Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.0% → 83.8%

Time: 20.5s

Alternatives: 23

Speedup: 0.5×

• 57.5% 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: 73.0% 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: 83.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot \frac{\mathsf{fma}\left(y, x, a \cdot \left(b \cdot \frac{i}{z}\right) - b \cdot c\right) - i \cdot \left(j \cdot \frac{y}{z}\right)}{t} + z \cdot \left(c \cdot \frac{j}{z} - a \cdot \frac{x}{z}\right)\right)\\ \end{array} \end{array} \]

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
     (*
      t
      (+
       (*
        z
        (/
         (- (fma y x (- (* a (* b (/ i z))) (* b c))) (* i (* j (/ y z))))
         t))
       (* z (- (* c (/ j z)) (* a (/ x z)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((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 = t * ((z * ((fma(y, x, ((a * (b * (i / z))) - (b * c))) - (i * (j * (y / z)))) / t)) + (z * ((c * (j / z)) - (a * (x / z)))));
	}
	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(t * Float64(Float64(z * Float64(Float64(fma(y, x, Float64(Float64(a * Float64(b * Float64(i / z))) - Float64(b * c))) - Float64(i * Float64(j * Float64(y / z)))) / t)) + Float64(z * Float64(Float64(c * Float64(j / z)) - Float64(a * Float64(x / z))))));
	end
	return 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[(t * N[(N[(z * N[(N[(N[(y * x + N[(N[(a * N[(b * N[(i / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(i * N[(j * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(c * N[(j / z), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.0%

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

   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. Add Preprocessing

   3. Taylor expanded in z around inf 29.8%

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

   4. Taylor expanded in t around -inf 52.6%

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

   6. Simplified 52.6%

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

4. Final simplification 80.9%

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

Alternative 2: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double 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 = i * ((a * b) - (y * 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 = i * ((a * b) - (y * 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 = i * ((a * b) - (y * 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(i * Float64(Float64(a * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	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 = i * ((a * b) - (y * 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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * 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 89.0%

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

   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. Add Preprocessing

   3. Taylor expanded in i around inf 48.1%

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

      1. distribute-lft-out-- 48.1%

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

      2. *-commutative 48.1%

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

   5. Simplified 48.1%

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

4. Final simplification 79.9%

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

Alternative 3: 63.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-13}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.38 \cdot 10^{+54}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \end{array} \end{array} \]

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 a))))))
   (if (<= b -4.4e+79)
     (* b (- (* a i) (* z c)))
     (if (<= b -2.8e+34)
       t_2
       (if (<= b -1.75e-13)
         (* a (- (* b i) (* x t)))
         (if (<= b -1.22e-60)
           (* t (- (* c j) (* x a)))
           (if (<= b 2.05e-80)
             t_2
             (if (<= b 1.38e+54)
               (+ t_1 (* a (* b i)))
               (* b (* i (- a (* c (/ z i)))))))))))))

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) - (t * a)));
	double tmp;
	if (b <= -4.4e+79) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -2.8e+34) {
		tmp = t_2;
	} else if (b <= -1.75e-13) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= -1.22e-60) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 2.05e-80) {
		tmp = t_2;
	} else if (b <= 1.38e+54) {
		tmp = t_1 + (a * (b * i));
	} else {
		tmp = b * (i * (a - (c * (z / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t_1 + (x * ((y * z) - (t * a)))
    if (b <= (-4.4d+79)) then
        tmp = b * ((a * i) - (z * c))
    else if (b <= (-2.8d+34)) then
        tmp = t_2
    else if (b <= (-1.75d-13)) then
        tmp = a * ((b * i) - (x * t))
    else if (b <= (-1.22d-60)) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 2.05d-80) then
        tmp = t_2
    else if (b <= 1.38d+54) then
        tmp = t_1 + (a * (b * i))
    else
        tmp = b * (i * (a - (c * (z / 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 t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (x * ((y * z) - (t * a)));
	double tmp;
	if (b <= -4.4e+79) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -2.8e+34) {
		tmp = t_2;
	} else if (b <= -1.75e-13) {
		tmp = a * ((b * i) - (x * t));
	} else if (b <= -1.22e-60) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 2.05e-80) {
		tmp = t_2;
	} else if (b <= 1.38e+54) {
		tmp = t_1 + (a * (b * i));
	} else {
		tmp = b * (i * (a - (c * (z / i))));
	}
	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 * a)))
	tmp = 0
	if b <= -4.4e+79:
		tmp = b * ((a * i) - (z * c))
	elif b <= -2.8e+34:
		tmp = t_2
	elif b <= -1.75e-13:
		tmp = a * ((b * i) - (x * t))
	elif b <= -1.22e-60:
		tmp = t * ((c * j) - (x * a))
	elif b <= 2.05e-80:
		tmp = t_2
	elif b <= 1.38e+54:
		tmp = t_1 + (a * (b * i))
	else:
		tmp = b * (i * (a - (c * (z / i))))
	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(Float64(y * z) - Float64(t * a))))
	tmp = 0.0
	if (b <= -4.4e+79)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (b <= -2.8e+34)
		tmp = t_2;
	elseif (b <= -1.75e-13)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (b <= -1.22e-60)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 2.05e-80)
		tmp = t_2;
	elseif (b <= 1.38e+54)
		tmp = Float64(t_1 + Float64(a * Float64(b * i)));
	else
		tmp = Float64(b * Float64(i * Float64(a - Float64(c * Float64(z / i)))));
	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 * a)));
	tmp = 0.0;
	if (b <= -4.4e+79)
		tmp = b * ((a * i) - (z * c));
	elseif (b <= -2.8e+34)
		tmp = t_2;
	elseif (b <= -1.75e-13)
		tmp = a * ((b * i) - (x * t));
	elseif (b <= -1.22e-60)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 2.05e-80)
		tmp = t_2;
	elseif (b <= 1.38e+54)
		tmp = t_1 + (a * (b * i));
	else
		tmp = b * (i * (a - (c * (z / i))));
	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[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.4e+79], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e+34], t$95$2, If[LessEqual[b, -1.75e-13], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.22e-60], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.05e-80], t$95$2, If[LessEqual[b, 1.38e+54], N[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(i * N[(a - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -4.3999999999999998e79

   1. Initial program 74.8%

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

   3. Taylor expanded in b around inf 76.6%

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

   if -4.3999999999999998e79 < b < -2.80000000000000008e34 or -1.22e-60 < b < 2.05e-80

   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. Add Preprocessing

   3. Taylor expanded in b around 0 78.2%

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

   if -2.80000000000000008e34 < b < -1.7500000000000001e-13

   1. Initial program 90.8%

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

   3. Taylor expanded in a around inf 80.0%

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

      1. distribute-lft-out-- 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in a around 0 80.0%

