Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.8% → 81.3%

Time: 25.6s

Alternatives: 20

Speedup: 0.5×

• 57.8% 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: 72.8% 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: 81.3% accurate, 0.2× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. fma-def 90.5%

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

      3. *-commutative 90.5%

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

      4. *-commutative 90.5%

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

      5. *-commutative 90.5%

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

      6. *-commutative 90.5%

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

   3. Simplified 90.5%

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

   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. Step-by-step derivation

      1. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. remove-double-neg 0.0%

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

      6. *-commutative 0.0%

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

      7. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in y around inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

   6. Simplified 49.5%

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

4. Final simplification 83.0%

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

Alternative 2: 81.3% accurate, 0.5× speedup

Math

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

FPCore

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y * ((x * z) - (i * j))
	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(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * 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))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y * ((x * z) - (i * j));
	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[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.5%

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

   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. Step-by-step derivation

      1. cancel-sign-sub 0.0%

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

      2. cancel-sign-sub-inv 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. remove-double-neg 0.0%

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

      6. *-commutative 0.0%

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

      7. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in y around inf 49.5%

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

      1. +-commutative 49.5%

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

      2. mul-1-neg 49.5%

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

      3. unsub-neg 49.5%

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

   6. Simplified 49.5%

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

4. Final simplification 83.0%

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

Alternative 3: 61.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-151}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-98}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ t_1 (* b (- (* a i) (* z c))))))
   (if (<= b -9e-105)
     t_2
     (if (<= b -3.5e-151)
       (* c (- (* t j) (* z b)))
       (if (<= b -2.05e-199)
         t_1
         (if (<= b 2.35e-98)
           (- (* j (- (* t c) (* y i))) (* a (* x t)))
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double tmp;
	if (b <= -9e-105) {
		tmp = t_2;
	} else if (b <= -3.5e-151) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= -2.05e-199) {
		tmp = t_1;
	} else if (b <= 2.35e-98) {
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 + (b * ((a * i) - (z * c)))
    if (b <= (-9d-105)) then
        tmp = t_2
    else if (b <= (-3.5d-151)) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= (-2.05d-199)) then
        tmp = t_1
    else if (b <= 2.35d-98) then
        tmp = (j * ((t * c) - (y * i))) - (a * (x * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double tmp;
	if (b <= -9e-105) {
		tmp = t_2;
	} else if (b <= -3.5e-151) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= -2.05e-199) {
		tmp = t_1;
	} else if (b <= 2.35e-98) {
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	} 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))
	t_2 = t_1 + (b * ((a * i) - (z * c)))
	tmp = 0
	if b <= -9e-105:
		tmp = t_2
	elif b <= -3.5e-151:
		tmp = c * ((t * j) - (z * b))
	elif b <= -2.05e-199:
		tmp = t_1
	elif b <= 2.35e-98:
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t))
	else:
		tmp = t_2
	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(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (b <= -9e-105)
		tmp = t_2;
	elseif (b <= -3.5e-151)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= -2.05e-199)
		tmp = t_1;
	elseif (b <= 2.35e-98)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(a * Float64(x * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (b <= -9e-105)
		tmp = t_2;
	elseif (b <= -3.5e-151)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= -2.05e-199)
		tmp = t_1;
	elseif (b <= 2.35e-98)
		tmp = (j * ((t * c) - (y * i))) - (a * (x * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9e-105], t$95$2, If[LessEqual[b, -3.5e-151], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.05e-199], t$95$1, If[LessEqual[b, 2.35e-98], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.9999999999999995e-105 or 2.35000000000000003e-98 < b

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

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

      2. fma-def 79.9%

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

      3. *-commutative 79.9%

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

      4. *-commutative 79.9%

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

      5. *-commutative 79.9%

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

      6. *-commutative 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in j around 0 72.1%

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

   if -8.9999999999999995e-105 < b < -3.49999999999999995e-151

   1. Initial program 46.2%

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

      1. cancel-sign-sub 46.2%

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

      2. cancel-sign-sub-inv 46.2%

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

      3. *-commutative 46.2%

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

      4. *-commutative 46.2%

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

      5. remove-double-neg 46.2%

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

      6. *-commutative 46.2%

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

      7. *-commutative 46.2%

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

   3. Simplified 46.2%

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

   4. Taylor expanded in c around inf 77.6%

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

   if -3.49999999999999995e-151 < b < -2.05000000000000011e-199

   1. Initial program 83.1%

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

      1. cancel-sign-sub 83.1%

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

      2. cancel-sign-sub-inv 83.1%

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

      3. *-commutative 83.1%

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

      4. *-commutative 83.1%

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

      5. remove-double-neg 83.1%

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

      6. *-commutative 83.1%

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

      7. *-commutative 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in x around inf 99.7%

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

   if -2.05000000000000011e-199 < b < 2.35000000000000003e-98

   1. Initial program 72.1%

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

      1. cancel-sign-sub 72.1%

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

      2. cancel-sign-sub-inv 72.1%

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

      3. *-commutative 72.1%

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

      4. *-commutative 72.1%

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

      5. remove-double-neg 72.1%

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

      6. *-commutative 72.1%

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

      7. *-commutative 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in t around inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. *-commutative 74.2%

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

      3. distribute-rgt-neg-in 74.2%

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

   6. Simplified 74.2%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-151}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.35 \cdot 10^{-98}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 4: 59.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t_1 + x \cdot \left(y \cdot z\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+218}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-96}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (+ t_1 (* x (* y z))))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= a -1.05e+218)
     t_3
     (if (<= a -9e+190)
       t_2
       (if (<= a -8e+71)
         t_3
         (if (<= a 3.2e-96)
           (- t_1 (* c (* z b)))
           (if (<= a 1.9e+41) 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 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (x * (y * z));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.05e+218) {
		tmp = t_3;
	} else if (a <= -9e+190) {
		tmp = t_2;
	} else if (a <= -8e+71) {
		tmp = t_3;
	} else if (a <= 3.2e-96) {
		tmp = t_1 - (c * (z * b));
	} else if (a <= 1.9e+41) {
		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 = j * ((t * c) - (y * i))
    t_2 = t_1 + (x * (y * z))
    t_3 = a * ((b * i) - (x * t))
    if (a <= (-1.05d+218)) then
        tmp = t_3
    else if (a <= (-9d+190)) then
        tmp = t_2
    else if (a <= (-8d+71)) then
        tmp = t_3
    else if (a <= 3.2d-96) then
        tmp = t_1 - (c * (z * b))
    else if (a <= 1.9d+41) 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 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (x * (y * z));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.05e+218) {
		tmp = t_3;
	} else if (a <= -9e+190) {
		tmp = t_2;
	} else if (a <= -8e+71) {
		tmp = t_3;
	} else if (a <= 3.2e-96) {
		tmp = t_1 - (c * (z * b));
	} else if (a <= 1.9e+41) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = t_1 + (x * (y * z))
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1.05e+218:
		tmp = t_3
	elif a <= -9e+190:
		tmp = t_2
	elif a <= -8e+71:
		tmp = t_3
	elif a <= 3.2e-96:
		tmp = t_1 - (c * (z * b))
	elif a <= 1.9e+41:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(t_1 + Float64(x * Float64(y * z)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.05e+218)
		tmp = t_3;
	elseif (a <= -9e+190)
		tmp = t_2;
	elseif (a <= -8e+71)
		tmp = t_3;
	elseif (a <= 3.2e-96)
		tmp = Float64(t_1 - Float64(c * Float64(z * b)));
	elseif (a <= 1.9e+41)
		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 = j * ((t * c) - (y * i));
	t_2 = t_1 + (x * (y * z));
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.05e+218)
		tmp = t_3;
	elseif (a <= -9e+190)
		tmp = t_2;
	elseif (a <= -8e+71)
		tmp = t_3;
	elseif (a <= 3.2e-96)
		tmp = t_1 - (c * (z * b));
	elseif (a <= 1.9e+41)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e+218], t$95$3, If[LessEqual[a, -9e+190], t$95$2, If[LessEqual[a, -8e+71], t$95$3, If[LessEqual[a, 3.2e-96], N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e+41], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.0499999999999999e218 or -8.9999999999999999e190 < a < -8.0000000000000003e71 or 1.9000000000000001e41 < a

   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. Step-by-step derivation

      1. cancel-sign-sub 67.9%

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

      2. cancel-sign-sub-inv 67.9%

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

      3. *-commutative 67.9%

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

      4. *-commutative 67.9%

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

      5. remove-double-neg 67.9%

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

      6. *-commutative 67.9%

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

      7. *-commutative 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in a around inf 69.9%

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

      1. distribute-lft-out-- 69.9%

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

      2. mul-1-neg 69.9%

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

      3. mul-1-neg 69.9%

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

      4. distribute-lft-out-- 69.9%

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

      5. cancel-sign-sub-inv 69.9%

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

      6. metadata-eval 69.9%

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

      7. *-lft-identity 69.9%

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

      8. +-commutative 69.9%

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

      9. mul-1-neg 69.9%

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

      10. unsub-neg 69.9%

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

   6. Simplified 69.9%

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

   if -1.0499999999999999e218 < a < -8.9999999999999999e190 or 3.20000000000000012e-96 < a < 1.9000000000000001e41

   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. Step-by-step derivation

      1. cancel-sign-sub 73.3%

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

      2. cancel-sign-sub-inv 73.3%

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

      3. *-commutative 73.3%

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

      4. *-commutative 73.3%

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

      5. remove-double-neg 73.3%

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

      6. *-commutative 73.3%

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

      7. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in y around inf 69.9%

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

      1. associate-*r* 73.0%

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

   6. Simplified 73.0%

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

   if -8.0000000000000003e71 < a < 3.20000000000000012e-96

   1. Initial program 78.7%

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

      1. cancel-sign-sub 78.7%

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

      2. cancel-sign-sub-inv 78.7%

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

      3. *-commutative 78.7%

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

      4. *-commutative 78.7%

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

      5. remove-double-neg 78.7%

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

      6. *-commutative 78.7%

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

      7. *-commutative 78.7%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in c around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. distribute-rgt-neg-in 63.2%

