Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B

Percentage Accurate: 88.4% → 98.4%

Time: 17.9s

Alternatives: 24

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / ((y - z) * (t - z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

Python

def code(x, y, z, t):
	return x / ((y - z) * (t - z))

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(y - z) * Float64(t - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((y - z) * (t - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 88.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x (* (- y z) (- t z))))

C

double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / ((y - z) * (t - z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x / ((y - z) * (t - z));
}

Python

def code(x, y, z, t):
	return x / ((y - z) * (t - z))

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(y - z) * Float64(t - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((y - z) * (t - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \left(\frac{\sqrt{x\_m}}{y - z} \cdot \frac{\sqrt{x\_m}}{t - z}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (* (/ (sqrt x_m) (- y z)) (/ (sqrt x_m) (- t z)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * ((sqrt(x_m) / (y - z)) * (sqrt(x_m) / (t - z)));
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_s * ((sqrt(x_m) / (y - z)) * (sqrt(x_m) / (t - z)))
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * ((Math.sqrt(x_m) / (y - z)) * (Math.sqrt(x_m) / (t - z)));
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	return x_s * ((math.sqrt(x_m) / (y - z)) * (math.sqrt(x_m) / (t - z)))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * Float64(Float64(sqrt(x_m) / Float64(y - z)) * Float64(sqrt(x_m) / Float64(t - z))))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * ((sqrt(x_m) / (y - z)) * (sqrt(x_m) / (t - z)));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * N[(N[(N[Sqrt[x$95$m], $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[x$95$m], $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.6%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-sqr-sqrt 43.0%

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

   2. times-frac 49.4%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

4. Applied egg-rr 49.4%

   \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

5. Final simplification 49.4%

   \[\leadsto \frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z} \]
6. Add Preprocessing

Alternative 2: 49.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{y \cdot t}\\ t_2 := \frac{\frac{x\_m}{y}}{t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+284}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+249}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6600000000:\\ \;\;\;\;\frac{-x\_m}{y \cdot z}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{-x\_m}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ x_m (* y t))) (t_2 (/ (/ x_m y) t)))
   (*
    x_s
    (if (<= y -5.5e+284)
      t_2
      (if (<= y -3.1e+249)
        t_1
        (if (<= y -6.2e+32)
          t_2
          (if (<= y -6600000000.0)
            (/ (- x_m) (* y z))
            (if (<= y -8.2e-8)
              t_1
              (if (<= y 3.5e+16) (/ (/ (- x_m) t) z) (/ (/ x_m t) y))))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / (y * t);
	double t_2 = (x_m / y) / t;
	double tmp;
	if (y <= -5.5e+284) {
		tmp = t_2;
	} else if (y <= -3.1e+249) {
		tmp = t_1;
	} else if (y <= -6.2e+32) {
		tmp = t_2;
	} else if (y <= -6600000000.0) {
		tmp = -x_m / (y * z);
	} else if (y <= -8.2e-8) {
		tmp = t_1;
	} else if (y <= 3.5e+16) {
		tmp = (-x_m / t) / z;
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x_m / (y * t)
    t_2 = (x_m / y) / t
    if (y <= (-5.5d+284)) then
        tmp = t_2
    else if (y <= (-3.1d+249)) then
        tmp = t_1
    else if (y <= (-6.2d+32)) then
        tmp = t_2
    else if (y <= (-6600000000.0d0)) then
        tmp = -x_m / (y * z)
    else if (y <= (-8.2d-8)) then
        tmp = t_1
    else if (y <= 3.5d+16) then
        tmp = (-x_m / t) / z
    else
        tmp = (x_m / t) / y
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / (y * t);
	double t_2 = (x_m / y) / t;
	double tmp;
	if (y <= -5.5e+284) {
		tmp = t_2;
	} else if (y <= -3.1e+249) {
		tmp = t_1;
	} else if (y <= -6.2e+32) {
		tmp = t_2;
	} else if (y <= -6600000000.0) {
		tmp = -x_m / (y * z);
	} else if (y <= -8.2e-8) {
		tmp = t_1;
	} else if (y <= 3.5e+16) {
		tmp = (-x_m / t) / z;
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m / (y * t)
	t_2 = (x_m / y) / t
	tmp = 0
	if y <= -5.5e+284:
		tmp = t_2
	elif y <= -3.1e+249:
		tmp = t_1
	elif y <= -6.2e+32:
		tmp = t_2
	elif y <= -6600000000.0:
		tmp = -x_m / (y * z)
	elif y <= -8.2e-8:
		tmp = t_1
	elif y <= 3.5e+16:
		tmp = (-x_m / t) / z
	else:
		tmp = (x_m / t) / y
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m / Float64(y * t))
	t_2 = Float64(Float64(x_m / y) / t)
	tmp = 0.0
	if (y <= -5.5e+284)
		tmp = t_2;
	elseif (y <= -3.1e+249)
		tmp = t_1;
	elseif (y <= -6.2e+32)
		tmp = t_2;
	elseif (y <= -6600000000.0)
		tmp = Float64(Float64(-x_m) / Float64(y * z));
	elseif (y <= -8.2e-8)
		tmp = t_1;
	elseif (y <= 3.5e+16)
		tmp = Float64(Float64(Float64(-x_m) / t) / z);
	else
		tmp = Float64(Float64(x_m / t) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m / (y * t);
	t_2 = (x_m / y) / t;
	tmp = 0.0;
	if (y <= -5.5e+284)
		tmp = t_2;
	elseif (y <= -3.1e+249)
		tmp = t_1;
	elseif (y <= -6.2e+32)
		tmp = t_2;
	elseif (y <= -6600000000.0)
		tmp = -x_m / (y * z);
	elseif (y <= -8.2e-8)
		tmp = t_1;
	elseif (y <= 3.5e+16)
		tmp = (-x_m / t) / z;
	else
		tmp = (x_m / t) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -5.5e+284], t$95$2, If[LessEqual[y, -3.1e+249], t$95$1, If[LessEqual[y, -6.2e+32], t$95$2, If[LessEqual[y, -6600000000.0], N[((-x$95$m) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e-8], t$95$1, If[LessEqual[y, 3.5e+16], N[(N[((-x$95$m) / t), $MachinePrecision] / z), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]]]]]), $MachinePrecision]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.5e284 or -3.10000000000000015e249 < y < -6.19999999999999986e32

   1. Initial program 81.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 76.3%

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

      1. *-commutative 76.3%

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

      2. associate-/r* 85.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 85.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around inf 63.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]
   7. Step-by-step derivation

      1. associate-/l/ 52.6%

         \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]

      2. clear-num 52.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot t}{x}}} \]

      3. associate-*l/ 70.1%

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot t}} \]

      4. associate-/r* 70.1%

         \[\leadsto \color{blue}{\frac{\frac{1}{\frac{y}{x}}}{t}} \]

      5. div-inv 70.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}} \cdot \frac{1}{t}} \]

      6. clear-num 71.2%

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot \frac{1}{t} \]

   8. Applied egg-rr 71.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]
   9. Step-by-step derivation

      1. un-div-inv 71.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   10. Applied egg-rr 71.2%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   if -5.5e284 < y < -3.10000000000000015e249 or -6.6e9 < y < -8.20000000000000063e-8

   1. Initial program 81.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 61.5%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]

   if -6.19999999999999986e32 < y < -6.6e9

   1. Initial program 100.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 55.4%

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

      1. *-commutative 55.4%

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

      2. associate-/r* 55.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 55.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around 0 55.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 55.4%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{y \cdot z}} \]

      2. neg-mul-1 55.4%

         \[\leadsto \frac{\color{blue}{-x}}{y \cdot z} \]

      3. *-commutative 55.4%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot y}} \]

   8. Simplified 55.4%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot y}} \]

   if -8.20000000000000063e-8 < y < 3.5e16

   1. Initial program 88.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 69.7%

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

      1. associate-*r/ 69.7%

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

      2. neg-mul-1 69.7%

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

   5. Simplified 69.7%

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

   6. Taylor expanded in z around 0 42.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 42.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 42.8%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

      3. *-commutative 42.8%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot t}} \]

   8. Simplified 42.8%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot t}} \]
   9. Step-by-step derivation

      1. distribute-frac-neg 42.8%

         \[\leadsto \color{blue}{-\frac{x}{z \cdot t}} \]

      2. *-commutative 42.8%

         \[\leadsto -\frac{x}{\color{blue}{t \cdot z}} \]

      3. associate-/r* 45.6%

         \[\leadsto -\color{blue}{\frac{\frac{x}{t}}{z}} \]

