.4e-109)))
           t_1
           (+ (* y (- (* x z) (* i j))) (* c (- (* t j) (* z 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 = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	double tmp;
	if (a <= -7.1e+127) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -8.5e-19) {
		tmp = t_1;
	} else if (a <= -3.8e-75) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if ((a <= -3e-115) || !(a <= 2.4e-109)) {
		tmp = t_1;
	} else {
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * 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 = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
    if (a <= (-7.1d+127)) then
        tmp = a * ((b * i) - (x * t))
    else if (a <= (-8.5d-19)) then
        tmp = t_1
    else if (a <= (-3.8d-75)) then
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else if ((a <= (-3d-115)) .or. (.not. (a <= 2.4d-109))) then
        tmp = t_1
    else
        tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * 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 = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	double tmp;
	if (a <= -7.1e+127) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -8.5e-19) {
		tmp = t_1;
	} else if (a <= -3.8e-75) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else if ((a <= -3e-115) || !(a <= 2.4e-109)) {
		tmp = t_1;
	} else {
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)))
	tmp = 0
	if a <= -7.1e+127:
		tmp = a * ((b * i) - (x * t))
	elif a <= -8.5e-19:
		tmp = t_1
	elif a <= -3.8e-75:
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	elif (a <= -3e-115) or not (a <= 2.4e-109):
		tmp = t_1
	else:
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (a <= -7.1e+127)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (a <= -8.5e-19)
		tmp = t_1;
	elseif (a <= -3.8e-75)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif ((a <= -3e-115) || !(a <= 2.4e-109))
		tmp = t_1;
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(c * Float64(Float64(t * j) - Float64(z * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * ((c * j) - (x * a))) + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (a <= -7.1e+127)
		tmp = a * ((b * i) - (x * t));
	elseif (a <= -8.5e-19)
		tmp = t_1;
	elseif (a <= -3.8e-75)
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	elseif ((a <= -3e-115) || ~((a <= 2.4e-109)))
		tmp = t_1;
	else
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.1e+127], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.5e-19], t$95$1, If[LessEqual[a, -3.8e-75], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -3e-115], N[Not[LessEqual[a, 2.4e-109]], $MachinePrecision]], t$95$1, N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.0999999999999996e127

   1. Initial program 56.6%

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

   2. Taylor expanded in y around -inf 64.0%

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

   4. Simplified 55.7%

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

   5. Taylor expanded in a around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

      5. *-commutative 75.4%

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

   7. Simplified 75.4%

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

   if -7.0999999999999996e127 < a < -8.50000000000000003e-19 or -3.79999999999999994e-75 < a < -3.0000000000000002e-115 or 2.39999999999999989e-109 < a

   1. Initial program 64.1%

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

   2. Taylor expanded in y around 0 61.1%

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

   4. Simplified 69.4%

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

   if -8.50000000000000003e-19 < a < -3.79999999999999994e-75

   1. Initial program 81.7%

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

   2. Taylor expanded in b around 0 81.9%

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

   if -3.0000000000000002e-115 < a < 2.39999999999999989e-109

   1. Initial program 73.9%

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

   2. Taylor expanded in y around -inf 80.1%

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

   4. Simplified 85.7%

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

   5. Taylor expanded in a around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. associate-+l+ 81.5%

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

      3. +-commutative 81.5%

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

      4. associate-*r* 81.5%

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

      5. *-commutative 81.5%

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

      6. associate-*r* 84.7%

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

      7. associate-*r* 84.7%

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

      8. *-commutative 84.7%

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

      9. distribute-rgt-in 85.8%

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

   7. Simplified 85.8%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.1 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-19}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-75}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-115} \lor \neg \left(a \leq 2.4 \cdot 10^{-109}\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 7: 51.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+136}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-178}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+70} \lor \neg \left(a \leq 1.9 \cdot 10^{+94}\right):\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.95e+136)
   (* a (- (* b i) (* x t)))
   (if (<= a -1.25e-178)
     (* z (- (* x y) (* b c)))
     (if (<= a 4.8e-261)
       (* y (- (* x z) (* i j)))
       (if (<= a 8e-140)
         (* c (- (* t j) (* z b)))
         (if (or (<= a 3.7e+70) (not (<= a 1.9e+94)))
           (- (* i (* a b)) (* t (- (* x a) (* c j))))
           (* i (- (* a b) (* y j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.95e+136) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -1.25e-178) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 4.8e-261) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 8e-140) {
		tmp = c * ((t * j) - (z * b));
	} else if ((a <= 3.7e+70) || !(a <= 1.9e+94)) {
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)));
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	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 (a <= (-1.95d+136)) then
        tmp = a * ((b * i) - (x * t))
    else if (a <= (-1.25d-178)) then
        tmp = z * ((x * y) - (b * c))
    else if (a <= 4.8d-261) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 8d-140) then
        tmp = c * ((t * j) - (z * b))
    else if ((a <= 3.7d+70) .or. (.not. (a <= 1.9d+94))) then
        tmp = (i * (a * b)) - (t * ((x * a) - (c * j)))
    else
        tmp = i * ((a * b) - (y * j))
    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 (a <= -1.95e+136) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -1.25e-178) {
		tmp = z * ((x * y) - (b * c));
	} else if (a <= 4.8e-261) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 8e-140) {
		tmp = c * ((t * j) - (z * b));
	} else if ((a <= 3.7e+70) || !(a <= 1.9e+94)) {
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)));
	} else {
		tmp = i * ((a * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.95e+136:
		tmp = a * ((b * i) - (x * t))
	elif a <= -1.25e-178:
		tmp = z * ((x * y) - (b * c))
	elif a <= 4.8e-261:
		tmp = y * ((x * z) - (i * j))
	elif a <= 8e-140:
		tmp = c * ((t * j) - (z * b))
	elif (a <= 3.7e+70) or not (a <= 1.9e+94):
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)))
	else:
		tmp = i * ((a * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.95e+136)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (a <= -1.25e-178)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (a <= 4.8e-261)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 8e-140)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif ((a <= 3.7e+70) || !(a <= 1.9e+94))
		tmp = Float64(Float64(i * Float64(a * b)) - Float64(t * Float64(Float64(x * a) - Float64(c * j))));
	else
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.95e+136)
		tmp = a * ((b * i) - (x * t));
	elseif (a <= -1.25e-178)
		tmp = z * ((x * y) - (b * c));
	elseif (a <= 4.8e-261)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 8e-140)
		tmp = c * ((t * j) - (z * b));
	elseif ((a <= 3.7e+70) || ~((a <= 1.9e+94)))
		tmp = (i * (a * b)) - (t * ((x * a) - (c * j)));
	else
		tmp = i * ((a * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.95e+136], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.25e-178], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-261], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-140], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 3.7e+70], N[Not[LessEqual[a, 1.9e+94]], $MachinePrecision]], N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(x * a), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -1.9500000000000001e136

   1. Initial program 57.0%

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

   2. Taylor expanded in y around -inf 64.8%

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

   4. Simplified 56.0%

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

   5. Taylor expanded in a around inf 79.5%

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

      1. +-commutative 79.5%

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

      2. mul-1-neg 79.5%

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

      3. unsub-neg 79.5%

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

      4. *-commutative 79.5%

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

      5. *-commutative 79.5%

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

   7. Simplified 79.5%

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

   if -1.9500000000000001e136 < a < -1.24999999999999994e-178

   1. Initial program 72.9%

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

   2. Taylor expanded in z around inf 62.6%

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

      1. *-commutative 62.6%

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

      2. *-commutative 62.6%

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

   4. Simplified 62.6%

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

   if -1.24999999999999994e-178 < a < 4.80000000000000028e-261

   1. Initial program 71.6%

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

   2. Taylor expanded in y around -inf 60.9%

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

      1. mul-1-neg 60.9%

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

      2. *-commutative 60.9%

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

      3. distribute-rgt-neg-in 60.9%

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

      4. +-commutative 60.9%

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

      5. mul-1-neg 60.9%

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

      6. unsub-neg 60.9%

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

   4. Simplified 60.9%

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

   5. Taylor expanded in i around 0 47.9%

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

      1. associate-*r* 47.9%

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

      2. associate-*r* 50.8%

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

      3. associate-*r* 50.8%

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

      4. *-commutative 50.8%

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

      5. associate-*l* 60.9%

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

      6. distribute-rgt-in 60.9%

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

      7. +-commutative 60.9%

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

      8. mul-1-neg 60.9%

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

      9. *-commutative 60.9%

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

      10. unsub-neg 60.9%

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

      11. *-commutative 60.9%

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

   7. Simplified 60.9%

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

   if 4.80000000000000028e-261 < a < 7.9999999999999999e-140

   1. Initial program 79.8%

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

   2. Taylor expanded in c around inf 63.5%

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

      1. *-commutative 63.5%

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

   4. Simplified 63.5%

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

   if 7.9999999999999999e-140 < a < 3.69999999999999989e70 or 1.8999999999999998e94 < a

   1. Initial program 60.8%

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

   2. Taylor expanded in y around 0 48.8%

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

   4. Simplified 65.2%

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

   5. Taylor expanded in i around inf 64.8%

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

      1. associate-*r* 20.4%

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

      2. *-commutative 20.4%

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

   7. Simplified 65.3%

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

   if 3.69999999999999989e70 < a < 1.8999999999999998e94

   1. Initial program 57.9%

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

   2. Taylor expanded in i around inf 85.9%

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

      1. distribute-lft-out-- 85.9%

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

   4. Simplified 85.9%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - a \cdot b\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.95 \cdot 10^{+136}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-178}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+70} \lor \neg \left(a \leq 1.9 \cdot 10^{+94}\right):\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t \cdot \left(x \cdot a - c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 8: 68.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.65 \cdot 10^{+189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{+133} \lor \neg \left(b \leq -1.6 \cdot 10^{-14}\right) \land b \leq 2.2 \cdot 10^{-84}:\\ \;\;\;\;t_1 + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.65e+189)
     t_2
     (if (or (<= b -8.8e+133) (and (not (<= b -1.6e-14)) (<= b 2.2e-84)))
       (+ t_1 (* y (- (* x z) (* i j))))
       (+ 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 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.65e+189) {
		tmp = t_2;
	} else if ((b <= -8.8e+133) || (!(b <= -1.6e-14) && (b <= 2.2e-84))) {
		tmp = t_1 + (y * ((x * z) - (i * j)));
	} else {
		tmp = t_1 + 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 * ((c * j) - (x * a))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.65d+189)) then
        tmp = t_2
    else if ((b <= (-8.8d+133)) .or. (.not. (b <= (-1.6d-14))) .and. (b <= 2.2d-84)) then
        tmp = t_1 + (y * ((x * z) - (i * j)))
    else
        tmp = t_1 + 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 * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.65e+189) {
		tmp = t_2;
	} else if ((b <= -8.8e+133) || (!(b <= -1.6e-14) && (b <= 2.2e-84))) {
		tmp = t_1 + (y * ((x * z) - (i * j)));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.65e+189:
		tmp = t_2
	elif (b <= -8.8e+133) or (not (b <= -1.6e-14) and (b <= 2.2e-84)):
		tmp = t_1 + (y * ((x * z) - (i * j)))
	else:
		tmp = t_1 + t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.65e+189)
		tmp = t_2;
	elseif ((b <= -8.8e+133) || (!(b <= -1.6e-14) && (b <= 2.2e-84)))
		tmp = Float64(t_1 + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.65e+189)
		tmp = t_2;
	elseif ((b <= -8.8e+133) || (~((b <= -1.6e-14)) && (b <= 2.2e-84)))
		tmp = t_1 + (y * ((x * z) - (i * j)));
	else
		tmp = t_1 + 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[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.65e+189], t$95$2, If[Or[LessEqual[b, -8.8e+133], And[N[Not[LessEqual[b, -1.6e-14]], $MachinePrecision], LessEqual[b, 2.2e-84]]], N[(t$95$1 + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.6500000000000001e189

   1. Initial program 59.6%

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

   2. Taylor expanded in b around inf 72.9%

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

      1. *-commutative 72.9%

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

   4. Simplified 72.9%

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

   if -1.6500000000000001e189 < b < -8.8e133 or -1.6000000000000001e-14 < b < 2.1999999999999999e-84

   1. Initial program 64.3%

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

   2. Taylor expanded in y around -inf 67.4%

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

   4. Simplified 73.7%

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

   5. Taylor expanded in b around 0 76.0%

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

      1. +-commutative 76.0%

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

      2. *-commutative 76.0%

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

      3. *-commutative 76.0%

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

      4. mul-1-neg 76.0%

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

      5. unsub-neg 76.0%

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

   7. Simplified 76.0%

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

   if -8.8e133 < b < -1.6000000000000001e-14 or 2.1999999999999999e-84 < b

   1. Initial program 71.7%

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

   2. Taylor expanded in y around 0 71.0%

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

   4. Simplified 71.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+189}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{+133} \lor \neg \left(b \leq -1.6 \cdot 10^{-14}\right) \land b \leq 2.2 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 9: 54.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t_1 + j \cdot \left(t \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+169}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 40:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (+ t_1 (* j (* t c))))
        (t_3 (* y (- (* x z) (* i j))))
        (t_4 (* x (- (* y z) (* t a)))))
   (if (<= x -5.6e+169)
     t_4
     (if (<= x -3.6e+44)
       t_3
       (if (<= x -1.9e-95)
         t_2
         (if (<= x -4.2e-176)
           t_3
           (if (<= x 4.6e-165)
             t_2
             (if (<= x 40.0)
               (* i (- (* a b) (* y j)))
               (if (<= x 3.1e+105) t_1 t_4)))))))))

