Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 90.1% → 95.1%

Time: 8.7s

Alternatives: 13

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: 90.1% 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: 95.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -1 \cdot 10^{+169} \lor \neg \left(x \cdot 2 \leq 2 \cdot 10^{-166}\right):\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* x 2.0) -1e+169) (not (<= (* x 2.0) 2e-166)))
   (* (/ x (- y t)) (/ 2.0 z))
   (* 2.0 (/ (/ x z) (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) <= -1e+169) || !((x * 2.0) <= 2e-166)) {
		tmp = (x / (y - t)) * (2.0 / z);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	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) :: tmp
    if (((x * 2.0d0) <= (-1d+169)) .or. (.not. ((x * 2.0d0) <= 2d-166))) then
        tmp = (x / (y - t)) * (2.0d0 / z)
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) <= -1e+169) || !((x * 2.0) <= 2e-166)) {
		tmp = (x / (y - t)) * (2.0 / z);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * 2.0) <= -1e+169) or not ((x * 2.0) <= 2e-166):
		tmp = (x / (y - t)) * (2.0 / z)
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x * 2.0) <= -1e+169) || !(Float64(x * 2.0) <= 2e-166))
		tmp = Float64(Float64(x / Float64(y - t)) * Float64(2.0 / z));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * 2.0) <= -1e+169) || ~(((x * 2.0) <= 2e-166)))
		tmp = (x / (y - t)) * (2.0 / z);
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x * 2.0), $MachinePrecision], -1e+169], N[Not[LessEqual[N[(x * 2.0), $MachinePrecision], 2e-166]], $MachinePrecision]], N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < -9.99999999999999934e168 or 2.00000000000000008e-166 < (*.f64 x 2)

   1. Initial program 85.0%

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

      1. distribute-rgt-out-- 85.9%

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

   3. Simplified 85.9%

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

      1. *-commutative 85.9%

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

      2. times-frac 98.8%

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

   5. Applied egg-rr 98.8%

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

   if -9.99999999999999934e168 < (*.f64 x 2) < 2.00000000000000008e-166

   1. Initial program 90.4%

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

      1. associate-*l/ 90.4%

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

      2. *-commutative 90.4%

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

      3. distribute-rgt-out-- 94.9%

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

      4. associate-/r* 98.4%

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

   3. Simplified 98.4%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -1 \cdot 10^{+169} \lor \neg \left(x \cdot 2 \leq 2 \cdot 10^{-166}\right):\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 2: 96.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-31} \lor \neg \left(z \leq 4.6 \cdot 10^{-7}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t - y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.9e-31) (not (<= z 4.6e-7)))
   (* 2.0 (/ (/ x z) (- y t)))
   (* x (/ (/ -2.0 (- t y)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.9e-31) || !(z <= 4.6e-7)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * ((-2.0 / (t - y)) / z);
	}
	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) :: tmp
    if ((z <= (-5.9d-31)) .or. (.not. (z <= 4.6d-7))) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else
        tmp = x * (((-2.0d0) / (t - y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.9e-31) || !(z <= 4.6e-7)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * ((-2.0 / (t - y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.9e-31) or not (z <= 4.6e-7):
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = x * ((-2.0 / (t - y)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.9e-31) || !(z <= 4.6e-7))
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(x * Float64(Float64(-2.0 / Float64(t - y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.9e-31) || ~((z <= 4.6e-7)))
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = x * ((-2.0 / (t - y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.9e-31], N[Not[LessEqual[z, 4.6e-7]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-2.0 / N[(t - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.90000000000000032e-31 or 4.5999999999999999e-7 < z

   1. Initial program 83.2%

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

      1. associate-*l/ 83.2%

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

      2. *-commutative 83.2%

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

      3. distribute-rgt-out-- 86.9%

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

      4. associate-/r* 98.5%

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

   3. Simplified 98.5%

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

   if -5.90000000000000032e-31 < z < 4.5999999999999999e-7

   1. Initial program 93.2%

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

      1. associate-*r/ 93.1%

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

      2. distribute-rgt-out-- 94.8%

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

      3. associate-/l/ 94.8%

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

      4. sub-neg 94.8%

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

      5. +-commutative 94.8%

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

      6. neg-sub0 94.8%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 94.8%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 94.8%