   10. Applied egg-rr 45.6%

       \[\leadsto \color{blue}{-\frac{\frac{x}{t}}{z}} \]

   if 3.5e16 < y

   1. Initial program 87.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-/r* 87.5%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around inf 51.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+284}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -6600000000:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+284}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+245}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \mathbf{elif}\;y \leq -6.1 \cdot 10^{+85}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x\_m}}\\ \mathbf{elif}\;y \leq -62000000:\\ \;\;\;\;\frac{\frac{-x\_m}{y}}{z}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+17}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -5.5e+284)
    (/ (/ x_m y) t)
    (if (<= y -1.6e+245)
      (/ x_m (* y t))
      (if (<= y -6.1e+85)
        (/ 1.0 (* t (/ y x_m)))
        (if (<= y -62000000.0)
          (/ (/ (- x_m) y) z)
          (if (<= y 1.42e+17) (* (/ x_m z) (/ -1.0 t)) (/ (/ x_m t) y))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e+284) {
		tmp = (x_m / y) / t;
	} else if (y <= -1.6e+245) {
		tmp = x_m / (y * t);
	} else if (y <= -6.1e+85) {
		tmp = 1.0 / (t * (y / x_m));
	} else if (y <= -62000000.0) {
		tmp = (-x_m / y) / z;
	} else if (y <= 1.42e+17) {
		tmp = (x_m / z) * (-1.0 / t);
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.5d+284)) then
        tmp = (x_m / y) / t
    else if (y <= (-1.6d+245)) then
        tmp = x_m / (y * t)
    else if (y <= (-6.1d+85)) then
        tmp = 1.0d0 / (t * (y / x_m))
    else if (y <= (-62000000.0d0)) then
        tmp = (-x_m / y) / z
    else if (y <= 1.42d+17) then
        tmp = (x_m / z) * ((-1.0d0) / t)
    else
        tmp = (x_m / t) / y
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e+284) {
		tmp = (x_m / y) / t;
	} else if (y <= -1.6e+245) {
		tmp = x_m / (y * t);
	} else if (y <= -6.1e+85) {
		tmp = 1.0 / (t * (y / x_m));
	} else if (y <= -62000000.0) {
		tmp = (-x_m / y) / z;
	} else if (y <= 1.42e+17) {
		tmp = (x_m / z) * (-1.0 / t);
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -5.5e+284:
		tmp = (x_m / y) / t
	elif y <= -1.6e+245:
		tmp = x_m / (y * t)
	elif y <= -6.1e+85:
		tmp = 1.0 / (t * (y / x_m))
	elif y <= -62000000.0:
		tmp = (-x_m / y) / z
	elif y <= 1.42e+17:
		tmp = (x_m / z) * (-1.0 / t)
	else:
		tmp = (x_m / t) / y
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -5.5e+284)
		tmp = Float64(Float64(x_m / y) / t);
	elseif (y <= -1.6e+245)
		tmp = Float64(x_m / Float64(y * t));
	elseif (y <= -6.1e+85)
		tmp = Float64(1.0 / Float64(t * Float64(y / x_m)));
	elseif (y <= -62000000.0)
		tmp = Float64(Float64(Float64(-x_m) / y) / z);
	elseif (y <= 1.42e+17)
		tmp = Float64(Float64(x_m / z) * Float64(-1.0 / t));
	else
		tmp = Float64(Float64(x_m / t) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e+284)
		tmp = (x_m / y) / t;
	elseif (y <= -1.6e+245)
		tmp = x_m / (y * t);
	elseif (y <= -6.1e+85)
		tmp = 1.0 / (t * (y / x_m));
	elseif (y <= -62000000.0)
		tmp = (-x_m / y) / z;
	elseif (y <= 1.42e+17)
		tmp = (x_m / z) * (-1.0 / t);
	else
		tmp = (x_m / t) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -5.5e+284], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, -1.6e+245], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.1e+85], N[(1.0 / N[(t * N[(y / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -62000000.0], N[(N[((-x$95$m) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.42e+17], N[(N[(x$95$m / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]]]]), $MachinePrecision]

Derivation

1. Split input into 6 regimes

2. if y < -5.5e284

   1. Initial program 69.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.0%

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

      1. *-commutative 69.0%

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

      2. associate-/r* 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around inf 69.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]
   7. Step-by-step derivation

      1. associate-/l/ 38.4%

         \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]

      2. clear-num 38.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot t}{x}}} \]

      3. associate-*l/ 99.7%

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot t}} \]

      4. associate-/r* 100.0%

         \[\leadsto \color{blue}{\frac{\frac{1}{\frac{y}{x}}}{t}} \]

      5. div-inv 100.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}} \cdot \frac{1}{t}} \]

      6. clear-num 100.0%

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot \frac{1}{t} \]

   8. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]
   9. Step-by-step derivation

      1. un-div-inv 100.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   10. Applied egg-rr 100.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   if -5.5e284 < y < -1.60000000000000012e245

   1. Initial program 83.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 69.4%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]

   if -1.60000000000000012e245 < y < -6.09999999999999981e85

   1. Initial program 77.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 52.5%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   4. Step-by-step derivation

      1. clear-num 52.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{t \cdot y}{x}}} \]

      2. inv-pow 52.5%

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

      3. *-commutative 52.5%

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

      4. associate-/l* 66.8%

         \[\leadsto {\color{blue}{\left(\frac{y}{\frac{x}{t}}\right)}}^{-1} \]

   5. Applied egg-rr 66.8%

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

      1. unpow-1 66.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{\frac{x}{t}}}} \]

      2. associate-/r/ 72.5%

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot t}} \]

   7. Simplified 72.5%

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{x} \cdot t}} \]

   if -6.09999999999999981e85 < y < -6.2e7

   1. Initial program 94.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 47.7%

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

      2. times-frac 52.8%

         \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

   4. Applied egg-rr 52.8%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 52.7%

         \[\leadsto \color{blue}{\frac{\frac{\sqrt{x}}{y - z} \cdot \sqrt{x}}{t - z}} \]

      2. clear-num 52.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t - z}{\frac{\sqrt{x}}{y - z} \cdot \sqrt{x}}}} \]

      3. associate-*l/ 52.7%

         \[\leadsto \frac{1}{\frac{t - z}{\color{blue}{\frac{\sqrt{x} \cdot \sqrt{x}}{y - z}}}} \]

      4. add-sqr-sqrt 99.7%

         \[\leadsto \frac{1}{\frac{t - z}{\frac{\color{blue}{x}}{y - z}}} \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{t - z}{\frac{x}{y - z}}}} \]

   7. Taylor expanded in y around inf 74.6%

      \[\leadsto \frac{1}{\frac{t - z}{\color{blue}{\frac{x}{y}}}} \]

   8. Taylor expanded in t around 0 38.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 38.9%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. associate-/r* 38.8%

         \[\leadsto -\color{blue}{\frac{\frac{x}{y}}{z}} \]

      3. distribute-neg-frac 38.8%

         \[\leadsto \color{blue}{\frac{-\frac{x}{y}}{z}} \]

      4. mul-1-neg 38.8%

         \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{y}}}{z} \]

      5. *-commutative 38.8%

         \[\leadsto \frac{\color{blue}{\frac{x}{y} \cdot -1}}{z} \]

      6. associate-*l/ 38.8%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot -1}{y}}}{z} \]

      7. *-commutative 38.8%

         \[\leadsto \frac{\frac{\color{blue}{-1 \cdot x}}{y}}{z} \]

      8. neg-mul-1 38.8%

         \[\leadsto \frac{\frac{\color{blue}{-x}}{y}}{z} \]

   10. Simplified 38.8%

       \[\leadsto \color{blue}{\frac{\frac{-x}{y}}{z}} \]

   if -6.2e7 < y < 1.42e17

   1. Initial program 88.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 69.9%

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

      1. associate-*r/ 69.9%

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

      2. neg-mul-1 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in z around 0 43.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 43.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 43.1%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

      3. *-commutative 43.1%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot t}} \]

   8. Simplified 43.1%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot t}} \]
   9. Step-by-step derivation

      1. neg-mul-1 43.1%

         \[\leadsto \frac{\color{blue}{-1 \cdot x}}{z \cdot t} \]

      2. *-commutative 43.1%

         \[\leadsto \frac{-1 \cdot x}{\color{blue}{t \cdot z}} \]

      3. times-frac 47.3%

         \[\leadsto \color{blue}{\frac{-1}{t} \cdot \frac{x}{z}} \]