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 * ((a * i) - (z * c));
	double t_2 = t_1 + (j * (t * c));
	double t_3 = y * ((x * z) - (i * j));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5.6e+169) {
		tmp = t_4;
	} else if (x <= -3.6e+44) {
		tmp = t_3;
	} else if (x <= -1.9e-95) {
		tmp = t_2;
	} else if (x <= -4.2e-176) {
		tmp = t_3;
	} else if (x <= 4.6e-165) {
		tmp = t_2;
	} else if (x <= 40.0) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 3.1e+105) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = t_1 + (j * (t * c))
    t_3 = y * ((x * z) - (i * j))
    t_4 = x * ((y * z) - (t * a))
    if (x <= (-5.6d+169)) then
        tmp = t_4
    else if (x <= (-3.6d+44)) then
        tmp = t_3
    else if (x <= (-1.9d-95)) then
        tmp = t_2
    else if (x <= (-4.2d-176)) then
        tmp = t_3
    else if (x <= 4.6d-165) then
        tmp = t_2
    else if (x <= 40.0d0) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 3.1d+105) then
        tmp = t_1
    else
        tmp = t_4
    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 * ((a * i) - (z * c));
	double t_2 = t_1 + (j * (t * c));
	double t_3 = y * ((x * z) - (i * j));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -5.6e+169) {
		tmp = t_4;
	} else if (x <= -3.6e+44) {
		tmp = t_3;
	} else if (x <= -1.9e-95) {
		tmp = t_2;
	} else if (x <= -4.2e-176) {
		tmp = t_3;
	} else if (x <= 4.6e-165) {
		tmp = t_2;
	} else if (x <= 40.0) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 3.1e+105) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t_1 + (j * (t * c))
	t_3 = y * ((x * z) - (i * j))
	t_4 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -5.6e+169:
		tmp = t_4
	elif x <= -3.6e+44:
		tmp = t_3
	elif x <= -1.9e-95:
		tmp = t_2
	elif x <= -4.2e-176:
		tmp = t_3
	elif x <= 4.6e-165:
		tmp = t_2
	elif x <= 40.0:
		tmp = i * ((a * b) - (y * j))
	elif x <= 3.1e+105:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t_1 + Float64(j * Float64(t * c)))
	t_3 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_4 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -5.6e+169)
		tmp = t_4;
	elseif (x <= -3.6e+44)
		tmp = t_3;
	elseif (x <= -1.9e-95)
		tmp = t_2;
	elseif (x <= -4.2e-176)
		tmp = t_3;
	elseif (x <= 4.6e-165)
		tmp = t_2;
	elseif (x <= 40.0)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 3.1e+105)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t_1 + (j * (t * c));
	t_3 = y * ((x * z) - (i * j));
	t_4 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -5.6e+169)
		tmp = t_4;
	elseif (x <= -3.6e+44)
		tmp = t_3;
	elseif (x <= -1.9e-95)
		tmp = t_2;
	elseif (x <= -4.2e-176)
		tmp = t_3;
	elseif (x <= 4.6e-165)
		tmp = t_2;
	elseif (x <= 40.0)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 3.1e+105)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.6e+169], t$95$4, If[LessEqual[x, -3.6e+44], t$95$3, If[LessEqual[x, -1.9e-95], t$95$2, If[LessEqual[x, -4.2e-176], t$95$3, If[LessEqual[x, 4.6e-165], t$95$2, If[LessEqual[x, 40.0], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.1e+105], t$95$1, t$95$4]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.6000000000000003e169 or 3.10000000000000004e105 < x

   1. Initial program 63.2%

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

   2. Taylor expanded in y around -inf 51.2%

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

   4. Simplified 65.0%

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

   5. Taylor expanded in x around inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

   7. Simplified 76.1%

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

   if -5.6000000000000003e169 < x < -3.6e44 or -1.8999999999999999e-95 < x < -4.19999999999999984e-176

   1. Initial program 66.9%

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

   2. Taylor expanded in y around -inf 58.7%

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

      1. mul-1-neg 58.7%

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

      2. *-commutative 58.7%

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

      3. distribute-rgt-neg-in 58.7%

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

      4. +-commutative 58.7%

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

      5. mul-1-neg 58.7%

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

      6. unsub-neg 58.7%

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

   4. Simplified 58.7%

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

   5. Taylor expanded in i around 0 50.6%

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

      1. associate-*r* 50.6%

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

      2. associate-*r* 50.6%

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

      3. associate-*r* 50.6%

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

      4. *-commutative 50.6%

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

      5. associate-*l* 58.7%

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

      6. distribute-rgt-in 58.7%

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

      7. +-commutative 58.7%

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

      8. mul-1-neg 58.7%

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

      9. *-commutative 58.7%

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

      10. unsub-neg 58.7%

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

      11. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   if -3.6e44 < x < -1.8999999999999999e-95 or -4.19999999999999984e-176 < x < 4.6000000000000001e-165

   1. Initial program 69.0%

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

   2. Taylor expanded in y around 0 76.4%

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

   4. Simplified 77.5%

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

   5. Taylor expanded in j around inf 71.7%

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

      1. associate-*r* 32.6%

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

      2. *-commutative 32.6%

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

      3. associate-*r* 26.1%

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

   7. Simplified 69.7%

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

   if 4.6000000000000001e-165 < x < 40

   1. Initial program 64.7%

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

   2. Taylor expanded in i around inf 54.1%

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

      1. distribute-lft-out-- 54.1%

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

   4. Simplified 54.1%

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

   if 40 < x < 3.10000000000000004e105

   1. Initial program 78.1%

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

   2. Taylor expanded in b around inf 62.4%

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

      1. *-commutative 62.4%

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

   4. Simplified 62.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-95}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-165}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 40:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+105}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 10: 59.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+47}:\\ \;\;\;\;t_2 - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* c (* z b))))
        (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -3e+156)
     t_2
     (if (<= t -1.6e+92)
       t_1
       (if (<= t -9e+47)
         (- t_2 (* y (* i j)))
         (if (<= t -1.4e-193)
           t_1
           (if (<= t 1.46e+68)
             (+ (* b (- (* a i) (* z c))) (* y (* x 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 = (y * ((x * z) - (i * j))) - (c * (z * b));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3e+156) {
		tmp = t_2;
	} else if (t <= -1.6e+92) {
		tmp = t_1;
	} else if (t <= -9e+47) {
		tmp = t_2 - (y * (i * j));
	} else if (t <= -1.4e-193) {
		tmp = t_1;
	} else if (t <= 1.46e+68) {
		tmp = (b * ((a * i) - (z * c))) + (y * (x * 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 = (y * ((x * z) - (i * j))) - (c * (z * b))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-3d+156)) then
        tmp = t_2
    else if (t <= (-1.6d+92)) then
        tmp = t_1
    else if (t <= (-9d+47)) then
        tmp = t_2 - (y * (i * j))
    else if (t <= (-1.4d-193)) then
        tmp = t_1
    else if (t <= 1.46d+68) then
        tmp = (b * ((a * i) - (z * c))) + (y * (x * 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 = (y * ((x * z) - (i * j))) - (c * (z * b));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3e+156) {
		tmp = t_2;
	} else if (t <= -1.6e+92) {
		tmp = t_1;
	} else if (t <= -9e+47) {
		tmp = t_2 - (y * (i * j));
	} else if (t <= -1.4e-193) {
		tmp = t_1;
	} else if (t <= 1.46e+68) {
		tmp = (b * ((a * i) - (z * c))) + (y * (x * z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) - (c * (z * b))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -3e+156:
		tmp = t_2
	elif t <= -1.6e+92:
		tmp = t_1
	elif t <= -9e+47:
		tmp = t_2 - (y * (i * j))
	elif t <= -1.4e-193:
		tmp = t_1
	elif t <= 1.46e+68:
		tmp = (b * ((a * i) - (z * c))) + (y * (x * z))
	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(i * j))) - Float64(c * Float64(z * b)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -3e+156)
		tmp = t_2;
	elseif (t <= -1.6e+92)
		tmp = t_1;
	elseif (t <= -9e+47)
		tmp = Float64(t_2 - Float64(y * Float64(i * j)));
	elseif (t <= -1.4e-193)
		tmp = t_1;
	elseif (t <= 1.46e+68)
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + Float64(y * Float64(x * 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 = (y * ((x * z) - (i * j))) - (c * (z * b));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -3e+156)
		tmp = t_2;
	elseif (t <= -1.6e+92)
		tmp = t_1;
	elseif (t <= -9e+47)
		tmp = t_2 - (y * (i * j));
	elseif (t <= -1.4e-193)
		tmp = t_1;
	elseif (t <= 1.46e+68)
		tmp = (b * ((a * i) - (z * c))) + (y * (x * 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[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+156], t$95$2, If[LessEqual[t, -1.6e+92], t$95$1, If[LessEqual[t, -9e+47], N[(t$95$2 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.4e-193], t$95$1, If[LessEqual[t, 1.46e+68], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3e156 or 1.45999999999999992e68 < t

   1. Initial program 51.6%

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

   2. Taylor expanded in t around inf 74.4%

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

      1. +-commutative 74.4%

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

      2. mul-1-neg 74.4%

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

      3. unsub-neg 74.4%

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

      4. *-commutative 74.4%

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

      5. *-commutative 74.4%

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

   4. Simplified 74.4%

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

   if -3e156 < t < -1.60000000000000013e92 or -8.99999999999999958e47 < t < -1.4000000000000001e-193

   1. Initial program 70.4%

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

   2. Taylor expanded in y around -inf 76.6%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in a around 0 70.5%

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

      1. +-commutative 70.5%

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

      2. associate-+l+ 70.5%

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

      3. +-commutative 70.5%

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

      4. associate-*r* 70.5%

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

      5. *-commutative 70.5%

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

      6. associate-*r* 71.7%

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

      7. associate-*r* 71.7%

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

      8. *-commutative 71.7%

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

      9. distribute-rgt-in 73.0%

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

   7. Simplified 73.0%

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

   8. Taylor expanded in j around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. *-commutative 68.6%

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

      3. distribute-rgt-neg-in 68.6%

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

   10. Simplified 68.6%

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

   if -1.60000000000000013e92 < t < -8.99999999999999958e47

   1. Initial program 74.1%

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

   2. Taylor expanded in y around -inf 55.6%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in b around 0 56.0%

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

      1. +-commutative 56.0%

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

      2. *-commutative 56.0%

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

      3. *-commutative 56.0%

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

      4. mul-1-neg 56.0%

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

      5. unsub-neg 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in i around inf 73.6%

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

      1. associate-*r* 73.6%

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

      2. *-commutative 73.6%

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

   10. Simplified 73.6%

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

   if -1.4000000000000001e-193 < t < 1.45999999999999992e68

   1. Initial program 77.1%

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

   2. Taylor expanded in y around inf 73.5%

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

      1. associate-*r* 74.5%

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

      2. *-commutative 74.5%

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

      3. associate-*r* 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in j around 0 70.1%

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

      1. *-commutative 70.1%

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

      2. associate-*l* 70.2%

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

      3. *-commutative 70.2%

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

      4. *-commutative 70.2%

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

      5. *-commutative 70.2%

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

   7. Simplified 70.2%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq -9 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-193}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 11: 51.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -3.9e+127)
     t_2
     (if (<= a -1.26e-62)
       (* b (- (* a i) (* z c)))
       (if (<= a 1.6e-299)
         t_1
         (if (<= a 1.8e-269)
           (* y (* x z))
           (if (<= a 7.2e-140)
             t_1
             (if (<= a 1.42e+16)
               (* j (- (* t c) (* y i)))
               (if (<= a 2.1e+69) 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 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3.9e+127) {
		tmp = t_2;
	} else if (a <= -1.26e-62) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 1.6e-299) {
		tmp = t_1;
	} else if (a <= 1.8e-269) {
		tmp = y * (x * z);
	} else if (a <= 7.2e-140) {
		tmp = t_1;
	} else if (a <= 1.42e+16) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 2.1e+69) {
		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 = c * ((t * j) - (z * b))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-3.9d+127)) then
        tmp = t_2
    else if (a <= (-1.26d-62)) then
        tmp = b * ((a * i) - (z * c))
    else if (a <= 1.6d-299) then
        tmp = t_1
    else if (a <= 1.8d-269) then
        tmp = y * (x * z)
    else if (a <= 7.2d-140) then
        tmp = t_1
    else if (a <= 1.42d+16) then
        tmp = j * ((t * c) - (y * i))
    else if (a <= 2.1d+69) 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 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3.9e+127) {
		tmp = t_2;
	} else if (a <= -1.26e-62) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 1.6e-299) {
		tmp = t_1;
	} else if (a <= 1.8e-269) {
		tmp = y * (x * z);
	} else if (a <= 7.2e-140) {
		tmp = t_1;
	} else if (a <= 1.42e+16) {
		tmp = j * ((t * c) - (y * i));
	} else if (a <= 2.1e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -3.9e+127:
		tmp = t_2
	elif a <= -1.26e-62:
		tmp = b * ((a * i) - (z * c))
	elif a <= 1.6e-299:
		tmp = t_1
	elif a <= 1.8e-269:
		tmp = y * (x * z)
	elif a <= 7.2e-140:
		tmp = t_1
	elif a <= 1.42e+16:
		tmp = j * ((t * c) - (y * i))
	elif a <= 2.1e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.9e+127)
		tmp = t_2;
	elseif (a <= -1.26e-62)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (a <= 1.6e-299)
		tmp = t_1;
	elseif (a <= 1.8e-269)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 7.2e-140)
		tmp = t_1;
	elseif (a <= 1.42e+16)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (a <= 2.1e+69)
		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 = c * ((t * j) - (z * b));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -3.9e+127)
		tmp = t_2;
	elseif (a <= -1.26e-62)
		tmp = b * ((a * i) - (z * c));
	elseif (a <= 1.6e-299)
		tmp = t_1;
	elseif (a <= 1.8e-269)
		tmp = y * (x * z);
	elseif (a <= 7.2e-140)
		tmp = t_1;
	elseif (a <= 1.42e+16)
		tmp = j * ((t * c) - (y * i));
	elseif (a <= 2.1e+69)
		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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.9e+127], t$95$2, If[LessEqual[a, -1.26e-62], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-299], t$95$1, If[LessEqual[a, 1.8e-269], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e-140], t$95$1, If[LessEqual[a, 1.42e+16], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e+69], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.89999999999999981e127 or 2.10000000000000015e69 < a