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

   6. Simplified 63.2%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+218}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+190}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+71}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-96}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 5: 52.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+87}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -8.6e+31)
     t_3
     (if (<= t -5.4e-234)
       t_2
       (if (<= t 1.8e-280)
         t_1
         (if (<= t 4.6e-172)
           t_2
           (if (<= t 2.8e-117)
             t_1
             (if (<= t 1.42e-24)
               t_2
               (if (<= t 1.7e+87) (* j (- (* t c) (* y i))) t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -8.6e+31) {
		tmp = t_3;
	} else if (t <= -5.4e-234) {
		tmp = t_2;
	} else if (t <= 1.8e-280) {
		tmp = t_1;
	} else if (t <= 4.6e-172) {
		tmp = t_2;
	} else if (t <= 2.8e-117) {
		tmp = t_1;
	} else if (t <= 1.42e-24) {
		tmp = t_2;
	} else if (t <= 1.7e+87) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = b * ((a * i) - (z * c))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-8.6d+31)) then
        tmp = t_3
    else if (t <= (-5.4d-234)) then
        tmp = t_2
    else if (t <= 1.8d-280) then
        tmp = t_1
    else if (t <= 4.6d-172) then
        tmp = t_2
    else if (t <= 2.8d-117) then
        tmp = t_1
    else if (t <= 1.42d-24) then
        tmp = t_2
    else if (t <= 1.7d+87) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -8.6e+31) {
		tmp = t_3;
	} else if (t <= -5.4e-234) {
		tmp = t_2;
	} else if (t <= 1.8e-280) {
		tmp = t_1;
	} else if (t <= 4.6e-172) {
		tmp = t_2;
	} else if (t <= 2.8e-117) {
		tmp = t_1;
	} else if (t <= 1.42e-24) {
		tmp = t_2;
	} else if (t <= 1.7e+87) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = b * ((a * i) - (z * c))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -8.6e+31:
		tmp = t_3
	elif t <= -5.4e-234:
		tmp = t_2
	elif t <= 1.8e-280:
		tmp = t_1
	elif t <= 4.6e-172:
		tmp = t_2
	elif t <= 2.8e-117:
		tmp = t_1
	elif t <= 1.42e-24:
		tmp = t_2
	elif t <= 1.7e+87:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -8.6e+31)
		tmp = t_3;
	elseif (t <= -5.4e-234)
		tmp = t_2;
	elseif (t <= 1.8e-280)
		tmp = t_1;
	elseif (t <= 4.6e-172)
		tmp = t_2;
	elseif (t <= 2.8e-117)
		tmp = t_1;
	elseif (t <= 1.42e-24)
		tmp = t_2;
	elseif (t <= 1.7e+87)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = b * ((a * i) - (z * c));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -8.6e+31)
		tmp = t_3;
	elseif (t <= -5.4e-234)
		tmp = t_2;
	elseif (t <= 1.8e-280)
		tmp = t_1;
	elseif (t <= 4.6e-172)
		tmp = t_2;
	elseif (t <= 2.8e-117)
		tmp = t_1;
	elseif (t <= 1.42e-24)
		tmp = t_2;
	elseif (t <= 1.7e+87)
		tmp = j * ((t * c) - (y * i));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.6e+31], t$95$3, If[LessEqual[t, -5.4e-234], t$95$2, If[LessEqual[t, 1.8e-280], t$95$1, If[LessEqual[t, 4.6e-172], t$95$2, If[LessEqual[t, 2.8e-117], t$95$1, If[LessEqual[t, 1.42e-24], t$95$2, If[LessEqual[t, 1.7e+87], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.59999999999999978e31 or 1.7000000000000001e87 < t

   1. Initial program 70.5%

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

      1. cancel-sign-sub 70.5%

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

      2. cancel-sign-sub-inv 70.5%

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

      3. *-commutative 70.5%

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

      4. *-commutative 70.5%

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

      5. remove-double-neg 70.5%

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

      6. *-commutative 70.5%

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

      7. *-commutative 70.5%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in t around inf 76.3%

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

      1. *-commutative 76.3%

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

      2. mul-1-neg 76.3%

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

      3. unsub-neg 76.3%

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

   6. Simplified 76.3%

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

   if -8.59999999999999978e31 < t < -5.4000000000000003e-234 or 1.79999999999999997e-280 < t < 4.5999999999999999e-172 or 2.8e-117 < t < 1.42e-24

   1. Initial program 81.5%

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

      1. cancel-sign-sub 81.5%

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

      2. cancel-sign-sub-inv 81.5%

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

      3. *-commutative 81.5%

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

      4. *-commutative 81.5%

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

      5. remove-double-neg 81.5%

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

      6. *-commutative 81.5%

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

      7. *-commutative 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in b around inf 62.7%

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

   if -5.4000000000000003e-234 < t < 1.79999999999999997e-280 or 4.5999999999999999e-172 < t < 2.8e-117

   1. Initial program 64.9%

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

      1. cancel-sign-sub 64.9%

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

      2. cancel-sign-sub-inv 64.9%

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

      3. *-commutative 64.9%

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

      4. *-commutative 64.9%

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

      5. remove-double-neg 64.9%

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

      6. *-commutative 64.9%

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

      7. *-commutative 64.9%

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

   3. Simplified 64.9%

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

   4. Taylor expanded in y around inf 63.7%

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

      1. +-commutative 63.7%

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

      2. mul-1-neg 63.7%

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

      3. unsub-neg 63.7%

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

   6. Simplified 63.7%

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

   if 1.42e-24 < t < 1.7000000000000001e87

   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. Step-by-step derivation

      1. cancel-sign-sub 67.9%

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

      2. cancel-sign-sub-inv 67.9%

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

      3. *-commutative 67.9%

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

      4. *-commutative 67.9%

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

      5. remove-double-neg 67.9%

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

      6. *-commutative 67.9%

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

      7. *-commutative 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in c around inf 58.8%

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

      1. mul-1-neg 58.8%

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

      2. distribute-rgt-neg-in 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in j around inf 53.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-234}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-172}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-24}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+87}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 6: 51.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -530000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-19}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+96}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -1e+106)
     t_1
     (if (<= c -530000.0)
       (* z (- (* x y) (* b c)))
       (if (<= c -2.1e-218)
         (* a (- (* b i) (* x t)))
         (if (<= c 1.7e-179)
           (+ (* j (- (* t c) (* y i))) (* x (* y z)))
           (if (<= c 4.5e-19)
             (* b (- (* a i) (* z c)))
             (if (<= c 5.9e+51)
               (* t (- (* c j) (* x a)))
               (if (<= c 1.1e+96) (* i (- (* a b) (* 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1e+106) {
		tmp = t_1;
	} else if (c <= -530000.0) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -2.1e-218) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 1.7e-179) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (c <= 4.5e-19) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 5.9e+51) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 1.1e+96) {
		tmp = i * ((a * b) - (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 = c * ((t * j) - (z * b))
    if (c <= (-1d+106)) then
        tmp = t_1
    else if (c <= (-530000.0d0)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= (-2.1d-218)) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 1.7d-179) then
        tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
    else if (c <= 4.5d-19) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= 5.9d+51) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= 1.1d+96) then
        tmp = i * ((a * b) - (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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1e+106) {
		tmp = t_1;
	} else if (c <= -530000.0) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -2.1e-218) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 1.7e-179) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else if (c <= 4.5e-19) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 5.9e+51) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 1.1e+96) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1e+106:
		tmp = t_1
	elif c <= -530000.0:
		tmp = z * ((x * y) - (b * c))
	elif c <= -2.1e-218:
		tmp = a * ((b * i) - (x * t))
	elif c <= 1.7e-179:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	elif c <= 4.5e-19:
		tmp = b * ((a * i) - (z * c))
	elif c <= 5.9e+51:
		tmp = t * ((c * j) - (x * a))
	elif c <= 1.1e+96:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_1
	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)))
	tmp = 0.0
	if (c <= -1e+106)
		tmp = t_1;
	elseif (c <= -530000.0)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= -2.1e-218)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 1.7e-179)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	elseif (c <= 4.5e-19)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= 5.9e+51)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= 1.1e+96)
		tmp = Float64(i * Float64(Float64(a * b) - 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 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1e+106)
		tmp = t_1;
	elseif (c <= -530000.0)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= -2.1e-218)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 1.7e-179)
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	elseif (c <= 4.5e-19)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= 5.9e+51)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= 1.1e+96)
		tmp = i * ((a * b) - (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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1e+106], t$95$1, If[LessEqual[c, -530000.0], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.1e-218], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e-179], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.5e-19], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.9e+51], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.1e+96], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -1.00000000000000009e106 or 1.0999999999999999e96 < c

   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. Step-by-step derivation

      1. cancel-sign-sub 63.7%

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

      2. cancel-sign-sub-inv 63.7%

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

      3. *-commutative 63.7%

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

      4. *-commutative 63.7%

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

      5. remove-double-neg 63.7%

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

      6. *-commutative 63.7%

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

      7. *-commutative 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in c around inf 71.4%

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

   if -1.00000000000000009e106 < c < -5.3e5

   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. Step-by-step derivation

      1. cancel-sign-sub 85.0%

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

      2. cancel-sign-sub-inv 85.0%

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

      3. *-commutative 85.0%

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

      4. *-commutative 85.0%

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

      5. remove-double-neg 85.0%

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

      6. *-commutative 85.0%

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

      7. *-commutative 85.0%

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

   3. Simplified 85.0%

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

   4. Taylor expanded in z around inf 67.1%

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

   if -5.3e5 < c < -2.09999999999999994e-218

   1. Initial program 86.7%

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

      1. cancel-sign-sub 86.7%

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

      2. cancel-sign-sub-inv 86.7%

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

      3. *-commutative 86.7%

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

      4. *-commutative 86.7%

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

      5. remove-double-neg 86.7%

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

      6. *-commutative 86.7%

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

      7. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in a around inf 66.6%

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

      1. distribute-lft-out-- 66.6%

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

      2. mul-1-neg 66.6%

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

      3. mul-1-neg 66.6%

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

      4. distribute-lft-out-- 66.6%

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

      5. cancel-sign-sub-inv 66.6%

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

      6. metadata-eval 66.6%

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

      7. *-lft-identity 66.6%

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

      8. +-commutative 66.6%

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

      9. mul-1-neg 66.6%

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

      10. unsub-neg 66.6%

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

   6. Simplified 66.6%

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

   if -2.09999999999999994e-218 < c < 1.6999999999999999e-179

   1. Initial program 76.6%

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

      1. cancel-sign-sub 76.6%

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

      2. cancel-sign-sub-inv 76.6%

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

      3. *-commutative 76.6%

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

      4. *-commutative 76.6%

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

      5. remove-double-neg 76.6%

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

      6. *-commutative 76.6%

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

      7. *-commutative 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in y around inf 63.0%

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

      1. associate-*r* 62.8%

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

   6. Simplified 62.8%

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

   if 1.6999999999999999e-179 < c < 4.50000000000000013e-19

   1. Initial program 82.9%

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

      1. cancel-sign-sub 82.9%

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

      2. cancel-sign-sub-inv 82.9%

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

      3. *-commutative 82.9%

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

      4. *-commutative 82.9%

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

      5. remove-double-neg 82.9%

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

      6. *-commutative 82.9%

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

      7. *-commutative 82.9%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in b around inf 69.8%