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

      1. associate-*r* 80.0%

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

      2. neg-mul-1 80.0%

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

      3. *-commutative 80.0%

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

   8. Simplified 80.0%

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

   if -1.7500000000000001e-13 < b < -1.22e-60

   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. Add Preprocessing

   3. Taylor expanded in t around inf 57.8%

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

      1. +-commutative 57.8%

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

      2. mul-1-neg 57.8%

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

      3. unsub-neg 57.8%

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

   5. Simplified 57.8%

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

   if 2.05e-80 < b < 1.38e54

   1. Initial program 69.8%

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

   3. Taylor expanded in x around 0 81.8%

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

   4. Taylor expanded in c around 0 81.4%

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

      1. associate-*r* 81.4%

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

      2. neg-mul-1 81.4%

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

      3. *-commutative 81.4%

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

   6. Simplified 81.4%

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

   if 1.38e54 < b

   1. Initial program 65.5%

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

   3. Taylor expanded in b around inf 72.3%

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

   4. Taylor expanded in i around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

      3. associate-/l* 73.9%

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

   6. Simplified 73.9%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{+34}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-13}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-80}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 1.38 \cdot 10^{+54}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 28.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{+211}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-290}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* x (* y z))))
   (if (<= z -1.16e+211)
     t_2
     (if (<= z -2.8e+84)
       (* a (* t (- x)))
       (if (<= z -6.4e-158)
         t_1
         (if (<= z 5.2e-290)
           (* y (* i (- j)))
           (if (<= z 7.5e-136)
             t_1
             (if (<= z 1.5e+77)
               (* t (* c j))
               (if (<= z 1.2e+135) t_2 (* z (* c (- b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -1.16e+211) {
		tmp = t_2;
	} else if (z <= -2.8e+84) {
		tmp = a * (t * -x);
	} else if (z <= -6.4e-158) {
		tmp = t_1;
	} else if (z <= 5.2e-290) {
		tmp = y * (i * -j);
	} else if (z <= 7.5e-136) {
		tmp = t_1;
	} else if (z <= 1.5e+77) {
		tmp = t * (c * j);
	} else if (z <= 1.2e+135) {
		tmp = t_2;
	} else {
		tmp = z * (c * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = x * (y * z)
    if (z <= (-1.16d+211)) then
        tmp = t_2
    else if (z <= (-2.8d+84)) then
        tmp = a * (t * -x)
    else if (z <= (-6.4d-158)) then
        tmp = t_1
    else if (z <= 5.2d-290) then
        tmp = y * (i * -j)
    else if (z <= 7.5d-136) then
        tmp = t_1
    else if (z <= 1.5d+77) then
        tmp = t * (c * j)
    else if (z <= 1.2d+135) then
        tmp = t_2
    else
        tmp = z * (c * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -1.16e+211) {
		tmp = t_2;
	} else if (z <= -2.8e+84) {
		tmp = a * (t * -x);
	} else if (z <= -6.4e-158) {
		tmp = t_1;
	} else if (z <= 5.2e-290) {
		tmp = y * (i * -j);
	} else if (z <= 7.5e-136) {
		tmp = t_1;
	} else if (z <= 1.5e+77) {
		tmp = t * (c * j);
	} else if (z <= 1.2e+135) {
		tmp = t_2;
	} else {
		tmp = z * (c * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = x * (y * z)
	tmp = 0
	if z <= -1.16e+211:
		tmp = t_2
	elif z <= -2.8e+84:
		tmp = a * (t * -x)
	elif z <= -6.4e-158:
		tmp = t_1
	elif z <= 5.2e-290:
		tmp = y * (i * -j)
	elif z <= 7.5e-136:
		tmp = t_1
	elif z <= 1.5e+77:
		tmp = t * (c * j)
	elif z <= 1.2e+135:
		tmp = t_2
	else:
		tmp = z * (c * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -1.16e+211)
		tmp = t_2;
	elseif (z <= -2.8e+84)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (z <= -6.4e-158)
		tmp = t_1;
	elseif (z <= 5.2e-290)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (z <= 7.5e-136)
		tmp = t_1;
	elseif (z <= 1.5e+77)
		tmp = Float64(t * Float64(c * j));
	elseif (z <= 1.2e+135)
		tmp = t_2;
	else
		tmp = Float64(z * Float64(c * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (z <= -1.16e+211)
		tmp = t_2;
	elseif (z <= -2.8e+84)
		tmp = a * (t * -x);
	elseif (z <= -6.4e-158)
		tmp = t_1;
	elseif (z <= 5.2e-290)
		tmp = y * (i * -j);
	elseif (z <= 7.5e-136)
		tmp = t_1;
	elseif (z <= 1.5e+77)
		tmp = t * (c * j);
	elseif (z <= 1.2e+135)
		tmp = t_2;
	else
		tmp = z * (c * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.16e+211], t$95$2, If[LessEqual[z, -2.8e+84], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.4e-158], t$95$1, If[LessEqual[z, 5.2e-290], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e-136], t$95$1, If[LessEqual[z, 1.5e+77], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+135], t$95$2, N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.15999999999999997e211 or 1.4999999999999999e77 < z < 1.19999999999999999e135

   1. Initial program 45.7%

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

   3. Taylor expanded in x around inf 55.6%

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

      1. *-commutative 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

   8. Simplified 58.4%

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

   if -1.15999999999999997e211 < z < -2.79999999999999982e84

   1. Initial program 72.9%

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

   3. Taylor expanded in x around inf 42.4%

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

      1. *-commutative 42.4%

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

   5. Simplified 42.4%

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

   6. Taylor expanded in z around 0 38.5%

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

      1. associate-*r* 38.5%

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

      2. neg-mul-1 38.5%

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

   8. Simplified 38.5%

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

   if -2.79999999999999982e84 < z < -6.39999999999999993e-158 or 5.20000000000000002e-290 < z < 7.5000000000000003e-136

   1. Initial program 80.2%

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

   3. Taylor expanded in b around inf 50.2%

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

   4. Taylor expanded in a around inf 41.7%

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

      1. *-commutative 41.7%

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

   6. Simplified 41.7%

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

   if -6.39999999999999993e-158 < z < 5.20000000000000002e-290

   1. Initial program 62.6%

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

   3. Taylor expanded in b around 0 58.6%

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

   4. Taylor expanded in i around inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. *-commutative 44.4%

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

      3. distribute-rgt-neg-in 44.4%

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

      4. *-commutative 44.4%

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

      5. associate-*l* 47.5%

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

   6. Simplified 47.5%

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

   if 7.5000000000000003e-136 < z < 1.4999999999999999e77

   1. Initial program 73.8%

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

   3. Taylor expanded in b around 0 57.4%

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

   4. Taylor expanded in c around inf 31.7%

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

      1. *-commutative 31.7%

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

      2. *-commutative 31.7%

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

      3. associate-*r* 36.5%

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

   6. Simplified 36.5%

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

   if 1.19999999999999999e135 < z

   1. Initial program 64.0%

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

   3. Taylor expanded in z around inf 78.1%

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

   4. Taylor expanded in z around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. *-commutative 66.5%

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

   6. Simplified 66.5%

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

   7. Taylor expanded in y around 0 49.8%

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

      1. mul-1-neg 49.8%

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

      2. *-commutative 49.8%

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

      3. distribute-rgt-neg-in 49.8%

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

   9. Simplified 49.8%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+211}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+84}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-158}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-290}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-136}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := t\_3 + t\_2\\ \mathbf{if}\;x \leq -1.2 \cdot 10^{+139}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-123}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+52}:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(t\_2 - i \cdot \left(y \cdot j\right)\right) + a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* t c) (* y i))))
        (t_4 (+ t_3 t_2)))
   (if (<= x -1.2e+139)
     t_4
     (if (<= x -9.2e-89)
       t_1
       (if (<= x -6.5e-123)
         t_4
         (if (<= x 7.5e+52)
           (+ t_3 t_1)
           (+ (- t_2 (* i (* y 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 t_1 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = t_3 + t_2;
	double tmp;
	if (x <= -1.2e+139) {
		tmp = t_4;
	} else if (x <= -9.2e-89) {
		tmp = t_1;
	} else if (x <= -6.5e-123) {
		tmp = t_4;
	} else if (x <= 7.5e+52) {
		tmp = t_3 + t_1;
	} else {
		tmp = (t_2 - (i * (y * j))) + (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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((t * c) - (y * i))
    t_4 = t_3 + t_2
    if (x <= (-1.2d+139)) then
        tmp = t_4
    else if (x <= (-9.2d-89)) then
        tmp = t_1
    else if (x <= (-6.5d-123)) then
        tmp = t_4
    else if (x <= 7.5d+52) then
        tmp = t_3 + t_1
    else
        tmp = (t_2 - (i * (y * j))) + (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 t_1 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = t_3 + t_2;
	double tmp;
	if (x <= -1.2e+139) {
		tmp = t_4;
	} else if (x <= -9.2e-89) {
		tmp = t_1;
	} else if (x <= -6.5e-123) {
		tmp = t_4;
	} else if (x <= 7.5e+52) {
		tmp = t_3 + t_1;
	} else {
		tmp = (t_2 - (i * (y * j))) + (a * (b * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((t * c) - (y * i))
	t_4 = t_3 + t_2
	tmp = 0
	if x <= -1.2e+139:
		tmp = t_4
	elif x <= -9.2e-89:
		tmp = t_1
	elif x <= -6.5e-123:
		tmp = t_4
	elif x <= 7.5e+52:
		tmp = t_3 + t_1
	else:
		tmp = (t_2 - (i * (y * j))) + (a * (b * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_4 = Float64(t_3 + t_2)
	tmp = 0.0
	if (x <= -1.2e+139)
		tmp = t_4;
	elseif (x <= -9.2e-89)
		tmp = t_1;
	elseif (x <= -6.5e-123)
		tmp = t_4;
	elseif (x <= 7.5e+52)
		tmp = Float64(t_3 + t_1);
	else
		tmp = Float64(Float64(t_2 - Float64(i * Float64(y * j))) + Float64(a * Float64(b * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((t * c) - (y * i));
	t_4 = t_3 + t_2;
	tmp = 0.0;
	if (x <= -1.2e+139)
		tmp = t_4;
	elseif (x <= -9.2e-89)
		tmp = t_1;
	elseif (x <= -6.5e-123)
		tmp = t_4;
	elseif (x <= 7.5e+52)
		tmp = t_3 + t_1;
	else
		tmp = (t_2 - (i * (y * j))) + (a * (b * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + t$95$2), $MachinePrecision]}, If[LessEqual[x, -1.2e+139], t$95$4, If[LessEqual[x, -9.2e-89], t$95$1, If[LessEqual[x, -6.5e-123], t$95$4, If[LessEqual[x, 7.5e+52], N[(t$95$3 + t$95$1), $MachinePrecision], N[(N[(t$95$2 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.20000000000000004e139 or -9.200000000000001e-89 < x < -6.49999999999999938e-123

