Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.7% → 95.7%

Time: 11.3s

Alternatives: 12

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot 2}{y \cdot z - t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((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 * 2.0d0) / ((y * z) - (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Python

def code(x, y, z, t):
	return (x * 2.0) / ((y * z) - (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * 2.0) / ((y * z) - (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot 2}{y \cdot z - t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x 2.0) (- (* y z) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((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 * 2.0d0) / ((y * z) - (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * 2.0) / ((y * z) - (t * z));
}

Python

def code(x, y, z, t):
	return (x * 2.0) / ((y * z) - (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * 2.0) / ((y * z) - (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \cdot 2 \leq 10^{-111}:\\ \;\;\;\;\frac{\frac{x_m}{z}}{\left(y - t\right) \cdot 0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m \cdot \frac{2}{y - t}}{z}\\ \end{array} \end{array} \]

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 (<= (* x_m 2.0) 1e-111)
    (/ (/ x_m z) (* (- y t) 0.5))
    (/ (* x_m (/ 2.0 (- y 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) {
	double tmp;
	if ((x_m * 2.0) <= 1e-111) {
		tmp = (x_m / z) / ((y - t) * 0.5);
	} else {
		tmp = (x_m * (2.0 / (y - t))) / 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 ((x_m * 2.0d0) <= 1d-111) then
        tmp = (x_m / z) / ((y - t) * 0.5d0)
    else
        tmp = (x_m * (2.0d0 / (y - t))) / 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 ((x_m * 2.0) <= 1e-111) {
		tmp = (x_m / z) / ((y - t) * 0.5);
	} else {
		tmp = (x_m * (2.0 / (y - t))) / 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 (x_m * 2.0) <= 1e-111:
		tmp = (x_m / z) / ((y - t) * 0.5)
	else:
		tmp = (x_m * (2.0 / (y - t))) / 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 (Float64(x_m * 2.0) <= 1e-111)
		tmp = Float64(Float64(x_m / z) / Float64(Float64(y - t) * 0.5));
	else
		tmp = Float64(Float64(x_m * Float64(2.0 / Float64(y - t))) / 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 ((x_m * 2.0) <= 1e-111)
		tmp = (x_m / z) / ((y - t) * 0.5);
	else
		tmp = (x_m * (2.0 / (y - t))) / 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[N[(x$95$m * 2.0), $MachinePrecision], 1e-111], N[(N[(x$95$m / z), $MachinePrecision] / N[(N[(y - t), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < 1.00000000000000009e-111

   1. Initial program 86.7%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.7%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*l/ 86.5%

         \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

      3. *-commutative 86.5%

         \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

      4. distribute-rgt-out-- 90.2%

         \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      5. associate-/l/ 91.7%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 93.0%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{2}{y - t}}{z}} \]

      2. associate-*l/ 96.9%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

      3. clear-num 96.9%

         \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{1}{\frac{y - t}{2}}} \]

      4. un-div-inv 97.0%

         \[\leadsto \color{blue}{\frac{\frac{x}{z}}{\frac{y - t}{2}}} \]

      5. div-inv 97.0%

         \[\leadsto \frac{\frac{x}{z}}{\color{blue}{\left(y - t\right) \cdot \frac{1}{2}}} \]

      6. metadata-eval 97.0%

         \[\leadsto \frac{\frac{x}{z}}{\left(y - t\right) \cdot \color{blue}{0.5}} \]

   6. Applied egg-rr 97.0%

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{\left(y - t\right) \cdot 0.5}} \]

   if 1.00000000000000009e-111 < (*.f64 x 2)

   1. Initial program 86.8%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.8%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*l/ 86.8%

         \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

      3. *-commutative 86.8%

         \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

      4. distribute-rgt-out-- 89.2%

         \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      5. associate-/l/ 91.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 97.5%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{2}{y - t}}{z}} \]

   6. Applied egg-rr 97.5%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq 10^{-111}:\\ \;\;\;\;\frac{\frac{x}{z}}{\left(y - t\right) \cdot 0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+20} \lor \neg \left(y \leq -1.3 \cdot 10^{-158}\right) \land \left(y \leq -2.15 \cdot 10^{-170} \lor \neg \left(y \leq 2.4 \cdot 10^{-8}\right)\right):\\ \;\;\;\;\frac{x_m}{y} \cdot \frac{2}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x_m}{t}}{z}\\ \end{array} \end{array} \]