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

      9. neg-mul-1 94.8%

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

      10. associate-/r* 94.8%

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

      11. metadata-eval 94.8%

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

   3. Simplified 94.8%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-31} \lor \neg \left(z \leq 4.6 \cdot 10^{-7}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{t - y}}{z}\\ \end{array} \]

Alternative 3: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{-34} \lor \neg \left(t \leq 4.1 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.6e-34) (not (<= t 4.1e+34)))
   (* x (/ (/ -2.0 t) z))
   (* x (/ 2.0 (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.6e-34) || !(t <= 4.1e+34)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = x * (2.0 / (y * z));
	}
	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) :: tmp
    if ((t <= (-9.6d-34)) .or. (.not. (t <= 4.1d+34))) then
        tmp = x * (((-2.0d0) / t) / z)
    else
        tmp = x * (2.0d0 / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.6e-34) || !(t <= 4.1e+34)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = x * (2.0 / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9.6e-34) or not (t <= 4.1e+34):
		tmp = x * ((-2.0 / t) / z)
	else:
		tmp = x * (2.0 / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9.6e-34) || !(t <= 4.1e+34))
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	else
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9.6e-34) || ~((t <= 4.1e+34)))
		tmp = x * ((-2.0 / t) / z);
	else
		tmp = x * (2.0 / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9.6e-34], N[Not[LessEqual[t, 4.1e+34]], $MachinePrecision]], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.59999999999999965e-34 or 4.0999999999999998e34 < t

   1. Initial program 85.5%

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

      1. associate-*r/ 85.4%

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

      2. distribute-rgt-out-- 89.4%

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

      3. associate-/l/ 89.3%

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

      4. sub-neg 89.3%

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

      5. +-commutative 89.3%

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

      6. neg-sub0 89.3%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 89.3%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 89.3%

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

      9. neg-mul-1 89.3%

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

      10. associate-/r* 89.3%

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

      11. metadata-eval 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around inf 72.8%

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

   if -9.59999999999999965e-34 < t < 4.0999999999999998e34

   1. Initial program 90.1%

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

      1. associate-*r/ 90.1%

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

      2. distribute-rgt-out-- 91.6%

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

      3. associate-/l/ 91.7%

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

      4. sub-neg 91.7%

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

      5. +-commutative 91.7%

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

      6. neg-sub0 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 91.7%

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

      9. neg-mul-1 91.7%

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

      10. associate-/r* 91.7%

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

      11. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around 0 74.8%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{-34} \lor \neg \left(t \leq 4.1 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \end{array} \]

Alternative 4: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-33} \lor \neg \left(t \leq 4.2 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.1e-33) (not (<= t 4.2e+34)))
   (* x (/ (/ -2.0 t) z))
   (* x (/ (/ 2.0 y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.1e-33) || !(t <= 4.2e+34)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = x * ((2.0 / y) / z);
	}
	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) :: tmp
    if ((t <= (-2.1d-33)) .or. (.not. (t <= 4.2d+34))) then
        tmp = x * (((-2.0d0) / t) / z)
    else
        tmp = x * ((2.0d0 / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.1e-33) || !(t <= 4.2e+34)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = x * ((2.0 / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.1e-33) or not (t <= 4.2e+34):
		tmp = x * ((-2.0 / t) / z)
	else:
		tmp = x * ((2.0 / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.1e-33) || !(t <= 4.2e+34))
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	else
		tmp = Float64(x * Float64(Float64(2.0 / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.1e-33) || ~((t <= 4.2e+34)))
		tmp = x * ((-2.0 / t) / z);
	else
		tmp = x * ((2.0 / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.1e-33], N[Not[LessEqual[t, 4.2e+34]], $MachinePrecision]], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1e-33 or 4.20000000000000035e34 < t