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

   if 4.50000000000000013e-19 < c < 5.89999999999999983e51

   1. Initial program 73.7%

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

      1. cancel-sign-sub 73.7%

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

      2. cancel-sign-sub-inv 73.7%

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

      3. *-commutative 73.7%

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

      4. *-commutative 73.7%

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

      5. remove-double-neg 73.7%

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

      6. *-commutative 73.7%

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

      7. *-commutative 73.7%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in t around inf 65.4%

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

      1. *-commutative 65.4%

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

      2. mul-1-neg 65.4%

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

      3. unsub-neg 65.4%

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

   6. Simplified 65.4%

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

   if 5.89999999999999983e51 < c < 1.0999999999999999e96

   1. Initial program 63.1%

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

      1. cancel-sign-sub 63.1%

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

      2. cancel-sign-sub-inv 63.1%

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

      3. *-commutative 63.1%

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

      4. *-commutative 63.1%

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

      5. remove-double-neg 63.1%

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

      6. *-commutative 63.1%

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

      7. *-commutative 63.1%

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

   3. Simplified 63.1%

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

   4. Taylor expanded in i around inf 87.7%

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

      1. *-commutative 87.7%

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

      2. distribute-lft-out-- 87.7%

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

      3. *-commutative 87.7%

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

   6. Simplified 87.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j - b \cdot a\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{+106}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -530000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-218}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-179}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-19}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{+96}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 7: 30.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-27}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-219}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-174}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= z -3.7e+198)
     (* x (* y z))
     (if (<= z -2.25e-27)
       (* c (* z (- b)))
       (if (<= z -2.7e-170)
         t_1
         (if (<= z -8.5e-219)
           (* j (* t c))
           (if (<= z -6.2e-304)
             t_1
             (if (<= z 7e-174)
               (* c (* t j))
               (if (<= z 3.4e-9) t_1 (* b (* z (- c))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (z <= -3.7e+198) {
		tmp = x * (y * z);
	} else if (z <= -2.25e-27) {
		tmp = c * (z * -b);
	} else if (z <= -2.7e-170) {
		tmp = t_1;
	} else if (z <= -8.5e-219) {
		tmp = j * (t * c);
	} else if (z <= -6.2e-304) {
		tmp = t_1;
	} else if (z <= 7e-174) {
		tmp = c * (t * j);
	} else if (z <= 3.4e-9) {
		tmp = t_1;
	} else {
		tmp = b * (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) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (z <= (-3.7d+198)) then
        tmp = x * (y * z)
    else if (z <= (-2.25d-27)) then
        tmp = c * (z * -b)
    else if (z <= (-2.7d-170)) then
        tmp = t_1
    else if (z <= (-8.5d-219)) then
        tmp = j * (t * c)
    else if (z <= (-6.2d-304)) then
        tmp = t_1
    else if (z <= 7d-174) then
        tmp = c * (t * j)
    else if (z <= 3.4d-9) then
        tmp = t_1
    else
        tmp = b * (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 t_1 = b * (a * i);
	double tmp;
	if (z <= -3.7e+198) {
		tmp = x * (y * z);
	} else if (z <= -2.25e-27) {
		tmp = c * (z * -b);
	} else if (z <= -2.7e-170) {
		tmp = t_1;
	} else if (z <= -8.5e-219) {
		tmp = j * (t * c);
	} else if (z <= -6.2e-304) {
		tmp = t_1;
	} else if (z <= 7e-174) {
		tmp = c * (t * j);
	} else if (z <= 3.4e-9) {
		tmp = t_1;
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if z <= -3.7e+198:
		tmp = x * (y * z)
	elif z <= -2.25e-27:
		tmp = c * (z * -b)
	elif z <= -2.7e-170:
		tmp = t_1
	elif z <= -8.5e-219:
		tmp = j * (t * c)
	elif z <= -6.2e-304:
		tmp = t_1
	elif z <= 7e-174:
		tmp = c * (t * j)
	elif z <= 3.4e-9:
		tmp = t_1
	else:
		tmp = b * (z * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (z <= -3.7e+198)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -2.25e-27)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (z <= -2.7e-170)
		tmp = t_1;
	elseif (z <= -8.5e-219)
		tmp = Float64(j * Float64(t * c));
	elseif (z <= -6.2e-304)
		tmp = t_1;
	elseif (z <= 7e-174)
		tmp = Float64(c * Float64(t * j));
	elseif (z <= 3.4e-9)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(z * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	tmp = 0.0;
	if (z <= -3.7e+198)
		tmp = x * (y * z);
	elseif (z <= -2.25e-27)
		tmp = c * (z * -b);
	elseif (z <= -2.7e-170)
		tmp = t_1;
	elseif (z <= -8.5e-219)
		tmp = j * (t * c);
	elseif (z <= -6.2e-304)
		tmp = t_1;
	elseif (z <= 7e-174)
		tmp = c * (t * j);
	elseif (z <= 3.4e-9)
		tmp = t_1;
	else
		tmp = b * (z * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.7e+198], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e-27], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-170], t$95$1, If[LessEqual[z, -8.5e-219], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-304], t$95$1, If[LessEqual[z, 7e-174], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-9], t$95$1, N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.6999999999999998e198

   1. Initial program 68.1%

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

      1. +-commutative 68.1%

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

      2. fma-def 72.7%

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

      3. *-commutative 72.7%

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

      4. *-commutative 72.7%

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

      5. *-commutative 72.7%

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

      6. *-commutative 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in j around 0 81.7%

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

   5. Taylor expanded in y around inf 65.1%

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

      1. associate-*r* 77.9%

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

      2. *-commutative 77.9%

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

   7. Simplified 77.9%

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

   if -3.6999999999999998e198 < z < -2.2500000000000001e-27

   1. Initial program 67.6%

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

      1. +-commutative 67.6%

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

      2. fma-def 71.7%

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

      3. *-commutative 71.7%

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

      4. *-commutative 71.7%

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

      5. *-commutative 71.7%

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

      6. *-commutative 71.7%

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

   3. Simplified 71.7%

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

   4. Taylor expanded in j around 0 67.7%

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

   5. Taylor expanded in c around inf 41.0%

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

      1. *-commutative 41.0%

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

      2. mul-1-neg 41.0%

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

      3. distribute-rgt-neg-in 41.0%

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

      4. distribute-rgt-neg-out 41.0%

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

   7. Simplified 41.0%

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

   if -2.2500000000000001e-27 < z < -2.6999999999999999e-170 or -8.49999999999999964e-219 < z < -6.1999999999999997e-304 or 6.99999999999999975e-174 < z < 3.3999999999999998e-9

   1. Initial program 78.7%

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

      1. cancel-sign-sub 78.7%

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

      2. cancel-sign-sub-inv 78.7%

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

      3. *-commutative 78.7%

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

      4. *-commutative 78.7%

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

      5. remove-double-neg 78.7%

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

      6. *-commutative 78.7%

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

      7. *-commutative 78.7%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in b around inf 42.1%

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

   5. Taylor expanded in a around inf 38.3%

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

   if -2.6999999999999999e-170 < z < -8.49999999999999964e-219

   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. Step-by-step derivation

      1. cancel-sign-sub 70.4%

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

      2. cancel-sign-sub-inv 70.4%

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

      3. *-commutative 70.4%

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

      4. *-commutative 70.4%

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

      5. remove-double-neg 70.4%

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

      6. *-commutative 70.4%

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

      7. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in c around inf 61.3%

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

      1. mul-1-neg 61.3%

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

      2. distribute-rgt-neg-in 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in j around inf 61.3%

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

   8. Taylor expanded in c around inf 60.9%

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

   if -6.1999999999999997e-304 < z < 6.99999999999999975e-174

   1. Initial program 85.1%

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

      1. cancel-sign-sub 85.1%

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

      2. cancel-sign-sub-inv 85.1%

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

      3. *-commutative 85.1%

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

      4. *-commutative 85.1%

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

      5. remove-double-neg 85.1%

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

      6. *-commutative 85.1%

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

      7. *-commutative 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in c around inf 60.5%

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

      1. mul-1-neg 60.5%

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

      2. distribute-rgt-neg-in 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in t around inf 42.7%

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

   if 3.3999999999999998e-9 < z

   1. Initial program 71.0%

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

      1. +-commutative 71.0%

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

      2. fma-def 73.8%

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

      3. *-commutative 73.8%

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

      4. *-commutative 73.8%

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

      5. *-commutative 73.8%

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

      6. *-commutative 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in j around 0 60.1%

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

   5. Taylor expanded in c around inf 38.1%

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

      1. neg-mul-1 38.1%

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

      2. *-commutative 38.1%

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

      3. associate-*r* 38.1%

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

      4. distribute-rgt-neg-in 38.1%

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

      5. *-commutative 38.1%

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

      6. associate-*l* 40.9%

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

   7. Simplified 40.9%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-27}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-170}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-219}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-304}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-174}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 8: 39.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-174}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= z -5.8e+198)
     (* x (* y z))
     (if (<= z -5e-22)
       (* c (* z (- b)))
       (if (<= z 6.5e-254)
         t_1
         (if (<= z 2.1e-174)
           (* c (* t j))
           (if (<= z 4e+129) t_1 (* b (* z (- c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (z <= -5.8e+198) {
		tmp = x * (y * z);
	} else if (z <= -5e-22) {
		tmp = c * (z * -b);
	} else if (z <= 6.5e-254) {
		tmp = t_1;
	} else if (z <= 2.1e-174) {
		tmp = c * (t * j);
	} else if (z <= 4e+129) {
		tmp = t_1;
	} else {
		tmp = b * (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) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (z <= (-5.8d+198)) then
        tmp = x * (y * z)
    else if (z <= (-5d-22)) then
        tmp = c * (z * -b)
    else if (z <= 6.5d-254) then
        tmp = t_1
    else if (z <= 2.1d-174) then
        tmp = c * (t * j)
    else if (z <= 4d+129) then
        tmp = t_1
    else
        tmp = b * (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 t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (z <= -5.8e+198) {
		tmp = x * (y * z);
	} else if (z <= -5e-22) {
		tmp = c * (z * -b);
	} else if (z <= 6.5e-254) {
		tmp = t_1;
	} else if (z <= 2.1e-174) {
		tmp = c * (t * j);
	} else if (z <= 4e+129) {
		tmp = t_1;
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if z <= -5.8e+198:
		tmp = x * (y * z)
	elif z <= -5e-22:
		tmp = c * (z * -b)
	elif z <= 6.5e-254:
		tmp = t_1
	elif z <= 2.1e-174:
		tmp = c * (t * j)
	elif z <= 4e+129:
		tmp = t_1
	else:
		tmp = b * (z * -c)
	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 (z <= -5.8e+198)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -5e-22)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (z <= 6.5e-254)
		tmp = t_1;
	elseif (z <= 2.1e-174)
		tmp = Float64(c * Float64(t * j));
	elseif (z <= 4e+129)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(z * Float64(-c)));
	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 (z <= -5.8e+198)
		tmp = x * (y * z);
	elseif (z <= -5e-22)
		tmp = c * (z * -b);
	elseif (z <= 6.5e-254)
		tmp = t_1;
	elseif (z <= 2.1e-174)
		tmp = c * (t * j);
	elseif (z <= 4e+129)
		tmp = t_1;
	else
		tmp = b * (z * -c);
	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[z, -5.8e+198], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-22], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-254], t$95$1, If[LessEqual[z, 2.1e-174], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+129], t$95$1, N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.8000000000000002e198