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 (or (<= y -1.3e+20)
          (and (not (<= y -1.3e-158))
               (or (<= y -2.15e-170) (not (<= y 2.4e-8)))))
    (* (/ x_m y) (/ 2.0 z))
    (* -2.0 (/ (/ 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) {
	double tmp;
	if ((y <= -1.3e+20) || (!(y <= -1.3e-158) && ((y <= -2.15e-170) || !(y <= 2.4e-8)))) {
		tmp = (x_m / y) * (2.0 / z);
	} else {
		tmp = -2.0 * ((x_m / t) / 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 <= (-1.3d+20)) .or. (.not. (y <= (-1.3d-158))) .and. (y <= (-2.15d-170)) .or. (.not. (y <= 2.4d-8))) then
        tmp = (x_m / y) * (2.0d0 / z)
    else
        tmp = (-2.0d0) * ((x_m / t) / 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 <= -1.3e+20) || (!(y <= -1.3e-158) && ((y <= -2.15e-170) || !(y <= 2.4e-8)))) {
		tmp = (x_m / y) * (2.0 / z);
	} else {
		tmp = -2.0 * ((x_m / t) / 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 <= -1.3e+20) or (not (y <= -1.3e-158) and ((y <= -2.15e-170) or not (y <= 2.4e-8))):
		tmp = (x_m / y) * (2.0 / z)
	else:
		tmp = -2.0 * ((x_m / t) / 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 <= -1.3e+20) || (!(y <= -1.3e-158) && ((y <= -2.15e-170) || !(y <= 2.4e-8))))
		tmp = Float64(Float64(x_m / y) * Float64(2.0 / z));
	else
		tmp = Float64(-2.0 * Float64(Float64(x_m / t) / 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 <= -1.3e+20) || (~((y <= -1.3e-158)) && ((y <= -2.15e-170) || ~((y <= 2.4e-8)))))
		tmp = (x_m / y) * (2.0 / z);
	else
		tmp = -2.0 * ((x_m / t) / 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[Or[LessEqual[y, -1.3e+20], And[N[Not[LessEqual[y, -1.3e-158]], $MachinePrecision], Or[LessEqual[y, -2.15e-170], N[Not[LessEqual[y, 2.4e-8]], $MachinePrecision]]]], N[(N[(x$95$m / y), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x$95$m / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e20 or -1.3e-158 < y < -2.1499999999999999e-170 or 2.39999999999999998e-8 < y

   1. Initial program 85.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 88.7%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 88.7%

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

   5. Taylor expanded in y around inf 80.6%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 80.6%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]

   7. Simplified 80.6%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]
   8. Step-by-step derivation

      1. *-commutative 80.6%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z}} \]

      2. times-frac 87.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   9. Applied egg-rr 87.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   if -1.3e20 < y < -1.3e-158 or -2.1499999999999999e-170 < y < 2.39999999999999998e-8

   1. Initial program 88.7%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 88.7%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*l/ 88.6%

         \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

      3. *-commutative 88.6%

         \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

      4. distribute-rgt-out-- 91.3%

         \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      5. associate-/l/ 91.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

   3. Simplified 91.9%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.5%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 80.0%

         \[\leadsto -2 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

   7. Simplified 80.0%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+20} \lor \neg \left(y \leq -1.3 \cdot 10^{-158}\right) \land \left(y \leq -2.15 \cdot 10^{-170} \lor \neg \left(y \leq 2.4 \cdot 10^{-8}\right)\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{2}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{x_m}{y} \cdot \frac{2}{z}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-159}:\\ \;\;\;\;\frac{x_m}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-170} \lor \neg \left(y \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x_m}{t}}{z}\\ \end{array} \end{array} \end{array} \]

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 y) (/ 2.0 z))))
   (*
    x_s
    (if (<= y -1.3e+20)
      t_1
      (if (<= y -7e-159)
        (* (/ x_m z) (/ -2.0 t))
        (if (or (<= y -2.15e-170) (not (<= y 2e-8)))
          t_1
          (* -2.0 (/ (/ 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) {
	double t_1 = (x_m / y) * (2.0 / z);
	double tmp;
	if (y <= -1.3e+20) {
		tmp = t_1;
	} else if (y <= -7e-159) {
		tmp = (x_m / z) * (-2.0 / t);
	} else if ((y <= -2.15e-170) || !(y <= 2e-8)) {
		tmp = t_1;
	} else {
		tmp = -2.0 * ((x_m / t) / 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) :: t_1
    real(8) :: tmp
    t_1 = (x_m / y) * (2.0d0 / z)
    if (y <= (-1.3d+20)) then
        tmp = t_1
    else if (y <= (-7d-159)) then
        tmp = (x_m / z) * ((-2.0d0) / t)
    else if ((y <= (-2.15d-170)) .or. (.not. (y <= 2d-8))) then
        tmp = t_1
    else
        tmp = (-2.0d0) * ((x_m / t) / 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 t_1 = (x_m / y) * (2.0 / z);
	double tmp;
	if (y <= -1.3e+20) {
		tmp = t_1;
	} else if (y <= -7e-159) {
		tmp = (x_m / z) * (-2.0 / t);
	} else if ((y <= -2.15e-170) || !(y <= 2e-8)) {
		tmp = t_1;
	} else {
		tmp = -2.0 * ((x_m / t) / 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 / y) * (2.0 / z)
	tmp = 0
	if y <= -1.3e+20:
		tmp = t_1
	elif y <= -7e-159:
		tmp = (x_m / z) * (-2.0 / t)
	elif (y <= -2.15e-170) or not (y <= 2e-8):
		tmp = t_1
	else:
		tmp = -2.0 * ((x_m / t) / 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(Float64(x_m / y) * Float64(2.0 / z))
	tmp = 0.0
	if (y <= -1.3e+20)
		tmp = t_1;
	elseif (y <= -7e-159)
		tmp = Float64(Float64(x_m / z) * Float64(-2.0 / t));
	elseif ((y <= -2.15e-170) || !(y <= 2e-8))
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(Float64(x_m / t) / 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 / y) * (2.0 / z);
	tmp = 0.0;
	if (y <= -1.3e+20)
		tmp = t_1;
	elseif (y <= -7e-159)
		tmp = (x_m / z) * (-2.0 / t);
	elseif ((y <= -2.15e-170) || ~((y <= 2e-8)))
		tmp = t_1;
	else
		tmp = -2.0 * ((x_m / t) / 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[(N[(x$95$m / y), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[y, -1.3e+20], t$95$1, If[LessEqual[y, -7e-159], N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.15e-170], N[Not[LessEqual[y, 2e-8]], $MachinePrecision]], t$95$1, N[(-2.0 * N[(N[(x$95$m / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e20 or -7.00000000000000005e-159 < y < -2.1499999999999999e-170 or 2e-8 < y