   1. Initial program 71.8%

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

   3. Taylor expanded in b around 0 79.9%

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

   if -1.20000000000000004e139 < x < -9.200000000000001e-89

   1. Initial program 65.0%

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

   3. Taylor expanded in b around inf 69.7%

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

   if -6.49999999999999938e-123 < x < 7.49999999999999995e52

   1. Initial program 69.1%

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

   3. Taylor expanded in x around 0 70.7%

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

   if 7.49999999999999995e52 < x

   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. Add Preprocessing

   3. Taylor expanded in c around 0 76.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z - a \cdot t\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+139}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-89}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-123}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+52}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\right) + a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 30.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+83}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-287}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+134}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))) (t_2 (* x (* y z))))
   (if (<= z -7.5e+83)
     t_2
     (if (<= z -6e-160)
       t_1
       (if (<= z 4.5e-287)
         (* y (* i (- j)))
         (if (<= z 1.6e-137)
           t_1
           (if (<= z 2e+79)
             (* t (* c j))
             (if (<= z 9e+134) t_2 (* z (* c (- b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -7.5e+83) {
		tmp = t_2;
	} else if (z <= -6e-160) {
		tmp = t_1;
	} else if (z <= 4.5e-287) {
		tmp = y * (i * -j);
	} else if (z <= 1.6e-137) {
		tmp = t_1;
	} else if (z <= 2e+79) {
		tmp = t * (c * j);
	} else if (z <= 9e+134) {
		tmp = t_2;
	} else {
		tmp = z * (c * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (a * i)
    t_2 = x * (y * z)
    if (z <= (-7.5d+83)) then
        tmp = t_2
    else if (z <= (-6d-160)) then
        tmp = t_1
    else if (z <= 4.5d-287) then
        tmp = y * (i * -j)
    else if (z <= 1.6d-137) then
        tmp = t_1
    else if (z <= 2d+79) then
        tmp = t * (c * j)
    else if (z <= 9d+134) then
        tmp = t_2
    else
        tmp = z * (c * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -7.5e+83) {
		tmp = t_2;
	} else if (z <= -6e-160) {
		tmp = t_1;
	} else if (z <= 4.5e-287) {
		tmp = y * (i * -j);
	} else if (z <= 1.6e-137) {
		tmp = t_1;
	} else if (z <= 2e+79) {
		tmp = t * (c * j);
	} else if (z <= 9e+134) {
		tmp = t_2;
	} else {
		tmp = z * (c * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	t_2 = x * (y * z)
	tmp = 0
	if z <= -7.5e+83:
		tmp = t_2
	elif z <= -6e-160:
		tmp = t_1
	elif z <= 4.5e-287:
		tmp = y * (i * -j)
	elif z <= 1.6e-137:
		tmp = t_1
	elif z <= 2e+79:
		tmp = t * (c * j)
	elif z <= 9e+134:
		tmp = t_2
	else:
		tmp = z * (c * -b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(a * i))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -7.5e+83)
		tmp = t_2;
	elseif (z <= -6e-160)
		tmp = t_1;
	elseif (z <= 4.5e-287)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (z <= 1.6e-137)
		tmp = t_1;
	elseif (z <= 2e+79)
		tmp = Float64(t * Float64(c * j));
	elseif (z <= 9e+134)
		tmp = t_2;
	else
		tmp = Float64(z * Float64(c * Float64(-b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (z <= -7.5e+83)
		tmp = t_2;
	elseif (z <= -6e-160)
		tmp = t_1;
	elseif (z <= 4.5e-287)
		tmp = y * (i * -j);
	elseif (z <= 1.6e-137)
		tmp = t_1;
	elseif (z <= 2e+79)
		tmp = t * (c * j);
	elseif (z <= 9e+134)
		tmp = t_2;
	else
		tmp = z * (c * -b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+83], t$95$2, If[LessEqual[z, -6e-160], t$95$1, If[LessEqual[z, 4.5e-287], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-137], t$95$1, If[LessEqual[z, 2e+79], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+134], t$95$2, N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.49999999999999989e83 or 1.99999999999999993e79 < z < 8.9999999999999995e134

   1. Initial program 56.6%

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

   3. Taylor expanded in x around inf 50.3%

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

      1. *-commutative 50.3%

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

   5. Simplified 50.3%

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

   6. Taylor expanded in z around inf 43.1%

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

      1. *-commutative 43.1%

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

   8. Simplified 43.1%

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

   if -7.49999999999999989e83 < z < -5.99999999999999993e-160 or 4.50000000000000017e-287 < z < 1.60000000000000011e-137

   1. Initial program 80.2%

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

   3. Taylor expanded in b around inf 50.2%

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

   4. Taylor expanded in a around inf 41.7%

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

      1. *-commutative 41.7%

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

   6. Simplified 41.7%

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

   if -5.99999999999999993e-160 < z < 4.50000000000000017e-287

   1. Initial program 62.6%

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

   3. Taylor expanded in b around 0 58.6%

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

   4. Taylor expanded in i around inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. *-commutative 44.4%

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

      3. distribute-rgt-neg-in 44.4%

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

      4. *-commutative 44.4%

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

      5. associate-*l* 47.5%

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

   6. Simplified 47.5%

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

   if 1.60000000000000011e-137 < z < 1.99999999999999993e79

   1. Initial program 73.8%

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

   3. Taylor expanded in b around 0 57.4%

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

   4. Taylor expanded in c around inf 31.7%

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

      1. *-commutative 31.7%

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

      2. *-commutative 31.7%

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

      3. associate-*r* 36.5%

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

   6. Simplified 36.5%

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

   if 8.9999999999999995e134 < z

   1. Initial program 64.0%

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

   3. Taylor expanded in z around inf 78.1%

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

   4. Taylor expanded in z around inf 66.5%

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

      1. *-commutative 66.5%

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

      2. *-commutative 66.5%

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

   6. Simplified 66.5%

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

   7. Taylor expanded in y around 0 49.8%

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

      1. mul-1-neg 49.8%

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

      2. *-commutative 49.8%

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

      3. distribute-rgt-neg-in 49.8%

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

   9. Simplified 49.8%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-160}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-287}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-137}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+79}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;b \leq -0.72:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-278}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= b -0.72)
     (* b (- (* a i) (* z c)))
     (if (<= b -9e-290)
       t_1
       (if (<= b 2e-278)
         (* y (- (* x z) (* i j)))
         (if (<= b 1.15e-265)
           t_1
           (if (<= b 4.5e+53)
             (* j (- (* t c) (* y i)))
             (* b (* i (- a (* c (/ z i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (b <= -0.72) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -9e-290) {
		tmp = t_1;
	} else if (b <= 2e-278) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.15e-265) {
		tmp = t_1;
	} else if (b <= 4.5e+53) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = b * (i * (a - (c * (z / 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) :: t_1
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    if (b <= (-0.72d0)) then
        tmp = b * ((a * i) - (z * c))
    else if (b <= (-9d-290)) then
        tmp = t_1
    else if (b <= 2d-278) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 1.15d-265) then
        tmp = t_1
    else if (b <= 4.5d+53) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = b * (i * (a - (c * (z / 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 t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (b <= -0.72) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= -9e-290) {
		tmp = t_1;
	} else if (b <= 2e-278) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.15e-265) {
		tmp = t_1;
	} else if (b <= 4.5e+53) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = b * (i * (a - (c * (z / i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	tmp = 0
	if b <= -0.72:
		tmp = b * ((a * i) - (z * c))
	elif b <= -9e-290:
		tmp = t_1
	elif b <= 2e-278:
		tmp = y * ((x * z) - (i * j))
	elif b <= 1.15e-265:
		tmp = t_1
	elif b <= 4.5e+53:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = b * (i * (a - (c * (z / i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (b <= -0.72)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (b <= -9e-290)
		tmp = t_1;
	elseif (b <= 2e-278)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 1.15e-265)
		tmp = t_1;
	elseif (b <= 4.5e+53)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(b * Float64(i * Float64(a - Float64(c * Float64(z / i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (b <= -0.72)
		tmp = b * ((a * i) - (z * c));
	elseif (b <= -9e-290)
		tmp = t_1;
	elseif (b <= 2e-278)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 1.15e-265)
		tmp = t_1;
	elseif (b <= 4.5e+53)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = b * (i * (a - (c * (z / i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.72], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9e-290], t$95$1, If[LessEqual[b, 2e-278], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-265], t$95$1, If[LessEqual[b, 4.5e+53], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(i * N[(a - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -0.71999999999999997

