Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.6% → 96.1%

Time: 13.0s

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: 89.6% 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: 96.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \cdot 2 \leq 6 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{x\_m \cdot 2}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y - t}}{\frac{z}{2}}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= (* x_m 2.0) 6e-113)
    (/ (/ (* x_m 2.0) z) (- y t))
    (/ (/ x_m (- y t)) (/ z 2.0)))))

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) <= 6e-113) {
		tmp = ((x_m * 2.0) / z) / (y - t);
	} else {
		tmp = (x_m / (y - t)) / (z / 2.0);
	}
	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) <= 6d-113) then
        tmp = ((x_m * 2.0d0) / z) / (y - t)
    else
        tmp = (x_m / (y - t)) / (z / 2.0d0)
    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) <= 6e-113) {
		tmp = ((x_m * 2.0) / z) / (y - t);
	} else {
		tmp = (x_m / (y - t)) / (z / 2.0);
	}
	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) <= 6e-113:
		tmp = ((x_m * 2.0) / z) / (y - t)
	else:
		tmp = (x_m / (y - t)) / (z / 2.0)
	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) <= 6e-113)
		tmp = Float64(Float64(Float64(x_m * 2.0) / z) / Float64(y - t));
	else
		tmp = Float64(Float64(x_m / Float64(y - t)) / Float64(z / 2.0));
	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) <= 6e-113)
		tmp = ((x_m * 2.0) / z) / (y - t);
	else
		tmp = (x_m / (y - t)) / (z / 2.0);
	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], 6e-113], N[(N[(N[(x$95$m * 2.0), $MachinePrecision] / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(y - t), $MachinePrecision]), $MachinePrecision] / N[(z / 2.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < 6.0000000000000002e-113

   1. Initial program 93.2%

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

      1. distribute-rgt-out-- N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot 2}{z}\right), \color{blue}{\left(y - t\right)}\right) \]

      4. /-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{1}}{z}\right), \left(y - t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{\mathsf{neg}\left(-1\right)}}{z}\right), \left(y - t\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot 2}{\mathsf{neg}\left(-1\right)}\right), z\right), \left(\color{blue}{y} - t\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot 2}{1}\right), z\right), \left(y - t\right)\right) \]

      8. /-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), z\right), \left(y - t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \left(y - t\right)\right) \]

      10. --lowering--.f64 91.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \mathsf{\_.f64}\left(y, \color{blue}{t}\right)\right) \]

   3. Simplified 91.7%

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

   if 6.0000000000000002e-113 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 86.0%

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

      1. distribute-rgt-out-- N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y - t}\right), \color{blue}{\left(\frac{z}{2}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - t\right)\right), \left(\frac{\color{blue}{z}}{2}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, t\right)\right), \left(\frac{z}{2}\right)\right) \]

      9. /-lowering-/.f64 97.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, t\right)\right), \mathsf{/.f64}\left(z, \color{blue}{2}\right)\right) \]

   4. Applied egg-rr 97.4%

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

Alternative 2: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-86}:\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x\_m}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{x\_m \cdot 2}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t} \cdot \frac{-2}{z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -3.4e-86)
    (/ -2.0 (* z (/ t x_m)))
    (if (<= t 2.6e-39) (/ (/ (* x_m 2.0) z) y) (* (/ x_m t) (/ -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 (t <= -3.4e-86) {
		tmp = -2.0 / (z * (t / x_m));
	} else if (t <= 2.6e-39) {
		tmp = ((x_m * 2.0) / z) / y;
	} else {
		tmp = (x_m / t) * (-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 (t <= (-3.4d-86)) then
        tmp = (-2.0d0) / (z * (t / x_m))
    else if (t <= 2.6d-39) then
        tmp = ((x_m * 2.0d0) / z) / y
    else
        tmp = (x_m / t) * ((-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 (t <= -3.4e-86) {
		tmp = -2.0 / (z * (t / x_m));
	} else if (t <= 2.6e-39) {
		tmp = ((x_m * 2.0) / z) / y;
	} else {
		tmp = (x_m / t) * (-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 t <= -3.4e-86:
		tmp = -2.0 / (z * (t / x_m))
	elif t <= 2.6e-39:
		tmp = ((x_m * 2.0) / z) / y
	else:
		tmp = (x_m / t) * (-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 (t <= -3.4e-86)
		tmp = Float64(-2.0 / Float64(z * Float64(t / x_m)));
	elseif (t <= 2.6e-39)
		tmp = Float64(Float64(Float64(x_m * 2.0) / z) / y);
	else
		tmp = Float64(Float64(x_m / t) * Float64(-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 (t <= -3.4e-86)
		tmp = -2.0 / (z * (t / x_m));
	elseif (t <= 2.6e-39)
		tmp = ((x_m * 2.0) / z) / y;
	else
		tmp = (x_m / t) * (-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[t, -3.4e-86], N[(-2.0 / N[(z * N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-39], N[(N[(N[(x$95$m * 2.0), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -3.4e-86