   1. Initial program 85.1%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 88.7%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 88.7%

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

   5. Taylor expanded in y around inf 80.6%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 80.6%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]

   7. Simplified 80.6%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]
   8. Step-by-step derivation

      1. *-commutative 80.6%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z}} \]

      2. times-frac 87.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   9. Applied egg-rr 87.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   if -1.3e20 < y < -7.00000000000000005e-159

   1. Initial program 85.9%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 88.7%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      2. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.2%

      \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{-2}{t}} \]

   if -2.1499999999999999e-170 < y < 2e-8

   1. Initial program 90.0%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 90.0%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*l/ 89.8%

         \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

      3. *-commutative 89.8%

         \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

      4. distribute-rgt-out-- 92.5%

         \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      5. associate-/l/ 93.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

   3. Simplified 93.4%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.6%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 83.9%

         \[\leadsto -2 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

   7. Simplified 83.9%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{2}{z}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-159}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-170} \lor \neg \left(y \leq 2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{2}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+35}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x_m}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-159}:\\ \;\;\;\;\frac{x_m}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-170} \lor \neg \left(y \leq 1.8 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x_m}{y} \cdot \frac{2}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x_m}{t}}{z}\\ \end{array} \end{array} \]

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 -1e+35)
    (/ 2.0 (* z (/ y x_m)))
    (if (<= y -7e-159)
      (* (/ x_m z) (/ -2.0 t))
      (if (or (<= y -2.15e-170) (not (<= y 1.8e-8)))
        (* (/ x_m y) (/ 2.0 z))
        (* -2.0 (/ (/ 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) {
	double tmp;
	if (y <= -1e+35) {
		tmp = 2.0 / (z * (y / x_m));
	} else if (y <= -7e-159) {
		tmp = (x_m / z) * (-2.0 / t);
	} else if ((y <= -2.15e-170) || !(y <= 1.8e-8)) {
		tmp = (x_m / y) * (2.0 / z);
	} else {
		tmp = -2.0 * ((x_m / t) / 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 <= (-1d+35)) then
        tmp = 2.0d0 / (z * (y / x_m))
    else if (y <= (-7d-159)) then
        tmp = (x_m / z) * ((-2.0d0) / t)
    else if ((y <= (-2.15d-170)) .or. (.not. (y <= 1.8d-8))) then
        tmp = (x_m / y) * (2.0d0 / z)
    else
        tmp = (-2.0d0) * ((x_m / t) / 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 <= -1e+35) {
		tmp = 2.0 / (z * (y / x_m));
	} else if (y <= -7e-159) {
		tmp = (x_m / z) * (-2.0 / t);
	} else if ((y <= -2.15e-170) || !(y <= 1.8e-8)) {
		tmp = (x_m / y) * (2.0 / z);
	} else {
		tmp = -2.0 * ((x_m / t) / 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 <= -1e+35:
		tmp = 2.0 / (z * (y / x_m))
	elif y <= -7e-159:
		tmp = (x_m / z) * (-2.0 / t)
	elif (y <= -2.15e-170) or not (y <= 1.8e-8):
		tmp = (x_m / y) * (2.0 / z)
	else:
		tmp = -2.0 * ((x_m / t) / 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 <= -1e+35)
		tmp = Float64(2.0 / Float64(z * Float64(y / x_m)));
	elseif (y <= -7e-159)
		tmp = Float64(Float64(x_m / z) * Float64(-2.0 / t));
	elseif ((y <= -2.15e-170) || !(y <= 1.8e-8))
		tmp = Float64(Float64(x_m / y) * Float64(2.0 / z));
	else
		tmp = Float64(-2.0 * Float64(Float64(x_m / t) / 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 <= -1e+35)
		tmp = 2.0 / (z * (y / x_m));
	elseif (y <= -7e-159)
		tmp = (x_m / z) * (-2.0 / t);
	elseif ((y <= -2.15e-170) || ~((y <= 1.8e-8)))
		tmp = (x_m / y) * (2.0 / z);
	else
		tmp = -2.0 * ((x_m / t) / 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, -1e+35], N[(2.0 / N[(z * N[(y / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-159], N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.15e-170], N[Not[LessEqual[y, 1.8e-8]], $MachinePrecision]], N[(N[(x$95$m / y), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x$95$m / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if y < -9.9999999999999997e34