   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. Add Preprocessing

   3. Taylor expanded in b around inf 69.8%

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

   if -0.71999999999999997 < b < -9e-290 or 1.99999999999999988e-278 < b < 1.1499999999999999e-265

   1. Initial program 66.8%

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

   3. Taylor expanded in t around inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

   5. Simplified 60.7%

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

   if -9e-290 < b < 1.99999999999999988e-278

   1. Initial program 50.0%

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

   3. Taylor expanded in y around inf 83.5%

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

      1. +-commutative 83.5%

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

      2. mul-1-neg 83.5%

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

      3. unsub-neg 83.5%

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

      4. *-commutative 83.5%

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

   5. Simplified 83.5%

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

   if 1.1499999999999999e-265 < b < 4.5000000000000002e53

   1. Initial program 72.2%

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

   3. Taylor expanded in z around inf 80.0%

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

   4. Taylor expanded in j around -inf 56.2%

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

   if 4.5000000000000002e53 < b

   1. Initial program 65.5%

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

   3. Taylor expanded in b around inf 72.3%

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

   4. Taylor expanded in i around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

      3. associate-/l* 73.9%

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

   6. Simplified 73.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.72:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9 \cdot 10^{-290}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-278}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-265}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -2.45e-9)
     t_2
     (if (<= b -1.75e-293)
       t_1
       (if (<= b 2.8e-282)
         (* y (- (* x z) (* i j)))
         (if (<= b 1.18e-265)
           t_1
           (if (<= b 7e+53) (* j (- (* t c) (* y i))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.45e-9) {
		tmp = t_2;
	} else if (b <= -1.75e-293) {
		tmp = t_1;
	} else if (b <= 2.8e-282) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.18e-265) {
		tmp = t_1;
	} else if (b <= 7e+53) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-2.45d-9)) then
        tmp = t_2
    else if (b <= (-1.75d-293)) then
        tmp = t_1
    else if (b <= 2.8d-282) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 1.18d-265) then
        tmp = t_1
    else if (b <= 7d+53) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -2.45e-9) {
		tmp = t_2;
	} else if (b <= -1.75e-293) {
		tmp = t_1;
	} else if (b <= 2.8e-282) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 1.18e-265) {
		tmp = t_1;
	} else if (b <= 7e+53) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -2.45e-9:
		tmp = t_2
	elif b <= -1.75e-293:
		tmp = t_1
	elif b <= 2.8e-282:
		tmp = y * ((x * z) - (i * j))
	elif b <= 1.18e-265:
		tmp = t_1
	elif b <= 7e+53:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.45e-9)
		tmp = t_2;
	elseif (b <= -1.75e-293)
		tmp = t_1;
	elseif (b <= 2.8e-282)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 1.18e-265)
		tmp = t_1;
	elseif (b <= 7e+53)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.45e-9)
		tmp = t_2;
	elseif (b <= -1.75e-293)
		tmp = t_1;
	elseif (b <= 2.8e-282)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 1.18e-265)
		tmp = t_1;
	elseif (b <= 7e+53)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.45e-9], t$95$2, If[LessEqual[b, -1.75e-293], t$95$1, If[LessEqual[b, 2.8e-282], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.18e-265], t$95$1, If[LessEqual[b, 7e+53], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.45000000000000002e-9 or 7.00000000000000038e53 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 70.9%

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

   if -2.45000000000000002e-9 < b < -1.7500000000000001e-293 or 2.7999999999999999e-282 < b < 1.18000000000000005e-265

   1. Initial program 66.8%

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

   3. Taylor expanded in t around inf 60.7%

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

      1. +-commutative 60.7%

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

      2. mul-1-neg 60.7%

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

      3. unsub-neg 60.7%

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

   5. Simplified 60.7%

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

   if -1.7500000000000001e-293 < b < 2.7999999999999999e-282

   1. Initial program 50.0%

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

   3. Taylor expanded in y around inf 83.5%

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

      1. +-commutative 83.5%

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

      2. mul-1-neg 83.5%

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

      3. unsub-neg 83.5%

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

      4. *-commutative 83.5%

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

   5. Simplified 83.5%

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

   if 1.18000000000000005e-265 < b < 7.00000000000000038e53

   1. Initial program 72.2%

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

   3. Taylor expanded in z around inf 80.0%

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

   4. Taylor expanded in j around -inf 56.2%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{-9}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-293}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{-265}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -0.0108:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-273}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-150}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -0.0108)
     t_2
     (if (<= b -5.8e-273)
       (* t (- (* c j) (* x a)))
       (if (<= b 2.1e-203)
         t_1
         (if (<= b 3.4e-150)
           (* x (- (* y z) (* t a)))
           (if (<= b 5.8e+53) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -0.0108) {
		tmp = t_2;
	} else if (b <= -5.8e-273) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 2.1e-203) {
		tmp = t_1;
	} else if (b <= 3.4e-150) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 5.8e+53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-0.0108d0)) then
        tmp = t_2
    else if (b <= (-5.8d-273)) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 2.1d-203) then
        tmp = t_1
    else if (b <= 3.4d-150) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 5.8d+53) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -0.0108) {
		tmp = t_2;
	} else if (b <= -5.8e-273) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 2.1e-203) {
		tmp = t_1;
	} else if (b <= 3.4e-150) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 5.8e+53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -0.0108:
		tmp = t_2
	elif b <= -5.8e-273:
		tmp = t * ((c * j) - (x * a))
	elif b <= 2.1e-203:
		tmp = t_1
	elif b <= 3.4e-150:
		tmp = x * ((y * z) - (t * a))
	elif b <= 5.8e+53:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -0.0108)
		tmp = t_2;
	elseif (b <= -5.8e-273)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 2.1e-203)
		tmp = t_1;
	elseif (b <= 3.4e-150)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 5.8e+53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -0.0108)
		tmp = t_2;
	elseif (b <= -5.8e-273)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 2.1e-203)
		tmp = t_1;
	elseif (b <= 3.4e-150)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 5.8e+53)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -0.0108], t$95$2, If[LessEqual[b, -5.8e-273], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-203], t$95$1, If[LessEqual[b, 3.4e-150], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+53], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -0.010800000000000001 or 5.8000000000000004e53 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 70.9%

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

   if -0.010800000000000001 < b < -5.79999999999999973e-273

   1. Initial program 65.6%

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

   3. Taylor expanded in t around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. mul-1-neg 58.4%

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

      3. unsub-neg 58.4%

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

   5. Simplified 58.4%

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

   if -5.79999999999999973e-273 < b < 2.10000000000000002e-203 or 3.39999999999999999e-150 < b < 5.8000000000000004e53