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-2 \cdot \frac{x}{z}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \left(\frac{x}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 73.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \mathsf{/.f64}\left(x, z\right)\right), t\right) \]

   5. Simplified 73.7%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-2, \color{blue}{\left(\frac{t}{\frac{x}{z}}\right)}\right) \]

      5. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-2, \left(\frac{t}{x} \cdot \color{blue}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-2, \mathsf{*.f64}\left(\left(\frac{t}{x}\right), \color{blue}{z}\right)\right) \]

      7. /-lowering-/.f64 75.1%

         \[\leadsto \mathsf{/.f64}\left(-2, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, x\right), z\right)\right) \]

   7. Applied egg-rr 75.1%

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

   if -3.4e-86 < t < 2.6e-39

   1. Initial program 89.5%

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

      1. distribute-rgt-out-- N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot 2}{z}\right), \color{blue}{\left(y - t\right)}\right) \]

      4. /-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{1}}{z}\right), \left(y - t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{\mathsf{neg}\left(-1\right)}}{z}\right), \left(y - t\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot 2}{\mathsf{neg}\left(-1\right)}\right), z\right), \left(\color{blue}{y} - t\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot 2}{1}\right), z\right), \left(y - t\right)\right) \]

      8. /-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), z\right), \left(y - t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \left(y - t\right)\right) \]

      10. --lowering--.f64 94.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \mathsf{\_.f64}\left(y, \color{blue}{t}\right)\right) \]

   3. Simplified 94.2%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \color{blue}{y}\right) \]
   6. Step-by-step derivation

   7. Simplified 84.2%

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

   if 2.6e-39 < t

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-2 \cdot \frac{x}{z}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \left(\frac{x}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 66.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \mathsf{/.f64}\left(x, z\right)\right), t\right) \]

   5. Simplified 66.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-/l/ N/A

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

      4. associate-*l/ N/A

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

      5. times-frac N/A

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

      6. metadata-eval N/A

         \[\leadsto \frac{x}{t} \cdot \frac{\mathsf{neg}\left(2\right)}{z} \]

      7. distribute-neg-frac N/A

         \[\leadsto \frac{x}{t} \cdot \left(\mathsf{neg}\left(\frac{2}{z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{2}{z}\right)\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\mathsf{neg}\left(\color{blue}{\frac{2}{z}}\right)\right)\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\frac{\mathsf{neg}\left(2\right)}{\color{blue}{z}}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\frac{-2}{z}\right)\right) \]

      12. /-lowering-/.f64 74.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{/.f64}\left(-2, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 74.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-86}:\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{x \cdot 2}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-86}:\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x\_m}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{x\_m \cdot \frac{2}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t} \cdot \frac{-2}{z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -4.1e-86)
    (/ -2.0 (* z (/ t x_m)))
    (if (<= t 2.6e-39) (/ (* x_m (/ 2.0 z)) y) (* (/ x_m t) (/ -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 (t <= -4.1e-86) {
		tmp = -2.0 / (z * (t / x_m));
	} else if (t <= 2.6e-39) {
		tmp = (x_m * (2.0 / z)) / y;
	} else {
		tmp = (x_m / t) * (-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 (t <= (-4.1d-86)) then
        tmp = (-2.0d0) / (z * (t / x_m))
    else if (t <= 2.6d-39) then
        tmp = (x_m * (2.0d0 / z)) / y
    else
        tmp = (x_m / t) * ((-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 (t <= -4.1e-86) {
		tmp = -2.0 / (z * (t / x_m));
	} else if (t <= 2.6e-39) {
		tmp = (x_m * (2.0 / z)) / y;
	} else {
		tmp = (x_m / t) * (-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 t <= -4.1e-86:
		tmp = -2.0 / (z * (t / x_m))
	elif t <= 2.6e-39:
		tmp = (x_m * (2.0 / z)) / y
	else:
		tmp = (x_m / t) * (-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 (t <= -4.1e-86)
		tmp = Float64(-2.0 / Float64(z * Float64(t / x_m)));
	elseif (t <= 2.6e-39)
		tmp = Float64(Float64(x_m * Float64(2.0 / z)) / y);
	else
		tmp = Float64(Float64(x_m / t) * Float64(-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 (t <= -4.1e-86)
		tmp = -2.0 / (z * (t / x_m));
	elseif (t <= 2.6e-39)
		tmp = (x_m * (2.0 / z)) / y;
	else
		tmp = (x_m / t) * (-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[t, -4.1e-86], N[(-2.0 / N[(z * N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-39], N[(N[(x$95$m * N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -4.09999999999999979e-86