   1. Initial program 55.0%

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

   2. Taylor expanded in y around -inf 54.0%

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

   4. Simplified 56.8%

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

   5. Taylor expanded in a around inf 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. unsub-neg 66.5%

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

      4. *-commutative 66.5%

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

      5. *-commutative 66.5%

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

   7. Simplified 66.5%

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

   if -3.89999999999999981e127 < a < -1.26e-62

   1. Initial program 73.3%

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

   2. Taylor expanded in b around inf 53.3%

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

      1. *-commutative 53.3%

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

   4. Simplified 53.3%

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

   if -1.26e-62 < a < 1.60000000000000004e-299 or 1.79999999999999999e-269 < a < 7.2000000000000001e-140 or 1.42e16 < a < 2.10000000000000015e69

   1. Initial program 73.1%

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

   2. Taylor expanded in c around inf 56.9%

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

      1. *-commutative 56.9%

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

   4. Simplified 56.9%

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

   if 1.60000000000000004e-299 < a < 1.79999999999999999e-269

   1. Initial program 75.0%

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

   2. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in i around 0 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-*l* 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 7.2000000000000001e-140 < a < 1.42e16

   1. Initial program 74.3%

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

   2. Taylor expanded in y around -inf 56.9%

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

   4. Simplified 78.1%

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

   5. Taylor expanded in j around inf 48.5%

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

      1. neg-mul-1 48.5%

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

      2. +-commutative 48.5%

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

      3. fma-udef 48.5%

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

      4. fma-neg 48.5%

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

      5. *-commutative 48.5%

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

   7. Simplified 48.5%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - y \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 12: 50.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+165}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+47}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -2e+165)
     t_3
     (if (<= t -4.4e+91)
       t_2
       (if (<= t -4e+47)
         t_3
         (if (<= t -1.1e-98)
           t_1
           (if (<= t -1.08e-147)
             (* y (- (* x z) (* i j)))
             (if (<= t 5.6e-64) t_1 (if (<= t 1.8e+114) t_2 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 = b * ((a * i) - (z * c));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2e+165) {
		tmp = t_3;
	} else if (t <= -4.4e+91) {
		tmp = t_2;
	} else if (t <= -4e+47) {
		tmp = t_3;
	} else if (t <= -1.1e-98) {
		tmp = t_1;
	} else if (t <= -1.08e-147) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 5.6e-64) {
		tmp = t_1;
	} else if (t <= 1.8e+114) {
		tmp = t_2;
	} 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 = b * ((a * i) - (z * c))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-2d+165)) then
        tmp = t_3
    else if (t <= (-4.4d+91)) then
        tmp = t_2
    else if (t <= (-4d+47)) then
        tmp = t_3
    else if (t <= (-1.1d-98)) then
        tmp = t_1
    else if (t <= (-1.08d-147)) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 5.6d-64) then
        tmp = t_1
    else if (t <= 1.8d+114) then
        tmp = t_2
    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 = b * ((a * i) - (z * c));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2e+165) {
		tmp = t_3;
	} else if (t <= -4.4e+91) {
		tmp = t_2;
	} else if (t <= -4e+47) {
		tmp = t_3;
	} else if (t <= -1.1e-98) {
		tmp = t_1;
	} else if (t <= -1.08e-147) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 5.6e-64) {
		tmp = t_1;
	} else if (t <= 1.8e+114) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -2e+165:
		tmp = t_3
	elif t <= -4.4e+91:
		tmp = t_2
	elif t <= -4e+47:
		tmp = t_3
	elif t <= -1.1e-98:
		tmp = t_1
	elif t <= -1.08e-147:
		tmp = y * ((x * z) - (i * j))
	elif t <= 5.6e-64:
		tmp = t_1
	elif t <= 1.8e+114:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2e+165)
		tmp = t_3;
	elseif (t <= -4.4e+91)
		tmp = t_2;
	elseif (t <= -4e+47)
		tmp = t_3;
	elseif (t <= -1.1e-98)
		tmp = t_1;
	elseif (t <= -1.08e-147)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 5.6e-64)
		tmp = t_1;
	elseif (t <= 1.8e+114)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -2e+165)
		tmp = t_3;
	elseif (t <= -4.4e+91)
		tmp = t_2;
	elseif (t <= -4e+47)
		tmp = t_3;
	elseif (t <= -1.1e-98)
		tmp = t_1;
	elseif (t <= -1.08e-147)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 5.6e-64)
		tmp = t_1;
	elseif (t <= 1.8e+114)
		tmp = t_2;
	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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+165], t$95$3, If[LessEqual[t, -4.4e+91], t$95$2, If[LessEqual[t, -4e+47], t$95$3, If[LessEqual[t, -1.1e-98], t$95$1, If[LessEqual[t, -1.08e-147], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e-64], t$95$1, If[LessEqual[t, 1.8e+114], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.9999999999999998e165 or -4.39999999999999999e91 < t < -4.0000000000000002e47 or 1.8e114 < t

   1. Initial program 54.9%

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

   2. Taylor expanded in t around inf 77.1%

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

      1. +-commutative 77.1%

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

      2. mul-1-neg 77.1%

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

      3. unsub-neg 77.1%

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

      4. *-commutative 77.1%

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

      5. *-commutative 77.1%

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

   4. Simplified 77.1%

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

   if -1.9999999999999998e165 < t < -4.39999999999999999e91 or 5.60000000000000008e-64 < t < 1.8e114

   1. Initial program 59.0%

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

   2. Taylor expanded in z around inf 59.6%

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

      1. *-commutative 59.6%

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

      2. *-commutative 59.6%

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

   4. Simplified 59.6%

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

   if -4.0000000000000002e47 < t < -1.09999999999999998e-98 or -1.07999999999999995e-147 < t < 5.60000000000000008e-64

   1. Initial program 78.8%

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

   2. Taylor expanded in b around inf 58.9%

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

      1. *-commutative 58.9%

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

   4. Simplified 58.9%

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

   if -1.09999999999999998e-98 < t < -1.07999999999999995e-147

   1. Initial program 79.3%

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

   2. Taylor expanded in y around -inf 64.9%

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

      1. mul-1-neg 64.9%

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

      2. *-commutative 64.9%

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

      3. distribute-rgt-neg-in 64.9%

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

      4. +-commutative 64.9%

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

      5. mul-1-neg 64.9%

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

      6. unsub-neg 64.9%

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

   4. Simplified 64.9%

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

   5. Taylor expanded in i around 0 64.6%

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

      1. associate-*r* 64.6%

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

      2. associate-*r* 69.5%

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

      3. associate-*r* 69.5%

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

      4. *-commutative 69.5%

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

      5. associate-*l* 64.9%

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

      6. distribute-rgt-in 64.9%

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

      7. +-commutative 64.9%

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

      8. mul-1-neg 64.9%

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

      9. *-commutative 64.9%

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

      10. unsub-neg 64.9%

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

      11. *-commutative 64.9%

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

   7. Simplified 64.9%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-98}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-64}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+114}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 13: 54.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-212}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-165}:\\ \;\;\;\;t_2 + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 82:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= x -5.8e+164)
     t_1
     (if (<= x -3.1e+87)
       (* z (- (* x y) (* b c)))
       (if (<= x -7.8e-212)
         (- (* t (- (* c j) (* x a))) (* y (* i j)))
         (if (<= x 4.6e-165)
           (+ t_2 (* j (* t c)))
           (if (<= x 82.0)
             (* i (- (* a b) (* y j)))
             (if (<= x 3.7e+105) t_2 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 * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (x <= -5.8e+164) {
		tmp = t_1;
	} else if (x <= -3.1e+87) {
		tmp = z * ((x * y) - (b * c));
	} else if (x <= -7.8e-212) {
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j));
	} else if (x <= 4.6e-165) {
		tmp = t_2 + (j * (t * c));
	} else if (x <= 82.0) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 3.7e+105) {
		tmp = t_2;
	} 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 * ((y * z) - (t * a))
    t_2 = b * ((a * i) - (z * c))
    if (x <= (-5.8d+164)) then
        tmp = t_1
    else if (x <= (-3.1d+87)) then
        tmp = z * ((x * y) - (b * c))
    else if (x <= (-7.8d-212)) then
        tmp = (t * ((c * j) - (x * a))) - (y * (i * j))
    else if (x <= 4.6d-165) then
        tmp = t_2 + (j * (t * c))
    else if (x <= 82.0d0) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= 3.7d+105) then
        tmp = t_2
    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 * ((y * z) - (t * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (x <= -5.8e+164) {
		tmp = t_1;
	} else if (x <= -3.1e+87) {
		tmp = z * ((x * y) - (b * c));
	} else if (x <= -7.8e-212) {
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j));
	} else if (x <= 4.6e-165) {
		tmp = t_2 + (j * (t * c));
	} else if (x <= 82.0) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= 3.7e+105) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if x <= -5.8e+164:
		tmp = t_1
	elif x <= -3.1e+87:
		tmp = z * ((x * y) - (b * c))
	elif x <= -7.8e-212:
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j))
	elif x <= 4.6e-165:
		tmp = t_2 + (j * (t * c))
	elif x <= 82.0:
		tmp = i * ((a * b) - (y * j))
	elif x <= 3.7e+105:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (x <= -5.8e+164)
		tmp = t_1;
	elseif (x <= -3.1e+87)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (x <= -7.8e-212)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(y * Float64(i * j)));
	elseif (x <= 4.6e-165)
		tmp = Float64(t_2 + Float64(j * Float64(t * c)));
	elseif (x <= 82.0)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= 3.7e+105)
		tmp = t_2;
	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 * ((y * z) - (t * a));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (x <= -5.8e+164)
		tmp = t_1;
	elseif (x <= -3.1e+87)
		tmp = z * ((x * y) - (b * c));
	elseif (x <= -7.8e-212)
		tmp = (t * ((c * j) - (x * a))) - (y * (i * j));
	elseif (x <= 4.6e-165)
		tmp = t_2 + (j * (t * c));
	elseif (x <= 82.0)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= 3.7e+105)
		tmp = t_2;
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.8e+164], t$95$1, If[LessEqual[x, -3.1e+87], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.8e-212], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e-165], N[(t$95$2 + N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 82.0], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+105], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -5.7999999999999997e164 or 3.69999999999999985e105 < x