   1. Initial program 85.5%

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

      1. associate-*r/ 85.4%

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

      2. distribute-rgt-out-- 89.4%

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

      3. associate-/l/ 89.3%

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

      4. sub-neg 89.3%

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

      5. +-commutative 89.3%

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

      6. neg-sub0 89.3%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 89.3%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 89.3%

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

      9. neg-mul-1 89.3%

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

      10. associate-/r* 89.3%

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

      11. metadata-eval 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around inf 72.8%

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

   if -2.1e-33 < t < 4.20000000000000035e34

   1. Initial program 90.1%

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

      1. associate-*r/ 90.1%

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

      2. distribute-rgt-out-- 91.6%

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

      3. associate-/l/ 91.7%

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

      4. sub-neg 91.7%

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

      5. +-commutative 91.7%

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

      6. neg-sub0 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 91.7%

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

      9. neg-mul-1 91.7%

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

      10. associate-/r* 91.7%

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

      11. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around 0 74.8%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-33} \lor \neg \left(t \leq 4.2 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \]

Alternative 5: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+53} \lor \neg \left(t \leq 8.5 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3e+53) (not (<= t 8.5e+34)))
   (* x (/ (/ -2.0 t) z))
   (* (/ x z) (/ 2.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3e+53) || !(t <= 8.5e+34)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	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) :: tmp
    if ((t <= (-3d+53)) .or. (.not. (t <= 8.5d+34))) then
        tmp = x * (((-2.0d0) / t) / z)
    else
        tmp = (x / z) * (2.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3e+53) || !(t <= 8.5e+34)) {
		tmp = x * ((-2.0 / t) / z);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3e+53) or not (t <= 8.5e+34):
		tmp = x * ((-2.0 / t) / z)
	else:
		tmp = (x / z) * (2.0 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3e+53) || !(t <= 8.5e+34))
		tmp = Float64(x * Float64(Float64(-2.0 / t) / z));
	else
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3e+53) || ~((t <= 8.5e+34)))
		tmp = x * ((-2.0 / t) / z);
	else
		tmp = (x / z) * (2.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3e+53], N[Not[LessEqual[t, 8.5e+34]], $MachinePrecision]], N[(x * N[(N[(-2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.99999999999999998e53 or 8.5000000000000003e34 < t

   1. Initial program 84.5%

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

      1. associate-*r/ 84.3%

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

      2. distribute-rgt-out-- 88.8%

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

      3. associate-/l/ 88.8%

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

      4. sub-neg 88.8%

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

      5. +-commutative 88.8%

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

      6. neg-sub0 88.8%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 88.8%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 88.8%

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

      9. neg-mul-1 88.8%

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

      10. associate-/r* 88.8%

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

      11. metadata-eval 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in t around inf 75.1%

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

   if -2.99999999999999998e53 < t < 8.5000000000000003e34

   1. Initial program 90.4%

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

      1. associate-*r/ 90.4%

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

      2. distribute-rgt-out-- 91.8%

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

      3. associate-/l/ 91.9%

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

      4. sub-neg 91.9%

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

      5. +-commutative 91.9%

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

      6. neg-sub0 91.9%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 91.9%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 91.9%

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

      9. neg-mul-1 91.9%

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

      10. associate-/r* 91.9%

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

      11. metadata-eval 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in t around 0 71.9%