   1. Initial program 68.1%

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

      1. +-commutative 68.1%

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

      2. fma-def 72.7%

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

      3. *-commutative 72.7%

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

      4. *-commutative 72.7%

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

      5. *-commutative 72.7%

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

      6. *-commutative 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in j around 0 81.7%

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

   5. Taylor expanded in y around inf 65.1%

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

      1. associate-*r* 77.9%

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

      2. *-commutative 77.9%

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

   7. Simplified 77.9%

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

   if -5.8000000000000002e198 < z < -4.99999999999999954e-22

   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. Step-by-step derivation

      1. +-commutative 69.0%

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

      2. fma-def 73.2%

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

      3. *-commutative 73.2%

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

      4. *-commutative 73.2%

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

      5. *-commutative 73.2%

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

      6. *-commutative 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in j around 0 67.0%

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

   5. Taylor expanded in c around inf 41.8%

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

      1. *-commutative 41.8%

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

      2. mul-1-neg 41.8%

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

      3. distribute-rgt-neg-in 41.8%

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

      4. distribute-rgt-neg-out 41.8%

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

   7. Simplified 41.8%

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

   if -4.99999999999999954e-22 < z < 6.5e-254 or 2.1000000000000001e-174 < z < 4e129

   1. Initial program 77.7%

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

      1. cancel-sign-sub 77.7%

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

      2. cancel-sign-sub-inv 77.7%

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

      3. *-commutative 77.7%

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

      4. *-commutative 77.7%

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

      5. remove-double-neg 77.7%

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

      6. *-commutative 77.7%

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

      7. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in a around inf 51.1%

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

      1. distribute-lft-out-- 51.1%

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

      2. mul-1-neg 51.1%

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

      3. mul-1-neg 51.1%

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

      4. distribute-lft-out-- 51.1%

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

      5. cancel-sign-sub-inv 51.1%

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

      6. metadata-eval 51.1%

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

      7. *-lft-identity 51.1%

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

      8. +-commutative 51.1%

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

      9. mul-1-neg 51.1%

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

      10. unsub-neg 51.1%

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

   6. Simplified 51.1%

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

   if 6.5e-254 < z < 2.1000000000000001e-174

   1. Initial program 83.5%

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

      1. cancel-sign-sub 83.5%

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

      2. cancel-sign-sub-inv 83.5%

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

      3. *-commutative 83.5%

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

      4. *-commutative 83.5%

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

      5. remove-double-neg 83.5%

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

      6. *-commutative 83.5%

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

      7. *-commutative 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in c around inf 75.5%

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

      1. mul-1-neg 75.5%

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

      2. distribute-rgt-neg-in 75.5%

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

   6. Simplified 75.5%

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

   7. Taylor expanded in t around inf 67.4%

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

   if 4e129 < z

   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. Step-by-step derivation

      1. +-commutative 67.9%

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

      2. fma-def 70.3%

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

      3. *-commutative 70.3%

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

      4. *-commutative 70.3%

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

      5. *-commutative 70.3%

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

      6. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   4. Taylor expanded in j around 0 59.3%

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

   5. Taylor expanded in c around inf 38.9%

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

      1. neg-mul-1 38.9%

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

      2. *-commutative 38.9%

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

      3. associate-*r* 41.1%

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

      4. distribute-rgt-neg-in 41.1%

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

      5. *-commutative 41.1%

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

      6. associate-*l* 45.8%

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

   7. Simplified 45.8%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+198}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-22}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-254}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-174}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 9: 28.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+95}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-223}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.9e+95)
   (* c (* z (- b)))
   (if (<= b -5.8e+20)
     (* i (* a b))
     (if (<= b -1.75e-48)
       (* b (* z (- c)))
       (if (<= b -1.9e-103)
         (* a (* b i))
         (if (<= b 3.4e-223)
           (* c (* t j))
           (if (<= b 5.2e-30) (* y (* i (- j))) (* 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 <= -1.9e+95) {
		tmp = c * (z * -b);
	} else if (b <= -5.8e+20) {
		tmp = i * (a * b);
	} else if (b <= -1.75e-48) {
		tmp = b * (z * -c);
	} else if (b <= -1.9e-103) {
		tmp = a * (b * i);
	} else if (b <= 3.4e-223) {
		tmp = c * (t * j);
	} else if (b <= 5.2e-30) {
		tmp = y * (i * -j);
	} 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 <= (-1.9d+95)) then
        tmp = c * (z * -b)
    else if (b <= (-5.8d+20)) then
        tmp = i * (a * b)
    else if (b <= (-1.75d-48)) then
        tmp = b * (z * -c)
    else if (b <= (-1.9d-103)) then
        tmp = a * (b * i)
    else if (b <= 3.4d-223) then
        tmp = c * (t * j)
    else if (b <= 5.2d-30) then
        tmp = y * (i * -j)
    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 <= -1.9e+95) {
		tmp = c * (z * -b);
	} else if (b <= -5.8e+20) {
		tmp = i * (a * b);
	} else if (b <= -1.75e-48) {
		tmp = b * (z * -c);
	} else if (b <= -1.9e-103) {
		tmp = a * (b * i);
	} else if (b <= 3.4e-223) {
		tmp = c * (t * j);
	} else if (b <= 5.2e-30) {
		tmp = y * (i * -j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.9e+95:
		tmp = c * (z * -b)
	elif b <= -5.8e+20:
		tmp = i * (a * b)
	elif b <= -1.75e-48:
		tmp = b * (z * -c)
	elif b <= -1.9e-103:
		tmp = a * (b * i)
	elif b <= 3.4e-223:
		tmp = c * (t * j)
	elif b <= 5.2e-30:
		tmp = y * (i * -j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.9e+95)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (b <= -5.8e+20)
		tmp = Float64(i * Float64(a * b));
	elseif (b <= -1.75e-48)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (b <= -1.9e-103)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= 3.4e-223)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 5.2e-30)
		tmp = Float64(y * Float64(i * Float64(-j)));
	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 <= -1.9e+95)
		tmp = c * (z * -b);
	elseif (b <= -5.8e+20)
		tmp = i * (a * b);
	elseif (b <= -1.75e-48)
		tmp = b * (z * -c);
	elseif (b <= -1.9e-103)
		tmp = a * (b * i);
	elseif (b <= 3.4e-223)
		tmp = c * (t * j);
	elseif (b <= 5.2e-30)
		tmp = y * (i * -j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.9e+95], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.8e+20], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.75e-48], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.9e-103], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e-223], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e-30], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.9e95

   1. Initial program 73.6%

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

      1. +-commutative 73.6%

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

      2. fma-def 80.8%

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

      3. *-commutative 80.8%

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

      4. *-commutative 80.8%

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

      5. *-commutative 80.8%

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

      6. *-commutative 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in j around 0 62.5%

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

   5. Taylor expanded in c around inf 44.3%

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

      1. *-commutative 44.3%

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

      2. mul-1-neg 44.3%

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

      3. distribute-rgt-neg-in 44.3%

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

      4. distribute-rgt-neg-out 44.3%

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

   7. Simplified 44.3%

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

   if -1.9e95 < b < -5.8e20

   1. Initial program 83.3%

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

      1. cancel-sign-sub 83.3%

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

      2. cancel-sign-sub-inv 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

      5. remove-double-neg 83.3%

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

      6. *-commutative 83.3%

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

      7. *-commutative 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in a around inf 83.6%

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

      1. distribute-lft-out-- 83.6%

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

      2. mul-1-neg 83.6%

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

      3. mul-1-neg 83.6%

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

      4. distribute-lft-out-- 83.6%

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

      5. cancel-sign-sub-inv 83.6%

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

      6. metadata-eval 83.6%

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

      7. *-lft-identity 83.6%

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

      8. +-commutative 83.6%

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

      9. mul-1-neg 83.6%

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

      10. unsub-neg 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in b around inf 59.3%

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

   if -5.8e20 < b < -1.74999999999999996e-48

   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. Step-by-step derivation

      1. +-commutative 71.6%

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

      2. fma-def 76.3%

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

      3. *-commutative 76.3%

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

      4. *-commutative 76.3%

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

      5. *-commutative 76.3%

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

      6. *-commutative 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in j around 0 66.2%

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

   5. Taylor expanded in c around inf 43.5%

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

      1. neg-mul-1 43.5%

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

      2. *-commutative 43.5%

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

      3. associate-*r* 43.6%

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

      4. distribute-rgt-neg-in 43.6%

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

      5. *-commutative 43.6%

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

      6. associate-*l* 43.6%

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

   7. Simplified 43.6%

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

   if -1.74999999999999996e-48 < b < -1.9e-103

   1. Initial program 86.0%

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

      1. +-commutative 86.0%

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

      2. fma-def 86.0%

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

      3. *-commutative 86.0%

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

      4. *-commutative 86.0%

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

      5. *-commutative 86.0%

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

      6. *-commutative 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in j around 0 72.3%

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

   5. Taylor expanded in i around inf 43.9%

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

   if -1.9e-103 < b < 3.3999999999999998e-223

   1. Initial program 72.6%

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

      1. cancel-sign-sub 72.6%

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

      2. cancel-sign-sub-inv 72.6%

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

      3. *-commutative 72.6%

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

      4. *-commutative 72.6%

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

      5. remove-double-neg 72.6%

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

      6. *-commutative 72.6%

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

      7. *-commutative 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in c around inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. distribute-rgt-neg-in 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in t around inf 45.8%

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

   if 3.3999999999999998e-223 < b < 5.19999999999999973e-30

   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. Step-by-step derivation

      1. cancel-sign-sub 68.5%

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

      2. cancel-sign-sub-inv 68.5%

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

      3. *-commutative 68.5%

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

      4. *-commutative 68.5%

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

      5. remove-double-neg 68.5%

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

      6. *-commutative 68.5%

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

      7. *-commutative 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in y around inf 53.8%