   1. Initial program 85.2%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 90.3%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 90.3%

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

   5. Taylor expanded in y around inf 81.0%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 81.0%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]

   7. Simplified 81.0%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]
   8. Step-by-step derivation

      1. *-commutative 81.0%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z}} \]

      2. times-frac 87.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   9. Applied egg-rr 87.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]
   10. Step-by-step derivation

       1. clear-num 87.5%

          \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \cdot \frac{2}{z} \]

       2. frac-times 88.3%

          \[\leadsto \color{blue}{\frac{1 \cdot 2}{\frac{y}{x} \cdot z}} \]

       3. metadata-eval 88.3%

          \[\leadsto \frac{\color{blue}{2}}{\frac{y}{x} \cdot z} \]

   11. Applied egg-rr 88.3%

       \[\leadsto \color{blue}{\frac{2}{\frac{y}{x} \cdot z}} \]

   if -9.9999999999999997e34 < y < -7.00000000000000005e-159

   1. Initial program 85.9%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 88.7%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      2. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.2%

      \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{-2}{t}} \]

   if -7.00000000000000005e-159 < y < -2.1499999999999999e-170 or 1.79999999999999991e-8 < y

   1. Initial program 85.0%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 87.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 87.5%

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

   5. Taylor expanded in y around inf 80.2%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 80.2%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]

   7. Simplified 80.2%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]
   8. Step-by-step derivation

      1. *-commutative 80.2%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z}} \]

      2. times-frac 88.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   9. Applied egg-rr 88.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   if -2.1499999999999999e-170 < y < 1.79999999999999991e-8

   1. Initial program 90.0%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 90.0%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*l/ 89.8%

         \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

      3. *-commutative 89.8%

         \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

      4. distribute-rgt-out-- 92.5%

         \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      5. associate-/l/ 93.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

   3. Simplified 93.4%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.6%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 83.9%

         \[\leadsto -2 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

   7. Simplified 83.9%

      \[\leadsto \color{blue}{-2 \cdot \frac{\frac{x}{t}}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+35}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-159}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-170} \lor \neg \left(y \leq 1.8 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{2}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x_m}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-159}:\\ \;\;\;\;\frac{x_m}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-170}:\\ \;\;\;\;\frac{x_m}{y} \cdot \frac{2}{z}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-7}:\\ \;\;\;\;-2 \cdot \frac{\frac{x_m}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x_m}{\frac{y}{2}}}{z}\\ \end{array} \end{array} \]

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 -7.2e+23)
    (/ 2.0 (* z (/ y x_m)))
    (if (<= y -7.5e-159)
      (* (/ x_m z) (/ -2.0 t))
      (if (<= y -2.15e-170)
        (* (/ x_m y) (/ 2.0 z))
        (if (<= y 4.3e-7)
          (* -2.0 (/ (/ x_m t) z))
          (/ (/ x_m (/ y 2.0)) 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 tmp;
	if (y <= -7.2e+23) {
		tmp = 2.0 / (z * (y / x_m));
	} else if (y <= -7.5e-159) {
		tmp = (x_m / z) * (-2.0 / t);
	} else if (y <= -2.15e-170) {
		tmp = (x_m / y) * (2.0 / z);
	} else if (y <= 4.3e-7) {
		tmp = -2.0 * ((x_m / t) / z);
	} else {
		tmp = (x_m / (y / 2.0)) / 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 <= (-7.2d+23)) then
        tmp = 2.0d0 / (z * (y / x_m))
    else if (y <= (-7.5d-159)) then
        tmp = (x_m / z) * ((-2.0d0) / t)
    else if (y <= (-2.15d-170)) then
        tmp = (x_m / y) * (2.0d0 / z)
    else if (y <= 4.3d-7) then
        tmp = (-2.0d0) * ((x_m / t) / z)
    else
        tmp = (x_m / (y / 2.0d0)) / 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 <= -7.2e+23) {
		tmp = 2.0 / (z * (y / x_m));
	} else if (y <= -7.5e-159) {
		tmp = (x_m / z) * (-2.0 / t);
	} else if (y <= -2.15e-170) {
		tmp = (x_m / y) * (2.0 / z);
	} else if (y <= 4.3e-7) {
		tmp = -2.0 * ((x_m / t) / z);
	} else {
		tmp = (x_m / (y / 2.0)) / 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):
	tmp = 0
	if y <= -7.2e+23:
		tmp = 2.0 / (z * (y / x_m))
	elif y <= -7.5e-159:
		tmp = (x_m / z) * (-2.0 / t)
	elif y <= -2.15e-170:
		tmp = (x_m / y) * (2.0 / z)
	elif y <= 4.3e-7:
		tmp = -2.0 * ((x_m / t) / z)
	else:
		tmp = (x_m / (y / 2.0)) / 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)
	tmp = 0.0
	if (y <= -7.2e+23)
		tmp = Float64(2.0 / Float64(z * Float64(y / x_m)));
	elseif (y <= -7.5e-159)
		tmp = Float64(Float64(x_m / z) * Float64(-2.0 / t));
	elseif (y <= -2.15e-170)
		tmp = Float64(Float64(x_m / y) * Float64(2.0 / z));
	elseif (y <= 4.3e-7)
		tmp = Float64(-2.0 * Float64(Float64(x_m / t) / z));
	else
		tmp = Float64(Float64(x_m / Float64(y / 2.0)) / 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)
	tmp = 0.0;
	if (y <= -7.2e+23)
		tmp = 2.0 / (z * (y / x_m));
	elseif (y <= -7.5e-159)
		tmp = (x_m / z) * (-2.0 / t);
	elseif (y <= -2.15e-170)
		tmp = (x_m / y) * (2.0 / z);
	elseif (y <= 4.3e-7)
		tmp = -2.0 * ((x_m / t) / z);
	else
		tmp = (x_m / (y / 2.0)) / 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_] := N[(x$95$s * If[LessEqual[y, -7.2e+23], N[(2.0 / N[(z * N[(y / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-159], N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e-170], N[(N[(x$95$m / y), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e-7], N[(-2.0 * N[(N[(x$95$m / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(y / 2.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]), $MachinePrecision]