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

      1. associate-*r/ 71.9%

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

      2. times-frac 73.2%

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

   6. Simplified 73.2%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+53} \lor \neg \left(t \leq 8.5 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \frac{\frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 6: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-33} \lor \neg \left(t \leq 4.1 \cdot 10^{+34}\right):\\ \;\;\;\;-2 \cdot \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.25e-33) (not (<= t 4.1e+34)))
   (* -2.0 (/ x (* t z)))
   (* x (/ (/ 2.0 y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.25e-33) || !(t <= 4.1e+34)) {
		tmp = -2.0 * (x / (t * z));
	} else {
		tmp = x * ((2.0 / y) / z);
	}
	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) :: tmp
    if ((t <= (-1.25d-33)) .or. (.not. (t <= 4.1d+34))) then
        tmp = (-2.0d0) * (x / (t * z))
    else
        tmp = x * ((2.0d0 / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.25e-33) || !(t <= 4.1e+34)) {
		tmp = -2.0 * (x / (t * z));
	} else {
		tmp = x * ((2.0 / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.25e-33) or not (t <= 4.1e+34):
		tmp = -2.0 * (x / (t * z))
	else:
		tmp = x * ((2.0 / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.25e-33) || !(t <= 4.1e+34))
		tmp = Float64(-2.0 * Float64(x / Float64(t * z)));
	else
		tmp = Float64(x * Float64(Float64(2.0 / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.25e-33) || ~((t <= 4.1e+34)))
		tmp = -2.0 * (x / (t * z));
	else
		tmp = x * ((2.0 / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.25e-33], N[Not[LessEqual[t, 4.1e+34]], $MachinePrecision]], N[(-2.0 * N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(2.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25000000000000007e-33 or 4.0999999999999998e34 < t

   1. Initial program 85.5%

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

      1. associate-*r/ 85.4%

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

      2. distribute-rgt-out-- 89.4%

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

      3. associate-/l/ 89.3%

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

      4. sub-neg 89.3%

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

      5. +-commutative 89.3%

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

      6. neg-sub0 89.3%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 89.3%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 89.3%

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

      9. neg-mul-1 89.3%

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

      10. associate-/r* 89.3%

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

      11. metadata-eval 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in t around inf 73.7%

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

      1. *-commutative 73.7%

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

   6. Simplified 73.7%

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

   if -1.25000000000000007e-33 < t < 4.0999999999999998e34

   1. Initial program 90.1%

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

      1. associate-*r/ 90.1%

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

      2. distribute-rgt-out-- 91.6%

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

      3. associate-/l/ 91.7%

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

      4. sub-neg 91.7%

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

      5. +-commutative 91.7%

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

      6. neg-sub0 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 91.7%

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

      9. neg-mul-1 91.7%

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

      10. associate-/r* 91.7%

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

      11. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around 0 74.8%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-33} \lor \neg \left(t \leq 4.1 \cdot 10^{+34}\right):\\ \;\;\;\;-2 \cdot \frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{2}{y}}{z}\\ \end{array} \]

Alternative 7: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+89} \lor \neg \left(t \leq 5.8 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x \cdot \frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.2e+89) (not (<= t 5.8e+34)))
   (/ (* x (/ -2.0 t)) z)
   (* (/ x z) (/ 2.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.2e+89) || !(t <= 5.8e+34)) {
		tmp = (x * (-2.0 / t)) / z;
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	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) :: tmp
    if ((t <= (-2.2d+89)) .or. (.not. (t <= 5.8d+34))) then
        tmp = (x * ((-2.0d0) / t)) / z
    else
        tmp = (x / z) * (2.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.2e+89) || !(t <= 5.8e+34)) {
		tmp = (x * (-2.0 / t)) / z;
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.2e+89) or not (t <= 5.8e+34):
		tmp = (x * (-2.0 / t)) / z
	else:
		tmp = (x / z) * (2.0 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.2e+89) || !(t <= 5.8e+34))
		tmp = Float64(Float64(x * Float64(-2.0 / t)) / z);
	else
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.2e+89) || ~((t <= 5.8e+34)))
		tmp = (x * (-2.0 / t)) / z;
	else
		tmp = (x / z) * (2.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.2e+89], N[Not[LessEqual[t, 5.8e+34]], $MachinePrecision]], N[(N[(x * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2e89 or 5.8000000000000003e34 < t