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

      1. +-commutative 53.8%

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

      2. mul-1-neg 53.8%

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

      3. unsub-neg 53.8%

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

   6. Simplified 53.8%

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

   7. Taylor expanded in z around 0 37.6%

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

      1. neg-mul-1 37.6%

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

      2. distribute-lft-neg-in 37.6%

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

      3. *-commutative 37.6%

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

   9. Simplified 37.6%

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

   if 5.19999999999999973e-30 < b

   1. Initial program 74.9%

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

      1. cancel-sign-sub 74.9%

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

      2. cancel-sign-sub-inv 74.9%

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

      3. *-commutative 74.9%

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

      4. *-commutative 74.9%

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

      5. remove-double-neg 74.9%

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

      6. *-commutative 74.9%

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

      7. *-commutative 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in b around inf 65.8%

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

   5. Taylor expanded in a around inf 39.6%

      \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]
3. Recombined 7 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+95}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-48}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-223}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 10: 29.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2600000:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-219}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{-178}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-22} \lor \neg \left(c \leq 3 \cdot 10^{+49}\right) \land c \leq 3.2 \cdot 10^{+158}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -2600000.0)
   (* b (* z (- c)))
   (if (<= c -1.15e-219)
     (* a (* b i))
     (if (<= c 2.35e-178)
       (* z (* x y))
       (if (or (<= c 1.1e-22) (and (not (<= c 3e+49)) (<= c 3.2e+158)))
         (* b (* a i))
         (* j (* t c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2600000.0) {
		tmp = b * (z * -c);
	} else if (c <= -1.15e-219) {
		tmp = a * (b * i);
	} else if (c <= 2.35e-178) {
		tmp = z * (x * y);
	} else if ((c <= 1.1e-22) || (!(c <= 3e+49) && (c <= 3.2e+158))) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-2600000.0d0)) then
        tmp = b * (z * -c)
    else if (c <= (-1.15d-219)) then
        tmp = a * (b * i)
    else if (c <= 2.35d-178) then
        tmp = z * (x * y)
    else if ((c <= 1.1d-22) .or. (.not. (c <= 3d+49)) .and. (c <= 3.2d+158)) then
        tmp = b * (a * i)
    else
        tmp = j * (t * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2600000.0) {
		tmp = b * (z * -c);
	} else if (c <= -1.15e-219) {
		tmp = a * (b * i);
	} else if (c <= 2.35e-178) {
		tmp = z * (x * y);
	} else if ((c <= 1.1e-22) || (!(c <= 3e+49) && (c <= 3.2e+158))) {
		tmp = b * (a * i);
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -2600000.0:
		tmp = b * (z * -c)
	elif c <= -1.15e-219:
		tmp = a * (b * i)
	elif c <= 2.35e-178:
		tmp = z * (x * y)
	elif (c <= 1.1e-22) or (not (c <= 3e+49) and (c <= 3.2e+158)):
		tmp = b * (a * i)
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -2600000.0)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= -1.15e-219)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 2.35e-178)
		tmp = Float64(z * Float64(x * y));
	elseif ((c <= 1.1e-22) || (!(c <= 3e+49) && (c <= 3.2e+158)))
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -2600000.0)
		tmp = b * (z * -c);
	elseif (c <= -1.15e-219)
		tmp = a * (b * i);
	elseif (c <= 2.35e-178)
		tmp = z * (x * y);
	elseif ((c <= 1.1e-22) || (~((c <= 3e+49)) && (c <= 3.2e+158)))
		tmp = b * (a * i);
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -2600000.0], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.15e-219], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.35e-178], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 1.1e-22], And[N[Not[LessEqual[c, 3e+49]], $MachinePrecision], LessEqual[c, 3.2e+158]]], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -2.6e6

   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. Step-by-step derivation

      1. +-commutative 63.7%

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

      2. fma-def 66.9%

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

      3. *-commutative 66.9%

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

      4. *-commutative 66.9%

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

      5. *-commutative 66.9%

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

      6. *-commutative 66.9%

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

   3. Simplified 66.9%

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

   4. Taylor expanded in j around 0 62.2%

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

   5. Taylor expanded in c around inf 40.3%

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

      1. neg-mul-1 40.3%

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

      2. *-commutative 40.3%

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

      3. associate-*r* 42.0%

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

      4. distribute-rgt-neg-in 42.0%

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

      5. *-commutative 42.0%

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

      6. associate-*l* 42.0%

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

   7. Simplified 42.0%

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

   if -2.6e6 < c < -1.14999999999999994e-219

   1. Initial program 87.1%

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

      1. +-commutative 87.1%

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

      2. fma-def 87.1%

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

      3. *-commutative 87.1%

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

      4. *-commutative 87.1%

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

      5. *-commutative 87.1%

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

      6. *-commutative 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in j around 0 73.6%

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

   5. Taylor expanded in i around inf 32.6%

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

   if -1.14999999999999994e-219 < c < 2.35e-178

   1. Initial program 76.1%

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

      1. +-commutative 76.1%

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

      2. fma-def 76.1%

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

      3. *-commutative 76.1%

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

      4. *-commutative 76.1%

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

      5. *-commutative 76.1%

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

      6. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in j around 0 55.3%

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

   5. Taylor expanded in y around inf 28.1%

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

      1. *-commutative 28.1%

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

      2. associate-*l* 33.3%

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

   7. Simplified 33.3%

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

   if 2.35e-178 < c < 1.1e-22 or 3.0000000000000002e49 < c < 3.19999999999999995e158

   1. Initial program 77.0%

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

      1. cancel-sign-sub 77.0%

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

      2. cancel-sign-sub-inv 77.0%

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

      3. *-commutative 77.0%

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

      4. *-commutative 77.0%

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

      5. remove-double-neg 77.0%

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

      6. *-commutative 77.0%

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

      7. *-commutative 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in b around inf 62.6%

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

   5. Taylor expanded in a around inf 48.8%

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

   if 1.1e-22 < c < 3.0000000000000002e49 or 3.19999999999999995e158 < c

   1. Initial program 71.3%

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

      1. cancel-sign-sub 71.3%

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

      2. cancel-sign-sub-inv 71.3%

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

      3. *-commutative 71.3%

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

      4. *-commutative 71.3%

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

      5. remove-double-neg 71.3%

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

      6. *-commutative 71.3%

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

      7. *-commutative 71.3%

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

   3. Simplified 71.3%

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

   4. Taylor expanded in c around inf 62.0%

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

      1. mul-1-neg 62.0%

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

      2. distribute-rgt-neg-in 62.0%

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

   6. Simplified 62.0%

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

   7. Taylor expanded in j around inf 51.2%

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

   8. Taylor expanded in c around inf 49.3%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2600000:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-219}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{-178}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-22} \lor \neg \left(c \leq 3 \cdot 10^{+49}\right) \land c \leq 3.2 \cdot 10^{+158}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 11: 29.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(t \cdot \left(-x\right)\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;c \leq -14500000:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 9.6 \cdot 10^{-177}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+158}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* t (- x)))) (t_2 (* b (* a i))))
   (if (<= c -14500000.0)
     (* (* b c) (- z))
     (if (<= c -2.1e-242)
       t_1
       (if (<= c 9.6e-177)
         (* (* y i) (- j))
         (if (<= c 2.9e-15)
           t_2
           (if (<= c 1.15e+61)
             t_1
             (if (<= c 3.2e+158) t_2 (* j (* t c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (t * -x);
	double t_2 = b * (a * i);
	double tmp;
	if (c <= -14500000.0) {
		tmp = (b * c) * -z;
	} else if (c <= -2.1e-242) {
		tmp = t_1;
	} else if (c <= 9.6e-177) {
		tmp = (y * i) * -j;
	} else if (c <= 2.9e-15) {
		tmp = t_2;
	} else if (c <= 1.15e+61) {
		tmp = t_1;
	} else if (c <= 3.2e+158) {
		tmp = t_2;
	} else {
		tmp = j * (t * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (t * -x)
    t_2 = b * (a * i)
    if (c <= (-14500000.0d0)) then
        tmp = (b * c) * -z
    else if (c <= (-2.1d-242)) then
        tmp = t_1
    else if (c <= 9.6d-177) then
        tmp = (y * i) * -j
    else if (c <= 2.9d-15) then
        tmp = t_2
    else if (c <= 1.15d+61) then
        tmp = t_1
    else if (c <= 3.2d+158) then
        tmp = t_2
    else
        tmp = j * (t * 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 t_1 = a * (t * -x);
	double t_2 = b * (a * i);
	double tmp;
	if (c <= -14500000.0) {
		tmp = (b * c) * -z;
	} else if (c <= -2.1e-242) {
		tmp = t_1;
	} else if (c <= 9.6e-177) {
		tmp = (y * i) * -j;
	} else if (c <= 2.9e-15) {
		tmp = t_2;
	} else if (c <= 1.15e+61) {
		tmp = t_1;
	} else if (c <= 3.2e+158) {
		tmp = t_2;
	} else {
		tmp = j * (t * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (t * -x)
	t_2 = b * (a * i)
	tmp = 0
	if c <= -14500000.0:
		tmp = (b * c) * -z
	elif c <= -2.1e-242:
		tmp = t_1
	elif c <= 9.6e-177:
		tmp = (y * i) * -j
	elif c <= 2.9e-15:
		tmp = t_2
	elif c <= 1.15e+61:
		tmp = t_1
	elif c <= 3.2e+158:
		tmp = t_2
	else:
		tmp = j * (t * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(t * Float64(-x)))
	t_2 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (c <= -14500000.0)
		tmp = Float64(Float64(b * c) * Float64(-z));
	elseif (c <= -2.1e-242)
		tmp = t_1;
	elseif (c <= 9.6e-177)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (c <= 2.9e-15)
		tmp = t_2;
	elseif (c <= 1.15e+61)
		tmp = t_1;
	elseif (c <= 3.2e+158)
		tmp = t_2;
	else
		tmp = Float64(j * Float64(t * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (t * -x);
	t_2 = b * (a * i);
	tmp = 0.0;
	if (c <= -14500000.0)
		tmp = (b * c) * -z;
	elseif (c <= -2.1e-242)
		tmp = t_1;
	elseif (c <= 9.6e-177)
		tmp = (y * i) * -j;
	elseif (c <= 2.9e-15)
		tmp = t_2;
	elseif (c <= 1.15e+61)
		tmp = t_1;
	elseif (c <= 3.2e+158)
		tmp = t_2;
	else
		tmp = j * (t * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -14500000.0], N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[c, -2.1e-242], t$95$1, If[LessEqual[c, 9.6e-177], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[c, 2.9e-15], t$95$2, If[LessEqual[c, 1.15e+61], t$95$1, If[LessEqual[c, 3.2e+158], t$95$2, N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.45e7