Derivation

1. Split input into 5 regimes

2. if y < -7.1999999999999997e23

   1. Initial program 85.2%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 90.3%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 90.3%

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

   5. Taylor expanded in y around inf 81.0%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 81.0%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]

   7. Simplified 81.0%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]
   8. Step-by-step derivation

      1. *-commutative 81.0%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z}} \]

      2. times-frac 87.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   9. Applied egg-rr 87.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]
   10. Step-by-step derivation

       1. clear-num 87.5%

          \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \cdot \frac{2}{z} \]

       2. frac-times 88.3%

          \[\leadsto \color{blue}{\frac{1 \cdot 2}{\frac{y}{x} \cdot z}} \]

       3. metadata-eval 88.3%

          \[\leadsto \frac{\color{blue}{2}}{\frac{y}{x} \cdot z} \]

   11. Applied egg-rr 88.3%

       \[\leadsto \color{blue}{\frac{2}{\frac{y}{x} \cdot z}} \]

   if -7.1999999999999997e23 < y < -7.5e-159

   1. Initial program 85.9%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 88.7%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      2. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.2%

      \[\leadsto \frac{x}{z} \cdot \color{blue}{\frac{-2}{t}} \]

   if -7.5e-159 < y < -2.1499999999999999e-170

   1. Initial program 81.0%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 81.0%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 81.0%

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

   5. Taylor expanded in y around inf 79.5%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 79.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]

   7. Simplified 79.5%

      \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot y}} \]
   8. Step-by-step derivation

      1. *-commutative 79.5%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{y \cdot z}} \]

      2. times-frac 98.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   9. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{2}{z}} \]

   if -2.1499999999999999e-170 < y < 4.3000000000000001e-7

   1. Initial program 90.0%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 90.0%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*l/ 89.8%

         \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

      3. *-commutative 89.8%

         \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

      4. distribute-rgt-out-- 92.5%

         \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      5. associate-/l/ 93.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

   3. Simplified 93.4%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.6%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 83.9%

         \[\leadsto -2 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

   7. Simplified 83.9%

      \[\leadsto \color{blue}{-2 \cdot \frac{\frac{x}{t}}{z}} \]

   if 4.3000000000000001e-7 < y

   1. Initial program 85.3%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 85.3%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*l/ 85.2%

         \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

      3. *-commutative 85.2%

         \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

      4. distribute-rgt-out-- 87.9%

         \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      5. associate-/l/ 91.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 93.7%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{2}{y - t}}{z}} \]

   6. Applied egg-rr 93.7%

      \[\leadsto \color{blue}{\frac{x \cdot \frac{2}{y - t}}{z}} \]

   7. Taylor expanded in y around inf 87.5%

      \[\leadsto \frac{\color{blue}{2 \cdot \frac{x}{y}}}{z} \]
   8. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto \frac{\color{blue}{\frac{x}{y} \cdot 2}}{z} \]

      2. associate-/r/ 87.5%

         \[\leadsto \frac{\color{blue}{\frac{x}{\frac{y}{2}}}}{z} \]

   9. Simplified 87.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{\frac{y}{2}}}}{z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+23}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-159}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{2}{z}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-7}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{2}}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+20} \lor \neg \left(y \leq 8.5 \cdot 10^{-8}\right):\\ \;\;\;\;x_m \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x_m}{t}}{z}\\ \end{array} \end{array} \]