   1. Initial program 63.7%

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

   2. Taylor expanded in y around -inf 51.9%

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

   4. Simplified 65.5%

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

   5. Taylor expanded in x around inf 75.0%

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

      1. +-commutative 75.0%

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

      2. mul-1-neg 75.0%

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

      3. unsub-neg 75.0%

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

   7. Simplified 75.0%

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

   if -5.7999999999999997e164 < x < -3.1e87

   1. Initial program 85.0%

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

   2. Taylor expanded in z around inf 69.8%

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

      1. *-commutative 69.8%

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

      2. *-commutative 69.8%

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

   4. Simplified 69.8%

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

   if -3.1e87 < x < -7.8e-212

   1. Initial program 59.6%

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

   2. Taylor expanded in y around -inf 78.4%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in b around 0 74.7%

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

      1. +-commutative 74.7%

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

      2. *-commutative 74.7%

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

      3. *-commutative 74.7%

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

      4. mul-1-neg 74.7%

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

      5. unsub-neg 74.7%

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

   7. Simplified 74.7%

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

   8. Taylor expanded in i around inf 56.4%

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

      1. associate-*r* 58.0%

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

      2. *-commutative 58.0%

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

   10. Simplified 58.0%

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

   if -7.8e-212 < x < 4.6000000000000001e-165

   1. Initial program 71.2%

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

   2. Taylor expanded in y around 0 82.6%

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

   4. Simplified 82.5%

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

   5. Taylor expanded in j around inf 80.8%

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

      1. associate-*r* 32.9%

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

      2. *-commutative 32.9%

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

      3. associate-*r* 23.9%

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

   7. Simplified 79.0%

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

   if 4.6000000000000001e-165 < x < 82

   1. Initial program 64.7%

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

   2. Taylor expanded in i around inf 54.1%

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

      1. distribute-lft-out-- 54.1%

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

   4. Simplified 54.1%

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

   if 82 < x < 3.69999999999999985e105

   1. Initial program 78.1%

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

   2. Taylor expanded in b around inf 62.4%

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

      1. *-commutative 62.4%

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

   4. Simplified 62.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-212}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-165}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq 82:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+105}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 14: 58.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+49}:\\ \;\;\;\;t_1 - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= t -3.8e+165)
     t_1
     (if (<= t -2.35e+91)
       (* z (- (* x y) (* b c)))
       (if (<= t -4.8e+49)
         (- t_1 (* y (* i j)))
         (if (<= t 1.6e+68)
           (+ (* b (- (* a i) (* z c))) (* y (* x z)))
           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 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.8e+165) {
		tmp = t_1;
	} else if (t <= -2.35e+91) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= -4.8e+49) {
		tmp = t_1 - (y * (i * j));
	} else if (t <= 1.6e+68) {
		tmp = (b * ((a * i) - (z * c))) + (y * (x * z));
	} 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 = t * ((c * j) - (x * a))
    if (t <= (-3.8d+165)) then
        tmp = t_1
    else if (t <= (-2.35d+91)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= (-4.8d+49)) then
        tmp = t_1 - (y * (i * j))
    else if (t <= 1.6d+68) then
        tmp = (b * ((a * i) - (z * c))) + (y * (x * z))
    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 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.8e+165) {
		tmp = t_1;
	} else if (t <= -2.35e+91) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= -4.8e+49) {
		tmp = t_1 - (y * (i * j));
	} else if (t <= 1.6e+68) {
		tmp = (b * ((a * i) - (z * c))) + (y * (x * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -3.8e+165:
		tmp = t_1
	elif t <= -2.35e+91:
		tmp = z * ((x * y) - (b * c))
	elif t <= -4.8e+49:
		tmp = t_1 - (y * (i * j))
	elif t <= 1.6e+68:
		tmp = (b * ((a * i) - (z * c))) + (y * (x * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -3.8e+165)
		tmp = t_1;
	elseif (t <= -2.35e+91)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= -4.8e+49)
		tmp = Float64(t_1 - Float64(y * Float64(i * j)));
	elseif (t <= 1.6e+68)
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) + Float64(y * Float64(x * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -3.8e+165)
		tmp = t_1;
	elseif (t <= -2.35e+91)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= -4.8e+49)
		tmp = t_1 - (y * (i * j));
	elseif (t <= 1.6e+68)
		tmp = (b * ((a * i) - (z * c))) + (y * (x * z));
	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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+165], t$95$1, If[LessEqual[t, -2.35e+91], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.8e+49], N[(t$95$1 - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e+68], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.7999999999999999e165 or 1.59999999999999997e68 < t

   1. Initial program 52.3%

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

   2. Taylor expanded in t around inf 74.0%

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

      1. +-commutative 74.0%

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

      2. mul-1-neg 74.0%

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

      3. unsub-neg 74.0%

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

      4. *-commutative 74.0%

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

      5. *-commutative 74.0%

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

   4. Simplified 74.0%

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

   if -3.7999999999999999e165 < t < -2.3499999999999999e91

   1. Initial program 57.9%

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

   2. Taylor expanded in z around inf 58.5%

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

      1. *-commutative 58.5%

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

      2. *-commutative 58.5%

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

   4. Simplified 58.5%

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

   if -2.3499999999999999e91 < t < -4.8e49

   1. Initial program 74.1%

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

   2. Taylor expanded in y around -inf 55.6%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in b around 0 56.0%

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

      1. +-commutative 56.0%

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

      2. *-commutative 56.0%

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

      3. *-commutative 56.0%

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

      4. mul-1-neg 56.0%

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

      5. unsub-neg 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in i around inf 73.6%

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

      1. associate-*r* 73.6%

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

      2. *-commutative 73.6%

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

   10. Simplified 73.6%

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

   if -4.8e49 < t < 1.59999999999999997e68

   1. Initial program 75.9%

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

   2. Taylor expanded in y around inf 72.3%

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

      1. associate-*r* 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r* 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in j around 0 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-*l* 65.7%

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

      3. *-commutative 65.7%

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

      4. *-commutative 65.7%

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

      5. *-commutative 65.7%

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

   7. Simplified 65.7%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+165}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{+91}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+49}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 15: 29.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot \left(-x\right)\right)\\ t_2 := b \cdot \left(-z \cdot c\right)\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{+247}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{+209}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{+177}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.52 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+126}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* a (- x)))) (t_2 (* b (- (* z c)))))
   (if (<= c -3.8e+247)
     (* j (* t c))
     (if (<= c -5.6e+209)
       (* i (* a b))
       (if (<= c -3.6e+177)
         (* z (- (* b c)))
         (if (<= c -1.5e+163)
           t_1
           (if (<= c -1.52e+66)
             t_2
             (if (<= c -2.5e-271)
               t_1
               (if (<= c 2.7e-22)
                 (* y (* x z))
                 (if (<= c 3.4e+126) t_2 (* t (* c j))))))))))))

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 * (a * -x);
	double t_2 = b * -(z * c);
	double tmp;
	if (c <= -3.8e+247) {
		tmp = j * (t * c);
	} else if (c <= -5.6e+209) {
		tmp = i * (a * b);
	} else if (c <= -3.6e+177) {
		tmp = z * -(b * c);
	} else if (c <= -1.5e+163) {
		tmp = t_1;
	} else if (c <= -1.52e+66) {
		tmp = t_2;
	} else if (c <= -2.5e-271) {
		tmp = t_1;
	} else if (c <= 2.7e-22) {
		tmp = y * (x * z);
	} else if (c <= 3.4e+126) {
		tmp = t_2;
	} else {
		tmp = t * (c * j);
	}
	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 * (a * -x)
    t_2 = b * -(z * c)
    if (c <= (-3.8d+247)) then
        tmp = j * (t * c)
    else if (c <= (-5.6d+209)) then
        tmp = i * (a * b)
    else if (c <= (-3.6d+177)) then
        tmp = z * -(b * c)
    else if (c <= (-1.5d+163)) then
        tmp = t_1
    else if (c <= (-1.52d+66)) then
        tmp = t_2
    else if (c <= (-2.5d-271)) then
        tmp = t_1
    else if (c <= 2.7d-22) then
        tmp = y * (x * z)
    else if (c <= 3.4d+126) then
        tmp = t_2
    else
        tmp = t * (c * j)
    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 * (a * -x);
	double t_2 = b * -(z * c);
	double tmp;
	if (c <= -3.8e+247) {
		tmp = j * (t * c);
	} else if (c <= -5.6e+209) {
		tmp = i * (a * b);
	} else if (c <= -3.6e+177) {
		tmp = z * -(b * c);
	} else if (c <= -1.5e+163) {
		tmp = t_1;
	} else if (c <= -1.52e+66) {
		tmp = t_2;
	} else if (c <= -2.5e-271) {
		tmp = t_1;
	} else if (c <= 2.7e-22) {
		tmp = y * (x * z);
	} else if (c <= 3.4e+126) {
		tmp = t_2;
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (a * -x)
	t_2 = b * -(z * c)
	tmp = 0
	if c <= -3.8e+247:
		tmp = j * (t * c)
	elif c <= -5.6e+209:
		tmp = i * (a * b)
	elif c <= -3.6e+177:
		tmp = z * -(b * c)
	elif c <= -1.5e+163:
		tmp = t_1
	elif c <= -1.52e+66:
		tmp = t_2
	elif c <= -2.5e-271:
		tmp = t_1
	elif c <= 2.7e-22:
		tmp = y * (x * z)
	elif c <= 3.4e+126:
		tmp = t_2
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(a * Float64(-x)))
	t_2 = Float64(b * Float64(-Float64(z * c)))
	tmp = 0.0
	if (c <= -3.8e+247)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= -5.6e+209)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= -3.6e+177)
		tmp = Float64(z * Float64(-Float64(b * c)));
	elseif (c <= -1.5e+163)
		tmp = t_1;
	elseif (c <= -1.52e+66)
		tmp = t_2;
	elseif (c <= -2.5e-271)
		tmp = t_1;
	elseif (c <= 2.7e-22)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 3.4e+126)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (a * -x);
	t_2 = b * -(z * c);
	tmp = 0.0;
	if (c <= -3.8e+247)
		tmp = j * (t * c);
	elseif (c <= -5.6e+209)
		tmp = i * (a * b);
	elseif (c <= -3.6e+177)
		tmp = z * -(b * c);
	elseif (c <= -1.5e+163)
		tmp = t_1;
	elseif (c <= -1.52e+66)
		tmp = t_2;
	elseif (c <= -2.5e-271)
		tmp = t_1;
	elseif (c <= 2.7e-22)
		tmp = y * (x * z);
	elseif (c <= 3.4e+126)
		tmp = t_2;
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * (-N[(z * c), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[c, -3.8e+247], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.6e+209], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.6e+177], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[c, -1.5e+163], t$95$1, If[LessEqual[c, -1.52e+66], t$95$2, If[LessEqual[c, -2.5e-271], t$95$1, If[LessEqual[c, 2.7e-22], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e+126], t$95$2, N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -3.80000000000000022e247

   1. Initial program 53.8%

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

   2. Taylor expanded in t around inf 69.9%

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

      1. +-commutative 69.9%

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

      2. mul-1-neg 69.9%

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

      3. unsub-neg 69.9%

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

      4. *-commutative 69.9%

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

      5. *-commutative 69.9%

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

   4. Simplified 69.9%

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

   5. Taylor expanded in j around inf 85.0%

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

      1. associate-*r* 78.0%

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

      2. *-commutative 78.0%

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

      3. associate-*r* 92.3%

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

   7. Simplified 92.3%

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

   if -3.80000000000000022e247 < c < -5.60000000000000026e209

   1. Initial program 62.5%

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

   2. Taylor expanded in b around inf 75.0%

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

      1. *-commutative 75.0%

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

   4. Simplified 75.0%

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

   5. Taylor expanded in i around inf 50.8%

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

      1. associate-*r* 62.7%

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

      2. *-commutative 62.7%

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

   7. Simplified 62.7%

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

   if -5.60000000000000026e209 < c < -3.60000000000000003e177

   1. Initial program 55.4%

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

   2. Taylor expanded in b around inf 67.3%

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

      1. *-commutative 67.3%

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

   4. Simplified 67.3%

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

   5. Taylor expanded in i around 0 57.4%

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

      1. associate-*r* 78.2%

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

      2. associate-*r* 78.2%

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

      3. *-commutative 78.2%

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

      4. mul-1-neg 78.2%

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

      5. distribute-rgt-neg-in 78.2%

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

   7. Simplified 78.2%

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

   if -3.60000000000000003e177 < c < -1.50000000000000007e163 or -1.52000000000000004e66 < c < -2.5000000000000001e-271

   1. Initial program 72.3%

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

   2. Taylor expanded in t around inf 50.3%

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

      1. +-commutative 50.3%

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

      2. mul-1-neg 50.3%

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

      3. unsub-neg 50.3%

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

      4. *-commutative 50.3%

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

      5. *-commutative 50.3%

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

   4. Simplified 50.3%

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

   5. Taylor expanded in j around 0 39.7%

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

      1. associate-*r* 39.7%

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

      2. neg-mul-1 39.7%

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

      3. *-commutative 39.7%

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

   7. Simplified 39.7%

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

   if -1.50000000000000007e163 < c < -1.52000000000000004e66 or 2.7000000000000002e-22 < c < 3.39999999999999989e126

   1. Initial program 72.4%

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

   2. Taylor expanded in b around inf 55.5%

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

      1. *-commutative 55.5%

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

   4. Simplified 55.5%

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

   5. Taylor expanded in i around 0 50.2%

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

      1. neg-mul-1 50.2%

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

      2. distribute-lft-neg-in 50.2%

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

      3. *-commutative 50.2%

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

   7. Simplified 50.2%

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

   if -2.5000000000000001e-271 < c < 2.7000000000000002e-22

   1. Initial program 76.4%

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

   2. Taylor expanded in y around -inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. *-commutative 54.3%

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

      3. distribute-rgt-neg-in 54.3%

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

      4. +-commutative 54.3%

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

      5. mul-1-neg 54.3%

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

      6. unsub-neg 54.3%

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

   4. Simplified 54.3%

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

   5. Taylor expanded in i around 0 30.8%

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

      1. *-commutative 30.8%

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

      2. associate-*l* 34.0%

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

      3. *-commutative 34.0%

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

   7. Simplified 34.0%

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

   if 3.39999999999999989e126 < c

   1. Initial program 44.8%

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

   2. Taylor expanded in t around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. mul-1-neg 56.9%

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

      3. unsub-neg 56.9%

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

      4. *-commutative 56.9%

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

      5. *-commutative 56.9%

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

   4. Simplified 56.9%

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

   5. Taylor expanded in j around inf 49.3%

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

      1. *-commutative 49.3%

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

   7. Simplified 49.3%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+247}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{+209}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{+177}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;c \leq -1.5 \cdot 10^{+163}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq -1.52 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+126}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 16: 30.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(-z \cdot c\right)\\ t_2 := t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -0.0066:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 75:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+173} \lor \neg \left(x \leq 1.25 \cdot 10^{+264}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* z c)))) (t_2 (* t (* a (- x)))))
   (if (<= x -3.2e+190)
     t_2
     (if (<= x -0.0066)
       (* y (* x z))
       (if (<= x 5.8e-166)
         t_1
         (if (<= x 75.0)
           (* i (- (* y j)))
           (if (<= x 1.7e+110)
             t_1
             (if (or (<= x 3.5e+173) (not (<= x 1.25e+264)))
               t_2
               (* x (* y z))))))))))