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-2 \cdot \frac{x}{z}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \left(\frac{x}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 73.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \mathsf{/.f64}\left(x, z\right)\right), t\right) \]

   5. Simplified 73.7%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-2, \color{blue}{\left(\frac{t}{\frac{x}{z}}\right)}\right) \]

      5. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-2, \left(\frac{t}{x} \cdot \color{blue}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-2, \mathsf{*.f64}\left(\left(\frac{t}{x}\right), \color{blue}{z}\right)\right) \]

      7. /-lowering-/.f64 75.1%

         \[\leadsto \mathsf{/.f64}\left(-2, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, x\right), z\right)\right) \]

   7. Applied egg-rr 75.1%

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

   if -4.09999999999999979e-86 < t < 2.6e-39

   1. Initial program 89.5%

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

      1. distribute-rgt-out-- N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot 2}{z}\right), \color{blue}{\left(y - t\right)}\right) \]

      4. /-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{1}}{z}\right), \left(y - t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{\mathsf{neg}\left(-1\right)}}{z}\right), \left(y - t\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot 2}{\mathsf{neg}\left(-1\right)}\right), z\right), \left(\color{blue}{y} - t\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot 2}{1}\right), z\right), \left(y - t\right)\right) \]

      8. /-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), z\right), \left(y - t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \left(y - t\right)\right) \]

      10. --lowering--.f64 94.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \mathsf{\_.f64}\left(y, \color{blue}{t}\right)\right) \]

   3. Simplified 94.2%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \color{blue}{y}\right) \]
   6. Step-by-step derivation

   7. Simplified 84.2%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{2}{z}\right), y\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{z} \cdot x\right), y\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\frac{2}{z}\right), x\right), y\right) \]

      4. /-lowering-/.f64 84.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(2, z\right), x\right), y\right) \]

   9. Applied egg-rr 84.1%

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

   if 2.6e-39 < t

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-2 \cdot \frac{x}{z}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \left(\frac{x}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 66.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \mathsf{/.f64}\left(x, z\right)\right), t\right) \]

   5. Simplified 66.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-/l/ N/A

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

      4. associate-*l/ N/A

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

      5. times-frac N/A

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

      6. metadata-eval N/A

         \[\leadsto \frac{x}{t} \cdot \frac{\mathsf{neg}\left(2\right)}{z} \]

      7. distribute-neg-frac N/A

         \[\leadsto \frac{x}{t} \cdot \left(\mathsf{neg}\left(\frac{2}{z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{2}{z}\right)\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\mathsf{neg}\left(\color{blue}{\frac{2}{z}}\right)\right)\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\frac{\mathsf{neg}\left(2\right)}{\color{blue}{z}}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\frac{-2}{z}\right)\right) \]

      12. /-lowering-/.f64 74.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{/.f64}\left(-2, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 74.9%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-86}:\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{x \cdot \frac{2}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-86}:\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x\_m}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{2}{\frac{y}{\frac{x\_m}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t} \cdot \frac{-2}{z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= t -2.95e-86)
    (/ -2.0 (* z (/ t x_m)))
    (if (<= t 2.6e-39) (/ 2.0 (/ y (/ x_m z))) (* (/ x_m t) (/ -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 (t <= -2.95e-86) {
		tmp = -2.0 / (z * (t / x_m));
	} else if (t <= 2.6e-39) {
		tmp = 2.0 / (y / (x_m / z));
	} else {
		tmp = (x_m / t) * (-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 (t <= (-2.95d-86)) then
        tmp = (-2.0d0) / (z * (t / x_m))
    else if (t <= 2.6d-39) then
        tmp = 2.0d0 / (y / (x_m / z))
    else
        tmp = (x_m / t) * ((-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 (t <= -2.95e-86) {
		tmp = -2.0 / (z * (t / x_m));
	} else if (t <= 2.6e-39) {
		tmp = 2.0 / (y / (x_m / z));
	} else {
		tmp = (x_m / t) * (-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 t <= -2.95e-86:
		tmp = -2.0 / (z * (t / x_m))
	elif t <= 2.6e-39:
		tmp = 2.0 / (y / (x_m / z))
	else:
		tmp = (x_m / t) * (-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 (t <= -2.95e-86)
		tmp = Float64(-2.0 / Float64(z * Float64(t / x_m)));
	elseif (t <= 2.6e-39)
		tmp = Float64(2.0 / Float64(y / Float64(x_m / z)));
	else
		tmp = Float64(Float64(x_m / t) * Float64(-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 (t <= -2.95e-86)
		tmp = -2.0 / (z * (t / x_m));
	elseif (t <= 2.6e-39)
		tmp = 2.0 / (y / (x_m / z));
	else
		tmp = (x_m / t) * (-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[t, -2.95e-86], N[(-2.0 / N[(z * N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-39], N[(2.0 / N[(y / N[(x$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if t < -2.94999999999999999e-86