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 (or (<= y -1.3e+20) (not (<= y 8.5e-8)))
    (* x_m (/ (/ 2.0 y) z))
    (* -2.0 (/ (/ 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) {
	double tmp;
	if ((y <= -1.3e+20) || !(y <= 8.5e-8)) {
		tmp = x_m * ((2.0 / y) / z);
	} else {
		tmp = -2.0 * ((x_m / t) / 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 <= (-1.3d+20)) .or. (.not. (y <= 8.5d-8))) then
        tmp = x_m * ((2.0d0 / y) / z)
    else
        tmp = (-2.0d0) * ((x_m / t) / 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 <= -1.3e+20) || !(y <= 8.5e-8)) {
		tmp = x_m * ((2.0 / y) / z);
	} else {
		tmp = -2.0 * ((x_m / t) / 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 <= -1.3e+20) or not (y <= 8.5e-8):
		tmp = x_m * ((2.0 / y) / z)
	else:
		tmp = -2.0 * ((x_m / t) / 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 <= -1.3e+20) || !(y <= 8.5e-8))
		tmp = Float64(x_m * Float64(Float64(2.0 / y) / z));
	else
		tmp = Float64(-2.0 * Float64(Float64(x_m / t) / 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 <= -1.3e+20) || ~((y <= 8.5e-8)))
		tmp = x_m * ((2.0 / y) / z);
	else
		tmp = -2.0 * ((x_m / t) / 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[Or[LessEqual[y, -1.3e+20], N[Not[LessEqual[y, 8.5e-8]], $MachinePrecision]], N[(x$95$m * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x$95$m / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e20 or 8.49999999999999935e-8 < y

   1. Initial program 85.3%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 85.3%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*l/ 85.2%

         \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

      3. *-commutative 85.2%

         \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

      4. distribute-rgt-out-- 88.9%

         \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      5. associate-/l/ 91.7%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 80.5%

      \[\leadsto x \cdot \color{blue}{\frac{2}{y \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 83.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y}}{z}} \]

   7. Simplified 83.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y}}{z}} \]

   if -1.3e20 < y < 8.49999999999999935e-8

   1. Initial program 88.4%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 88.4%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*l/ 88.3%

         \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

      3. *-commutative 88.3%

         \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

      4. distribute-rgt-out-- 90.9%

         \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      5. associate-/l/ 91.5%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 72.4%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   6. Step-by-step derivation

      1. associate-/r* 76.7%

         \[\leadsto -2 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

   7. Simplified 76.7%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+20} \lor \neg \left(y \leq 8.5 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{2}{y - t}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;x_m \cdot 2 \leq 10^{-111}:\\ \;\;\;\;\frac{x_m}{z} \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m \cdot t_1}{z}\\ \end{array} \end{array} \end{array} \]

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 (/ 2.0 (- y t))))
   (* x_s (if (<= (* x_m 2.0) 1e-111) (* (/ x_m z) t_1) (/ (* x_m t_1) 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 = 2.0 / (y - t);
	double tmp;
	if ((x_m * 2.0) <= 1e-111) {
		tmp = (x_m / z) * t_1;
	} else {
		tmp = (x_m * t_1) / 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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 / (y - t)
    if ((x_m * 2.0d0) <= 1d-111) then
        tmp = (x_m / z) * t_1
    else
        tmp = (x_m * t_1) / 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 t_1 = 2.0 / (y - t);
	double tmp;
	if ((x_m * 2.0) <= 1e-111) {
		tmp = (x_m / z) * t_1;
	} else {
		tmp = (x_m * t_1) / 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 = 2.0 / (y - t)
	tmp = 0
	if (x_m * 2.0) <= 1e-111:
		tmp = (x_m / z) * t_1
	else:
		tmp = (x_m * t_1) / 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(2.0 / Float64(y - t))
	tmp = 0.0
	if (Float64(x_m * 2.0) <= 1e-111)
		tmp = Float64(Float64(x_m / z) * t_1);
	else
		tmp = Float64(Float64(x_m * t_1) / 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 = 2.0 / (y - t);
	tmp = 0.0;
	if ((x_m * 2.0) <= 1e-111)
		tmp = (x_m / z) * t_1;
	else
		tmp = (x_m * t_1) / 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[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[N[(x$95$m * 2.0), $MachinePrecision], 1e-111], N[(N[(x$95$m / z), $MachinePrecision] * t$95$1), $MachinePrecision], N[(N[(x$95$m * t$95$1), $MachinePrecision] / z), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < 1.00000000000000009e-111

   1. Initial program 86.7%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 90.3%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      2. times-frac 96.9%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]
   4. Add Preprocessing

   if 1.00000000000000009e-111 < (*.f64 x 2)

   1. Initial program 86.8%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 86.8%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*l/ 86.8%

         \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

      3. *-commutative 86.8%

         \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

      4. distribute-rgt-out-- 89.2%

         \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      5. associate-/l/ 91.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 97.5%

         \[\leadsto \color{blue}{\frac{x \cdot \frac{2}{y - t}}{z}} \]

   6. Applied egg-rr 97.5%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq 10^{-111}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{2}{y - t}\\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 3 \cdot 10^{-48}:\\ \;\;\;\;x_m \cdot \frac{t_1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z} \cdot t_1\\ \end{array} \end{array} \end{array} \]

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 (/ 2.0 (- y t))))
   (* x_s (if (<= z 3e-48) (* x_m (/ t_1 z)) (* (/ x_m z) t_1)))))