   10. Applied egg-rr 47.3%

       \[\leadsto \color{blue}{\frac{-1}{t} \cdot \frac{x}{z}} \]

   if 1.42e17 < y

   1. Initial program 87.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-/r* 87.5%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around inf 51.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+284}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+245}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq -6.1 \cdot 10^{+85}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq -62000000:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{\frac{x\_m}{y}}{t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+249}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -240000:\\ \;\;\;\;\frac{\frac{-x\_m}{y}}{z}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{-x\_m}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x_m y) t)))
   (*
    x_s
    (if (<= y -5.5e+284)
      t_1
      (if (<= y -3e+249)
        (/ x_m (* y t))
        (if (<= y -2.7e+85)
          t_1
          (if (<= y -240000.0)
            (/ (/ (- x_m) y) z)
            (if (<= y 3.1e+16) (/ (/ (- x_m) t) z) (/ (/ x_m t) y)))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / y) / t;
	double tmp;
	if (y <= -5.5e+284) {
		tmp = t_1;
	} else if (y <= -3e+249) {
		tmp = x_m / (y * t);
	} else if (y <= -2.7e+85) {
		tmp = t_1;
	} else if (y <= -240000.0) {
		tmp = (-x_m / y) / z;
	} else if (y <= 3.1e+16) {
		tmp = (-x_m / t) / z;
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x_m / y) / t
    if (y <= (-5.5d+284)) then
        tmp = t_1
    else if (y <= (-3d+249)) then
        tmp = x_m / (y * t)
    else if (y <= (-2.7d+85)) then
        tmp = t_1
    else if (y <= (-240000.0d0)) then
        tmp = (-x_m / y) / z
    else if (y <= 3.1d+16) then
        tmp = (-x_m / t) / z
    else
        tmp = (x_m / t) / y
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / y) / t;
	double tmp;
	if (y <= -5.5e+284) {
		tmp = t_1;
	} else if (y <= -3e+249) {
		tmp = x_m / (y * t);
	} else if (y <= -2.7e+85) {
		tmp = t_1;
	} else if (y <= -240000.0) {
		tmp = (-x_m / y) / z;
	} else if (y <= 3.1e+16) {
		tmp = (-x_m / t) / z;
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / y) / t
	tmp = 0
	if y <= -5.5e+284:
		tmp = t_1
	elif y <= -3e+249:
		tmp = x_m / (y * t)
	elif y <= -2.7e+85:
		tmp = t_1
	elif y <= -240000.0:
		tmp = (-x_m / y) / z
	elif y <= 3.1e+16:
		tmp = (-x_m / t) / z
	else:
		tmp = (x_m / t) / y
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / y) / t)
	tmp = 0.0
	if (y <= -5.5e+284)
		tmp = t_1;
	elseif (y <= -3e+249)
		tmp = Float64(x_m / Float64(y * t));
	elseif (y <= -2.7e+85)
		tmp = t_1;
	elseif (y <= -240000.0)
		tmp = Float64(Float64(Float64(-x_m) / y) / z);
	elseif (y <= 3.1e+16)
		tmp = Float64(Float64(Float64(-x_m) / t) / z);
	else
		tmp = Float64(Float64(x_m / t) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / y) / t;
	tmp = 0.0;
	if (y <= -5.5e+284)
		tmp = t_1;
	elseif (y <= -3e+249)
		tmp = x_m / (y * t);
	elseif (y <= -2.7e+85)
		tmp = t_1;
	elseif (y <= -240000.0)
		tmp = (-x_m / y) / z;
	elseif (y <= 3.1e+16)
		tmp = (-x_m / t) / z;
	else
		tmp = (x_m / t) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -5.5e+284], t$95$1, If[LessEqual[y, -3e+249], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e+85], t$95$1, If[LessEqual[y, -240000.0], N[(N[((-x$95$m) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 3.1e+16], N[(N[((-x$95$m) / t), $MachinePrecision] / z), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]]]]), $MachinePrecision]]

Derivation

1. Split input into 5 regimes

2. if y < -5.5e284 or -3.00000000000000016e249 < y < -2.69999999999999983e85

   1. Initial program 76.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-/r* 90.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 90.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around inf 65.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]
   7. Step-by-step derivation

      1. associate-/l/ 49.4%

         \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]

      2. clear-num 49.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot t}{x}}} \]

      3. associate-*l/ 75.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot t}} \]

      4. associate-/r* 75.1%

         \[\leadsto \color{blue}{\frac{\frac{1}{\frac{y}{x}}}{t}} \]

      5. div-inv 75.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}} \cdot \frac{1}{t}} \]

      6. clear-num 76.5%

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot \frac{1}{t} \]

   8. Applied egg-rr 76.5%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]
   9. Step-by-step derivation

      1. un-div-inv 76.5%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   10. Applied egg-rr 76.5%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   if -5.5e284 < y < -3.00000000000000016e249

   1. Initial program 81.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.0%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]

   if -2.69999999999999983e85 < y < -2.4e5

   1. Initial program 94.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 47.7%

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

      2. times-frac 52.8%

         \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

   4. Applied egg-rr 52.8%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 52.7%

         \[\leadsto \color{blue}{\frac{\frac{\sqrt{x}}{y - z} \cdot \sqrt{x}}{t - z}} \]

      2. clear-num 52.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t - z}{\frac{\sqrt{x}}{y - z} \cdot \sqrt{x}}}} \]

      3. associate-*l/ 52.7%

         \[\leadsto \frac{1}{\frac{t - z}{\color{blue}{\frac{\sqrt{x} \cdot \sqrt{x}}{y - z}}}} \]

      4. add-sqr-sqrt 99.7%

         \[\leadsto \frac{1}{\frac{t - z}{\frac{\color{blue}{x}}{y - z}}} \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{t - z}{\frac{x}{y - z}}}} \]

   7. Taylor expanded in y around inf 74.6%

      \[\leadsto \frac{1}{\frac{t - z}{\color{blue}{\frac{x}{y}}}} \]

   8. Taylor expanded in t around 0 38.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y \cdot z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 38.9%

         \[\leadsto \color{blue}{-\frac{x}{y \cdot z}} \]

      2. associate-/r* 38.8%

         \[\leadsto -\color{blue}{\frac{\frac{x}{y}}{z}} \]

      3. distribute-neg-frac 38.8%

         \[\leadsto \color{blue}{\frac{-\frac{x}{y}}{z}} \]

      4. mul-1-neg 38.8%

         \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{y}}}{z} \]

      5. *-commutative 38.8%

         \[\leadsto \frac{\color{blue}{\frac{x}{y} \cdot -1}}{z} \]

      6. associate-*l/ 38.8%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot -1}{y}}}{z} \]

      7. *-commutative 38.8%

         \[\leadsto \frac{\frac{\color{blue}{-1 \cdot x}}{y}}{z} \]

      8. neg-mul-1 38.8%

         \[\leadsto \frac{\frac{\color{blue}{-x}}{y}}{z} \]

   10. Simplified 38.8%

       \[\leadsto \color{blue}{\frac{\frac{-x}{y}}{z}} \]

   if -2.4e5 < y < 3.1e16

   1. Initial program 88.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 69.9%

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

      1. associate-*r/ 69.9%

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

      2. neg-mul-1 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in z around 0 43.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 43.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 43.1%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

      3. *-commutative 43.1%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot t}} \]

   8. Simplified 43.1%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot t}} \]
   9. Step-by-step derivation

      1. distribute-frac-neg 43.1%

         \[\leadsto \color{blue}{-\frac{x}{z \cdot t}} \]

      2. *-commutative 43.1%

         \[\leadsto -\frac{x}{\color{blue}{t \cdot z}} \]

      3. associate-/r* 45.8%

         \[\leadsto -\color{blue}{\frac{\frac{x}{t}}{z}} \]

   10. Applied egg-rr 45.8%

       \[\leadsto \color{blue}{-\frac{\frac{x}{t}}{z}} \]

   if 3.1e16 < y

   1. Initial program 87.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-/r* 87.5%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around inf 51.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+284}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+85}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -240000:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x\_m}{t - z}\\ t_2 := \left(y - z\right) \cdot \left(t - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{t\_1}{y}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\frac{x\_m}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \frac{-1}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ x_m (- t z))) (t_2 (* (- y z) (- t z))))
   (*
    x_s
    (if (<= t_2 (- INFINITY))
      (/ t_1 y)
      (if (<= t_2 2e+303) (/ x_m t_2) (* t_1 (/ -1.0 z)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / (t - z);
	double t_2 = (y - z) * (t - z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1 / y;
	} else if (t_2 <= 2e+303) {
		tmp = x_m / t_2;
	} else {
		tmp = t_1 * (-1.0 / z);
	}
	return x_s * tmp;
}

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = x_m / (t - z);
	double t_2 = (y - z) * (t - z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1 / y;
	} else if (t_2 <= 2e+303) {
		tmp = x_m / t_2;
	} else {
		tmp = t_1 * (-1.0 / z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = x_m / (t - z)
	t_2 = (y - z) * (t - z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1 / y
	elif t_2 <= 2e+303:
		tmp = x_m / t_2
	else:
		tmp = t_1 * (-1.0 / z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(x_m / Float64(t - z))
	t_2 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(t_1 / y);
	elseif (t_2 <= 2e+303)
		tmp = Float64(x_m / t_2);
	else
		tmp = Float64(t_1 * Float64(-1.0 / z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = x_m / (t - z);
	t_2 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1 / y;
	elseif (t_2 <= 2e+303)
		tmp = x_m / t_2;
	else
		tmp = t_1 * (-1.0 / z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$2, (-Infinity)], N[(t$95$1 / y), $MachinePrecision], If[LessEqual[t$95$2, 2e+303], N[(x$95$m / t$95$2), $MachinePrecision], N[(t$95$1 * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 56.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 40.3%