   1. Initial program 91.4%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-2 \cdot \frac{x}{z}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \left(\frac{x}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 73.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \mathsf{/.f64}\left(x, z\right)\right), t\right) \]

   5. Simplified 73.7%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-2, \color{blue}{\left(\frac{t}{\frac{x}{z}}\right)}\right) \]

      5. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-2, \left(\frac{t}{x} \cdot \color{blue}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-2, \mathsf{*.f64}\left(\left(\frac{t}{x}\right), \color{blue}{z}\right)\right) \]

      7. /-lowering-/.f64 75.1%

         \[\leadsto \mathsf{/.f64}\left(-2, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, x\right), z\right)\right) \]

   7. Applied egg-rr 75.1%

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

   if -2.94999999999999999e-86 < t < 2.6e-39

   1. Initial program 89.5%

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

      1. distribute-rgt-out-- N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot 2}{z}\right), \color{blue}{\left(y - t\right)}\right) \]

      4. /-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{1}}{z}\right), \left(y - t\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{\mathsf{neg}\left(-1\right)}}{z}\right), \left(y - t\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot 2}{\mathsf{neg}\left(-1\right)}\right), z\right), \left(\color{blue}{y} - t\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot 2}{1}\right), z\right), \left(y - t\right)\right) \]

      8. /-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), z\right), \left(y - t\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \left(y - t\right)\right) \]

      10. --lowering--.f64 94.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \mathsf{\_.f64}\left(y, \color{blue}{t}\right)\right) \]

   3. Simplified 94.2%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \color{blue}{y}\right) \]
   6. Step-by-step derivation

   7. Simplified 84.2%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{2}{z}\right), y\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{z} \cdot x\right), y\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\frac{2}{z}\right), x\right), y\right) \]

      4. /-lowering-/.f64 84.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(2, z\right), x\right), y\right) \]

   9. Applied egg-rr 84.1%

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

       1. associate-/r/ N/A

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

       2. associate-/l/ N/A

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

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(2, \color{blue}{\left(y \cdot \frac{z}{x}\right)}\right) \]

       4. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(2, \left(y \cdot \frac{1}{\color{blue}{\frac{x}{z}}}\right)\right) \]

       5. un-div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(2, \left(\frac{y}{\color{blue}{\frac{x}{z}}}\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(2, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{x}{z}\right)}\right)\right) \]

       7. /-lowering-/.f64 83.4%

          \[\leadsto \mathsf{/.f64}\left(2, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{z}\right)\right)\right) \]

   11. Applied egg-rr 83.4%

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

   if 2.6e-39 < t

   1. Initial program 92.4%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-2 \cdot \frac{x}{z}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \left(\frac{x}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 66.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \mathsf{/.f64}\left(x, z\right)\right), t\right) \]

   5. Simplified 66.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-/l/ N/A

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

      4. associate-*l/ N/A

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

      5. times-frac N/A

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

      6. metadata-eval N/A

         \[\leadsto \frac{x}{t} \cdot \frac{\mathsf{neg}\left(2\right)}{z} \]

      7. distribute-neg-frac N/A

         \[\leadsto \frac{x}{t} \cdot \left(\mathsf{neg}\left(\frac{2}{z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{2}{z}\right)\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\mathsf{neg}\left(\color{blue}{\frac{2}{z}}\right)\right)\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\frac{\mathsf{neg}\left(2\right)}{\color{blue}{z}}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\frac{-2}{z}\right)\right) \]