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 * -(z * c);
	double t_2 = t * (a * -x);
	double tmp;
	if (x <= -3.2e+190) {
		tmp = t_2;
	} else if (x <= -0.0066) {
		tmp = y * (x * z);
	} else if (x <= 5.8e-166) {
		tmp = t_1;
	} else if (x <= 75.0) {
		tmp = i * -(y * j);
	} else if (x <= 1.7e+110) {
		tmp = t_1;
	} else if ((x <= 3.5e+173) || !(x <= 1.25e+264)) {
		tmp = t_2;
	} else {
		tmp = x * (y * z);
	}
	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 = b * -(z * c)
    t_2 = t * (a * -x)
    if (x <= (-3.2d+190)) then
        tmp = t_2
    else if (x <= (-0.0066d0)) then
        tmp = y * (x * z)
    else if (x <= 5.8d-166) then
        tmp = t_1
    else if (x <= 75.0d0) then
        tmp = i * -(y * j)
    else if (x <= 1.7d+110) then
        tmp = t_1
    else if ((x <= 3.5d+173) .or. (.not. (x <= 1.25d+264))) then
        tmp = t_2
    else
        tmp = x * (y * z)
    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 * -(z * c);
	double t_2 = t * (a * -x);
	double tmp;
	if (x <= -3.2e+190) {
		tmp = t_2;
	} else if (x <= -0.0066) {
		tmp = y * (x * z);
	} else if (x <= 5.8e-166) {
		tmp = t_1;
	} else if (x <= 75.0) {
		tmp = i * -(y * j);
	} else if (x <= 1.7e+110) {
		tmp = t_1;
	} else if ((x <= 3.5e+173) || !(x <= 1.25e+264)) {
		tmp = t_2;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * -(z * c)
	t_2 = t * (a * -x)
	tmp = 0
	if x <= -3.2e+190:
		tmp = t_2
	elif x <= -0.0066:
		tmp = y * (x * z)
	elif x <= 5.8e-166:
		tmp = t_1
	elif x <= 75.0:
		tmp = i * -(y * j)
	elif x <= 1.7e+110:
		tmp = t_1
	elif (x <= 3.5e+173) or not (x <= 1.25e+264):
		tmp = t_2
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(-Float64(z * c)))
	t_2 = Float64(t * Float64(a * Float64(-x)))
	tmp = 0.0
	if (x <= -3.2e+190)
		tmp = t_2;
	elseif (x <= -0.0066)
		tmp = Float64(y * Float64(x * z));
	elseif (x <= 5.8e-166)
		tmp = t_1;
	elseif (x <= 75.0)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (x <= 1.7e+110)
		tmp = t_1;
	elseif ((x <= 3.5e+173) || !(x <= 1.25e+264))
		tmp = t_2;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * -(z * c);
	t_2 = t * (a * -x);
	tmp = 0.0;
	if (x <= -3.2e+190)
		tmp = t_2;
	elseif (x <= -0.0066)
		tmp = y * (x * z);
	elseif (x <= 5.8e-166)
		tmp = t_1;
	elseif (x <= 75.0)
		tmp = i * -(y * j);
	elseif (x <= 1.7e+110)
		tmp = t_1;
	elseif ((x <= 3.5e+173) || ~((x <= 1.25e+264)))
		tmp = t_2;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * (-N[(z * c), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+190], t$95$2, If[LessEqual[x, -0.0066], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-166], t$95$1, If[LessEqual[x, 75.0], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 1.7e+110], t$95$1, If[Or[LessEqual[x, 3.5e+173], N[Not[LessEqual[x, 1.25e+264]], $MachinePrecision]], t$95$2, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.2000000000000001e190 or 1.7000000000000001e110 < x < 3.4999999999999999e173 or 1.25000000000000008e264 < x

   1. Initial program 55.0%

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

   2. Taylor expanded in t around inf 74.9%

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

      1. +-commutative 74.9%

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

      2. mul-1-neg 74.9%

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

      3. unsub-neg 74.9%

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

      4. *-commutative 74.9%

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

      5. *-commutative 74.9%

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

   4. Simplified 74.9%

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

   5. Taylor expanded in j around 0 70.7%

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

      1. associate-*r* 70.7%

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

      2. neg-mul-1 70.7%

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

      3. *-commutative 70.7%

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

   7. Simplified 70.7%

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

   if -3.2000000000000001e190 < x < -0.0066

   1. Initial program 78.9%

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

   2. Taylor expanded in y around -inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. *-commutative 55.0%

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

      3. distribute-rgt-neg-in 55.0%

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

      4. +-commutative 55.0%

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

      5. mul-1-neg 55.0%

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

      6. unsub-neg 55.0%

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

   4. Simplified 55.0%

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

   5. Taylor expanded in i around 0 35.4%

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

      1. *-commutative 35.4%

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

      2. associate-*l* 37.4%

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

      3. *-commutative 37.4%

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

   7. Simplified 37.4%

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

   if -0.0066 < x < 5.8e-166 or 75 < x < 1.7000000000000001e110

   1. Initial program 66.6%

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

   2. Taylor expanded in b around inf 56.3%

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

      1. *-commutative 56.3%

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

   4. Simplified 56.3%

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

   5. Taylor expanded in i around 0 40.7%

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

      1. neg-mul-1 40.7%

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

      2. distribute-lft-neg-in 40.7%

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

      3. *-commutative 40.7%

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

   7. Simplified 40.7%

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

   if 5.8e-166 < x < 75

   1. Initial program 64.7%

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

   2. Taylor expanded in y around -inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. *-commutative 46.2%

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

      3. distribute-rgt-neg-in 46.2%

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

      4. +-commutative 46.2%

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

      5. mul-1-neg 46.2%

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

      6. unsub-neg 46.2%

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

   4. Simplified 46.2%

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

   5. Taylor expanded in i around inf 30.7%

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

      1. mul-1-neg 30.7%

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

      2. *-commutative 30.7%

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

   7. Simplified 30.7%

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

   if 3.4999999999999999e173 < x < 1.25000000000000008e264

   1. Initial program 77.8%

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

   2. Taylor expanded in y around -inf 56.8%

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

      1. mul-1-neg 56.8%

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

      2. *-commutative 56.8%

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

      3. distribute-rgt-neg-in 56.8%

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

      4. +-commutative 56.8%

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

      5. mul-1-neg 56.8%

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

      6. unsub-neg 56.8%

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

   4. Simplified 56.8%

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

   5. Taylor expanded in i around 0 61.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+190}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq -0.0066:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-166}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{elif}\;x \leq 75:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+173} \lor \neg \left(x \leq 1.25 \cdot 10^{+264}\right):\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 17: 43.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.45 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-67}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -5.6e-56)
     t_1
     (if (<= a -2.1e-131)
       (* x (* y z))
       (if (<= a -1.9e-271)
         (* b (- (* z c)))
         (if (<= a 4.45e-261)
           (* y (* x z))
           (if (<= a 2.15e-67) (* t (* c j)) 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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -5.6e-56) {
		tmp = t_1;
	} else if (a <= -2.1e-131) {
		tmp = x * (y * z);
	} else if (a <= -1.9e-271) {
		tmp = b * -(z * c);
	} else if (a <= 4.45e-261) {
		tmp = y * (x * z);
	} else if (a <= 2.15e-67) {
		tmp = t * (c * j);
	} 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 = a * ((b * i) - (x * t))
    if (a <= (-5.6d-56)) then
        tmp = t_1
    else if (a <= (-2.1d-131)) then
        tmp = x * (y * z)
    else if (a <= (-1.9d-271)) then
        tmp = b * -(z * c)
    else if (a <= 4.45d-261) then
        tmp = y * (x * z)
    else if (a <= 2.15d-67) then
        tmp = t * (c * j)
    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 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -5.6e-56) {
		tmp = t_1;
	} else if (a <= -2.1e-131) {
		tmp = x * (y * z);
	} else if (a <= -1.9e-271) {
		tmp = b * -(z * c);
	} else if (a <= 4.45e-261) {
		tmp = y * (x * z);
	} else if (a <= 2.15e-67) {
		tmp = t * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -5.6e-56:
		tmp = t_1
	elif a <= -2.1e-131:
		tmp = x * (y * z)
	elif a <= -1.9e-271:
		tmp = b * -(z * c)
	elif a <= 4.45e-261:
		tmp = y * (x * z)
	elif a <= 2.15e-67:
		tmp = t * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -5.6e-56)
		tmp = t_1;
	elseif (a <= -2.1e-131)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= -1.9e-271)
		tmp = Float64(b * Float64(-Float64(z * c)));
	elseif (a <= 4.45e-261)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 2.15e-67)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -5.6e-56)
		tmp = t_1;
	elseif (a <= -2.1e-131)
		tmp = x * (y * z);
	elseif (a <= -1.9e-271)
		tmp = b * -(z * c);
	elseif (a <= 4.45e-261)
		tmp = y * (x * z);
	elseif (a <= 2.15e-67)
		tmp = t * (c * j);
	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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.6e-56], t$95$1, If[LessEqual[a, -2.1e-131], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.9e-271], N[(b * (-N[(z * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, 4.45e-261], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.15e-67], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -5.59999999999999986e-56 or 2.15000000000000013e-67 < a

   1. Initial program 62.9%

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

   2. Taylor expanded in y around -inf 63.2%

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

   4. Simplified 66.1%

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

   5. Taylor expanded in a around inf 54.9%

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

      1. +-commutative 54.9%

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

      2. mul-1-neg 54.9%

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

      3. unsub-neg 54.9%

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

      4. *-commutative 54.9%

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

      5. *-commutative 54.9%

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

   7. Simplified 54.9%

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

   if -5.59999999999999986e-56 < a < -2.09999999999999997e-131

   1. Initial program 70.6%

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

   2. Taylor expanded in y around -inf 59.1%

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

      1. mul-1-neg 59.1%

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

      2. *-commutative 59.1%

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

      3. distribute-rgt-neg-in 59.1%

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

      4. +-commutative 59.1%

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

      5. mul-1-neg 59.1%

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

      6. unsub-neg 59.1%

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

   4. Simplified 59.1%

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

   5. Taylor expanded in i around 0 59.2%

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

   if -2.09999999999999997e-131 < a < -1.90000000000000005e-271

   1. Initial program 71.8%

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

   2. Taylor expanded in b around inf 51.4%

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

      1. *-commutative 51.4%

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

   4. Simplified 51.4%

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

   5. Taylor expanded in i around 0 47.3%

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

      1. neg-mul-1 47.3%

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

      2. distribute-lft-neg-in 47.3%

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

      3. *-commutative 47.3%

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

   7. Simplified 47.3%

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

   if -1.90000000000000005e-271 < a < 4.45000000000000022e-261

   1. Initial program 69.7%

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

   2. Taylor expanded in y around -inf 69.3%

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

      1. mul-1-neg 69.3%

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

      2. *-commutative 69.3%

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

      3. distribute-rgt-neg-in 69.3%

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

      4. +-commutative 69.3%

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

      5. mul-1-neg 69.3%

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

      6. unsub-neg 69.3%

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

   4. Simplified 69.3%

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

   5. Taylor expanded in i around 0 42.8%

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

      1. *-commutative 42.8%

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

      2. associate-*l* 51.5%

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

      3. *-commutative 51.5%

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

   7. Simplified 51.5%

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

   if 4.45000000000000022e-261 < a < 2.15000000000000013e-67

   1. Initial program 76.0%

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

   2. Taylor expanded in t around inf 49.4%

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

      1. +-commutative 49.4%

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

      2. mul-1-neg 49.4%

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

      3. unsub-neg 49.4%

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

      4. *-commutative 49.4%

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

      5. *-commutative 49.4%

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

   4. Simplified 49.4%

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

   5. Taylor expanded in j around inf 39.7%

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

      1. *-commutative 39.7%

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

   7. Simplified 39.7%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-131}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.45 \cdot 10^{-261}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-67}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 18: 51.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.1 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.7 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -4.1e+127)
     t_2
     (if (<= a -6.7e-62)
       (* b (- (* a i) (* z c)))
       (if (<= a 1.8e-299)
         t_1
         (if (<= a 1.3e-269) (* y (* x z)) (if (<= a 6.2e+69) 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 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.1e+127) {
		tmp = t_2;
	} else if (a <= -6.7e-62) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 1.8e-299) {
		tmp = t_1;
	} else if (a <= 1.3e-269) {
		tmp = y * (x * z);
	} else if (a <= 6.2e+69) {
		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 = c * ((t * j) - (z * b))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-4.1d+127)) then
        tmp = t_2
    else if (a <= (-6.7d-62)) then
        tmp = b * ((a * i) - (z * c))
    else if (a <= 1.8d-299) then
        tmp = t_1
    else if (a <= 1.3d-269) then
        tmp = y * (x * z)
    else if (a <= 6.2d+69) 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 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.1e+127) {
		tmp = t_2;
	} else if (a <= -6.7e-62) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= 1.8e-299) {
		tmp = t_1;
	} else if (a <= 1.3e-269) {
		tmp = y * (x * z);
	} else if (a <= 6.2e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -4.1e+127:
		tmp = t_2
	elif a <= -6.7e-62:
		tmp = b * ((a * i) - (z * c))
	elif a <= 1.8e-299:
		tmp = t_1
	elif a <= 1.3e-269:
		tmp = y * (x * z)
	elif a <= 6.2e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.1e+127)
		tmp = t_2;
	elseif (a <= -6.7e-62)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (a <= 1.8e-299)
		tmp = t_1;
	elseif (a <= 1.3e-269)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 6.2e+69)
		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 = c * ((t * j) - (z * b));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -4.1e+127)
		tmp = t_2;
	elseif (a <= -6.7e-62)
		tmp = b * ((a * i) - (z * c));
	elseif (a <= 1.8e-299)
		tmp = t_1;
	elseif (a <= 1.3e-269)
		tmp = y * (x * z);
	elseif (a <= 6.2e+69)
		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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.1e+127], t$95$2, If[LessEqual[a, -6.7e-62], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-299], t$95$1, If[LessEqual[a, 1.3e-269], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e+69], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.09999999999999983e127 or 6.1999999999999997e69 < a