   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. Step-by-step derivation

      1. cancel-sign-sub 63.7%

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

      2. cancel-sign-sub-inv 63.7%

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

      3. *-commutative 63.7%

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

      4. *-commutative 63.7%

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

      5. remove-double-neg 63.7%

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

      6. *-commutative 63.7%

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

      7. *-commutative 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in c around inf 54.4%

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

      1. mul-1-neg 54.4%

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

      2. distribute-rgt-neg-in 54.4%

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

   6. Simplified 54.4%

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

      1. add-cbrt-cube 45.5%

         \[\leadsto c \cdot \left(-b \cdot z\right) + j \cdot \color{blue}{\sqrt[3]{\left(\left(t \cdot c - y \cdot i\right) \cdot \left(t \cdot c - y \cdot i\right)\right) \cdot \left(t \cdot c - y \cdot i\right)}} \]

      2. *-commutative 45.5%

         \[\leadsto c \cdot \left(-b \cdot z\right) + j \cdot \sqrt[3]{\left(\left(\color{blue}{c \cdot t} - y \cdot i\right) \cdot \left(t \cdot c - y \cdot i\right)\right) \cdot \left(t \cdot c - y \cdot i\right)} \]

      3. *-commutative 45.5%

         \[\leadsto c \cdot \left(-b \cdot z\right) + j \cdot \sqrt[3]{\left(\left(c \cdot t - \color{blue}{i \cdot y}\right) \cdot \left(t \cdot c - y \cdot i\right)\right) \cdot \left(t \cdot c - y \cdot i\right)} \]

      4. *-commutative 45.5%

         \[\leadsto c \cdot \left(-b \cdot z\right) + j \cdot \sqrt[3]{\left(\left(c \cdot t - i \cdot y\right) \cdot \left(\color{blue}{c \cdot t} - y \cdot i\right)\right) \cdot \left(t \cdot c - y \cdot i\right)} \]

      5. *-commutative 45.5%

         \[\leadsto c \cdot \left(-b \cdot z\right) + j \cdot \sqrt[3]{\left(\left(c \cdot t - i \cdot y\right) \cdot \left(c \cdot t - \color{blue}{i \cdot y}\right)\right) \cdot \left(t \cdot c - y \cdot i\right)} \]

      6. *-commutative 45.5%

         \[\leadsto c \cdot \left(-b \cdot z\right) + j \cdot \sqrt[3]{\left(\left(c \cdot t - i \cdot y\right) \cdot \left(c \cdot t - i \cdot y\right)\right) \cdot \left(\color{blue}{c \cdot t} - y \cdot i\right)} \]

      7. *-commutative 45.5%

         \[\leadsto c \cdot \left(-b \cdot z\right) + j \cdot \sqrt[3]{\left(\left(c \cdot t - i \cdot y\right) \cdot \left(c \cdot t - i \cdot y\right)\right) \cdot \left(c \cdot t - \color{blue}{i \cdot y}\right)} \]

   8. Applied egg-rr 45.5%

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

      1. associate-*l* 45.5%

         \[\leadsto c \cdot \left(-b \cdot z\right) + j \cdot \sqrt[3]{\color{blue}{\left(c \cdot t - i \cdot y\right) \cdot \left(\left(c \cdot t - i \cdot y\right) \cdot \left(c \cdot t - i \cdot y\right)\right)}} \]

   10. Simplified 45.5%

       \[\leadsto c \cdot \left(-b \cdot z\right) + j \cdot \color{blue}{\sqrt[3]{\left(c \cdot t - i \cdot y\right) \cdot \left(\left(c \cdot t - i \cdot y\right) \cdot \left(c \cdot t - i \cdot y\right)\right)}} \]

   11. Taylor expanded in b around inf 40.3%

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

       1. mul-1-neg 40.3%

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

       2. *-commutative 40.3%

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

       3. distribute-rgt-neg-in 40.3%

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

       4. mul-1-neg 40.3%

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

       5. associate-*r* 40.3%

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

       6. associate-*r* 42.0%

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

       7. neg-mul-1 42.0%

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

   13. Simplified 42.0%

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

   if -1.45e7 < c < -2.10000000000000019e-242 or 2.90000000000000019e-15 < c < 1.15e61

   1. Initial program 80.4%

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

      1. +-commutative 80.4%

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

      2. fma-def 80.4%

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

      3. *-commutative 80.4%

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

      4. *-commutative 80.4%

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

      5. *-commutative 80.4%

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

      6. *-commutative 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in j around 0 69.3%

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

   5. Taylor expanded in t around inf 38.7%

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

      1. mul-1-neg 38.7%

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

      2. *-commutative 38.7%

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

      3. distribute-rgt-neg-in 38.7%

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

   7. Simplified 38.7%

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

   if -2.10000000000000019e-242 < c < 9.5999999999999995e-177

   1. Initial program 76.2%

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

      1. cancel-sign-sub 76.2%

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

      2. cancel-sign-sub-inv 76.2%

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

      3. *-commutative 76.2%

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

      4. *-commutative 76.2%

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

      5. remove-double-neg 76.2%

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

      6. *-commutative 76.2%

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

      7. *-commutative 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in c around inf 42.5%

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

      1. mul-1-neg 42.5%

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

      2. distribute-rgt-neg-in 42.5%

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

   6. Simplified 42.5%

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

   7. Taylor expanded in j around inf 43.8%

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

   8. Taylor expanded in c around 0 36.1%

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

      1. mul-1-neg 36.1%

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

      2. distribute-rgt-neg-in 36.1%

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

   10. Simplified 36.1%

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

   if 9.5999999999999995e-177 < c < 2.90000000000000019e-15 or 1.15e61 < c < 3.19999999999999995e158

   1. Initial program 80.5%

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

      1. cancel-sign-sub 80.5%

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

      2. cancel-sign-sub-inv 80.5%

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

      3. *-commutative 80.5%

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

      4. *-commutative 80.5%

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

      5. remove-double-neg 80.5%

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

      6. *-commutative 80.5%

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

      7. *-commutative 80.5%

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

   3. Simplified 80.5%

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

   4. Taylor expanded in b around inf 64.0%

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

   5. Taylor expanded in a around inf 52.7%

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

   if 3.19999999999999995e158 < c

   1. Initial program 69.3%

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

      1. cancel-sign-sub 69.3%

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

      2. cancel-sign-sub-inv 69.3%

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

      3. *-commutative 69.3%

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

      4. *-commutative 69.3%

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

      5. remove-double-neg 69.3%

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

      6. *-commutative 69.3%

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

      7. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in c around inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. distribute-rgt-neg-in 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in j around inf 54.8%

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

   8. Taylor expanded in c around inf 52.6%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -14500000:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;c \leq -2.1 \cdot 10^{-242}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 9.6 \cdot 10^{-177}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-15}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+61}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{+158}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \end{array} \]

Alternative 12: 51.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -4.2e+106)
     t_2
     (if (<= c -7.5e-217)
       t_1
       (if (<= c 1.02e-178)
         (* y (- (* x z) (* i j)))
         (if (<= c 2.2e+114) 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 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.2e+106) {
		tmp = t_2;
	} else if (c <= -7.5e-217) {
		tmp = t_1;
	} else if (c <= 1.02e-178) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 2.2e+114) {
		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 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-4.2d+106)) then
        tmp = t_2
    else if (c <= (-7.5d-217)) then
        tmp = t_1
    else if (c <= 1.02d-178) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 2.2d+114) 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 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.2e+106) {
		tmp = t_2;
	} else if (c <= -7.5e-217) {
		tmp = t_1;
	} else if (c <= 1.02e-178) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 2.2e+114) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -4.2e+106:
		tmp = t_2
	elif c <= -7.5e-217:
		tmp = t_1
	elif c <= 1.02e-178:
		tmp = y * ((x * z) - (i * j))
	elif c <= 2.2e+114:
		tmp = t_1
	else:
		tmp = t_2
	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)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.2e+106)
		tmp = t_2;
	elseif (c <= -7.5e-217)
		tmp = t_1;
	elseif (c <= 1.02e-178)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 2.2e+114)
		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 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.2e+106)
		tmp = t_2;
	elseif (c <= -7.5e-217)
		tmp = t_1;
	elseif (c <= 1.02e-178)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 2.2e+114)
		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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.2e+106], t$95$2, If[LessEqual[c, -7.5e-217], t$95$1, If[LessEqual[c, 1.02e-178], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e+114], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.2000000000000001e106 or 2.2e114 < c

   1. Initial program 63.6%

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

      1. cancel-sign-sub 63.6%

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

      2. cancel-sign-sub-inv 63.6%

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

      3. *-commutative 63.6%

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

      4. *-commutative 63.6%

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

      5. remove-double-neg 63.6%

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

      6. *-commutative 63.6%

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

      7. *-commutative 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in c around inf 73.5%

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

   if -4.2000000000000001e106 < c < -7.50000000000000031e-217 or 1.02000000000000006e-178 < c < 2.2e114

   1. Initial program 81.3%

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

      1. cancel-sign-sub 81.3%

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

      2. cancel-sign-sub-inv 81.3%

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

      3. *-commutative 81.3%

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

      4. *-commutative 81.3%

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

      5. remove-double-neg 81.3%

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

      6. *-commutative 81.3%

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

      7. *-commutative 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in a around inf 55.7%

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

      1. distribute-lft-out-- 55.7%

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

      2. mul-1-neg 55.7%

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

      3. mul-1-neg 55.7%

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

      4. distribute-lft-out-- 55.7%

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

      5. cancel-sign-sub-inv 55.7%

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

      6. metadata-eval 55.7%

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

      7. *-lft-identity 55.7%

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

      8. +-commutative 55.7%

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

      9. mul-1-neg 55.7%

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

      10. unsub-neg 55.7%

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

   6. Simplified 55.7%

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

   if -7.50000000000000031e-217 < c < 1.02000000000000006e-178

   1. Initial program 76.6%

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

      1. cancel-sign-sub 76.6%

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

      2. cancel-sign-sub-inv 76.6%

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

      3. *-commutative 76.6%

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

      4. *-commutative 76.6%

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

      5. remove-double-neg 76.6%

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

      6. *-commutative 76.6%

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

      7. *-commutative 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in y around inf 54.5%