   1. Initial program 68.4%

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

   3. Taylor expanded in z around inf 74.3%

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

   4. Taylor expanded in j around -inf 61.1%

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

   if 2.10000000000000002e-203 < b < 3.39999999999999999e-150

   1. Initial program 71.5%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. *-commutative 83.2%

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

   5. Simplified 83.2%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0108:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-273}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-203}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-150}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 41.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.9 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.255 \cdot 10^{-253}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-279}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-270}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -3.9e-75)
     t_1
     (if (<= b -1.255e-253)
       (* c (* t j))
       (if (<= b 1.45e-279)
         (* z (* x y))
         (if (<= b 1.65e-270)
           (* t (* c j))
           (if (<= b 4.5e+53) (* y (* 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 <= -3.9e-75) {
		tmp = t_1;
	} else if (b <= -1.255e-253) {
		tmp = c * (t * j);
	} else if (b <= 1.45e-279) {
		tmp = z * (x * y);
	} else if (b <= 1.65e-270) {
		tmp = t * (c * j);
	} else if (b <= 4.5e+53) {
		tmp = y * (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 <= (-3.9d-75)) then
        tmp = t_1
    else if (b <= (-1.255d-253)) then
        tmp = c * (t * j)
    else if (b <= 1.45d-279) then
        tmp = z * (x * y)
    else if (b <= 1.65d-270) then
        tmp = t * (c * j)
    else if (b <= 4.5d+53) then
        tmp = y * (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 <= -3.9e-75) {
		tmp = t_1;
	} else if (b <= -1.255e-253) {
		tmp = c * (t * j);
	} else if (b <= 1.45e-279) {
		tmp = z * (x * y);
	} else if (b <= 1.65e-270) {
		tmp = t * (c * j);
	} else if (b <= 4.5e+53) {
		tmp = y * (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 <= -3.9e-75:
		tmp = t_1
	elif b <= -1.255e-253:
		tmp = c * (t * j)
	elif b <= 1.45e-279:
		tmp = z * (x * y)
	elif b <= 1.65e-270:
		tmp = t * (c * j)
	elif b <= 4.5e+53:
		tmp = y * (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 <= -3.9e-75)
		tmp = t_1;
	elseif (b <= -1.255e-253)
		tmp = Float64(c * Float64(t * j));
	elseif (b <= 1.45e-279)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 1.65e-270)
		tmp = Float64(t * Float64(c * j));
	elseif (b <= 4.5e+53)
		tmp = Float64(y * Float64(i * Float64(-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 <= -3.9e-75)
		tmp = t_1;
	elseif (b <= -1.255e-253)
		tmp = c * (t * j);
	elseif (b <= 1.45e-279)
		tmp = z * (x * y);
	elseif (b <= 1.65e-270)
		tmp = t * (c * j);
	elseif (b <= 4.5e+53)
		tmp = y * (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, -3.9e-75], t$95$1, If[LessEqual[b, -1.255e-253], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.45e-279], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e-270], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+53], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.9000000000000001e-75 or 4.5000000000000002e53 < b

   1. Initial program 68.6%

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

   3. Taylor expanded in b around inf 65.2%

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

   if -3.9000000000000001e-75 < b < -1.25500000000000007e-253

   1. Initial program 71.8%

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

   3. Taylor expanded in x around 0 50.0%

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

   4. Taylor expanded in t around inf 38.8%

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

   if -1.25500000000000007e-253 < b < 1.45e-279

   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. Add Preprocessing

   3. Taylor expanded in z around inf 65.3%

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

   4. Taylor expanded in z around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. *-commutative 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in y around inf 51.1%

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

   if 1.45e-279 < b < 1.65000000000000009e-270

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

   4. Taylor expanded in c around inf 68.1%

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

      1. *-commutative 68.1%

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

      2. *-commutative 68.1%

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

      3. associate-*r* 68.3%

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

   6. Simplified 68.3%

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

   if 1.65000000000000009e-270 < b < 4.5000000000000002e53

   1. Initial program 68.8%

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

   3. Taylor expanded in b around 0 68.2%

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

   4. Taylor expanded in i around inf 35.9%

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

      1. mul-1-neg 35.9%

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

      2. *-commutative 35.9%

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

      3. distribute-rgt-neg-in 35.9%

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

      4. *-commutative 35.9%

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

      5. associate-*l* 38.1%

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

   6. Simplified 38.1%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.9 \cdot 10^{-75}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.255 \cdot 10^{-253}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-279}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-270}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.85 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 4.05 \cdot 10^{-81}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 10^{+204}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \end{array} \end{array} \]

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 (* b (- (* a i) (* z c))))))
   (if (<= b -1.85e-10)
     t_2
     (if (<= b 4.05e-81)
       (+ t_1 (* x (- (* y z) (* t a))))
       (if (<= b 1e+204) t_2 (* b (* i (- a (* c (/ z i))))))))))

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 + (b * ((a * i) - (z * c)));
	double tmp;
	if (b <= -1.85e-10) {
		tmp = t_2;
	} else if (b <= 4.05e-81) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (b <= 1e+204) {
		tmp = t_2;
	} else {
		tmp = b * (i * (a - (c * (z / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = t_1 + (b * ((a * i) - (z * c)))
    if (b <= (-1.85d-10)) then
        tmp = t_2
    else if (b <= 4.05d-81) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else if (b <= 1d+204) then
        tmp = t_2
    else
        tmp = b * (i * (a - (c * (z / 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 t_1 = j * ((t * c) - (y * i));
	double t_2 = t_1 + (b * ((a * i) - (z * c)));
	double tmp;
	if (b <= -1.85e-10) {
		tmp = t_2;
	} else if (b <= 4.05e-81) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else if (b <= 1e+204) {
		tmp = t_2;
	} else {
		tmp = b * (i * (a - (c * (z / i))));
	}
	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 + (b * ((a * i) - (z * c)))
	tmp = 0
	if b <= -1.85e-10:
		tmp = t_2
	elif b <= 4.05e-81:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	elif b <= 1e+204:
		tmp = t_2
	else:
		tmp = b * (i * (a - (c * (z / i))))
	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(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (b <= -1.85e-10)
		tmp = t_2;
	elseif (b <= 4.05e-81)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	elseif (b <= 1e+204)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(i * Float64(a - Float64(c * Float64(z / i)))));
	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 + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (b <= -1.85e-10)
		tmp = t_2;
	elseif (b <= 4.05e-81)
		tmp = t_1 + (x * ((y * z) - (t * a)));
	elseif (b <= 1e+204)
		tmp = t_2;
	else
		tmp = b * (i * (a - (c * (z / i))));
	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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.85e-10], t$95$2, If[LessEqual[b, 4.05e-81], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+204], t$95$2, N[(b * N[(i * N[(a - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.85000000000000007e-10 or 4.0500000000000001e-81 < b < 9.99999999999999989e203

   1. Initial program 77.6%

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

   3. Taylor expanded in x around 0 77.2%

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

   if -1.85000000000000007e-10 < b < 4.0500000000000001e-81

   1. Initial program 66.9%

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

   3. Taylor expanded in b around 0 73.5%

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

   if 9.99999999999999989e203 < b

   1. Initial program 44.6%

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

   3. Taylor expanded in b around inf 77.8%

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

   4. Taylor expanded in i around inf 81.5%

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

      1. mul-1-neg 81.5%

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

      2. unsub-neg 81.5%

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

      3. associate-/l* 81.5%

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

   6. Simplified 81.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.85 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 4.05 \cdot 10^{-81}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 10^{+204}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 27.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{+211}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+86}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-293}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-149}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= z -1.16e+211)
     (* x (* y z))
     (if (<= z -7.8e+86)
       (* a (* t (- x)))
       (if (<= z -2e-159)
         t_1
         (if (<= z 1.16e-293)
           (* y (* i (- j)))
           (if (<= z 9.5e-149) t_1 (* c (* z (- b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (z <= -1.16e+211) {
		tmp = x * (y * z);
	} else if (z <= -7.8e+86) {
		tmp = a * (t * -x);
	} else if (z <= -2e-159) {
		tmp = t_1;
	} else if (z <= 1.16e-293) {
		tmp = y * (i * -j);
	} else if (z <= 9.5e-149) {
		tmp = t_1;
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (z <= (-1.16d+211)) then
        tmp = x * (y * z)
    else if (z <= (-7.8d+86)) then
        tmp = a * (t * -x)
    else if (z <= (-2d-159)) then
        tmp = t_1
    else if (z <= 1.16d-293) then
        tmp = y * (i * -j)
    else if (z <= 9.5d-149) then
        tmp = t_1
    else
        tmp = c * (z * -b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (z <= -1.16e+211) {
		tmp = x * (y * z);
	} else if (z <= -7.8e+86) {
		tmp = a * (t * -x);
	} else if (z <= -2e-159) {
		tmp = t_1;
	} else if (z <= 1.16e-293) {
		tmp = y * (i * -j);
	} else if (z <= 9.5e-149) {
		tmp = t_1;
	} else {
		tmp = c * (z * -b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if z <= -1.16e+211:
		tmp = x * (y * z)
	elif z <= -7.8e+86:
		tmp = a * (t * -x)
	elif z <= -2e-159:
		tmp = t_1
	elif z <= 1.16e-293:
		tmp = y * (i * -j)
	elif z <= 9.5e-149:
		tmp = t_1
	else:
		tmp = c * (z * -b)
	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 <= -1.16e+211)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -7.8e+86)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (z <= -2e-159)
		tmp = t_1;
	elseif (z <= 1.16e-293)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (z <= 9.5e-149)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(z * Float64(-b)));
	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 <= -1.16e+211)
		tmp = x * (y * z);
	elseif (z <= -7.8e+86)
		tmp = a * (t * -x);
	elseif (z <= -2e-159)
		tmp = t_1;
	elseif (z <= 1.16e-293)
		tmp = y * (i * -j);
	elseif (z <= 9.5e-149)
		tmp = t_1;
	else
		tmp = c * (z * -b);
	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, -1.16e+211], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.8e+86], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e-159], t$95$1, If[LessEqual[z, 1.16e-293], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-149], t$95$1, N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.15999999999999997e211