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

      1. *-commutative 40.3%

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

      2. associate-/r* 80.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 80.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 2e303

   1. Initial program 96.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   if 2e303 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 76.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-un-lft-identity 76.3%

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

      2. times-frac 99.9%

         \[\leadsto \color{blue}{\frac{1}{y - z} \cdot \frac{x}{t - z}} \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{1}{y - z} \cdot \frac{x}{t - z}} \]

   5. Taylor expanded in y around 0 89.8%

      \[\leadsto \color{blue}{\frac{-1}{z}} \cdot \frac{x}{t - z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\frac{x\_m}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x\_m}}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (*
    x_s
    (if (<= t_1 (- INFINITY))
      (/ (/ x_m (- t z)) y)
      (if (<= t_1 2e+303) (/ x_m t_1) (/ (/ -1.0 z) (/ (- t z) x_m)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x_m / (t - z)) / y;
	} else if (t_1 <= 2e+303) {
		tmp = x_m / t_1;
	} else {
		tmp = (-1.0 / z) / ((t - z) / x_m);
	}
	return x_s * tmp;
}

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x_m / (t - z)) / y;
	} else if (t_1 <= 2e+303) {
		tmp = x_m / t_1;
	} else {
		tmp = (-1.0 / z) / ((t - z) / x_m);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x_m / (t - z)) / y
	elif t_1 <= 2e+303:
		tmp = x_m / t_1
	else:
		tmp = (-1.0 / z) / ((t - z) / x_m)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x_m / Float64(t - z)) / y);
	elseif (t_1 <= 2e+303)
		tmp = Float64(x_m / t_1);
	else
		tmp = Float64(Float64(-1.0 / z) / Float64(Float64(t - z) / x_m));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x_m / (t - z)) / y;
	elseif (t_1 <= 2e+303)
		tmp = x_m / t_1;
	else
		tmp = (-1.0 / z) / ((t - z) / x_m);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[t$95$1, (-Infinity)], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 2e+303], N[(x$95$m / t$95$1), $MachinePrecision], N[(N[(-1.0 / z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 56.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 40.3%

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

      1. *-commutative 40.3%

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

      2. associate-/r* 80.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 80.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 2e303

   1. Initial program 96.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   if 2e303 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 76.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 38.9%

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

      2. times-frac 51.8%

         \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

   4. Applied egg-rr 51.8%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]
   5. Step-by-step derivation

      1. frac-times 38.9%

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

      2. add-sqr-sqrt 76.3%

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

      3. *-un-lft-identity 76.3%

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

      4. frac-times 99.9%

         \[\leadsto \color{blue}{\frac{1}{y - z} \cdot \frac{x}{t - z}} \]

      5. clear-num 99.9%

         \[\leadsto \frac{1}{y - z} \cdot \color{blue}{\frac{1}{\frac{t - z}{x}}} \]

      6. un-div-inv 99.9%

         \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]

   7. Taylor expanded in y around 0 89.9%

      \[\leadsto \frac{\color{blue}{\frac{-1}{z}}}{\frac{t - z}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{z}}{\frac{t - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{\frac{x\_m}{y}}{t}\\ t_2 := \frac{x\_m}{z} \cdot \frac{-1}{t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-177}:\\ \;\;\;\;-\frac{x\_m}{z \cdot t}\\ \mathbf{elif}\;z \leq 1000000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x_m y) t)) (t_2 (* (/ x_m z) (/ -1.0 t))))
   (*
    x_s
    (if (<= z -8.5e-21)
      t_2
      (if (<= z -5.2e-120)
        t_1
        (if (<= z -1.55e-177)
          (- (/ x_m (* z t)))
          (if (<= z 1000000000000.0) t_1 t_2)))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / y) / t;
	double t_2 = (x_m / z) * (-1.0 / t);
	double tmp;
	if (z <= -8.5e-21) {
		tmp = t_2;
	} else if (z <= -5.2e-120) {
		tmp = t_1;
	} else if (z <= -1.55e-177) {
		tmp = -(x_m / (z * t));
	} else if (z <= 1000000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x_m / y) / t
    t_2 = (x_m / z) * ((-1.0d0) / t)
    if (z <= (-8.5d-21)) then
        tmp = t_2
    else if (z <= (-5.2d-120)) then
        tmp = t_1
    else if (z <= (-1.55d-177)) then
        tmp = -(x_m / (z * t))
    else if (z <= 1000000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / y) / t;
	double t_2 = (x_m / z) * (-1.0 / t);
	double tmp;
	if (z <= -8.5e-21) {
		tmp = t_2;
	} else if (z <= -5.2e-120) {
		tmp = t_1;
	} else if (z <= -1.55e-177) {
		tmp = -(x_m / (z * t));
	} else if (z <= 1000000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / y) / t
	t_2 = (x_m / z) * (-1.0 / t)
	tmp = 0
	if z <= -8.5e-21:
		tmp = t_2
	elif z <= -5.2e-120:
		tmp = t_1
	elif z <= -1.55e-177:
		tmp = -(x_m / (z * t))
	elif z <= 1000000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / y) / t)
	t_2 = Float64(Float64(x_m / z) * Float64(-1.0 / t))
	tmp = 0.0
	if (z <= -8.5e-21)
		tmp = t_2;
	elseif (z <= -5.2e-120)
		tmp = t_1;
	elseif (z <= -1.55e-177)
		tmp = Float64(-Float64(x_m / Float64(z * t)));
	elseif (z <= 1000000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / y) / t;
	t_2 = (x_m / z) * (-1.0 / t);
	tmp = 0.0;
	if (z <= -8.5e-21)
		tmp = t_2;
	elseif (z <= -5.2e-120)
		tmp = t_1;
	elseif (z <= -1.55e-177)
		tmp = -(x_m / (z * t));
	elseif (z <= 1000000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x$95$m / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, -8.5e-21], t$95$2, If[LessEqual[z, -5.2e-120], t$95$1, If[LessEqual[z, -1.55e-177], (-N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision]), If[LessEqual[z, 1000000000000.0], t$95$1, t$95$2]]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999993e-21 or 1e12 < z

   1. Initial program 86.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.8%

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

      1. associate-*r/ 74.8%

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

      2. neg-mul-1 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in z around 0 44.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 44.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 44.7%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

      3. *-commutative 44.7%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot t}} \]

   8. Simplified 44.7%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot t}} \]
   9. Step-by-step derivation

      1. neg-mul-1 44.7%

         \[\leadsto \frac{\color{blue}{-1 \cdot x}}{z \cdot t} \]

      2. *-commutative 44.7%

         \[\leadsto \frac{-1 \cdot x}{\color{blue}{t \cdot z}} \]

      3. times-frac 49.8%

         \[\leadsto \color{blue}{\frac{-1}{t} \cdot \frac{x}{z}} \]

   10. Applied egg-rr 49.8%

       \[\leadsto \color{blue}{\frac{-1}{t} \cdot \frac{x}{z}} \]

   if -8.4999999999999993e-21 < z < -5.2000000000000002e-120 or -1.55000000000000009e-177 < z < 1e12

   1. Initial program 85.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-/r* 82.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 82.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around inf 71.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]
   7. Step-by-step derivation

      1. associate-/l/ 62.6%

         \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]

      2. clear-num 62.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot t}{x}}} \]

      3. associate-*l/ 74.7%

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot t}} \]

      4. associate-/r* 75.3%

         \[\leadsto \color{blue}{\frac{\frac{1}{\frac{y}{x}}}{t}} \]

      5. div-inv 75.2%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}} \cdot \frac{1}{t}} \]

      6. clear-num 75.7%

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot \frac{1}{t} \]

   8. Applied egg-rr 75.7%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]
   9. Step-by-step derivation

      1. un-div-inv 75.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   10. Applied egg-rr 75.9%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   if -5.2000000000000002e-120 < z < -1.55000000000000009e-177

   1. Initial program 99.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 69.4%

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

      1. associate-*r/ 69.4%

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

      2. neg-mul-1 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in z around 0 50.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 50.8%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 50.8%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

      3. *-commutative 50.8%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot t}} \]