      12. /-lowering-/.f64 74.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{/.f64}\left(-2, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 74.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-86}:\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{2}{\frac{y}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \cdot 2 \leq 2 \cdot 10^{-134}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x\_m}{y - t}}{\frac{z}{2}}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= (* x_m 2.0) 2e-134)
    (* (/ x_m z) (/ 2.0 (- y t)))
    (/ (/ x_m (- y t)) (/ z 2.0)))))

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) <= 2e-134) {
		tmp = (x_m / z) * (2.0 / (y - t));
	} else {
		tmp = (x_m / (y - t)) / (z / 2.0);
	}
	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) <= 2d-134) then
        tmp = (x_m / z) * (2.0d0 / (y - t))
    else
        tmp = (x_m / (y - t)) / (z / 2.0d0)
    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) <= 2e-134) {
		tmp = (x_m / z) * (2.0 / (y - t));
	} else {
		tmp = (x_m / (y - t)) / (z / 2.0);
	}
	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) <= 2e-134:
		tmp = (x_m / z) * (2.0 / (y - t))
	else:
		tmp = (x_m / (y - t)) / (z / 2.0)
	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) <= 2e-134)
		tmp = Float64(Float64(x_m / z) * Float64(2.0 / Float64(y - t)));
	else
		tmp = Float64(Float64(x_m / Float64(y - t)) / Float64(z / 2.0));
	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) <= 2e-134)
		tmp = (x_m / z) * (2.0 / (y - t));
	else
		tmp = (x_m / (y - t)) / (z / 2.0);
	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], 2e-134], N[(N[(x$95$m / z), $MachinePrecision] * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / N[(y - t), $MachinePrecision]), $MachinePrecision] / N[(z / 2.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < 2.00000000000000008e-134

   1. Initial program 93.1%

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

      1. distribute-rgt-out-- N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{z}\right), \color{blue}{\left(\frac{2}{y - t}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\frac{\color{blue}{2}}{y - t}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{/.f64}\left(2, \color{blue}{\left(y - t\right)}\right)\right) \]

      6. --lowering--.f64 92.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{/.f64}\left(2, \mathsf{\_.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 92.0%

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

   if 2.00000000000000008e-134 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 86.4%

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

      1. distribute-rgt-out-- N/A

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

      2. *-commutative N/A

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

      3. times-frac N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y - t}\right), \color{blue}{\left(\frac{z}{2}\right)}\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - t\right)\right), \left(\frac{\color{blue}{z}}{2}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, t\right)\right), \left(\frac{z}{2}\right)\right) \]

      9. /-lowering-/.f64 97.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, t\right)\right), \mathsf{/.f64}\left(z, \color{blue}{2}\right)\right) \]

   4. Applied egg-rr 97.4%

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

Alternative 6: 95.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \cdot 2 \leq 2 \cdot 10^{-134}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z}}{\frac{y - t}{x\_m}}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= (* x_m 2.0) 2e-134)
    (* (/ x_m z) (/ 2.0 (- y t)))
    (/ (/ 2.0 z) (/ (- y t) 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 tmp;
	if ((x_m * 2.0) <= 2e-134) {
		tmp = (x_m / z) * (2.0 / (y - t));
	} else {
		tmp = (2.0 / z) / ((y - t) / x_m);
	}
	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) <= 2d-134) then
        tmp = (x_m / z) * (2.0d0 / (y - t))
    else
        tmp = (2.0d0 / z) / ((y - t) / x_m)
    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) <= 2e-134) {
		tmp = (x_m / z) * (2.0 / (y - t));
	} else {
		tmp = (2.0 / z) / ((y - t) / 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):
	tmp = 0
	if (x_m * 2.0) <= 2e-134:
		tmp = (x_m / z) * (2.0 / (y - t))
	else:
		tmp = (2.0 / z) / ((y - t) / 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)
	tmp = 0.0
	if (Float64(x_m * 2.0) <= 2e-134)
		tmp = Float64(Float64(x_m / z) * Float64(2.0 / Float64(y - t)));
	else
		tmp = Float64(Float64(2.0 / z) / Float64(Float64(y - t) / 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)
	tmp = 0.0;
	if ((x_m * 2.0) <= 2e-134)
		tmp = (x_m / z) * (2.0 / (y - t));
	else
		tmp = (2.0 / z) / ((y - t) / 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_] := N[(x$95$s * If[LessEqual[N[(x$95$m * 2.0), $MachinePrecision], 2e-134], N[(N[(x$95$m / z), $MachinePrecision] * N[(2.0 / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] / N[(N[(y - t), $MachinePrecision] / x$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < 2.00000000000000008e-134