   1. Initial program 47.5%

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

   3. Taylor expanded in x around inf 58.0%

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

      1. *-commutative 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in z around inf 62.4%

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

      1. *-commutative 62.4%

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

   8. Simplified 62.4%

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

   if -1.15999999999999997e211 < z < -7.8000000000000004e86

   1. Initial program 72.9%

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

   3. Taylor expanded in x around inf 42.4%

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

      1. *-commutative 42.4%

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

   5. Simplified 42.4%

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

   6. Taylor expanded in z around 0 38.5%

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

      1. associate-*r* 38.5%

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

      2. neg-mul-1 38.5%

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

   8. Simplified 38.5%

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

   if -7.8000000000000004e86 < z < -1.99999999999999998e-159 or 1.16e-293 < z < 9.50000000000000034e-149

   1. Initial program 79.9%

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

   3. Taylor expanded in b around inf 49.7%

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

   4. Taylor expanded in a around inf 42.1%

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

      1. *-commutative 42.1%

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

   6. Simplified 42.1%

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

   if -1.99999999999999998e-159 < z < 1.16e-293

   1. Initial program 62.6%

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

   3. Taylor expanded in b around 0 58.6%

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

   4. Taylor expanded in i around inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. *-commutative 44.4%

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

      3. distribute-rgt-neg-in 44.4%

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

      4. *-commutative 44.4%

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

      5. associate-*l* 47.5%

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

   6. Simplified 47.5%

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

   if 9.50000000000000034e-149 < z

   1. Initial program 65.9%

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

   3. Taylor expanded in b around inf 47.4%

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

   4. Taylor expanded in i around inf 41.6%

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

      1. +-commutative 41.6%

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

      2. mul-1-neg 41.6%

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

      3. unsub-neg 41.6%

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

      4. *-commutative 41.6%

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

      5. associate-/l* 42.7%

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

      6. associate-/l* 43.6%

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

   6. Simplified 43.6%

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

   7. Taylor expanded in i around 0 39.0%

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

      1. associate-*r* 39.0%

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

      2. neg-mul-1 39.0%

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

      3. *-commutative 39.0%

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

      4. associate-*r* 40.8%

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

      5. neg-mul-1 40.8%

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

      6. associate-*r* 40.8%

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

      7. *-commutative 40.8%

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

      8. associate-*l* 40.8%

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

      9. *-commutative 40.8%

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

      10. neg-mul-1 40.8%

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

   9. Simplified 40.8%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+211}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+86}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-159}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-293}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-149}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* a i))))
   (if (<= z -1.8e+87)
     (* x (* y z))
     (if (<= z -4e-159)
       t_1
       (if (<= z 9.5e-288)
         (* y (* i (- j)))
         (if (<= z 1.5e-138)
           t_1
           (if (<= z 8.4e+74) (* t (* c j)) (* z (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (z <= -1.8e+87) {
		tmp = x * (y * z);
	} else if (z <= -4e-159) {
		tmp = t_1;
	} else if (z <= 9.5e-288) {
		tmp = y * (i * -j);
	} else if (z <= 1.5e-138) {
		tmp = t_1;
	} else if (z <= 8.4e+74) {
		tmp = t * (c * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * i)
    if (z <= (-1.8d+87)) then
        tmp = x * (y * z)
    else if (z <= (-4d-159)) then
        tmp = t_1
    else if (z <= 9.5d-288) then
        tmp = y * (i * -j)
    else if (z <= 1.5d-138) then
        tmp = t_1
    else if (z <= 8.4d+74) then
        tmp = t * (c * j)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (a * i);
	double tmp;
	if (z <= -1.8e+87) {
		tmp = x * (y * z);
	} else if (z <= -4e-159) {
		tmp = t_1;
	} else if (z <= 9.5e-288) {
		tmp = y * (i * -j);
	} else if (z <= 1.5e-138) {
		tmp = t_1;
	} else if (z <= 8.4e+74) {
		tmp = t * (c * j);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (a * i)
	tmp = 0
	if z <= -1.8e+87:
		tmp = x * (y * z)
	elif z <= -4e-159:
		tmp = t_1
	elif z <= 9.5e-288:
		tmp = y * (i * -j)
	elif z <= 1.5e-138:
		tmp = t_1
	elif z <= 8.4e+74:
		tmp = t * (c * j)
	else:
		tmp = z * (x * y)
	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 <= -1.8e+87)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= -4e-159)
		tmp = t_1;
	elseif (z <= 9.5e-288)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (z <= 1.5e-138)
		tmp = t_1;
	elseif (z <= 8.4e+74)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (a * i);
	tmp = 0.0;
	if (z <= -1.8e+87)
		tmp = x * (y * z);
	elseif (z <= -4e-159)
		tmp = t_1;
	elseif (z <= 9.5e-288)
		tmp = y * (i * -j);
	elseif (z <= 1.5e-138)
		tmp = t_1;
	elseif (z <= 8.4e+74)
		tmp = t * (c * j);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+87], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-159], t$95$1, If[LessEqual[z, 9.5e-288], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-138], t$95$1, If[LessEqual[z, 8.4e+74], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.79999999999999997e87

   1. Initial program 60.5%

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

   3. Taylor expanded in x around inf 50.0%

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

      1. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in z around inf 40.7%

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

      1. *-commutative 40.7%

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

   8. Simplified 40.7%

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

   if -1.79999999999999997e87 < z < -3.99999999999999995e-159 or 9.49999999999999955e-288 < z < 1.5e-138

   1. Initial program 80.2%

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

   3. Taylor expanded in b around inf 50.2%

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

   4. Taylor expanded in a around inf 41.7%

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

      1. *-commutative 41.7%

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

   6. Simplified 41.7%

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

   if -3.99999999999999995e-159 < z < 9.49999999999999955e-288

   1. Initial program 62.6%

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

   3. Taylor expanded in b around 0 58.6%

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

   4. Taylor expanded in i around inf 44.4%

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

      1. mul-1-neg 44.4%

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

      2. *-commutative 44.4%

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

      3. distribute-rgt-neg-in 44.4%

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

      4. *-commutative 44.4%

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

      5. associate-*l* 47.5%

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

   6. Simplified 47.5%

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

   if 1.5e-138 < z < 8.3999999999999995e74

   1. Initial program 73.8%

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

   3. Taylor expanded in b around 0 57.4%

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

   4. Taylor expanded in c around inf 31.7%

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

      1. *-commutative 31.7%

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

      2. *-commutative 31.7%

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

      3. associate-*r* 36.5%

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

   6. Simplified 36.5%

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

   if 8.3999999999999995e74 < z

   1. Initial program 59.1%

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

   3. Taylor expanded in z around inf 73.6%

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

   4. Taylor expanded in z around inf 70.5%

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

      1. *-commutative 70.5%

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

      2. *-commutative 70.5%

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

   6. Simplified 70.5%

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

   7. Taylor expanded in y around inf 39.3%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-159}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-138}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 56.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{-38}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-163}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+54}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= b -3.4e-38)
     (* b (- (* a i) (* z c)))
     (if (<= b 1.7e-163)
       (+ t_1 (* x (* y z)))
       (if (<= b 1.35e+54)
         (+ t_1 (* a (* b i)))
         (* b (* i (- a (* c (/ z i))))))))))