   8. Simplified 50.8%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-177}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{elif}\;z \leq 1000000000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{\frac{x\_m}{y}}{t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+249}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{-x\_m}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x_m y) t)))
   (*
    x_s
    (if (<= y -5.5e+284)
      t_1
      (if (<= y -3.1e+249)
        (/ x_m (* y t))
        (if (<= y -1.9e+45)
          t_1
          (if (<= y 5.1e+16) (/ (/ (- x_m) t) z) (/ (/ x_m t) y))))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / y) / t;
	double tmp;
	if (y <= -5.5e+284) {
		tmp = t_1;
	} else if (y <= -3.1e+249) {
		tmp = x_m / (y * t);
	} else if (y <= -1.9e+45) {
		tmp = t_1;
	} else if (y <= 5.1e+16) {
		tmp = (-x_m / t) / z;
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x_m / y) / t
    if (y <= (-5.5d+284)) then
        tmp = t_1
    else if (y <= (-3.1d+249)) then
        tmp = x_m / (y * t)
    else if (y <= (-1.9d+45)) then
        tmp = t_1
    else if (y <= 5.1d+16) then
        tmp = (-x_m / t) / z
    else
        tmp = (x_m / t) / y
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double t_1 = (x_m / y) / t;
	double tmp;
	if (y <= -5.5e+284) {
		tmp = t_1;
	} else if (y <= -3.1e+249) {
		tmp = x_m / (y * t);
	} else if (y <= -1.9e+45) {
		tmp = t_1;
	} else if (y <= 5.1e+16) {
		tmp = (-x_m / t) / z;
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	t_1 = (x_m / y) / t
	tmp = 0
	if y <= -5.5e+284:
		tmp = t_1
	elif y <= -3.1e+249:
		tmp = x_m / (y * t)
	elif y <= -1.9e+45:
		tmp = t_1
	elif y <= 5.1e+16:
		tmp = (-x_m / t) / z
	else:
		tmp = (x_m / t) / y
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	t_1 = Float64(Float64(x_m / y) / t)
	tmp = 0.0
	if (y <= -5.5e+284)
		tmp = t_1;
	elseif (y <= -3.1e+249)
		tmp = Float64(x_m / Float64(y * t));
	elseif (y <= -1.9e+45)
		tmp = t_1;
	elseif (y <= 5.1e+16)
		tmp = Float64(Float64(Float64(-x_m) / t) / z);
	else
		tmp = Float64(Float64(x_m / t) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	t_1 = (x_m / y) / t;
	tmp = 0.0;
	if (y <= -5.5e+284)
		tmp = t_1;
	elseif (y <= -3.1e+249)
		tmp = x_m / (y * t);
	elseif (y <= -1.9e+45)
		tmp = t_1;
	elseif (y <= 5.1e+16)
		tmp = (-x_m / t) / z;
	else
		tmp = (x_m / t) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -5.5e+284], t$95$1, If[LessEqual[y, -3.1e+249], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e+45], t$95$1, If[LessEqual[y, 5.1e+16], N[(N[((-x$95$m) / t), $MachinePrecision] / z), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if y < -5.5e284 or -3.10000000000000015e249 < y < -1.9000000000000001e45

   1. Initial program 82.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-/r* 86.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 86.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around inf 63.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]
   7. Step-by-step derivation

      1. associate-/l/ 52.6%

         \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]

      2. clear-num 52.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot t}{x}}} \]

      3. associate-*l/ 70.8%

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot t}} \]

      4. associate-/r* 70.9%

         \[\leadsto \color{blue}{\frac{\frac{1}{\frac{y}{x}}}{t}} \]

      5. div-inv 70.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}} \cdot \frac{1}{t}} \]

      6. clear-num 72.0%

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot \frac{1}{t} \]

   8. Applied egg-rr 72.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]
   9. Step-by-step derivation

      1. un-div-inv 72.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   10. Applied egg-rr 72.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   if -5.5e284 < y < -3.10000000000000015e249

   1. Initial program 81.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.0%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]

   if -1.9000000000000001e45 < y < 5.1e16

   1. Initial program 88.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 68.3%

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

      1. associate-*r/ 68.3%

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

      2. neg-mul-1 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in z around 0 41.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 41.6%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{t \cdot z}} \]

      2. neg-mul-1 41.6%

         \[\leadsto \frac{\color{blue}{-x}}{t \cdot z} \]

      3. *-commutative 41.6%

         \[\leadsto \frac{-x}{\color{blue}{z \cdot t}} \]

   8. Simplified 41.6%

      \[\leadsto \color{blue}{\frac{-x}{z \cdot t}} \]
   9. Step-by-step derivation

      1. distribute-frac-neg 41.6%

         \[\leadsto \color{blue}{-\frac{x}{z \cdot t}} \]

      2. *-commutative 41.6%

         \[\leadsto -\frac{x}{\color{blue}{t \cdot z}} \]

      3. associate-/r* 44.2%

         \[\leadsto -\color{blue}{\frac{\frac{x}{t}}{z}} \]

   10. Applied egg-rr 44.2%

       \[\leadsto \color{blue}{-\frac{\frac{x}{t}}{z}} \]

   if 5.1e16 < y

   1. Initial program 87.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-/r* 87.5%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 87.5%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around inf 51.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+284}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+45}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{x\_m}{t - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -6.8e+18)
    (/ (/ x_m y) (- t z))
    (if (<= y 9.5e-201)
      (* (/ x_m (- t z)) (/ -1.0 z))
      (/ (/ x_m t) (- y z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+18) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 9.5e-201) {
		tmp = (x_m / (t - z)) * (-1.0 / z);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.8d+18)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 9.5d-201) then
        tmp = (x_m / (t - z)) * ((-1.0d0) / z)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+18) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 9.5e-201) {
		tmp = (x_m / (t - z)) * (-1.0 / z);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -6.8e+18:
		tmp = (x_m / y) / (t - z)
	elif y <= 9.5e-201:
		tmp = (x_m / (t - z)) * (-1.0 / z)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -6.8e+18)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 9.5e-201)
		tmp = Float64(Float64(x_m / Float64(t - z)) * Float64(-1.0 / z));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -6.8e+18)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 9.5e-201)
		tmp = (x_m / (t - z)) * (-1.0 / z);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -6.8e+18], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-201], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -6.8e18

   1. Initial program 81.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 44.8%

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

      2. times-frac 55.5%

         \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

   4. Applied egg-rr 55.5%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

   5. Taylor expanded in y around inf 77.1%

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

      1. associate-/r* 89.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   7. Simplified 89.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   if -6.8e18 < y < 9.5000000000000001e-201

   1. Initial program 87.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-un-lft-identity 87.9%

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

      2. times-frac 96.5%

         \[\leadsto \color{blue}{\frac{1}{y - z} \cdot \frac{x}{t - z}} \]

   4. Applied egg-rr 96.5%

      \[\leadsto \color{blue}{\frac{1}{y - z} \cdot \frac{x}{t - z}} \]

   5. Taylor expanded in y around 0 88.1%

      \[\leadsto \color{blue}{\frac{-1}{z}} \cdot \frac{x}{t - z} \]

   if 9.5000000000000001e-201 < y

   1. Initial program 88.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.5%

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

      1. associate-/r* 98.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   5. Simplified 98.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   6. Taylor expanded in t around inf 62.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-202}:\\ \;\;\;\;\frac{-x\_m}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -2.05e+16)
    (/ (/ x_m y) (- t z))
    (if (<= y 6.8e-202) (/ (- x_m) (* z (- t z))) (/ (/ x_m t) (- y z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.05e+16) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 6.8e-202) {
		tmp = -x_m / (z * (t - z));
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.05d+16)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 6.8d-202) then
        tmp = -x_m / (z * (t - z))
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -2.05e+16) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 6.8e-202) {
		tmp = -x_m / (z * (t - z));
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -2.05e+16:
		tmp = (x_m / y) / (t - z)
	elif y <= 6.8e-202:
		tmp = -x_m / (z * (t - z))
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -2.05e+16)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 6.8e-202)
		tmp = Float64(Float64(-x_m) / Float64(z * Float64(t - z)));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -2.05e+16)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 6.8e-202)
		tmp = -x_m / (z * (t - z));
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -2.05e+16], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-202], N[((-x$95$m) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -2.05e16

   1. Initial program 81.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 44.8%

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

      2. times-frac 55.5%

         \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

   4. Applied egg-rr 55.5%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

   5. Taylor expanded in y around inf 77.1%

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

      1. associate-/r* 89.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   7. Simplified 89.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   if -2.05e16 < y < 6.80000000000000025e-202

   1. Initial program 87.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.3%

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

      1. associate-*r/ 77.3%

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

      2. neg-mul-1 77.3%

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

   5. Simplified 77.3%

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

   if 6.80000000000000025e-202 < y

   1. Initial program 88.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.6%

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

      1. associate-/r* 98.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   5. Simplified 98.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   6. Taylor expanded in t around inf 61.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-202}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{-x\_m}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.95e-125)
    (/ (/ x_m (- t z)) y)
    (if (<= t 4.5e-22) (/ (/ (- x_m) z) (- y z)) (/ (/ x_m t) (- y z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.95e-125) {
		tmp = (x_m / (t - z)) / y;
	} else if (t <= 4.5e-22) {
		tmp = (-x_m / z) / (y - z);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.95d-125)) then
        tmp = (x_m / (t - z)) / y
    else if (t <= 4.5d-22) then
        tmp = (-x_m / z) / (y - z)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.95e-125) {
		tmp = (x_m / (t - z)) / y;
	} else if (t <= 4.5e-22) {
		tmp = (-x_m / z) / (y - z);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -1.95e-125:
		tmp = (x_m / (t - z)) / y
	elif t <= 4.5e-22:
		tmp = (-x_m / z) / (y - z)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -1.95e-125)
		tmp = Float64(Float64(x_m / Float64(t - z)) / y);
	elseif (t <= 4.5e-22)
		tmp = Float64(Float64(Float64(-x_m) / z) / Float64(y - z));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -1.95e-125)
		tmp = (x_m / (t - z)) / y;
	elseif (t <= 4.5e-22)
		tmp = (-x_m / z) / (y - z);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -1.95e-125], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4.5e-22], N[(N[((-x$95$m) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -1.94999999999999991e-125