   1. Initial program 93.1%

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

      1. distribute-rgt-out-- N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{z}\right), \color{blue}{\left(\frac{2}{y - t}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\frac{\color{blue}{2}}{y - t}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{/.f64}\left(2, \color{blue}{\left(y - t\right)}\right)\right) \]

      6. --lowering--.f64 92.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{/.f64}\left(2, \mathsf{\_.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 92.0%

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

   if 2.00000000000000008e-134 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 86.4%

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

      1. clear-num N/A

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

      2. distribute-rgt-out-- N/A

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

      3. *-commutative N/A

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

      4. times-frac N/A

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

      5. associate-/r* N/A

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

      6. clear-num N/A

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

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{z}\right), \color{blue}{\left(\frac{y - t}{x}\right)}\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, z\right), \left(\frac{\color{blue}{y - t}}{x}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, z\right), \mathsf{/.f64}\left(\left(y - t\right), \color{blue}{x}\right)\right) \]

      10. --lowering--.f64 97.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, z\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, t\right), x\right)\right) \]

   4. Applied egg-rr 97.5%

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

Alternative 7: 95.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ \begin{array}{l} t_1 := \frac{2}{y - t}\\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \cdot 2 \leq 2 \cdot 10^{-134}:\\ \;\;\;\;\frac{x\_m}{z} \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m \cdot t\_1}{z}\\ \end{array} \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) 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) 2e-134) (* (/ 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) <= 2e-134) {
		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) <= 2d-134) 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) <= 2e-134) {
		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) <= 2e-134:
		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) <= 2e-134)
		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) <= 2e-134)
		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], 2e-134], 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 #s(literal 2 binary64)) < 2.00000000000000008e-134

   1. Initial program 93.1%

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

      1. distribute-rgt-out-- N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{z}\right), \color{blue}{\left(\frac{2}{y - t}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\frac{\color{blue}{2}}{y - t}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{/.f64}\left(2, \color{blue}{\left(y - t\right)}\right)\right) \]

      6. --lowering--.f64 92.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{/.f64}\left(2, \mathsf{\_.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

   4. Applied egg-rr 92.0%

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

   if 2.00000000000000008e-134 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 86.4%

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

      1. *-commutative N/A

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

      2. distribute-rgt-out-- N/A

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

      3. *-commutative N/A

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

      4. times-frac N/A

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

      5. associate-*r/ N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{y - t} \cdot x\right), \color{blue}{z}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\frac{2}{y - t}\right), x\right), z\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(2, \left(y - t\right)\right), x\right), z\right) \]

      9. --lowering--.f64 97.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(2, \mathsf{\_.f64}\left(y, t\right)\right), x\right), z\right) \]

   4. Applied egg-rr 97.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq 2 \cdot 10^{-134}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y - t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 2.6 \cdot 10^{-91}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x\_m}}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 2.6e-91) (* (/ x_m z) (/ -2.0 t)) (/ -2.0 (* z (/ t 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 tmp;
	if (x_m <= 2.6e-91) {
		tmp = (x_m / z) * (-2.0 / t);
	} else {
		tmp = -2.0 / (z * (t / x_m));
	}
	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 <= 2.6d-91) then
        tmp = (x_m / z) * ((-2.0d0) / t)
    else
        tmp = (-2.0d0) / (z * (t / x_m))
    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 <= 2.6e-91) {
		tmp = (x_m / z) * (-2.0 / t);
	} else {
		tmp = -2.0 / (z * (t / 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):
	tmp = 0
	if x_m <= 2.6e-91:
		tmp = (x_m / z) * (-2.0 / t)
	else:
		tmp = -2.0 / (z * (t / 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)
	tmp = 0.0
	if (x_m <= 2.6e-91)
		tmp = Float64(Float64(x_m / z) * Float64(-2.0 / t));
	else
		tmp = Float64(-2.0 / Float64(z * Float64(t / 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)
	tmp = 0.0;
	if (x_m <= 2.6e-91)
		tmp = (x_m / z) * (-2.0 / t);
	else
		tmp = -2.0 / (z * (t / 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_] := N[(x$95$s * If[LessEqual[x$95$m, 2.6e-91], N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 / N[(z * N[(t / x$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 2.60000000000000014e-91

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-2 \cdot \frac{x}{z}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \left(\frac{x}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 57.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \mathsf{/.f64}\left(x, z\right)\right), t\right) \]