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 tmp;
	if (b <= -3.4e-38) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= 1.7e-163) {
		tmp = t_1 + (x * (y * z));
	} else if (b <= 1.35e+54) {
		tmp = t_1 + (a * (b * i));
	} else {
		tmp = b * (i * (a - (c * (z / 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) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (b <= (-3.4d-38)) then
        tmp = b * ((a * i) - (z * c))
    else if (b <= 1.7d-163) then
        tmp = t_1 + (x * (y * z))
    else if (b <= 1.35d+54) then
        tmp = t_1 + (a * (b * i))
    else
        tmp = b * (i * (a - (c * (z / 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 t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (b <= -3.4e-38) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= 1.7e-163) {
		tmp = t_1 + (x * (y * z));
	} else if (b <= 1.35e+54) {
		tmp = t_1 + (a * (b * i));
	} else {
		tmp = b * (i * (a - (c * (z / i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if b <= -3.4e-38:
		tmp = b * ((a * i) - (z * c))
	elif b <= 1.7e-163:
		tmp = t_1 + (x * (y * z))
	elif b <= 1.35e+54:
		tmp = t_1 + (a * (b * i))
	else:
		tmp = b * (i * (a - (c * (z / i))))
	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)))
	tmp = 0.0
	if (b <= -3.4e-38)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (b <= 1.7e-163)
		tmp = Float64(t_1 + Float64(x * Float64(y * z)));
	elseif (b <= 1.35e+54)
		tmp = Float64(t_1 + Float64(a * Float64(b * i)));
	else
		tmp = Float64(b * Float64(i * Float64(a - Float64(c * Float64(z / i)))));
	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));
	tmp = 0.0;
	if (b <= -3.4e-38)
		tmp = b * ((a * i) - (z * c));
	elseif (b <= 1.7e-163)
		tmp = t_1 + (x * (y * z));
	elseif (b <= 1.35e+54)
		tmp = t_1 + (a * (b * i));
	else
		tmp = b * (i * (a - (c * (z / i))));
	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]}, If[LessEqual[b, -3.4e-38], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-163], N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+54], N[(t$95$1 + N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(i * N[(a - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.4000000000000002e-38

   1. Initial program 74.1%

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

   3. Taylor expanded in b around inf 67.4%

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

   if -3.4000000000000002e-38 < b < 1.70000000000000007e-163

   1. Initial program 68.8%

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

   3. Taylor expanded in b around 0 76.3%

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

   4. Taylor expanded in y around inf 64.4%

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

   if 1.70000000000000007e-163 < b < 1.35000000000000005e54

   1. Initial program 64.6%

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

   3. Taylor expanded in x around 0 64.7%

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

   4. Taylor expanded in c around 0 70.8%

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

      1. associate-*r* 70.8%

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

      2. neg-mul-1 70.8%

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

      3. *-commutative 70.8%

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

   6. Simplified 70.8%

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

   if 1.35000000000000005e54 < b

   1. Initial program 65.5%

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

   3. Taylor expanded in b around inf 72.3%

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

   4. Taylor expanded in i around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

      3. associate-/l* 73.9%

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

   6. Simplified 73.9%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-38}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-163}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+54}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-282}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 3.55 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -1.25e-36)
     t_2
     (if (<= b -4.3e-240)
       t_1
       (if (<= b 1.6e-282) (* z (* x y)) (if (<= b 3.55e-75) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.25e-36) {
		tmp = t_2;
	} else if (b <= -4.3e-240) {
		tmp = t_1;
	} else if (b <= 1.6e-282) {
		tmp = z * (x * y);
	} else if (b <= 3.55e-75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-1.25d-36)) then
        tmp = t_2
    else if (b <= (-4.3d-240)) then
        tmp = t_1
    else if (b <= 1.6d-282) then
        tmp = z * (x * y)
    else if (b <= 3.55d-75) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.25e-36) {
		tmp = t_2;
	} else if (b <= -4.3e-240) {
		tmp = t_1;
	} else if (b <= 1.6e-282) {
		tmp = z * (x * y);
	} else if (b <= 3.55e-75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.25e-36:
		tmp = t_2
	elif b <= -4.3e-240:
		tmp = t_1
	elif b <= 1.6e-282:
		tmp = z * (x * y)
	elif b <= 3.55e-75:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.25e-36)
		tmp = t_2;
	elseif (b <= -4.3e-240)
		tmp = t_1;
	elseif (b <= 1.6e-282)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 3.55e-75)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.25e-36)
		tmp = t_2;
	elseif (b <= -4.3e-240)
		tmp = t_1;
	elseif (b <= 1.6e-282)
		tmp = z * (x * y);
	elseif (b <= 3.55e-75)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e-36], t$95$2, If[LessEqual[b, -4.3e-240], t$95$1, If[LessEqual[b, 1.6e-282], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.55e-75], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25000000000000001e-36 or 3.5500000000000002e-75 < b

   1. Initial program 70.6%

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

   3. Taylor expanded in b around inf 65.7%

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

   if -1.25000000000000001e-36 < b < -4.30000000000000013e-240 or 1.59999999999999991e-282 < b < 3.5500000000000002e-75

   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. Add Preprocessing

   3. Taylor expanded in c around inf 42.7%

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

   if -4.30000000000000013e-240 < b < 1.59999999999999991e-282

   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. Add Preprocessing

   3. Taylor expanded in z around inf 68.4%

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

   4. Taylor expanded in z around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. *-commutative 51.0%

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

   6. Simplified 51.0%

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

   7. Taylor expanded in y around inf 51.1%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{-36}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-240}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-282}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 3.55 \cdot 10^{-75}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 57.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{-38}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.95e-38)
   (* b (- (* a i) (* z c)))
   (if (<= b 6.2e+53)
     (+ (* j (- (* t c) (* y i))) (* x (* y z)))
     (* b (* i (- a (* c (/ z 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 <= -1.95e-38) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= 6.2e+53) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else {
		tmp = b * (i * (a - (c * (z / 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 <= (-1.95d-38)) then
        tmp = b * ((a * i) - (z * c))
    else if (b <= 6.2d+53) then
        tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
    else
        tmp = b * (i * (a - (c * (z / 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 <= -1.95e-38) {
		tmp = b * ((a * i) - (z * c));
	} else if (b <= 6.2e+53) {
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	} else {
		tmp = b * (i * (a - (c * (z / i))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.95e-38:
		tmp = b * ((a * i) - (z * c))
	elif b <= 6.2e+53:
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z))
	else:
		tmp = b * (i * (a - (c * (z / i))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.95e-38)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (b <= 6.2e+53)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)));
	else
		tmp = Float64(b * Float64(i * Float64(a - Float64(c * Float64(z / i)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.95e-38)
		tmp = b * ((a * i) - (z * c));
	elseif (b <= 6.2e+53)
		tmp = (j * ((t * c) - (y * i))) + (x * (y * z));
	else
		tmp = b * (i * (a - (c * (z / i))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.95e-38], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e+53], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(i * N[(a - N[(c * N[(z / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.95e-38

   1. Initial program 74.1%

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

   3. Taylor expanded in b around inf 67.4%

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

   if -1.95e-38 < b < 6.20000000000000038e53

   1. Initial program 67.8%

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

   3. Taylor expanded in b around 0 71.8%

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

   4. Taylor expanded in y around inf 61.2%

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

   if 6.20000000000000038e53 < b

   1. Initial program 65.5%

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

   3. Taylor expanded in b around inf 72.3%

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

   4. Taylor expanded in i around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

      3. associate-/l* 73.9%

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

   6. Simplified 73.9%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.95 \cdot 10^{-38}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(i \cdot \left(a - c \cdot \frac{z}{i}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.75 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -3.75e-7)
     t_1
     (if (<= b -3.5e-271)
       (* t (- (* c j) (* x a)))
       (if (<= b 4.7e+53) (* j (- (* t c) (* y i))) 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 <= -3.75e-7) {
		tmp = t_1;
	} else if (b <= -3.5e-271) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4.7e+53) {
		tmp = j * ((t * c) - (y * i));
	} 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 <= (-3.75d-7)) then
        tmp = t_1
    else if (b <= (-3.5d-271)) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 4.7d+53) then
        tmp = j * ((t * c) - (y * i))
    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 <= -3.75e-7) {
		tmp = t_1;
	} else if (b <= -3.5e-271) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 4.7e+53) {
		tmp = j * ((t * c) - (y * i));
	} 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 <= -3.75e-7:
		tmp = t_1
	elif b <= -3.5e-271:
		tmp = t * ((c * j) - (x * a))
	elif b <= 4.7e+53:
		tmp = j * ((t * c) - (y * i))
	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 <= -3.75e-7)
		tmp = t_1;
	elseif (b <= -3.5e-271)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 4.7e+53)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	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 <= -3.75e-7)
		tmp = t_1;
	elseif (b <= -3.5e-271)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 4.7e+53)
		tmp = j * ((t * c) - (y * i));
	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, -3.75e-7], t$95$1, If[LessEqual[b, -3.5e-271], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.7e+53], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.7500000000000001e-7 or 4.69999999999999976e53 < b