   1. Initial program 89.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 62.0%

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

      1. *-commutative 62.0%

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

      2. associate-/r* 68.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 68.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   if -1.94999999999999991e-125 < t < 4.49999999999999987e-22

   1. Initial program 85.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. associate-/r* 82.6%

         \[\leadsto -\color{blue}{\frac{\frac{x}{z}}{y - z}} \]

      3. distribute-neg-frac 82.6%

         \[\leadsto \color{blue}{\frac{-\frac{x}{z}}{y - z}} \]

   5. Simplified 82.6%

      \[\leadsto \color{blue}{\frac{-\frac{x}{z}}{y - z}} \]

   if 4.49999999999999987e-22 < t

   1. Initial program 84.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.2%

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

      1. associate-/r* 96.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   5. Simplified 96.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   6. Taylor expanded in t around inf 88.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-125}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{elif}\;y \leq 10^{-200}:\\ \;\;\;\;\frac{\frac{-x\_m}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= y -4.2e+15)
    (/ (/ x_m y) (- t z))
    (if (<= y 1e-200) (/ (/ (- x_m) z) (- t z)) (/ (/ x_m t) (- y z))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e+15) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 1e-200) {
		tmp = (-x_m / z) / (t - z);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.2d+15)) then
        tmp = (x_m / y) / (t - z)
    else if (y <= 1d-200) then
        tmp = (-x_m / z) / (t - z)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e+15) {
		tmp = (x_m / y) / (t - z);
	} else if (y <= 1e-200) {
		tmp = (-x_m / z) / (t - z);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -4.2e+15:
		tmp = (x_m / y) / (t - z)
	elif y <= 1e-200:
		tmp = (-x_m / z) / (t - z)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -4.2e+15)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	elseif (y <= 1e-200)
		tmp = Float64(Float64(Float64(-x_m) / z) / Float64(t - z));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -4.2e+15)
		tmp = (x_m / y) / (t - z);
	elseif (y <= 1e-200)
		tmp = (-x_m / z) / (t - z);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -4.2e+15], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-200], N[(N[((-x$95$m) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if y < -4.2e15

   1. Initial program 81.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 44.8%

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

      2. times-frac 55.5%

         \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

   4. Applied egg-rr 55.5%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

   5. Taylor expanded in y around inf 77.1%

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

      1. associate-/r* 89.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   7. Simplified 89.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   if -4.2e15 < y < 9.9999999999999998e-201

   1. Initial program 87.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 35.4%

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

      2. times-frac 39.9%

         \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

   4. Applied egg-rr 39.9%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]
   5. Step-by-step derivation

      1. frac-times 35.4%

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

      2. add-sqr-sqrt 87.9%

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

      3. *-un-lft-identity 87.9%

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

      4. frac-times 96.5%

         \[\leadsto \color{blue}{\frac{1}{y - z} \cdot \frac{x}{t - z}} \]

      5. clear-num 96.4%

         \[\leadsto \frac{1}{y - z} \cdot \color{blue}{\frac{1}{\frac{t - z}{x}}} \]

      6. un-div-inv 96.5%

         \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]

   6. Applied egg-rr 96.5%

      \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]

   7. Taylor expanded in y around 0 77.6%

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

      1. associate-/r* 85.2%

         \[\leadsto -1 \cdot \color{blue}{\frac{\frac{x}{z}}{t - z}} \]

      2. associate-*r/ 85.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{z}}{t - z}} \]

      3. associate-*r/ 85.2%

         \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{t - z} \]

      4. neg-mul-1 85.2%

         \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{t - z} \]

   9. Simplified 85.2%

      \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z}} \]

   if 9.9999999999999998e-201 < y

   1. Initial program 88.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.5%

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

      1. associate-/r* 98.1%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   5. Simplified 98.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   6. Taylor expanded in t around inf 62.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 10^{-200}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+155} \lor \neg \left(z \leq 1.15 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -1.4e+155) (not (<= z 1.15e+95)))
    (/ x_m (* z (- t z)))
    (/ x_m (* (- y z) t)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+155) || !(z <= 1.15e+95)) {
		tmp = x_m / (z * (t - z));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.4d+155)) .or. (.not. (z <= 1.15d+95))) then
        tmp = x_m / (z * (t - z))
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e+155) || !(z <= 1.15e+95)) {
		tmp = x_m / (z * (t - z));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -1.4e+155) or not (z <= 1.15e+95):
		tmp = x_m / (z * (t - z))
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -1.4e+155) || !(z <= 1.15e+95))
		tmp = Float64(x_m / Float64(z * Float64(t - z)));
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -1.4e+155) || ~((z <= 1.15e+95)))
		tmp = x_m / (z * (t - z));
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -1.4e+155], N[Not[LessEqual[z, 1.15e+95]], $MachinePrecision]], N[(x$95$m / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -1.40000000000000008e155 or 1.14999999999999999e95 < z

   1. Initial program 79.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 78.9%

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

      1. associate-*r/ 78.9%

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

      2. neg-mul-1 78.9%

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

   5. Simplified 78.9%

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

      1. associate-/r* 94.4%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z}} \]

      2. add0 94.4%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z} + 0} \]

      3. add-sqr-sqrt 48.5%

         \[\leadsto \frac{\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z}}{t - z} + 0 \]

      4. sqrt-unprod 68.1%

         \[\leadsto \frac{\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z}}{t - z} + 0 \]

      5. sqr-neg 68.1%

         \[\leadsto \frac{\frac{\sqrt{\color{blue}{x \cdot x}}}{z}}{t - z} + 0 \]

      6. sqrt-unprod 35.2%

         \[\leadsto \frac{\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z}}{t - z} + 0 \]

      7. add-sqr-sqrt 74.2%

         \[\leadsto \frac{\frac{\color{blue}{x}}{z}}{t - z} + 0 \]

   7. Applied egg-rr 74.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{t - z} + 0} \]
   8. Step-by-step derivation

      1. associate-/r* 74.4%

         \[\leadsto \color{blue}{\frac{x}{z \cdot \left(t - z\right)}} + 0 \]

      2. add0 74.4%

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

   9. Simplified 74.4%

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

   if -1.40000000000000008e155 < z < 1.14999999999999999e95

   1. Initial program 89.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 62.5%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+155} \lor \neg \left(z \leq 1.15 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-40}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-166}:\\ \;\;\;\;\frac{\frac{-x\_m}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -1.6e-40)
    (/ (/ x_m t) y)
    (if (<= t 1.3e-166) (/ (/ (- x_m) z) y) (/ x_m (* (- y z) t))))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e-40) {
		tmp = (x_m / t) / y;
	} else if (t <= 1.3e-166) {
		tmp = (-x_m / z) / y;
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.6d-40)) then
        tmp = (x_m / t) / y
    else if (t <= 1.3d-166) then
        tmp = (-x_m / z) / y
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e-40) {
		tmp = (x_m / t) / y;
	} else if (t <= 1.3e-166) {
		tmp = (-x_m / z) / y;
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= -1.6e-40:
		tmp = (x_m / t) / y
	elif t <= 1.3e-166:
		tmp = (-x_m / z) / y
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= -1.6e-40)
		tmp = Float64(Float64(x_m / t) / y);
	elseif (t <= 1.3e-166)
		tmp = Float64(Float64(Float64(-x_m) / z) / y);
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= -1.6e-40)
		tmp = (x_m / t) / y;
	elseif (t <= 1.3e-166)
		tmp = (-x_m / z) / y;
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, -1.6e-40], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.3e-166], N[(N[((-x$95$m) / z), $MachinePrecision] / y), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -1.60000000000000001e-40

   1. Initial program 91.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-/r* 71.3%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 71.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around inf 58.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]

   if -1.60000000000000001e-40 < t < 1.29999999999999995e-166

   1. Initial program 84.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 52.9%

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

      1. *-commutative 52.9%

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

      2. associate-/r* 60.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 60.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around 0 49.5%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{x}{z}}}{y} \]
   7. Step-by-step derivation

      1. associate-*r/ 49.5%

         \[\leadsto \frac{\color{blue}{\frac{-1 \cdot x}{z}}}{y} \]

      2. neg-mul-1 49.5%

         \[\leadsto \frac{\frac{\color{blue}{-x}}{z}}{y} \]