   1. Initial program 55.0%

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

   2. Taylor expanded in y around -inf 54.0%

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

   4. Simplified 56.8%

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

   5. Taylor expanded in a around inf 66.5%

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

      1. +-commutative 66.5%

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

      2. mul-1-neg 66.5%

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

      3. unsub-neg 66.5%

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

      4. *-commutative 66.5%

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

      5. *-commutative 66.5%

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

   7. Simplified 66.5%

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

   if -4.09999999999999983e127 < a < -6.69999999999999992e-62

   1. Initial program 73.3%

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

   2. Taylor expanded in b around inf 53.3%

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

      1. *-commutative 53.3%

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

   4. Simplified 53.3%

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

   if -6.69999999999999992e-62 < a < 1.8e-299 or 1.3e-269 < a < 6.1999999999999997e69

   1. Initial program 73.4%

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

   2. Taylor expanded in c around inf 51.0%

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

      1. *-commutative 51.0%

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

   4. Simplified 51.0%

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

   if 1.8e-299 < a < 1.3e-269

   1. Initial program 75.0%

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

   2. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. *-commutative 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in i around 0 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-*l* 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -6.7 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-269}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 19: 29.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := b \cdot \left(-z \cdot c\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+203}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* b (- (* z c)))))
   (if (<= b -3.4e+174)
     t_2
     (if (<= b -1.5e+130)
       t_1
       (if (<= b -2.15e-23)
         t_2
         (if (<= b -1.4e-116)
           (* t (* c j))
           (if (<= b 6.5e-85)
             t_1
             (if (<= b 2.55e+203) t_2 (* i (* a 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 = x * (y * z);
	double t_2 = b * -(z * c);
	double tmp;
	if (b <= -3.4e+174) {
		tmp = t_2;
	} else if (b <= -1.5e+130) {
		tmp = t_1;
	} else if (b <= -2.15e-23) {
		tmp = t_2;
	} else if (b <= -1.4e-116) {
		tmp = t * (c * j);
	} else if (b <= 6.5e-85) {
		tmp = t_1;
	} else if (b <= 2.55e+203) {
		tmp = t_2;
	} else {
		tmp = i * (a * 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) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = b * -(z * c)
    if (b <= (-3.4d+174)) then
        tmp = t_2
    else if (b <= (-1.5d+130)) then
        tmp = t_1
    else if (b <= (-2.15d-23)) then
        tmp = t_2
    else if (b <= (-1.4d-116)) then
        tmp = t * (c * j)
    else if (b <= 6.5d-85) then
        tmp = t_1
    else if (b <= 2.55d+203) then
        tmp = t_2
    else
        tmp = i * (a * 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 = x * (y * z);
	double t_2 = b * -(z * c);
	double tmp;
	if (b <= -3.4e+174) {
		tmp = t_2;
	} else if (b <= -1.5e+130) {
		tmp = t_1;
	} else if (b <= -2.15e-23) {
		tmp = t_2;
	} else if (b <= -1.4e-116) {
		tmp = t * (c * j);
	} else if (b <= 6.5e-85) {
		tmp = t_1;
	} else if (b <= 2.55e+203) {
		tmp = t_2;
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = b * -(z * c)
	tmp = 0
	if b <= -3.4e+174:
		tmp = t_2
	elif b <= -1.5e+130:
		tmp = t_1
	elif b <= -2.15e-23:
		tmp = t_2
	elif b <= -1.4e-116:
		tmp = t * (c * j)
	elif b <= 6.5e-85:
		tmp = t_1
	elif b <= 2.55e+203:
		tmp = t_2
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(b * Float64(-Float64(z * c)))
	tmp = 0.0
	if (b <= -3.4e+174)
		tmp = t_2;
	elseif (b <= -1.5e+130)
		tmp = t_1;
	elseif (b <= -2.15e-23)
		tmp = t_2;
	elseif (b <= -1.4e-116)
		tmp = Float64(t * Float64(c * j));
	elseif (b <= 6.5e-85)
		tmp = t_1;
	elseif (b <= 2.55e+203)
		tmp = t_2;
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = b * -(z * c);
	tmp = 0.0;
	if (b <= -3.4e+174)
		tmp = t_2;
	elseif (b <= -1.5e+130)
		tmp = t_1;
	elseif (b <= -2.15e-23)
		tmp = t_2;
	elseif (b <= -1.4e-116)
		tmp = t * (c * j);
	elseif (b <= 6.5e-85)
		tmp = t_1;
	elseif (b <= 2.55e+203)
		tmp = t_2;
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * (-N[(z * c), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[b, -3.4e+174], t$95$2, If[LessEqual[b, -1.5e+130], t$95$1, If[LessEqual[b, -2.15e-23], t$95$2, If[LessEqual[b, -1.4e-116], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e-85], t$95$1, If[LessEqual[b, 2.55e+203], t$95$2, N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.4000000000000001e174 or -1.5e130 < b < -2.15000000000000001e-23 or 6.5e-85 < b < 2.5500000000000001e203

   1. Initial program 73.1%

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

   2. Taylor expanded in b around inf 58.7%

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

      1. *-commutative 58.7%

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

   4. Simplified 58.7%

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

   5. Taylor expanded in i around 0 42.2%

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

      1. neg-mul-1 42.2%

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

      2. distribute-lft-neg-in 42.2%

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

      3. *-commutative 42.2%

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

   7. Simplified 42.2%

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

   if -3.4000000000000001e174 < b < -1.5e130 or -1.3999999999999999e-116 < b < 6.5e-85

   1. Initial program 63.9%

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

   2. Taylor expanded in y around -inf 58.3%

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

      1. mul-1-neg 58.3%

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

      2. *-commutative 58.3%

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

      3. distribute-rgt-neg-in 58.3%

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

      4. +-commutative 58.3%

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

      5. mul-1-neg 58.3%

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

      6. unsub-neg 58.3%

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

   4. Simplified 58.3%

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

   5. Taylor expanded in i around 0 39.1%

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

   if -2.15000000000000001e-23 < b < -1.3999999999999999e-116

   1. Initial program 58.4%

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

   2. Taylor expanded in t around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. mul-1-neg 58.4%

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

      3. unsub-neg 58.4%

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

      4. *-commutative 58.4%

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

      5. *-commutative 58.4%

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

   4. Simplified 58.4%

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

   5. Taylor expanded in j around inf 39.5%

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

      1. *-commutative 39.5%

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

   7. Simplified 39.5%

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

   if 2.5500000000000001e203 < b

   1. Initial program 60.3%

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

   2. Taylor expanded in b around inf 64.0%

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

      1. *-commutative 64.0%

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

   4. Simplified 64.0%

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

   5. Taylor expanded in i around inf 42.6%

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

      1. associate-*r* 52.9%

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

      2. *-commutative 52.9%

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

   7. Simplified 52.9%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+174}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+130}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -2.15 \cdot 10^{-23}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{+203}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 20: 52.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -1.3e+50)
     t_2
     (if (<= t -3.2e-99)
       t_1
       (if (<= t -5.3e-151)
         (* y (- (* x z) (* i j)))
         (if (<= t 2.35e+67) 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 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.3e+50) {
		tmp = t_2;
	} else if (t <= -3.2e-99) {
		tmp = t_1;
	} else if (t <= -5.3e-151) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 2.35e+67) {
		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 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-1.3d+50)) then
        tmp = t_2
    else if (t <= (-3.2d-99)) then
        tmp = t_1
    else if (t <= (-5.3d-151)) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 2.35d+67) 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 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.3e+50) {
		tmp = t_2;
	} else if (t <= -3.2e-99) {
		tmp = t_1;
	} else if (t <= -5.3e-151) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 2.35e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1.3e+50:
		tmp = t_2
	elif t <= -3.2e-99:
		tmp = t_1
	elif t <= -5.3e-151:
		tmp = y * ((x * z) - (i * j))
	elif t <= 2.35e+67:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.3e+50)
		tmp = t_2;
	elseif (t <= -3.2e-99)
		tmp = t_1;
	elseif (t <= -5.3e-151)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 2.35e+67)
		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 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1.3e+50)
		tmp = t_2;
	elseif (t <= -3.2e-99)
		tmp = t_1;
	elseif (t <= -5.3e-151)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 2.35e+67)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+50], t$95$2, If[LessEqual[t, -3.2e-99], t$95$1, If[LessEqual[t, -5.3e-151], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.35e+67], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3000000000000001e50 or 2.35000000000000009e67 < t

   1. Initial program 55.6%

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

   2. Taylor expanded in t around inf 66.3%

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

      1. +-commutative 66.3%

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

      2. mul-1-neg 66.3%

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

      3. unsub-neg 66.3%

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

      4. *-commutative 66.3%

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

      5. *-commutative 66.3%

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

   4. Simplified 66.3%

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

   if -1.3000000000000001e50 < t < -3.2000000000000001e-99 or -5.29999999999999978e-151 < t < 2.35000000000000009e67

   1. Initial program 75.4%

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

   2. Taylor expanded in b around inf 56.3%

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

      1. *-commutative 56.3%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 56.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   if -3.2000000000000001e-99 < t < -5.29999999999999978e-151

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around -inf 64.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 64.9%

         \[\leadsto \color{blue}{-y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)} \]

      2. *-commutative 64.9%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot y} \]

      3. distribute-rgt-neg-in 64.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot \left(-y\right)} \]

      4. +-commutative 64.9%

         \[\leadsto \color{blue}{\left(i \cdot j + -1 \cdot \left(x \cdot z\right)\right)} \cdot \left(-y\right) \]

      5. mul-1-neg 64.9%

         \[\leadsto \left(i \cdot j + \color{blue}{\left(-x \cdot z\right)}\right) \cdot \left(-y\right) \]

      6. unsub-neg 64.9%

         \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right)} \cdot \left(-y\right) \]

   4. Simplified 64.9%

      \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right) \cdot \left(-y\right)} \]

   5. Taylor expanded in i around 0 64.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 64.6%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} + x \cdot \left(y \cdot z\right) \]

      2. associate-*r* 69.5%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot i\right) \cdot j\right) \cdot y} + x \cdot \left(y \cdot z\right) \]

      3. associate-*r* 69.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \cdot y + x \cdot \left(y \cdot z\right) \]

      4. *-commutative 69.5%

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + x \cdot \color{blue}{\left(z \cdot y\right)} \]

      5. associate-*l* 64.9%

         \[\leadsto \left(-1 \cdot \left(i \cdot j\right)\right) \cdot y + \color{blue}{\left(x \cdot z\right) \cdot y} \]

      6. distribute-rgt-in 64.9%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

      7. +-commutative 64.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      8. mul-1-neg 64.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      9. *-commutative 64.9%

         \[\leadsto y \cdot \left(x \cdot z + \left(-\color{blue}{j \cdot i}\right)\right) \]

      10. unsub-neg 64.9%

          \[\leadsto y \cdot \color{blue}{\left(x \cdot z - j \cdot i\right)} \]

      11. *-commutative 64.9%

          \[\leadsto y \cdot \left(x \cdot z - \color{blue}{i \cdot j}\right) \]