   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. Add Preprocessing

   3. Taylor expanded in b around inf 70.9%

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

   if -3.7500000000000001e-7 < b < -3.4999999999999999e-271

   1. Initial program 65.6%

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

   3. Taylor expanded in t around inf 58.4%

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

      1. +-commutative 58.4%

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

      2. mul-1-neg 58.4%

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

      3. unsub-neg 58.4%

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

   5. Simplified 58.4%

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

   if -3.4999999999999999e-271 < b < 4.69999999999999976e53

   1. Initial program 68.7%

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

   3. Taylor expanded in z around inf 75.4%

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

   4. Taylor expanded in j around -inf 56.7%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.75 \cdot 10^{-7}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-271}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+53}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 25.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{-118}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 2200000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= c -1.15e+35)
     t_1
     (if (<= c 5.2e-118)
       (* i (* a b))
       (if (<= c 2200000.0) t_1 (* t (* c j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (c <= -1.15e+35) {
		tmp = t_1;
	} else if (c <= 5.2e-118) {
		tmp = i * (a * b);
	} else if (c <= 2200000.0) {
		tmp = t_1;
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x * y)
    if (c <= (-1.15d+35)) then
        tmp = t_1
    else if (c <= 5.2d-118) then
        tmp = i * (a * b)
    else if (c <= 2200000.0d0) then
        tmp = t_1
    else
        tmp = t * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (c <= -1.15e+35) {
		tmp = t_1;
	} else if (c <= 5.2e-118) {
		tmp = i * (a * b);
	} else if (c <= 2200000.0) {
		tmp = t_1;
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if c <= -1.15e+35:
		tmp = t_1
	elif c <= 5.2e-118:
		tmp = i * (a * b)
	elif c <= 2200000.0:
		tmp = t_1
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (c <= -1.15e+35)
		tmp = t_1;
	elseif (c <= 5.2e-118)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= 2200000.0)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (c <= -1.15e+35)
		tmp = t_1;
	elseif (c <= 5.2e-118)
		tmp = i * (a * b);
	elseif (c <= 2200000.0)
		tmp = t_1;
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+35], t$95$1, If[LessEqual[c, 5.2e-118], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2200000.0], t$95$1, N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.1499999999999999e35 or 5.2e-118 < c < 2.2e6

   1. Initial program 65.3%

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

   3. Taylor expanded in z around inf 60.2%

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

   4. Taylor expanded in z around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. *-commutative 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in y around inf 36.6%

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

   if -1.1499999999999999e35 < c < 5.2e-118

   1. Initial program 76.5%

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

   3. Taylor expanded in b around inf 43.4%

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

   4. Taylor expanded in i around inf 40.6%

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

      1. +-commutative 40.6%

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

      2. mul-1-neg 40.6%

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

      3. unsub-neg 40.6%

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

      4. *-commutative 40.6%

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

      5. associate-/l* 41.6%

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

      6. associate-/l* 41.5%

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

   6. Simplified 41.5%

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

   7. Taylor expanded in a around inf 36.8%

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

   if 2.2e6 < c

   1. Initial program 61.7%

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

   3. Taylor expanded in b around 0 51.9%

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

   4. Taylor expanded in c around inf 37.8%

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

      1. *-commutative 37.8%

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

      2. *-commutative 37.8%

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

      3. associate-*r* 39.3%

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

   6. Simplified 39.3%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{-118}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 2200000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{-74} \lor \neg \left(b \leq 1.2 \cdot 10^{+54}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -8.5e-74) (not (<= b 1.2e+54)))
   (* b (- (* a i) (* z c)))
   (* j (- (* t c) (* y 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 <= -8.5e-74) || !(b <= 1.2e+54)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = j * ((t * c) - (y * 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 <= (-8.5d-74)) .or. (.not. (b <= 1.2d+54))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = j * ((t * c) - (y * 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 <= -8.5e-74) || !(b <= 1.2e+54)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -8.5e-74) or not (b <= 1.2e+54):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = j * ((t * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -8.5e-74) || !(b <= 1.2e+54))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -8.5e-74) || ~((b <= 1.2e+54)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = j * ((t * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -8.5e-74], N[Not[LessEqual[b, 1.2e+54]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.50000000000000052e-74 or 1.19999999999999999e54 < b

   1. Initial program 68.6%

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

   3. Taylor expanded in b around inf 65.2%

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

   if -8.50000000000000052e-74 < b < 1.19999999999999999e54

   1. Initial program 69.9%

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

   3. Taylor expanded in z around inf 75.3%

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

   4. Taylor expanded in j around -inf 55.7%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{-74} \lor \neg \left(b \leq 1.2 \cdot 10^{+54}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 28.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-38}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-87}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -5.2e-38)
   (* i (* a b))
   (if (<= b 1.5e-87) (* 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 (b <= -5.2e-38) {
		tmp = i * (a * b);
	} else if (b <= 1.5e-87) {
		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 (b <= (-5.2d-38)) then
        tmp = i * (a * b)
    else if (b <= 1.5d-87) 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 (b <= -5.2e-38) {
		tmp = i * (a * b);
	} else if (b <= 1.5e-87) {
		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 b <= -5.2e-38:
		tmp = i * (a * b)
	elif b <= 1.5e-87:
		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 (b <= -5.2e-38)
		tmp = Float64(i * Float64(a * b));
	elseif (b <= 1.5e-87)
		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 (b <= -5.2e-38)
		tmp = i * (a * b);
	elseif (b <= 1.5e-87)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -5.2e-38], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e-87], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.20000000000000022e-38

   1. Initial program 74.1%

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

   3. Taylor expanded in b around inf 67.4%

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

   4. Taylor expanded in i around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. *-commutative 56.5%

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

      5. associate-/l* 57.8%

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

      6. associate-/l* 57.8%

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

   6. Simplified 57.8%

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

   7. Taylor expanded in a around inf 38.0%

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

   if -5.20000000000000022e-38 < b < 1.50000000000000008e-87

   1. Initial program 66.9%

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

   3. Taylor expanded in x around 0 50.1%

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

   4. Taylor expanded in t around inf 32.4%

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

   if 1.50000000000000008e-87 < b

   1. Initial program 67.4%

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

   3. Taylor expanded in b around inf 61.9%

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

   4. Taylor expanded in a around inf 42.4%

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

      1. *-commutative 42.4%

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

   6. Simplified 42.4%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-38}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-87}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{-38}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.9e-38)
   (* b (* a i))
   (if (<= b 7.5e-91) (* 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 (b <= -1.9e-38) {
		tmp = b * (a * i);
	} else if (b <= 7.5e-91) {
		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 (b <= (-1.9d-38)) then
        tmp = b * (a * i)
    else if (b <= 7.5d-91) 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 (b <= -1.9e-38) {
		tmp = b * (a * i);
	} else if (b <= 7.5e-91) {
		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 b <= -1.9e-38:
		tmp = b * (a * i)
	elif b <= 7.5e-91:
		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 (b <= -1.9e-38)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= 7.5e-91)
		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 (b <= -1.9e-38)
		tmp = b * (a * i);
	elseif (b <= 7.5e-91)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.9e-38], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e-91], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9e-38

   1. Initial program 74.1%

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

   3. Taylor expanded in b around inf 67.4%

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

   4. Taylor expanded in a around inf 35.5%

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

      1. *-commutative 35.5%

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

   6. Simplified 35.5%

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

   if -1.9e-38 < b < 7.50000000000000051e-91

   1. Initial program 66.9%

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

   3. Taylor expanded in x around 0 50.1%

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

   4. Taylor expanded in t around inf 32.4%

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

   if 7.50000000000000051e-91 < b

   1. Initial program 67.4%

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

   3. Taylor expanded in b around inf 61.9%

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

   4. Taylor expanded in a around inf 42.4%

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

      1. *-commutative 42.4%

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

   6. Simplified 42.4%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{-38}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 21.9% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.1%

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

3. Taylor expanded in b around inf 44.2%

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

4. Taylor expanded in a around inf 25.2%

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

   1. *-commutative 25.2%

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

6. Simplified 25.2%

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

7. Final simplification 25.2%

   \[\leadsto b \cdot \left(a \cdot i\right) \]
8. Add Preprocessing

Alternative 23: 21.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.1%

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

3. Taylor expanded in b around inf 44.2%

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

4. Taylor expanded in a around inf 24.8%

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

   1. *-commutative 24.8%

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

6. Simplified 24.8%

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

7. Final simplification 24.8%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 68.6% 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 2024087 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (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)))))