   8. Simplified 49.5%

      \[\leadsto \frac{\color{blue}{\frac{-x}{z}}}{y} \]

   if 1.29999999999999995e-166 < t

   1. Initial program 84.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 68.9%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-40}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-166}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+100} \lor \neg \left(z \leq 6.7 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -5.9e+100) (not (<= z 6.7e+100)))
    (/ x_m (* z t))
    (/ x_m (* y t)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -5.9e+100) || !(z <= 6.7e+100)) {
		tmp = x_m / (z * t);
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.9d+100)) .or. (.not. (z <= 6.7d+100))) then
        tmp = x_m / (z * t)
    else
        tmp = x_m / (y * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -5.9e+100) || !(z <= 6.7e+100)) {
		tmp = x_m / (z * t);
	} else {
		tmp = x_m / (y * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -5.9e+100) or not (z <= 6.7e+100):
		tmp = x_m / (z * t)
	else:
		tmp = x_m / (y * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -5.9e+100) || !(z <= 6.7e+100))
		tmp = Float64(x_m / Float64(z * t));
	else
		tmp = Float64(x_m / Float64(y * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -5.9e+100) || ~((z <= 6.7e+100)))
		tmp = x_m / (z * t);
	else
		tmp = x_m / (y * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -5.9e+100], N[Not[LessEqual[z, 6.7e+100]], $MachinePrecision]], N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -5.90000000000000027e100 or 6.6999999999999997e100 < z

   1. Initial program 79.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 78.0%

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

      1. associate-*r/ 78.0%

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

      2. neg-mul-1 78.0%

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

   5. Simplified 78.0%

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

      1. associate-/r* 93.9%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z}} \]

      2. add0 93.9%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z} + 0} \]

      3. add-sqr-sqrt 46.4%

         \[\leadsto \frac{\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z}}{t - z} + 0 \]

      4. sqrt-unprod 65.1%

         \[\leadsto \frac{\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z}}{t - z} + 0 \]

      5. sqr-neg 65.1%

         \[\leadsto \frac{\frac{\sqrt{\color{blue}{x \cdot x}}}{z}}{t - z} + 0 \]

      6. sqrt-unprod 33.6%

         \[\leadsto \frac{\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z}}{t - z} + 0 \]

      7. add-sqr-sqrt 71.6%

         \[\leadsto \frac{\frac{\color{blue}{x}}{z}}{t - z} + 0 \]

   7. Applied egg-rr 71.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{t - z} + 0} \]
   8. Step-by-step derivation

      1. add0 71.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{t - z}} \]

   9. Simplified 71.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{t - z}} \]

   10. Taylor expanded in z around 0 46.5%

       \[\leadsto \color{blue}{\frac{x}{t \cdot z}} \]

   if -5.90000000000000027e100 < z < 6.6999999999999997e100

   1. Initial program 90.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 48.6%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+100} \lor \neg \left(z \leq 6.7 \cdot 10^{+100}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+97} \lor \neg \left(z \leq 6.8 \cdot 10^{+108}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -2.3e+97) (not (<= z 6.8e+108)))
    (/ x_m (* z t))
    (/ (/ x_m t) y))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -2.3e+97) || !(z <= 6.8e+108)) {
		tmp = x_m / (z * t);
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.3d+97)) .or. (.not. (z <= 6.8d+108))) then
        tmp = x_m / (z * t)
    else
        tmp = (x_m / t) / y
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -2.3e+97) || !(z <= 6.8e+108)) {
		tmp = x_m / (z * t);
	} else {
		tmp = (x_m / t) / y;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -2.3e+97) or not (z <= 6.8e+108):
		tmp = x_m / (z * t)
	else:
		tmp = (x_m / t) / y
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -2.3e+97) || !(z <= 6.8e+108))
		tmp = Float64(x_m / Float64(z * t));
	else
		tmp = Float64(Float64(x_m / t) / y);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -2.3e+97) || ~((z <= 6.8e+108)))
		tmp = x_m / (z * t);
	else
		tmp = (x_m / t) / y;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -2.3e+97], N[Not[LessEqual[z, 6.8e+108]], $MachinePrecision]], N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / y), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -2.30000000000000006e97 or 6.79999999999999992e108 < z

   1. Initial program 80.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. neg-mul-1 78.6%

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

   5. Simplified 78.6%

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

      1. associate-/r* 94.9%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z}} \]

      2. add0 94.9%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z} + 0} \]

      3. add-sqr-sqrt 47.5%

         \[\leadsto \frac{\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z}}{t - z} + 0 \]

      4. sqrt-unprod 65.5%

         \[\leadsto \frac{\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z}}{t - z} + 0 \]

      5. sqr-neg 65.5%

         \[\leadsto \frac{\frac{\sqrt{\color{blue}{x \cdot x}}}{z}}{t - z} + 0 \]

      6. sqrt-unprod 33.2%

         \[\leadsto \frac{\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z}}{t - z} + 0 \]

      7. add-sqr-sqrt 72.0%

         \[\leadsto \frac{\frac{\color{blue}{x}}{z}}{t - z} + 0 \]

   7. Applied egg-rr 72.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{t - z} + 0} \]
   8. Step-by-step derivation

      1. add0 72.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{t - z}} \]

   9. Simplified 72.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{t - z}} \]

   10. Taylor expanded in z around 0 47.5%

       \[\leadsto \color{blue}{\frac{x}{t \cdot z}} \]

   if -2.30000000000000006e97 < z < 6.79999999999999992e108

   1. Initial program 89.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 62.7%

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

      1. *-commutative 62.7%

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

      2. associate-/r* 69.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 69.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around inf 54.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+97} \lor \neg \left(z \leq 6.8 \cdot 10^{+108}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 49.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+95} \lor \neg \left(z \leq 1.15 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{x\_m}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (or (<= z -3.3e+95) (not (<= z 1.15e+107)))
    (/ x_m (* z t))
    (/ (/ x_m y) t))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3e+95) || !(z <= 1.15e+107)) {
		tmp = x_m / (z * t);
	} else {
		tmp = (x_m / y) / t;
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.3d+95)) .or. (.not. (z <= 1.15d+107))) then
        tmp = x_m / (z * t)
    else
        tmp = (x_m / y) / t
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3e+95) || !(z <= 1.15e+107)) {
		tmp = x_m / (z * t);
	} else {
		tmp = (x_m / y) / t;
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if (z <= -3.3e+95) or not (z <= 1.15e+107):
		tmp = x_m / (z * t)
	else:
		tmp = (x_m / y) / t
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if ((z <= -3.3e+95) || !(z <= 1.15e+107))
		tmp = Float64(x_m / Float64(z * t));
	else
		tmp = Float64(Float64(x_m / y) / t);
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if ((z <= -3.3e+95) || ~((z <= 1.15e+107)))
		tmp = x_m / (z * t);
	else
		tmp = (x_m / y) / t;
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[Or[LessEqual[z, -3.3e+95], N[Not[LessEqual[z, 1.15e+107]], $MachinePrecision]], N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / y), $MachinePrecision] / t), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999998e95 or 1.15e107 < z

   1. Initial program 80.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. neg-mul-1 78.6%

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

   5. Simplified 78.6%

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

      1. associate-/r* 94.9%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z}} \]

      2. add0 94.9%

         \[\leadsto \color{blue}{\frac{\frac{-x}{z}}{t - z} + 0} \]

      3. add-sqr-sqrt 47.5%

         \[\leadsto \frac{\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z}}{t - z} + 0 \]

      4. sqrt-unprod 65.5%

         \[\leadsto \frac{\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{z}}{t - z} + 0 \]

      5. sqr-neg 65.5%

         \[\leadsto \frac{\frac{\sqrt{\color{blue}{x \cdot x}}}{z}}{t - z} + 0 \]

      6. sqrt-unprod 33.2%

         \[\leadsto \frac{\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z}}{t - z} + 0 \]

      7. add-sqr-sqrt 72.0%

         \[\leadsto \frac{\frac{\color{blue}{x}}{z}}{t - z} + 0 \]

   7. Applied egg-rr 72.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{t - z} + 0} \]
   8. Step-by-step derivation

      1. add0 72.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{t - z}} \]

   9. Simplified 72.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{t - z}} \]

   10. Taylor expanded in z around 0 47.5%

       \[\leadsto \color{blue}{\frac{x}{t \cdot z}} \]

   if -3.2999999999999998e95 < z < 1.15e107

   1. Initial program 89.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 62.7%

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

      1. *-commutative 62.7%

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

      2. associate-/r* 69.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 69.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   6. Taylor expanded in t around inf 54.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y} \]
   7. Step-by-step derivation

      1. associate-/l/ 48.0%

         \[\leadsto \color{blue}{\frac{x}{y \cdot t}} \]

      2. clear-num 48.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot t}{x}}} \]

      3. associate-*l/ 57.9%

         \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot t}} \]

      4. associate-/r* 58.2%

         \[\leadsto \color{blue}{\frac{\frac{1}{\frac{y}{x}}}{t}} \]

      5. div-inv 58.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}} \cdot \frac{1}{t}} \]

      6. clear-num 58.0%

         \[\leadsto \color{blue}{\frac{x}{y}} \cdot \frac{1}{t} \]