   7. Simplified 64.9%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 21: 43.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+184}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+205}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+243}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.7e+184)
   (* j (* t c))
   (if (<= t 2.25e+24)
     (* b (- (* a i) (* z c)))
     (if (<= t 6.8e+205)
       (* a (- (* b i) (* x t)))
       (if (<= t 3.2e+243) (* t (* c j)) (* t (* a (- x))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.7e+184) {
		tmp = j * (t * c);
	} else if (t <= 2.25e+24) {
		tmp = b * ((a * i) - (z * c));
	} else if (t <= 6.8e+205) {
		tmp = a * ((b * i) - (x * t));
	} else if (t <= 3.2e+243) {
		tmp = t * (c * j);
	} else {
		tmp = t * (a * -x);
	}
	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 (t <= (-4.7d+184)) then
        tmp = j * (t * c)
    else if (t <= 2.25d+24) then
        tmp = b * ((a * i) - (z * c))
    else if (t <= 6.8d+205) then
        tmp = a * ((b * i) - (x * t))
    else if (t <= 3.2d+243) then
        tmp = t * (c * j)
    else
        tmp = t * (a * -x)
    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 (t <= -4.7e+184) {
		tmp = j * (t * c);
	} else if (t <= 2.25e+24) {
		tmp = b * ((a * i) - (z * c));
	} else if (t <= 6.8e+205) {
		tmp = a * ((b * i) - (x * t));
	} else if (t <= 3.2e+243) {
		tmp = t * (c * j);
	} else {
		tmp = t * (a * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4.7e+184:
		tmp = j * (t * c)
	elif t <= 2.25e+24:
		tmp = b * ((a * i) - (z * c))
	elif t <= 6.8e+205:
		tmp = a * ((b * i) - (x * t))
	elif t <= 3.2e+243:
		tmp = t * (c * j)
	else:
		tmp = t * (a * -x)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4.7e+184)
		tmp = Float64(j * Float64(t * c));
	elseif (t <= 2.25e+24)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (t <= 6.8e+205)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (t <= 3.2e+243)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(t * Float64(a * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4.7e+184)
		tmp = j * (t * c);
	elseif (t <= 2.25e+24)
		tmp = b * ((a * i) - (z * c));
	elseif (t <= 6.8e+205)
		tmp = a * ((b * i) - (x * t));
	elseif (t <= 3.2e+243)
		tmp = t * (c * j);
	else
		tmp = t * (a * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4.7e+184], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.25e+24], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+205], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+243], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -4.7000000000000003e184

   1. Initial program 54.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around inf 78.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 78.8%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 78.8%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 78.8%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 78.8%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 78.8%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   4. Simplified 78.8%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   5. Taylor expanded in j around inf 57.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 57.6%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot t} \]

      2. *-commutative 57.6%

         \[\leadsto \color{blue}{\left(j \cdot c\right)} \cdot t \]

      3. associate-*r* 58.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

   7. Simplified 58.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

   if -4.7000000000000003e184 < t < 2.2500000000000001e24

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 48.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 48.7%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 48.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   if 2.2500000000000001e24 < t < 6.8e205

   1. Initial program 48.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around -inf 53.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + c \cdot \left(j \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   4. Simplified 62.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - x \cdot a\right) + \left(i \cdot j - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in a around inf 51.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]
   6. Step-by-step derivation

      1. +-commutative 51.4%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.4%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.4%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

      4. *-commutative 51.4%

         \[\leadsto a \cdot \left(\color{blue}{i \cdot b} - t \cdot x\right) \]

      5. *-commutative 51.4%

         \[\leadsto a \cdot \left(i \cdot b - \color{blue}{x \cdot t}\right) \]

   7. Simplified 51.4%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - x \cdot t\right)} \]

   if 6.8e205 < t < 3.20000000000000016e243

   1. Initial program 34.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around inf 66.5%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 66.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 66.5%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 66.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 66.5%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 66.5%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   4. Simplified 66.5%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   5. Taylor expanded in j around inf 67.1%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 67.1%

         \[\leadsto t \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 67.1%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot c\right)} \]

   if 3.20000000000000016e243 < t

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around inf 83.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 83.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 83.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 83.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 83.7%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 83.7%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   4. Simplified 83.7%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   5. Taylor expanded in j around 0 75.9%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 75.9%

         \[\leadsto t \cdot \color{blue}{\left(\left(-1 \cdot a\right) \cdot x\right)} \]

      2. neg-mul-1 75.9%

         \[\leadsto t \cdot \left(\color{blue}{\left(-a\right)} \cdot x\right) \]

      3. *-commutative 75.9%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   7. Simplified 75.9%

      \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+184}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+205}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+243}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 22: 30.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-221}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-214}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -5.4e+51)
   (* a (* b i))
   (if (<= b -3.5e-221)
     (* c (* t j))
     (if (<= b 1.2e-214)
       (* i (- (* y j)))
       (if (<= b 2e+55) (* y (* x z)) (* i (* a 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 <= -5.4e+51) {
		tmp = a * (b * i);
	} else if (b <= -3.5e-221) {
		tmp = c * (t * j);
	} else if (b <= 1.2e-214) {
		tmp = i * -(y * j);
	} else if (b <= 2e+55) {
		tmp = y * (x * z);
	} else {
		tmp = i * (a * 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 <= (-5.4d+51)) then
        tmp = a * (b * i)
    else if (b <= (-3.5d-221)) then
        tmp = c * (t * j)
    else if (b <= 1.2d-214) then
        tmp = i * -(y * j)
    else if (b <= 2d+55) then
        tmp = y * (x * z)
    else
        tmp = i * (a * 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 <= -5.4e+51) {
		tmp = a * (b * i);
	} else if (b <= -3.5e-221) {
		tmp = c * (t * j);
	} else if (b <= 1.2e-214) {
		tmp = i * -(y * j);
	} else if (b <= 2e+55) {
		tmp = y * (x * z);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -5.4e+51:
		tmp = a * (b * i)
	elif b <= -3.5e-221:
		tmp = c * (t * j)
	elif b <= 1.2e-214:
		tmp = i * -(y * j)
	elif b <= 2e+55:
		tmp = y * (x * z)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -5.4e+51)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= -3.5e-221)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 1.2e-214)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (b <= 2e+55)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -5.4e+51)
		tmp = a * (b * i);
	elseif (b <= -3.5e-221)
		tmp = c * (t * j);
	elseif (b <= 1.2e-214)
		tmp = i * -(y * j);
	elseif (b <= 2e+55)
		tmp = y * (x * z);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -5.4e+51], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.5e-221], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.2e-214], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 2e+55], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5.39999999999999983e51

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 53.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 53.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 31.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -5.39999999999999983e51 < b < -3.4999999999999999e-221

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around -inf 61.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + c \cdot \left(j \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   4. Simplified 72.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - x \cdot a\right) + \left(i \cdot j - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in b around 0 69.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) + t \cdot \left(c \cdot j - a \cdot x\right)} \]
   6. Step-by-step derivation

      1. +-commutative 69.0%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right)} \]

      2. *-commutative 69.0%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) \]

      3. *-commutative 69.0%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) \]

      4. mul-1-neg 69.0%

         \[\leadsto t \cdot \left(j \cdot c - x \cdot a\right) + \color{blue}{\left(-y \cdot \left(i \cdot j - x \cdot z\right)\right)} \]

      5. unsub-neg 69.0%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - y \cdot \left(i \cdot j - x \cdot z\right)} \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - y \cdot \left(i \cdot j - x \cdot z\right)} \]

   8. Taylor expanded in c around inf 33.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -3.4999999999999999e-221 < b < 1.2000000000000001e-214

   1. Initial program 65.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around -inf 72.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 72.5%

         \[\leadsto \color{blue}{-y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)} \]

      2. *-commutative 72.5%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot y} \]

      3. distribute-rgt-neg-in 72.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot \left(-y\right)} \]

      4. +-commutative 72.5%

         \[\leadsto \color{blue}{\left(i \cdot j + -1 \cdot \left(x \cdot z\right)\right)} \cdot \left(-y\right) \]

      5. mul-1-neg 72.5%

         \[\leadsto \left(i \cdot j + \color{blue}{\left(-x \cdot z\right)}\right) \cdot \left(-y\right) \]

      6. unsub-neg 72.5%

         \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right)} \cdot \left(-y\right) \]

   4. Simplified 72.5%

      \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right) \cdot \left(-y\right)} \]

   5. Taylor expanded in i around inf 45.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 45.0%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 45.0%

         \[\leadsto -i \cdot \color{blue}{\left(y \cdot j\right)} \]

   7. Simplified 45.0%

      \[\leadsto \color{blue}{-i \cdot \left(y \cdot j\right)} \]

   if 1.2000000000000001e-214 < b < 2.00000000000000002e55

   1. Initial program 69.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around -inf 44.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 44.0%

         \[\leadsto \color{blue}{-y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)} \]

      2. *-commutative 44.0%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot y} \]

      3. distribute-rgt-neg-in 44.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot \left(-y\right)} \]

      4. +-commutative 44.0%

         \[\leadsto \color{blue}{\left(i \cdot j + -1 \cdot \left(x \cdot z\right)\right)} \cdot \left(-y\right) \]

      5. mul-1-neg 44.0%

         \[\leadsto \left(i \cdot j + \color{blue}{\left(-x \cdot z\right)}\right) \cdot \left(-y\right) \]

      6. unsub-neg 44.0%

         \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right)} \cdot \left(-y\right) \]

   4. Simplified 44.0%

      \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right) \cdot \left(-y\right)} \]

   5. Taylor expanded in i around 0 31.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 31.0%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

      2. associate-*l* 32.7%

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot y} \]

      3. *-commutative 32.7%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   7. Simplified 32.7%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if 2.00000000000000002e55 < b

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 68.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 68.0%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 68.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 37.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 42.1%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

   7. Simplified 42.1%

      \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot i} \]
3. Recombined 5 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-221}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-214}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 23: 52.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+46} \lor \neg \left(t \leq 3.1 \cdot 10^{+67}\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.05e+46) (not (<= t 3.1e+67)))
   (* t (- (* c j) (* x a)))
   (* b (- (* a i) (* z 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 ((t <= -1.05e+46) || !(t <= 3.1e+67)) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = b * ((a * i) - (z * 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 ((t <= (-1.05d+46)) .or. (.not. (t <= 3.1d+67))) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = b * ((a * i) - (z * 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 ((t <= -1.05e+46) || !(t <= 3.1e+67)) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.05e+46) or not (t <= 3.1e+67):
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.05e+46) || !(t <= 3.1e+67))
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.05e+46) || ~((t <= 3.1e+67)))
		tmp = t * ((c * j) - (x * a));
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.05e+46], N[Not[LessEqual[t, 3.1e+67]], $MachinePrecision]], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e46 or 3.09999999999999996e67 < t

   1. Initial program 55.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around inf 65.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 65.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 65.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 65.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 65.7%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 65.7%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   4. Simplified 65.7%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   if -1.05e46 < t < 3.09999999999999996e67

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 53.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.0%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 53.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+46} \lor \neg \left(t \leq 3.1 \cdot 10^{+67}\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 24: 30.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-119}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.55e+45)
   (* a (* b i))
   (if (<= b -4.5e-119)
     (* c (* t j))
     (if (<= b 2.2e+55) (* x (* y z)) (* b (* a 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 (b <= -1.55e+45) {
		tmp = a * (b * i);
	} else if (b <= -4.5e-119) {
		tmp = c * (t * j);
	} else if (b <= 2.2e+55) {
		tmp = x * (y * z);
	} else {
		tmp = b * (a * 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 (b <= (-1.55d+45)) then
        tmp = a * (b * i)
    else if (b <= (-4.5d-119)) then
        tmp = c * (t * j)
    else if (b <= 2.2d+55) then
        tmp = x * (y * z)
    else
        tmp = b * (a * 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 (b <= -1.55e+45) {
		tmp = a * (b * i);
	} else if (b <= -4.5e-119) {
		tmp = c * (t * j);
	} else if (b <= 2.2e+55) {
		tmp = x * (y * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.55e+45:
		tmp = a * (b * i)
	elif b <= -4.5e-119:
		tmp = c * (t * j)
	elif b <= 2.2e+55:
		tmp = x * (y * z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.55e+45)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= -4.5e-119)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 2.2e+55)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.55e+45)
		tmp = a * (b * i);
	elseif (b <= -4.5e-119)
		tmp = c * (t * j);
	elseif (b <= 2.2e+55)
		tmp = x * (y * z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.55e+45], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.5e-119], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e+55], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.54999999999999994e45

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 53.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 53.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 31.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -1.54999999999999994e45 < b < -4.5000000000000003e-119

   1. Initial program 66.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around -inf 63.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + c \cdot \left(j \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   4. Simplified 72.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - x \cdot a\right) + \left(i \cdot j - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in b around 0 66.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) + t \cdot \left(c \cdot j - a \cdot x\right)} \]
   6. Step-by-step derivation

      1. +-commutative 66.3%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right)} \]

      2. *-commutative 66.3%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) \]

      3. *-commutative 66.3%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) \]

      4. mul-1-neg 66.3%

         \[\leadsto t \cdot \left(j \cdot c - x \cdot a\right) + \color{blue}{\left(-y \cdot \left(i \cdot j - x \cdot z\right)\right)} \]

      5. unsub-neg 66.3%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - y \cdot \left(i \cdot j - x \cdot z\right)} \]

   7. Simplified 66.3%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - y \cdot \left(i \cdot j - x \cdot z\right)} \]

   8. Taylor expanded in c around inf 30.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -4.5000000000000003e-119 < b < 2.2000000000000001e55

   1. Initial program 68.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around -inf 52.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 52.3%

         \[\leadsto \color{blue}{-y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)} \]

      2. *-commutative 52.3%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot y} \]

      3. distribute-rgt-neg-in 52.3%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot \left(-y\right)} \]