   5. Simplified 57.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{z}\right), \color{blue}{\left(\frac{-2}{t}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\frac{\color{blue}{-2}}{t}\right)\right) \]

      5. /-lowering-/.f64 57.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{/.f64}\left(-2, \color{blue}{t}\right)\right) \]

   7. Applied egg-rr 57.1%

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

   if 2.60000000000000014e-91 < x

   1. Initial program 85.5%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-2 \cdot \frac{x}{z}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \left(\frac{x}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 47.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \mathsf{/.f64}\left(x, z\right)\right), t\right) \]

   5. Simplified 47.1%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-2, \color{blue}{\left(\frac{t}{\frac{x}{z}}\right)}\right) \]

      5. associate-/r/ N/A

         \[\leadsto \mathsf{/.f64}\left(-2, \left(\frac{t}{x} \cdot \color{blue}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(-2, \mathsf{*.f64}\left(\left(\frac{t}{x}\right), \color{blue}{z}\right)\right) \]

      7. /-lowering-/.f64 53.9%

         \[\leadsto \mathsf{/.f64}\left(-2, \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, x\right), z\right)\right) \]

   7. Applied egg-rr 53.9%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.6 \cdot 10^{-91}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{z \cdot \frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} x\_m = \left|x\right| \\ x\_s = \mathsf{copysign}\left(1, x\right) \\ x\_s \cdot \begin{array}{l} \mathbf{if}\;x\_m \leq 2.85 \cdot 10^{-92}:\\ \;\;\;\;\frac{x\_m}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x\_m}{t} \cdot \frac{-2}{z}\\ \end{array} \end{array} \]

FPCore

x\_m = (fabs.f64 x)
x\_s = (copysign.f64 #s(literal 1 binary64) x)
(FPCore (x_s x_m y z t)
 :precision binary64
 (*
  x_s
  (if (<= x_m 2.85e-92) (* (/ x_m z) (/ -2.0 t)) (* (/ x_m t) (/ -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 (x_m <= 2.85e-92) {
		tmp = (x_m / z) * (-2.0 / t);
	} else {
		tmp = (x_m / t) * (-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 (x_m <= 2.85d-92) then
        tmp = (x_m / z) * ((-2.0d0) / t)
    else
        tmp = (x_m / t) * ((-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 (x_m <= 2.85e-92) {
		tmp = (x_m / z) * (-2.0 / t);
	} else {
		tmp = (x_m / t) * (-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 x_m <= 2.85e-92:
		tmp = (x_m / z) * (-2.0 / t)
	else:
		tmp = (x_m / t) * (-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 (x_m <= 2.85e-92)
		tmp = Float64(Float64(x_m / z) * Float64(-2.0 / t));
	else
		tmp = Float64(Float64(x_m / t) * Float64(-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 (x_m <= 2.85e-92)
		tmp = (x_m / z) * (-2.0 / t);
	else
		tmp = (x_m / t) * (-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[x$95$m, 2.85e-92], N[(N[(x$95$m / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x$95$m / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 2.85000000000000004e-92

   1. Initial program 93.3%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-2 \cdot \frac{x}{z}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \left(\frac{x}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 57.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \mathsf{/.f64}\left(x, z\right)\right), t\right) \]

   5. Simplified 57.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{z}\right), \color{blue}{\left(\frac{-2}{t}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\frac{\color{blue}{-2}}{t}\right)\right) \]

      5. /-lowering-/.f64 57.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{/.f64}\left(-2, \color{blue}{t}\right)\right) \]

   7. Applied egg-rr 57.1%

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

   if 2.85000000000000004e-92 < x

   1. Initial program 85.5%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l/ N/A

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

      2. associate-*r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-2 \cdot \frac{x}{z}\right), \color{blue}{t}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \left(\frac{x}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 47.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \mathsf{/.f64}\left(x, z\right)\right), t\right) \]

   5. Simplified 47.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-/l/ N/A

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

      4. associate-*l/ N/A

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

      5. times-frac N/A

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

      6. metadata-eval N/A

         \[\leadsto \frac{x}{t} \cdot \frac{\mathsf{neg}\left(2\right)}{z} \]

      7. distribute-neg-frac N/A

         \[\leadsto \frac{x}{t} \cdot \left(\mathsf{neg}\left(\frac{2}{z}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{2}{z}\right)\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\mathsf{neg}\left(\color{blue}{\frac{2}{z}}\right)\right)\right) \]

      10. distribute-neg-frac N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\frac{\mathsf{neg}\left(2\right)}{\color{blue}{z}}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\frac{-2}{z}\right)\right) \]