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

      1. +-commutative 54.5%

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

      2. mul-1-neg 54.5%

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

      3. unsub-neg 54.5%

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

   6. Simplified 54.5%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+106}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-217}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 13: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;b \leq -2 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2600000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* a (* b i))))
   (if (<= b -2e+20)
     (* i (* a b))
     (if (<= b -9.5e-45)
       t_1
       (if (<= b -1.9e-103)
         t_2
         (if (<= b 2.1e-189)
           t_1
           (if (<= b 2600000000000.0) (* 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 = c * (t * j);
	double t_2 = a * (b * i);
	double tmp;
	if (b <= -2e+20) {
		tmp = i * (a * b);
	} else if (b <= -9.5e-45) {
		tmp = t_1;
	} else if (b <= -1.9e-103) {
		tmp = t_2;
	} else if (b <= 2.1e-189) {
		tmp = t_1;
	} else if (b <= 2600000000000.0) {
		tmp = 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 = c * (t * j)
    t_2 = a * (b * i)
    if (b <= (-2d+20)) then
        tmp = i * (a * b)
    else if (b <= (-9.5d-45)) then
        tmp = t_1
    else if (b <= (-1.9d-103)) then
        tmp = t_2
    else if (b <= 2.1d-189) then
        tmp = t_1
    else if (b <= 2600000000000.0d0) then
        tmp = 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 = c * (t * j);
	double t_2 = a * (b * i);
	double tmp;
	if (b <= -2e+20) {
		tmp = i * (a * b);
	} else if (b <= -9.5e-45) {
		tmp = t_1;
	} else if (b <= -1.9e-103) {
		tmp = t_2;
	} else if (b <= 2.1e-189) {
		tmp = t_1;
	} else if (b <= 2600000000000.0) {
		tmp = y * (x * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = a * (b * i)
	tmp = 0
	if b <= -2e+20:
		tmp = i * (a * b)
	elif b <= -9.5e-45:
		tmp = t_1
	elif b <= -1.9e-103:
		tmp = t_2
	elif b <= 2.1e-189:
		tmp = t_1
	elif b <= 2600000000000.0:
		tmp = y * (x * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (b <= -2e+20)
		tmp = Float64(i * Float64(a * b));
	elseif (b <= -9.5e-45)
		tmp = t_1;
	elseif (b <= -1.9e-103)
		tmp = t_2;
	elseif (b <= 2.1e-189)
		tmp = t_1;
	elseif (b <= 2600000000000.0)
		tmp = 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 = c * (t * j);
	t_2 = a * (b * i);
	tmp = 0.0;
	if (b <= -2e+20)
		tmp = i * (a * b);
	elseif (b <= -9.5e-45)
		tmp = t_1;
	elseif (b <= -1.9e-103)
		tmp = t_2;
	elseif (b <= 2.1e-189)
		tmp = t_1;
	elseif (b <= 2600000000000.0)
		tmp = 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[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2e+20], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.5e-45], t$95$1, If[LessEqual[b, -1.9e-103], t$95$2, If[LessEqual[b, 2.1e-189], t$95$1, If[LessEqual[b, 2600000000000.0], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2e20

   1. Initial program 75.8%

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

      1. cancel-sign-sub 75.8%

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

      2. cancel-sign-sub-inv 75.8%

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

      3. *-commutative 75.8%

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

      4. *-commutative 75.8%

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

      5. remove-double-neg 75.8%

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

      6. *-commutative 75.8%

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

      7. *-commutative 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in a around inf 50.3%

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

      1. distribute-lft-out-- 50.3%

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

      2. mul-1-neg 50.3%

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

      3. mul-1-neg 50.3%

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

      4. distribute-lft-out-- 50.3%

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

      5. cancel-sign-sub-inv 50.3%

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

      6. metadata-eval 50.3%

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

      7. *-lft-identity 50.3%

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

      8. +-commutative 50.3%

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

      9. mul-1-neg 50.3%

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

      10. unsub-neg 50.3%

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

   6. Simplified 50.3%

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

   7. Taylor expanded in b around inf 34.7%

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

   if -2e20 < b < -9.5000000000000002e-45 or -1.9e-103 < b < 2.10000000000000016e-189

   1. Initial program 70.2%

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

      1. cancel-sign-sub 70.2%

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

      2. cancel-sign-sub-inv 70.2%

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

      3. *-commutative 70.2%

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

      4. *-commutative 70.2%

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

      5. remove-double-neg 70.2%

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

      6. *-commutative 70.2%

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

      7. *-commutative 70.2%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in c around inf 57.3%

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

      1. mul-1-neg 57.3%

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

      2. distribute-rgt-neg-in 57.3%

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

   6. Simplified 57.3%

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

   7. Taylor expanded in t around inf 41.1%

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

   if -9.5000000000000002e-45 < b < -1.9e-103 or 2.6e12 < b

   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. Step-by-step derivation

      1. +-commutative 74.7%

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

      2. fma-def 77.4%

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

      3. *-commutative 77.4%

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

      4. *-commutative 77.4%

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

      5. *-commutative 77.4%

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

      6. *-commutative 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in j around 0 72.8%

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

   5. Taylor expanded in i around inf 41.1%

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

   if 2.10000000000000016e-189 < b < 2.6e12

   1. Initial program 78.2%

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

      1. +-commutative 78.2%

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

      2. fma-def 78.2%

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

      3. *-commutative 78.2%

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

      4. *-commutative 78.2%

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

      5. *-commutative 78.2%

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

      6. *-commutative 78.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in j around 0 63.0%

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

   5. Taylor expanded in y around inf 33.5%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-45}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-189}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 2600000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 14: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-49}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-192}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 60000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= b -4.8e+20)
     (* i (* a b))
     (if (<= b -5.5e-49)
       (* j (* t c))
       (if (<= b -1.75e-103)
         t_1
         (if (<= b 1.25e-192)
           (* c (* t j))
           (if (<= b 60000000000.0) (* 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 = a * (b * i);
	double tmp;
	if (b <= -4.8e+20) {
		tmp = i * (a * b);
	} else if (b <= -5.5e-49) {
		tmp = j * (t * c);
	} else if (b <= -1.75e-103) {
		tmp = t_1;
	} else if (b <= 1.25e-192) {
		tmp = c * (t * j);
	} else if (b <= 60000000000.0) {
		tmp = 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 = a * (b * i)
    if (b <= (-4.8d+20)) then
        tmp = i * (a * b)
    else if (b <= (-5.5d-49)) then
        tmp = j * (t * c)
    else if (b <= (-1.75d-103)) then
        tmp = t_1
    else if (b <= 1.25d-192) then
        tmp = c * (t * j)
    else if (b <= 60000000000.0d0) then
        tmp = 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 = a * (b * i);
	double tmp;
	if (b <= -4.8e+20) {
		tmp = i * (a * b);
	} else if (b <= -5.5e-49) {
		tmp = j * (t * c);
	} else if (b <= -1.75e-103) {
		tmp = t_1;
	} else if (b <= 1.25e-192) {
		tmp = c * (t * j);
	} else if (b <= 60000000000.0) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if b <= -4.8e+20:
		tmp = i * (a * b)
	elif b <= -5.5e-49:
		tmp = j * (t * c)
	elif b <= -1.75e-103:
		tmp = t_1
	elif b <= 1.25e-192:
		tmp = c * (t * j)
	elif b <= 60000000000.0:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (b <= -4.8e+20)
		tmp = Float64(i * Float64(a * b));
	elseif (b <= -5.5e-49)
		tmp = Float64(j * Float64(t * c));
	elseif (b <= -1.75e-103)
		tmp = t_1;
	elseif (b <= 1.25e-192)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 60000000000.0)
		tmp = 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 = a * (b * i);
	tmp = 0.0;
	if (b <= -4.8e+20)
		tmp = i * (a * b);
	elseif (b <= -5.5e-49)
		tmp = j * (t * c);
	elseif (b <= -1.75e-103)
		tmp = t_1;
	elseif (b <= 1.25e-192)
		tmp = c * (t * j);
	elseif (b <= 60000000000.0)
		tmp = 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[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+20], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.5e-49], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.75e-103], t$95$1, If[LessEqual[b, 1.25e-192], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 60000000000.0], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.8e20

   1. Initial program 75.8%

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

      1. cancel-sign-sub 75.8%

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

      2. cancel-sign-sub-inv 75.8%

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

      3. *-commutative 75.8%

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

      4. *-commutative 75.8%

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

      5. remove-double-neg 75.8%

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

      6. *-commutative 75.8%

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

      7. *-commutative 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in a around inf 50.3%

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

      1. distribute-lft-out-- 50.3%

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

      2. mul-1-neg 50.3%

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

      3. mul-1-neg 50.3%

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

      4. distribute-lft-out-- 50.3%

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

      5. cancel-sign-sub-inv 50.3%

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

      6. metadata-eval 50.3%

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

      7. *-lft-identity 50.3%

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

      8. +-commutative 50.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      9. mul-1-neg 50.3%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      10. unsub-neg 50.3%

          \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 50.3%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 34.7%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -4.8e20 < b < -5.50000000000000031e-49

   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. Step-by-step derivation

      1. cancel-sign-sub 71.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 48.6%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 48.6%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. distribute-rgt-neg-in 48.6%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 48.6%

      \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 34.6%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   8. Taylor expanded in c around inf 35.0%

      \[\leadsto \color{blue}{\left(c \cdot t\right)} \cdot j \]

   if -5.50000000000000031e-49 < b < -1.75000000000000008e-103 or 6e10 < b

   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. Step-by-step derivation

      1. +-commutative 74.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 77.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 77.4%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 77.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 77.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 77.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 72.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in i around inf 41.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -1.75000000000000008e-103 < b < 1.25e-192

   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. Step-by-step derivation

      1. cancel-sign-sub 69.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 60.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 60.0%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. distribute-rgt-neg-in 60.0%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 60.0%

      \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in t around inf 43.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 1.25e-192 < b < 6e10