      4. +-commutative 52.3%

         \[\leadsto \color{blue}{\left(i \cdot j + -1 \cdot \left(x \cdot z\right)\right)} \cdot \left(-y\right) \]

      5. mul-1-neg 52.3%

         \[\leadsto \left(i \cdot j + \color{blue}{\left(-x \cdot z\right)}\right) \cdot \left(-y\right) \]

      6. unsub-neg 52.3%

         \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right)} \cdot \left(-y\right) \]

   4. Simplified 52.3%

      \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right) \cdot \left(-y\right)} \]

   5. Taylor expanded in i around 0 32.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 2.2000000000000001e55 < b

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 68.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 68.0%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 68.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 40.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.6%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   7. Simplified 40.6%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-119}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 25: 29.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3.2e+46)
   (* a (* b i))
   (if (<= b -1.95e-225)
     (* c (* t j))
     (if (<= b 8.5e+55) (* y (* x z)) (* b (* a 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 (b <= -3.2e+46) {
		tmp = a * (b * i);
	} else if (b <= -1.95e-225) {
		tmp = c * (t * j);
	} else if (b <= 8.5e+55) {
		tmp = y * (x * z);
	} else {
		tmp = b * (a * 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 (b <= (-3.2d+46)) then
        tmp = a * (b * i)
    else if (b <= (-1.95d-225)) then
        tmp = c * (t * j)
    else if (b <= 8.5d+55) then
        tmp = y * (x * z)
    else
        tmp = b * (a * 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 (b <= -3.2e+46) {
		tmp = a * (b * i);
	} else if (b <= -1.95e-225) {
		tmp = c * (t * j);
	} else if (b <= 8.5e+55) {
		tmp = y * (x * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3.2e+46:
		tmp = a * (b * i)
	elif b <= -1.95e-225:
		tmp = c * (t * j)
	elif b <= 8.5e+55:
		tmp = y * (x * z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3.2e+46)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= -1.95e-225)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 8.5e+55)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3.2e+46)
		tmp = a * (b * i);
	elseif (b <= -1.95e-225)
		tmp = c * (t * j);
	elseif (b <= 8.5e+55)
		tmp = y * (x * z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3.2e+46], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.95e-225], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+55], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.1999999999999998e46

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 53.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 53.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 31.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -3.1999999999999998e46 < b < -1.95e-225

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around -inf 61.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + c \cdot \left(j \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   4. Simplified 72.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - x \cdot a\right) + \left(i \cdot j - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in b around 0 69.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) + t \cdot \left(c \cdot j - a \cdot x\right)} \]
   6. Step-by-step derivation

      1. +-commutative 69.5%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right)} \]

      2. *-commutative 69.5%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) \]

      3. *-commutative 69.5%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) \]

      4. mul-1-neg 69.5%

         \[\leadsto t \cdot \left(j \cdot c - x \cdot a\right) + \color{blue}{\left(-y \cdot \left(i \cdot j - x \cdot z\right)\right)} \]

      5. unsub-neg 69.5%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - y \cdot \left(i \cdot j - x \cdot z\right)} \]

   7. Simplified 69.5%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - y \cdot \left(i \cdot j - x \cdot z\right)} \]

   8. Taylor expanded in c around inf 32.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -1.95e-225 < b < 8.50000000000000002e55

   1. Initial program 68.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around -inf 53.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 53.5%

         \[\leadsto \color{blue}{-y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)} \]

      2. *-commutative 53.5%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot y} \]

      3. distribute-rgt-neg-in 53.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot \left(-y\right)} \]

      4. +-commutative 53.5%

         \[\leadsto \color{blue}{\left(i \cdot j + -1 \cdot \left(x \cdot z\right)\right)} \cdot \left(-y\right) \]

      5. mul-1-neg 53.5%

         \[\leadsto \left(i \cdot j + \color{blue}{\left(-x \cdot z\right)}\right) \cdot \left(-y\right) \]

      6. unsub-neg 53.5%

         \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right)} \cdot \left(-y\right) \]

   4. Simplified 53.5%

      \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right) \cdot \left(-y\right)} \]

   5. Taylor expanded in i around 0 31.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 31.2%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

      2. associate-*l* 32.4%

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot y} \]

      3. *-commutative 32.4%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   7. Simplified 32.4%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if 8.50000000000000002e55 < b

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 68.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 68.0%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 68.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 40.6%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 40.6%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   7. Simplified 40.6%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-225}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 26: 30.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-224}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.42e+45)
   (* a (* b i))
   (if (<= b -3.6e-224)
     (* c (* t j))
     (if (<= b 1.15e+55) (* y (* x z)) (* i (* a 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 <= -1.42e+45) {
		tmp = a * (b * i);
	} else if (b <= -3.6e-224) {
		tmp = c * (t * j);
	} else if (b <= 1.15e+55) {
		tmp = y * (x * z);
	} else {
		tmp = i * (a * 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 <= (-1.42d+45)) then
        tmp = a * (b * i)
    else if (b <= (-3.6d-224)) then
        tmp = c * (t * j)
    else if (b <= 1.15d+55) then
        tmp = y * (x * z)
    else
        tmp = i * (a * 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 <= -1.42e+45) {
		tmp = a * (b * i);
	} else if (b <= -3.6e-224) {
		tmp = c * (t * j);
	} else if (b <= 1.15e+55) {
		tmp = y * (x * z);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.42e+45:
		tmp = a * (b * i)
	elif b <= -3.6e-224:
		tmp = c * (t * j)
	elif b <= 1.15e+55:
		tmp = y * (x * z)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.42e+45)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= -3.6e-224)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 1.15e+55)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.42e+45)
		tmp = a * (b * i);
	elseif (b <= -3.6e-224)
		tmp = c * (t * j);
	elseif (b <= 1.15e+55)
		tmp = y * (x * z);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.42e+45], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.6e-224], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+55], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.42e45

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 53.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.8%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 53.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 31.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -1.42e45 < b < -3.6e-224

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around -inf 61.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + c \cdot \left(j \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   4. Simplified 72.8%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - x \cdot a\right) + \left(i \cdot j - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in b around 0 69.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) + t \cdot \left(c \cdot j - a \cdot x\right)} \]
   6. Step-by-step derivation

      1. +-commutative 69.5%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right)} \]

      2. *-commutative 69.5%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) \]

      3. *-commutative 69.5%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) \]

      4. mul-1-neg 69.5%

         \[\leadsto t \cdot \left(j \cdot c - x \cdot a\right) + \color{blue}{\left(-y \cdot \left(i \cdot j - x \cdot z\right)\right)} \]

      5. unsub-neg 69.5%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - y \cdot \left(i \cdot j - x \cdot z\right)} \]

   7. Simplified 69.5%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - y \cdot \left(i \cdot j - x \cdot z\right)} \]

   8. Taylor expanded in c around inf 32.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -3.6e-224 < b < 1.14999999999999994e55

   1. Initial program 68.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around -inf 53.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 53.5%

         \[\leadsto \color{blue}{-y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)} \]

      2. *-commutative 53.5%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot y} \]

      3. distribute-rgt-neg-in 53.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right) \cdot \left(-y\right)} \]

      4. +-commutative 53.5%

         \[\leadsto \color{blue}{\left(i \cdot j + -1 \cdot \left(x \cdot z\right)\right)} \cdot \left(-y\right) \]

      5. mul-1-neg 53.5%

         \[\leadsto \left(i \cdot j + \color{blue}{\left(-x \cdot z\right)}\right) \cdot \left(-y\right) \]

      6. unsub-neg 53.5%

         \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right)} \cdot \left(-y\right) \]

   4. Simplified 53.5%

      \[\leadsto \color{blue}{\left(i \cdot j - x \cdot z\right) \cdot \left(-y\right)} \]

   5. Taylor expanded in i around 0 31.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 31.2%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

      2. associate-*l* 32.4%

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot y} \]

      3. *-commutative 32.4%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   7. Simplified 32.4%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if 1.14999999999999994e55 < b

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 68.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 68.0%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 68.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 37.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 42.1%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 42.1%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

   7. Simplified 42.1%

      \[\leadsto \color{blue}{\left(b \cdot a\right) \cdot i} \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.42 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-224}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+55}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 27: 30.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.18 \cdot 10^{-61} \lor \neg \left(a \leq 4.2 \cdot 10^{+45}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.18e-61) (not (<= a 4.2e+45))) (* b (* a i)) (* t (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.18e-61) || !(a <= 4.2e+45)) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	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 ((a <= (-1.18d-61)) .or. (.not. (a <= 4.2d+45))) then
        tmp = b * (a * i)
    else
        tmp = t * (c * j)
    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 ((a <= -1.18e-61) || !(a <= 4.2e+45)) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.18e-61) or not (a <= 4.2e+45):
		tmp = b * (a * i)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.18e-61) || !(a <= 4.2e+45))
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.18e-61) || ~((a <= 4.2e+45)))
		tmp = b * (a * i);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.18e-61], N[Not[LessEqual[a, 4.2e+45]], $MachinePrecision]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1800000000000001e-61 or 4.1999999999999999e45 < a

   1. Initial program 61.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 48.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 48.7%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 48.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 34.1%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 34.1%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   7. Simplified 34.1%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   if -1.1800000000000001e-61 < a < 4.1999999999999999e45

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around inf 39.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 39.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 39.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 39.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 39.4%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) \]

      5. *-commutative 39.4%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) \]

   4. Simplified 39.4%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right)} \]

   5. Taylor expanded in j around inf 29.6%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 29.6%

         \[\leadsto t \cdot \color{blue}{\left(j \cdot c\right)} \]

   7. Simplified 29.6%

      \[\leadsto t \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.18 \cdot 10^{-61} \lor \neg \left(a \leq 4.2 \cdot 10^{+45}\right):\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 28: 30.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{-22}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.3e-22)
   (* b (* a i))
   (if (<= i 2.8e+57) (* c (* t j)) (* a (* b 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 (i <= -3.3e-22) {
		tmp = b * (a * i);
	} else if (i <= 2.8e+57) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * 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 (i <= (-3.3d-22)) then
        tmp = b * (a * i)
    else if (i <= 2.8d+57) then
        tmp = c * (t * j)
    else
        tmp = a * (b * 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 (i <= -3.3e-22) {
		tmp = b * (a * i);
	} else if (i <= 2.8e+57) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.3e-22:
		tmp = b * (a * i)
	elif i <= 2.8e+57:
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.3e-22)
		tmp = Float64(b * Float64(a * i));
	elseif (i <= 2.8e+57)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3.3e-22)
		tmp = b * (a * i);
	elseif (i <= 2.8e+57)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.3e-22], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.8e+57], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.3000000000000001e-22

   1. Initial program 61.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 53.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.3%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 53.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 35.4%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   6. Step-by-step derivation

      1. *-commutative 35.4%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   7. Simplified 35.4%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   if -3.3000000000000001e-22 < i < 2.8e57

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around -inf 72.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(-1 \cdot \left(y \cdot \left(-1 \cdot \left(x \cdot z\right) + i \cdot j\right)\right) + c \cdot \left(j \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   4. Simplified 80.4%

      \[\leadsto \color{blue}{\left(t \cdot \left(j \cdot c - x \cdot a\right) + \left(i \cdot j - x \cdot z\right) \cdot \left(-y\right)\right) + b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in b around 0 66.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) + t \cdot \left(c \cdot j - a \cdot x\right)} \]
   6. Step-by-step derivation

      1. +-commutative 66.9%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right)} \]

      2. *-commutative 66.9%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} - a \cdot x\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) \]

      3. *-commutative 66.9%

         \[\leadsto t \cdot \left(j \cdot c - \color{blue}{x \cdot a}\right) + -1 \cdot \left(y \cdot \left(i \cdot j - x \cdot z\right)\right) \]

      4. mul-1-neg 66.9%

         \[\leadsto t \cdot \left(j \cdot c - x \cdot a\right) + \color{blue}{\left(-y \cdot \left(i \cdot j - x \cdot z\right)\right)} \]

      5. unsub-neg 66.9%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - y \cdot \left(i \cdot j - x \cdot z\right)} \]

   7. Simplified 66.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) - y \cdot \left(i \cdot j - x \cdot z\right)} \]

   8. Taylor expanded in c around inf 25.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if 2.8e57 < i

   1. Initial program 57.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 42.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 42.9%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 42.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 36.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.3 \cdot 10^{-22}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{+57}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 29: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * 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 = a * (b * 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 a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.3%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

2. Taylor expanded in b around inf 41.3%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
3. Step-by-step derivation

   1. *-commutative 41.3%

      \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

4. Simplified 41.3%

   \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

5. Taylor expanded in i around inf 20.3%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

6. Final simplification 20.3%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Alternative 30: 22.6% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* b (* a i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return b * (a * 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 = b * (a * 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 b * (a * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return b * (a * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(b * Float64(a * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = b * (a * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.3%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

2. Taylor expanded in b around inf 41.3%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
3. Step-by-step derivation

   1. *-commutative 41.3%

      \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

4. Simplified 41.3%

   \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

5. Taylor expanded in i around inf 21.4%

   \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
6. Step-by-step derivation

   1. *-commutative 21.4%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

7. Simplified 21.4%

   \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

8. Final simplification 21.4%

   \[\leadsto b \cdot \left(a \cdot i\right) \]

Developer target: 67.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		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(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))