      12. /-lowering-/.f64 54.0%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{/.f64}\left(-2, \color{blue}{z}\right)\right) \]

   7. Applied egg-rr 54.0%

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

Alternative 10: 91.9% accurate, 1.2× speedup

Math

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

FPCore

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

Derivation

1. Initial program 90.9%

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

   1. distribute-rgt-out-- N/A

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

   2. associate-/r* N/A

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

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{x \cdot 2}{z}\right), \color{blue}{\left(y - t\right)}\right) \]

   4. /-rgt-identity N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{1}}{z}\right), \left(y - t\right)\right) \]

   5. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{x \cdot 2}{\mathsf{neg}\left(-1\right)}}{z}\right), \left(y - t\right)\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot 2}{\mathsf{neg}\left(-1\right)}\right), z\right), \left(\color{blue}{y} - t\right)\right) \]

   7. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{x \cdot 2}{1}\right), z\right), \left(y - t\right)\right) \]

   8. /-rgt-identity N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot 2\right), z\right), \left(y - t\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \left(y - t\right)\right) \]

   10. --lowering--.f64 90.0%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, 2\right), z\right), \mathsf{\_.f64}\left(y, \color{blue}{t}\right)\right) \]

3. Simplified 90.0%

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

   1. associate-/l* N/A

      \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{2}{z}\right), \mathsf{\_.f64}\left(\color{blue}{y}, t\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{z} \cdot x\right), \mathsf{\_.f64}\left(\color{blue}{y}, t\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(\frac{2}{z}\right), x\right), \mathsf{\_.f64}\left(\color{blue}{y}, t\right)\right) \]

   4. /-lowering-/.f64 90.2%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(2, z\right), x\right), \mathsf{\_.f64}\left(y, t\right)\right) \]

6. Applied egg-rr 90.2%

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

7. Final simplification 90.2%

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

Alternative 11: 91.9% accurate, 1.2× speedup

Math

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

FPCore

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

Derivation

1. Initial program 90.9%

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

   1. distribute-rgt-out-- N/A

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

   2. times-frac N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{z}\right), \color{blue}{\left(\frac{2}{y - t}\right)}\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\frac{\color{blue}{2}}{y - t}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{/.f64}\left(2, \color{blue}{\left(y - t\right)}\right)\right) \]

   6. --lowering--.f64 90.2%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{/.f64}\left(2, \mathsf{\_.f64}\left(y, \color{blue}{t}\right)\right)\right) \]

4. Applied egg-rr 90.2%

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

Alternative 12: 53.6% accurate, 1.6× speedup

Math

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

FPCore

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

Derivation

1. Initial program 90.9%

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

3. Taylor expanded in y around 0

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

   1. associate-/l/ N/A

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

   2. associate-*r/ N/A

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

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(-2 \cdot \frac{x}{z}\right), \color{blue}{t}\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \left(\frac{x}{z}\right)\right), t\right) \]

   5. /-lowering-/.f64 54.0%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(-2, \mathsf{/.f64}\left(x, z\right)\right), t\right) \]

5. Simplified 54.0%

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

   1. associate-/l* N/A

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

   2. *-commutative N/A

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

   3. associate-/l/ N/A

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

   4. associate-*l/ N/A

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

   5. times-frac N/A

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

   6. metadata-eval N/A

      \[\leadsto \frac{x}{t} \cdot \frac{\mathsf{neg}\left(2\right)}{z} \]

   7. distribute-neg-frac N/A

      \[\leadsto \frac{x}{t} \cdot \left(\mathsf{neg}\left(\frac{2}{z}\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{2}{z}\right)\right)}\right) \]

   9. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\mathsf{neg}\left(\color{blue}{\frac{2}{z}}\right)\right)\right) \]

   10. distribute-neg-frac N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\frac{\mathsf{neg}\left(2\right)}{\color{blue}{z}}\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\frac{-2}{z}\right)\right) \]

   12. /-lowering-/.f64 52.9%

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{/.f64}\left(-2, \color{blue}{z}\right)\right) \]

7. Applied egg-rr 52.9%

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

Developer Target 1: 97.1% 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 2024138 
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (* x 2) (- (* y z) (* t z))) -2559141628295061/10000000000000000000000000000) (* (/ x (* (- y t) z)) 2) (if (< (/ (* x 2) (- (* y z) (* t z))) 522513913665063/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (* (/ x z) 2) (- y t)) (* (/ x (* (- y t) z)) 2))))

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