   1. Initial program 83.9%

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

      1. associate-*r/ 83.8%

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

      2. distribute-rgt-out-- 88.7%

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

      3. associate-/l/ 88.7%

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

      4. sub-neg 88.7%

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

      5. +-commutative 88.7%

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

      6. neg-sub0 88.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 88.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 88.7%

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

      9. neg-mul-1 88.7%

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

      10. associate-/r* 88.7%

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

      11. metadata-eval 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*l/ 79.9%

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

   6. Applied egg-rr 79.9%

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

   if -2.2e89 < t < 5.8000000000000003e34

   1. Initial program 90.4%

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

      1. associate-*r/ 90.4%

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

      2. distribute-rgt-out-- 91.7%

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

      3. associate-/l/ 91.7%

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

      4. sub-neg 91.7%

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

      5. +-commutative 91.7%

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

      6. neg-sub0 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 91.7%

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

      9. neg-mul-1 91.7%

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

      10. associate-/r* 91.7%

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

      11. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around 0 70.2%

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

      1. associate-*r/ 70.2%

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

      2. times-frac 72.1%

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

   6. Simplified 72.1%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+89} \lor \neg \left(t \leq 5.8 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x \cdot \frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 8: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+89} \lor \neg \left(t \leq 4.1 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x \cdot \frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.6e+89) (not (<= t 4.1e+34)))
   (/ (* x (/ -2.0 t)) z)
   (/ (/ x y) (* z 0.5))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e+89) || !(t <= 4.1e+34)) {
		tmp = (x * (-2.0 / t)) / z;
	} else {
		tmp = (x / y) / (z * 0.5);
	}
	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) :: tmp
    if ((t <= (-6.6d+89)) .or. (.not. (t <= 4.1d+34))) then
        tmp = (x * ((-2.0d0) / t)) / z
    else
        tmp = (x / y) / (z * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e+89) || !(t <= 4.1e+34)) {
		tmp = (x * (-2.0 / t)) / z;
	} else {
		tmp = (x / y) / (z * 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.6e+89) or not (t <= 4.1e+34):
		tmp = (x * (-2.0 / t)) / z
	else:
		tmp = (x / y) / (z * 0.5)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.6e+89) || !(t <= 4.1e+34))
		tmp = Float64(Float64(x * Float64(-2.0 / t)) / z);
	else
		tmp = Float64(Float64(x / y) / Float64(z * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.6e+89) || ~((t <= 4.1e+34)))
		tmp = (x * (-2.0 / t)) / z;
	else
		tmp = (x / y) / (z * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.6e+89], N[Not[LessEqual[t, 4.1e+34]], $MachinePrecision]], N[(N[(x * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / N[(z * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.59999999999999948e89 or 4.0999999999999998e34 < t

   1. Initial program 83.9%

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

      1. associate-*r/ 83.8%

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

      2. distribute-rgt-out-- 88.7%

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

      3. associate-/l/ 88.7%

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

      4. sub-neg 88.7%

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

      5. +-commutative 88.7%

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

      6. neg-sub0 88.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 88.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 88.7%

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

      9. neg-mul-1 88.7%

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

      10. associate-/r* 88.7%

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

      11. metadata-eval 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*l/ 79.9%

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

   6. Applied egg-rr 79.9%

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

   if -6.59999999999999948e89 < t < 4.0999999999999998e34

   1. Initial program 90.4%

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

      1. associate-*r/ 90.4%

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

      2. distribute-rgt-out-- 91.7%

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

      3. associate-/l/ 91.7%

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

      4. sub-neg 91.7%

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

      5. +-commutative 91.7%

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

      6. neg-sub0 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 91.7%

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

      9. neg-mul-1 91.7%

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

      10. associate-/r* 91.7%

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

      11. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around 0 70.2%

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

      1. associate-*r/ 70.2%

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

      2. times-frac 73.1%

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

      3. clear-num 73.1%

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

      4. un-div-inv 73.2%

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

      5. div-inv 73.2%

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

      6. metadata-eval 73.2%

         \[\leadsto \frac{\frac{x}{y}}{z \cdot \color{blue}{0.5}} \]