   8. Applied egg-rr 58.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{1}{t}} \]
   9. Step-by-step derivation

      1. un-div-inv 58.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]

   10. Applied egg-rr 58.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+95} \lor \neg \left(z \leq 1.15 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-5}:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= y -4.7e-5) (/ x_m (* y (- t z))) (/ x_m (* (- y z) t)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -4.7e-5) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.7d-5)) then
        tmp = x_m / (y * (t - z))
    else
        tmp = x_m / ((y - z) * t)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -4.7e-5) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = x_m / ((y - z) * t);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -4.7e-5:
		tmp = x_m / (y * (t - z))
	else:
		tmp = x_m / ((y - z) * t)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -4.7e-5)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x_m / Float64(Float64(y - z) * t));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -4.7e-5)
		tmp = x_m / (y * (t - z));
	else
		tmp = x_m / ((y - z) * t);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -4.7e-5], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$95$m / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -4.69999999999999972e-5

   1. Initial program 81.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.5%

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

      1. *-commutative 74.5%

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

   5. Simplified 74.5%

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

   if -4.69999999999999972e-5 < y

   1. Initial program 88.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 58.3%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 64.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -0.000185:\\ \;\;\;\;\frac{x\_m}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= y -0.000185) (/ x_m (* y (- t z))) (/ (/ x_m t) (- y z)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -0.000185) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-0.000185d0)) then
        tmp = x_m / (y * (t - z))
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -0.000185) {
		tmp = x_m / (y * (t - z));
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -0.000185:
		tmp = x_m / (y * (t - z))
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -0.000185)
		tmp = Float64(x_m / Float64(y * Float64(t - z)));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -0.000185)
		tmp = x_m / (y * (t - z));
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -0.000185], N[(x$95$m / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.85e-4

   1. Initial program 81.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.5%

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

      1. *-commutative 74.5%

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

   5. Simplified 74.5%

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

   if -1.85e-4 < y

   1. Initial program 88.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.4%

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

      1. associate-/r* 97.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   5. Simplified 97.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   6. Taylor expanded in t around inf 59.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000185:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -0.0002:\\ \;\;\;\;\frac{\frac{x\_m}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= y -0.0002) (/ (/ x_m y) (- t z)) (/ (/ x_m t) (- y z)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -0.0002) {
		tmp = (x_m / y) / (t - z);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-0.0002d0)) then
        tmp = (x_m / y) / (t - z)
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (y <= -0.0002) {
		tmp = (x_m / y) / (t - z);
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if y <= -0.0002:
		tmp = (x_m / y) / (t - z)
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (y <= -0.0002)
		tmp = Float64(Float64(x_m / y) / Float64(t - z));
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (y <= -0.0002)
		tmp = (x_m / y) / (t - z);
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[y, -0.0002], N[(N[(x$95$m / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -2.0000000000000001e-4

   1. Initial program 81.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-sqr-sqrt 46.0%

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

      2. times-frac 55.9%

         \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

   4. Applied egg-rr 55.9%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

   5. Taylor expanded in y around inf 74.5%

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

      1. associate-/r* 85.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   7. Simplified 85.6%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{t - z}} \]

   if -2.0000000000000001e-4 < y

   1. Initial program 88.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 88.4%

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

      1. associate-/r* 97.4%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   5. Simplified 97.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   6. Taylor expanded in t around inf 59.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0002:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq 2.9 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x\_m}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (if (<= t 2.9e-19) (/ (/ x_m (- t z)) y) (/ (/ x_m t) (- y z)))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= 2.9e-19) {
		tmp = (x_m / (t - z)) / y;
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 2.9d-19) then
        tmp = (x_m / (t - z)) / y
    else
        tmp = (x_m / t) / (y - z)
    end if
    code = x_s * tmp
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	double tmp;
	if (t <= 2.9e-19) {
		tmp = (x_m / (t - z)) / y;
	} else {
		tmp = (x_m / t) / (y - z);
	}
	return x_s * tmp;
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	tmp = 0
	if t <= 2.9e-19:
		tmp = (x_m / (t - z)) / y
	else:
		tmp = (x_m / t) / (y - z)
	return x_s * tmp

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	tmp = 0.0
	if (t <= 2.9e-19)
		tmp = Float64(Float64(x_m / Float64(t - z)) / y);
	else
		tmp = Float64(Float64(x_m / t) / Float64(y - z));
	end
	return Float64(x_s * tmp)
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp_2 = code(x_s, x_m, y, z, t)
	tmp = 0.0;
	if (t <= 2.9e-19)
		tmp = (x_m / (t - z)) / y;
	else
		tmp = (x_m / t) / (y - z);
	end
	tmp_2 = x_s * tmp;
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * If[LessEqual[t, 2.9e-19], N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 2.9e-19

   1. Initial program 87.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. associate-/r* 63.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   5. Simplified 63.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y}} \]

   if 2.9e-19 < t

   1. Initial program 84.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 84.2%

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

      1. associate-/r* 96.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   5. Simplified 96.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

   6. Taylor expanded in t around inf 88.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.9 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 96.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \frac{\frac{1}{y - z}}{\frac{t - z}{x\_m}} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (/ (/ 1.0 (- y z)) (/ (- t z) x_m))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * ((1.0 / (y - z)) / ((t - z) / x_m));
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_s * ((1.0d0 / (y - z)) / ((t - z) / x_m))
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * ((1.0 / (y - z)) / ((t - z) / x_m));
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	return x_s * ((1.0 / (y - z)) / ((t - z) / x_m))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * Float64(Float64(1.0 / Float64(y - z)) / Float64(Float64(t - z) / x_m)))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * ((1.0 / (y - z)) / ((t - z) / x_m));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * N[(N[(1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.6%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-sqr-sqrt 43.0%

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

   2. times-frac 49.4%

      \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]

4. Applied egg-rr 49.4%

   \[\leadsto \color{blue}{\frac{\sqrt{x}}{y - z} \cdot \frac{\sqrt{x}}{t - z}} \]
5. Step-by-step derivation

   1. frac-times 43.0%

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

   2. add-sqr-sqrt 86.6%

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

   3. *-un-lft-identity 86.6%

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

   4. frac-times 97.2%

      \[\leadsto \color{blue}{\frac{1}{y - z} \cdot \frac{x}{t - z}} \]

   5. clear-num 97.1%

      \[\leadsto \frac{1}{y - z} \cdot \color{blue}{\frac{1}{\frac{t - z}{x}}} \]

   6. un-div-inv 97.2%

      \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]

6. Applied egg-rr 97.2%

   \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]

7. Final simplification 97.2%

   \[\leadsto \frac{\frac{1}{y - z}}{\frac{t - z}{x}} \]
8. Add Preprocessing

Alternative 23: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \frac{\frac{x\_m}{t - z}}{y - z} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (/ (/ x_m (- t z)) (- y z))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * ((x_m / (t - z)) / (y - z));
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_s * ((x_m / (t - z)) / (y - z))
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * ((x_m / (t - z)) / (y - z));
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	return x_s * ((x_m / (t - z)) / (y - z))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * Float64(Float64(x_m / Float64(t - z)) / Float64(y - z)))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * ((x_m / (t - z)) / (y - z));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * N[(N[(x$95$m / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.6%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 86.6%

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

   1. associate-/r* 97.3%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

5. Simplified 97.3%

   \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]

6. Final simplification 97.3%

   \[\leadsto \frac{\frac{x}{t - z}}{y - z} \]
7. Add Preprocessing

Alternative 24: 39.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \frac{x\_m}{y \cdot t} \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t) :precision binary64 (* x_s (/ x_m (* y t))))

C

x_m = fabs(x);
x_s = copysign(1.0, x);
double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (x_m / (y * t));
}

Fortran

x_m = abs(x)
x_s = copysign(1.0d0, x)
real(8) function code(x_s, x_m, y, z, t)
    real(8), intent (in) :: x_s
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x_s * (x_m / (y * t))
end function

Java

x_m = Math.abs(x);
x_s = Math.copySign(1.0, x);
public static double code(double x_s, double x_m, double y, double z, double t) {
	return x_s * (x_m / (y * t));
}

Python

x_m = math.fabs(x)
x_s = math.copysign(1.0, x)
def code(x_s, x_m, y, z, t):
	return x_s * (x_m / (y * t))

Julia

x_m = abs(x)
x_s = copysign(1.0, x)
function code(x_s, x_m, y, z, t)
	return Float64(x_s * Float64(x_m / Float64(y * t)))
end

MATLAB

x_m = abs(x);
x_s = sign(x) * abs(1.0);
function tmp = code(x_s, x_m, y, z, t)
	tmp = x_s * (x_m / (y * t));
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
x_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$95$s_, x$95$m_, y_, z_, t_] := N[(x$95$s * N[(x$95$m / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.6%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 38.5%

   \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]

4. Final simplification 38.5%

   \[\leadsto \frac{x}{y \cdot t} \]
5. Add Preprocessing

Developer target: 87.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))