   1. Initial program 78.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 78.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 78.2%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 78.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 78.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 78.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 63.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 33.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-49}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-192}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 60000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 15: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 17500000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -2.1e+20)
   (* i (* a b))
   (if (<= b -3.6e-50)
     (* j (* t c))
     (if (<= b -1e-103)
       (* a (* b i))
       (if (<= b 7e-196)
         (* c (* t j))
         (if (<= b 17500000000000.0) (* 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 <= -2.1e+20) {
		tmp = i * (a * b);
	} else if (b <= -3.6e-50) {
		tmp = j * (t * c);
	} else if (b <= -1e-103) {
		tmp = a * (b * i);
	} else if (b <= 7e-196) {
		tmp = c * (t * j);
	} else if (b <= 17500000000000.0) {
		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 <= (-2.1d+20)) then
        tmp = i * (a * b)
    else if (b <= (-3.6d-50)) then
        tmp = j * (t * c)
    else if (b <= (-1d-103)) then
        tmp = a * (b * i)
    else if (b <= 7d-196) then
        tmp = c * (t * j)
    else if (b <= 17500000000000.0d0) 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 <= -2.1e+20) {
		tmp = i * (a * b);
	} else if (b <= -3.6e-50) {
		tmp = j * (t * c);
	} else if (b <= -1e-103) {
		tmp = a * (b * i);
	} else if (b <= 7e-196) {
		tmp = c * (t * j);
	} else if (b <= 17500000000000.0) {
		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 <= -2.1e+20:
		tmp = i * (a * b)
	elif b <= -3.6e-50:
		tmp = j * (t * c)
	elif b <= -1e-103:
		tmp = a * (b * i)
	elif b <= 7e-196:
		tmp = c * (t * j)
	elif b <= 17500000000000.0:
		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 <= -2.1e+20)
		tmp = Float64(i * Float64(a * b));
	elseif (b <= -3.6e-50)
		tmp = Float64(j * Float64(t * c));
	elseif (b <= -1e-103)
		tmp = Float64(a * Float64(b * i));
	elseif (b <= 7e-196)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 17500000000000.0)
		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 <= -2.1e+20)
		tmp = i * (a * b);
	elseif (b <= -3.6e-50)
		tmp = j * (t * c);
	elseif (b <= -1e-103)
		tmp = a * (b * i);
	elseif (b <= 7e-196)
		tmp = c * (t * j);
	elseif (b <= 17500000000000.0)
		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, -2.1e+20], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.6e-50], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1e-103], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-196], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 17500000000000.0], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.1e20

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 50.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 50.3%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      2. mul-1-neg 50.3%

         \[\leadsto a \cdot \color{blue}{\left(-\left(t \cdot x - i \cdot b\right)\right)} \]

      3. mul-1-neg 50.3%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      4. distribute-lft-out-- 50.3%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      5. cancel-sign-sub-inv 50.3%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(--1\right) \cdot \left(i \cdot b\right)\right)} \]

      6. metadata-eval 50.3%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{1} \cdot \left(i \cdot b\right)\right) \]

      7. *-lft-identity 50.3%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{i \cdot b}\right) \]

      8. +-commutative 50.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      9. mul-1-neg 50.3%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      10. unsub-neg 50.3%

          \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 50.3%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 34.7%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -2.1e20 < b < -3.59999999999999979e-50

   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. Step-by-step derivation

      1. cancel-sign-sub 71.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 48.6%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 48.6%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. distribute-rgt-neg-in 48.6%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 48.6%

      \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 34.6%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   8. Taylor expanded in c around inf 35.0%

      \[\leadsto \color{blue}{\left(c \cdot t\right)} \cdot j \]

   if -3.59999999999999979e-50 < b < -9.99999999999999958e-104

   1. Initial program 86.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 86.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 86.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 86.0%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 86.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 86.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 86.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 72.3%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in i around inf 43.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -9.99999999999999958e-104 < b < 7.00000000000000009e-196

   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. Step-by-step derivation

      1. cancel-sign-sub 69.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 60.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 60.0%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. distribute-rgt-neg-in 60.0%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 60.0%

      \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in t around inf 43.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 7.00000000000000009e-196 < b < 1.75e13

   1. Initial program 78.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 78.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 78.2%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 78.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 78.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 78.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 63.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 33.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 1.75e13 < b

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 72.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 72.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 72.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 72.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 72.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 72.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 72.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 68.4%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in a around inf 42.4%

      \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]
3. Recombined 6 regimes into one program.

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+20}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 17500000000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 16: 51.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2100000000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -7e-59)
     t_1
     (if (<= b 3.4e-138)
       (* t (- (* c j) (* x a)))
       (if (<= b 2100000000.0) (* 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7e-59) {
		tmp = t_1;
	} else if (b <= 3.4e-138) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 2100000000.0) {
		tmp = y * ((x * z) - (i * 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 = b * ((a * i) - (z * c))
    if (b <= (-7d-59)) then
        tmp = t_1
    else if (b <= 3.4d-138) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 2100000000.0d0) then
        tmp = y * ((x * z) - (i * 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -7e-59) {
		tmp = t_1;
	} else if (b <= 3.4e-138) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 2100000000.0) {
		tmp = 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 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -7e-59:
		tmp = t_1
	elif b <= 3.4e-138:
		tmp = t * ((c * j) - (x * a))
	elif b <= 2100000000.0:
		tmp = 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(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7e-59)
		tmp = t_1;
	elseif (b <= 3.4e-138)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 2100000000.0)
		tmp = 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 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -7e-59)
		tmp = t_1;
	elseif (b <= 3.4e-138)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 2100000000.0)
		tmp = 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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e-59], t$95$1, If[LessEqual[b, 3.4e-138], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2100000000.0], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.0000000000000002e-59 or 2.1e9 < b

   1. Initial program 74.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 74.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 74.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 74.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 74.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 74.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 74.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 74.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 63.4%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if -7.0000000000000002e-59 < b < 3.4000000000000001e-138

   1. Initial program 70.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 70.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 70.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 56.3%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 56.3%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 56.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 56.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 56.3%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if 3.4000000000000001e-138 < b < 2.1e9

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 80.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 63.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 63.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 63.1%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 63.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 63.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2100000000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 17: 51.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.7 \cdot 10^{+106} \lor \neg \left(c \leq 2.2 \cdot 10^{+114}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -2.7e+106) (not (<= c 2.2e+114)))
   (* c (- (* t j) (* z b)))
   (* a (- (* b i) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.7e+106) || !(c <= 2.2e+114)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-2.7d+106)) .or. (.not. (c <= 2.2d+114))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.7e+106) || !(c <= 2.2e+114)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -2.7e+106) or not (c <= 2.2e+114):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -2.7e+106) || !(c <= 2.2e+114))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -2.7e+106) || ~((c <= 2.2e+114)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -2.7e+106], N[Not[LessEqual[c, 2.2e+114]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.70000000000000006e106 or 2.2e114 < c

   1. Initial program 63.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 63.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 63.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 63.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 63.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 63.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 63.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 63.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 73.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -2.70000000000000006e106 < c < 2.2e114

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 47.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 47.4%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      2. mul-1-neg 47.4%

         \[\leadsto a \cdot \color{blue}{\left(-\left(t \cdot x - i \cdot b\right)\right)} \]

      3. mul-1-neg 47.4%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      4. distribute-lft-out-- 47.4%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      5. cancel-sign-sub-inv 47.4%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(--1\right) \cdot \left(i \cdot b\right)\right)} \]

      6. metadata-eval 47.4%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{1} \cdot \left(i \cdot b\right)\right) \]

      7. *-lft-identity 47.4%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{i \cdot b}\right) \]

      8. +-commutative 47.4%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      9. mul-1-neg 47.4%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      10. unsub-neg 47.4%

          \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 47.4%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.7 \cdot 10^{+106} \lor \neg \left(c \leq 2.2 \cdot 10^{+114}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 18: 28.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+66} \lor \neg \left(c \leq 2.15 \cdot 10^{+164}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -4.6e+66) (not (<= c 2.15e+164))) (* 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 ((c <= -4.6e+66) || !(c <= 2.15e+164)) {
		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 ((c <= (-4.6d+66)) .or. (.not. (c <= 2.15d+164))) 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 ((c <= -4.6e+66) || !(c <= 2.15e+164)) {
		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 (c <= -4.6e+66) or not (c <= 2.15e+164):
		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 ((c <= -4.6e+66) || !(c <= 2.15e+164))
		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 ((c <= -4.6e+66) || ~((c <= 2.15e+164)))
		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[Or[LessEqual[c, -4.6e+66], N[Not[LessEqual[c, 2.15e+164]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.6e66 or 2.15e164 < c

   1. Initial program 63.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 63.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 63.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 63.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 59.2%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 59.2%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. distribute-rgt-neg-in 59.2%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 59.2%

      \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -4.6e66 < c < 2.15e164

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 80.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 80.9%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 80.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 65.9%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in i around inf 29.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+66} \lor \neg \left(c \leq 2.15 \cdot 10^{+164}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 19: 28.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.42 \cdot 10^{+104} \lor \neg \left(c \leq 4.8 \cdot 10^{+161}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.42e+104) (not (<= c 4.8e+161))) (* c (* t j)) (* 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 ((c <= -1.42e+104) || !(c <= 4.8e+161)) {
		tmp = c * (t * j);
	} 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 ((c <= (-1.42d+104)) .or. (.not. (c <= 4.8d+161))) then
        tmp = c * (t * j)
    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 ((c <= -1.42e+104) || !(c <= 4.8e+161)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.42e+104) or not (c <= 4.8e+161):
		tmp = c * (t * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.42e+104) || !(c <= 4.8e+161))
		tmp = Float64(c * Float64(t * j));
	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 ((c <= -1.42e+104) || ~((c <= 4.8e+161)))
		tmp = c * (t * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.42e+104], N[Not[LessEqual[c, 4.8e+161]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.42e104 or 4.7999999999999998e161 < c

   1. Initial program 62.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 62.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 62.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 62.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 62.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 62.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 62.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 62.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 62.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 61.1%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 61.1%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. distribute-rgt-neg-in 61.1%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 61.1%

      \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in t around inf 45.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.42e104 < c < 4.7999999999999998e161

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 46.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. distribute-lft-out-- 46.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      2. mul-1-neg 46.8%

         \[\leadsto a \cdot \color{blue}{\left(-\left(t \cdot x - i \cdot b\right)\right)} \]

      3. mul-1-neg 46.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - i \cdot b\right)\right)} \]

      4. distribute-lft-out-- 46.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]

      5. cancel-sign-sub-inv 46.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + \left(--1\right) \cdot \left(i \cdot b\right)\right)} \]

      6. metadata-eval 46.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{1} \cdot \left(i \cdot b\right)\right) \]

      7. *-lft-identity 46.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) + \color{blue}{i \cdot b}\right) \]

      8. +-commutative 46.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      9. mul-1-neg 46.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      10. unsub-neg 46.8%

          \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 46.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 28.8%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.42 \cdot 10^{+104} \lor \neg \left(c \leq 4.8 \cdot 10^{+161}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 20: 22.6% 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 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. Step-by-step derivation

   1. +-commutative 73.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   2. fma-def 76.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   3. *-commutative 76.6%

      \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   4. *-commutative 76.6%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   5. *-commutative 76.6%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

   6. *-commutative 76.6%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

3. Simplified 76.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

4. Taylor expanded in j around 0 62.0%

   \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

5. Taylor expanded in i around inf 22.3%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

6. Final simplification 22.3%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 68.1% 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 2023240 
(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)))))