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 = 2.0 / (y - t);
	double tmp;
	if (z <= 3e-48) {
		tmp = x_m * (t_1 / z);
	} else {
		tmp = (x_m / z) * t_1;
	}
	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 = 2.0d0 / (y - t)
    if (z <= 3d-48) then
        tmp = x_m * (t_1 / z)
    else
        tmp = (x_m / z) * t_1
    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 = 2.0 / (y - t);
	double tmp;
	if (z <= 3e-48) {
		tmp = x_m * (t_1 / z);
	} else {
		tmp = (x_m / z) * t_1;
	}
	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 = 2.0 / (y - t)
	tmp = 0
	if z <= 3e-48:
		tmp = x_m * (t_1 / z)
	else:
		tmp = (x_m / z) * t_1
	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(2.0 / Float64(y - t))
	tmp = 0.0
	if (z <= 3e-48)
		tmp = Float64(x_m * Float64(t_1 / z));
	else
		tmp = Float64(Float64(x_m / z) * t_1);
	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 = 2.0 / (y - t);
	tmp = 0.0;
	if (z <= 3e-48)
		tmp = x_m * (t_1 / z);
	else
		tmp = (x_m / z) * t_1;
	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[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]}, N[(x$95$s * If[LessEqual[z, 3e-48], N[(x$95$m * N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * t$95$1), $MachinePrecision]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.9999999999999999e-48

   1. Initial program 87.3%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. *-commutative 87.3%

         \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

      2. associate-*l/ 87.1%

         \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

      3. *-commutative 87.1%

         \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

      4. distribute-rgt-out-- 90.8%

         \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      5. associate-/l/ 92.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
   4. Add Preprocessing

   if 2.9999999999999999e-48 < z

   1. Initial program 85.6%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 88.1%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      2. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   3. Simplified 99.7%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \begin{array}{l} \mathbf{if}\;z \leq 10^{+31}:\\ \;\;\;\;\frac{x_m \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x_m}{z} \cdot \frac{2}{y - t}\\ \end{array} \end{array} \]

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 (<= z 1e+31)
    (/ (* x_m 2.0) (* z (- y t)))
    (* (/ x_m z) (/ 2.0 (- 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 <= 1e+31) {
		tmp = (x_m * 2.0) / (z * (y - t));
	} else {
		tmp = (x_m / z) * (2.0 / (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 <= 1d+31) then
        tmp = (x_m * 2.0d0) / (z * (y - t))
    else
        tmp = (x_m / z) * (2.0d0 / (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 <= 1e+31) {
		tmp = (x_m * 2.0) / (z * (y - t));
	} else {
		tmp = (x_m / z) * (2.0 / (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 <= 1e+31:
		tmp = (x_m * 2.0) / (z * (y - t))
	else:
		tmp = (x_m / z) * (2.0 / (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 <= 1e+31)
		tmp = Float64(Float64(x_m * 2.0) / Float64(z * Float64(y - t)));
	else
		tmp = Float64(Float64(x_m / z) * Float64(2.0 / 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 <= 1e+31)
		tmp = (x_m * 2.0) / (z * (y - t));
	else
		tmp = (x_m / z) * (2.0 / (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[LessEqual[z, 1e+31], N[(N[(x$95$m * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / z), $MachinePrecision] * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if z < 9.9999999999999996e30

   1. Initial program 88.4%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 91.7%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   3. Simplified 91.7%

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

   if 9.9999999999999996e30 < z

   1. Initial program 82.2%

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 85.3%

         \[\leadsto \frac{x \cdot 2}{\color{blue}{z \cdot \left(y - t\right)}} \]

      2. times-frac 99.8%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{2}{y - t}} \]

   3. Simplified 99.8%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 10^{+31}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \left(x_m \cdot \frac{\frac{2}{y - t}}{z}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (* x_s (* x_m (/ (/ 2.0 (- y 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 * (x_m * ((2.0 / (y - 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 * (x_m * ((2.0d0 / (y - 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 * (x_m * ((2.0 / (y - 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 * (x_m * ((2.0 / (y - 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(x_m * Float64(Float64(2.0 / Float64(y - 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 * (x_m * ((2.0 / (y - 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[(x$95$m * N[(N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.7%

   \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
2. Step-by-step derivation

   1. *-commutative 86.7%

      \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

   2. associate-*l/ 86.6%

      \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

   3. *-commutative 86.6%

      \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

   4. distribute-rgt-out-- 89.8%

      \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   5. associate-/l/ 91.6%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

3. Simplified 91.6%

   \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
4. Add Preprocessing

5. Final simplification 91.6%

   \[\leadsto x \cdot \frac{\frac{2}{y - t}}{z} \]
6. Add Preprocessing

Alternative 11: 52.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \left(-2 \cdot \frac{x_m}{z \cdot t}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t) :precision binary64 (* x_s (* -2.0 (/ x_m (* 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) {
	return x_s * (-2.0 * (x_m / (z * 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 * ((-2.0d0) * (x_m / (z * 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 * (-2.0 * (x_m / (z * 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 * (-2.0 * (x_m / (z * 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(-2.0 * Float64(x_m / Float64(z * 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 * (-2.0 * (x_m / (z * 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[(-2.0 * N[(x$95$m / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.7%

   \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
2. Step-by-step derivation

   1. *-commutative 86.7%

      \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

   2. associate-*l/ 86.6%

      \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

   3. *-commutative 86.6%

      \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

   4. distribute-rgt-out-- 89.8%

      \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   5. associate-/l/ 91.6%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

3. Simplified 91.6%

   \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 47.4%

   \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]

6. Final simplification 47.4%

   \[\leadsto -2 \cdot \frac{x}{z \cdot t} \]
7. Add Preprocessing

Alternative 12: 52.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ x_s = \mathsf{copysign}\left(1, x\right) \\ x_s \cdot \left(-2 \cdot \frac{\frac{x_m}{t}}{z}\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
x_s = (copysign.f64 1 x)
(FPCore (x_s x_m y z t) :precision binary64 (* x_s (* -2.0 (/ (/ 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 * (-2.0 * ((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 * ((-2.0d0) * ((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 * (-2.0 * ((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 * (-2.0 * ((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(-2.0 * Float64(Float64(x_m / 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 * (-2.0 * ((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[(-2.0 * N[(N[(x$95$m / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.7%

   \[\frac{x \cdot 2}{y \cdot z - t \cdot z} \]
2. Step-by-step derivation

   1. *-commutative 86.7%

      \[\leadsto \frac{\color{blue}{2 \cdot x}}{y \cdot z - t \cdot z} \]

   2. associate-*l/ 86.6%

      \[\leadsto \color{blue}{\frac{2}{y \cdot z - t \cdot z} \cdot x} \]

   3. *-commutative 86.6%

      \[\leadsto \color{blue}{x \cdot \frac{2}{y \cdot z - t \cdot z}} \]

   4. distribute-rgt-out-- 89.8%

      \[\leadsto x \cdot \frac{2}{\color{blue}{z \cdot \left(y - t\right)}} \]

   5. associate-/l/ 91.6%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{2}{y - t}}{z}} \]

3. Simplified 91.6%

   \[\leadsto \color{blue}{x \cdot \frac{\frac{2}{y - t}}{z}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 47.4%

   \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
6. Step-by-step derivation

   1. associate-/r* 48.8%

      \[\leadsto -2 \cdot \color{blue}{\frac{\frac{x}{t}}{z}} \]

7. Simplified 48.8%

   \[\leadsto \color{blue}{-2 \cdot \frac{\frac{x}{t}}{z}} \]

8. Final simplification 48.8%

   \[\leadsto -2 \cdot \frac{\frac{x}{t}}{z} \]
9. Add Preprocessing

Developer target: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ t_2 := \frac{x \cdot 2}{y \cdot z - t \cdot z}\\ \mathbf{if}\;t_2 < -2.559141628295061 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 < 1.045027827330126 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x (* (- y t) z)) 2.0))
        (t_2 (/ (* x 2.0) (- (* y z) (* t z)))))
   (if (< t_2 -2.559141628295061e-13)
     t_1
     (if (< t_2 1.045027827330126e-269) (/ (* (/ x z) 2.0) (- y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / ((y - t) * z)) * 2.0;
	double t_2 = (x * 2.0) / ((y * z) - (t * z));
	double tmp;
	if (t_2 < -2.559141628295061e-13) {
		tmp = t_1;
	} else if (t_2 < 1.045027827330126e-269) {
		tmp = ((x / z) * 2.0) / (y - t);
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = (x / ((y - t) * z)) * 2.0d0
    t_2 = (x * 2.0d0) / ((y * z) - (t * z))
    if (t_2 < (-2.559141628295061d-13)) then
        tmp = t_1
    else if (t_2 < 1.045027827330126d-269) then
        tmp = ((x / z) * 2.0d0) / (y - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / ((y - t) * z)) * 2.0;
	double t_2 = (x * 2.0) / ((y * z) - (t * z));
	double tmp;
	if (t_2 < -2.559141628295061e-13) {
		tmp = t_1;
	} else if (t_2 < 1.045027827330126e-269) {
		tmp = ((x / z) * 2.0) / (y - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / ((y - t) * z)) * 2.0
	t_2 = (x * 2.0) / ((y * z) - (t * z))
	tmp = 0
	if t_2 < -2.559141628295061e-13:
		tmp = t_1
	elif t_2 < 1.045027827330126e-269:
		tmp = ((x / z) * 2.0) / (y - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(Float64(y - t) * z)) * 2.0)
	t_2 = Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(t * z)))
	tmp = 0.0
	if (t_2 < -2.559141628295061e-13)
		tmp = t_1;
	elseif (t_2 < 1.045027827330126e-269)
		tmp = Float64(Float64(Float64(x / z) * 2.0) / Float64(y - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / ((y - t) * z)) * 2.0;
	t_2 = (x * 2.0) / ((y * z) - (t * z));
	tmp = 0.0;
	if (t_2 < -2.559141628295061e-13)
		tmp = t_1;
	elseif (t_2 < 1.045027827330126e-269)
		tmp = ((x / z) * 2.0) / (y - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(N[(y - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -2.559141628295061e-13], t$95$1, If[Less[t$95$2, 1.045027827330126e-269], N[(N[(N[(x / z), $MachinePrecision] * 2.0), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024021 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (if (< (/ (* x 2.0) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2.0) (if (< (/ (* x 2.0) (- (* y z) (* t z))) 1.045027827330126e-269) (/ (* (/ x z) 2.0) (- y t)) (* (/ x (* (- y t) z)) 2.0)))

  (/ (* x 2.0) (- (* y z) (* t z))))