   6. Applied egg-rr 73.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{z \cdot 0.5}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+89} \lor \neg \left(t \leq 4.1 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{x \cdot \frac{-2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \end{array} \]

Alternative 9: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+89} \lor \neg \left(t \leq 7.8 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{\frac{x \cdot -2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5e+89) (not (<= t 7.8e+34)))
   (/ (/ (* x -2.0) t) z)
   (/ (/ x y) (* z 0.5))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e+89) || !(t <= 7.8e+34)) {
		tmp = ((x * -2.0) / t) / z;
	} else {
		tmp = (x / y) / (z * 0.5);
	}
	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) :: tmp
    if ((t <= (-5d+89)) .or. (.not. (t <= 7.8d+34))) then
        tmp = ((x * (-2.0d0)) / t) / z
    else
        tmp = (x / y) / (z * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5e+89) || !(t <= 7.8e+34)) {
		tmp = ((x * -2.0) / t) / z;
	} else {
		tmp = (x / y) / (z * 0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5e+89) or not (t <= 7.8e+34):
		tmp = ((x * -2.0) / t) / z
	else:
		tmp = (x / y) / (z * 0.5)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5e+89) || !(t <= 7.8e+34))
		tmp = Float64(Float64(Float64(x * -2.0) / t) / z);
	else
		tmp = Float64(Float64(x / y) / Float64(z * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5e+89) || ~((t <= 7.8e+34)))
		tmp = ((x * -2.0) / t) / z;
	else
		tmp = (x / y) / (z * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5e+89], N[Not[LessEqual[t, 7.8e+34]], $MachinePrecision]], N[(N[(N[(x * -2.0), $MachinePrecision] / t), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / N[(z * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.99999999999999983e89 or 7.80000000000000038e34 < t

   1. Initial program 83.9%

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

      1. associate-*r/ 83.8%

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

      2. distribute-rgt-out-- 88.7%

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

      3. associate-/l/ 88.7%

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

      4. sub-neg 88.7%

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

      5. +-commutative 88.7%

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

      6. neg-sub0 88.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 88.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 88.7%

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

      9. neg-mul-1 88.7%

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

      10. associate-/r* 88.7%

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

      11. metadata-eval 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*l/ 79.9%

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

   6. Applied egg-rr 79.9%

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

      1. *-commutative 79.9%

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

      2. associate-*r/ 80.0%

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

   8. Applied egg-rr 80.0%

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

   if -4.99999999999999983e89 < t < 7.80000000000000038e34

   1. Initial program 90.4%

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

      1. associate-*r/ 90.4%

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

      2. distribute-rgt-out-- 91.7%

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

      3. associate-/l/ 91.7%

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

      4. sub-neg 91.7%

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

      5. +-commutative 91.7%

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

      6. neg-sub0 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 91.7%

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

      9. neg-mul-1 91.7%

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

      10. associate-/r* 91.7%

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

      11. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around 0 70.2%

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

      1. associate-*r/ 70.2%

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

      2. times-frac 73.1%

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

      3. clear-num 73.1%

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

      4. un-div-inv 73.2%

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

      5. div-inv 73.2%

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

      6. metadata-eval 73.2%

         \[\leadsto \frac{\frac{x}{y}}{z \cdot \color{blue}{0.5}} \]

   6. Applied egg-rr 73.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{z \cdot 0.5}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+89} \lor \neg \left(t \leq 7.8 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{\frac{x \cdot -2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \end{array} \]

Alternative 10: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+89}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{-x}{t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.1e+89)
   (* (/ 2.0 z) (/ (- x) t))
   (if (<= t 1.05e+35) (/ (/ x y) (* z 0.5)) (/ (/ (* x -2.0) t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e+89) {
		tmp = (2.0 / z) * (-x / t);
	} else if (t <= 1.05e+35) {
		tmp = (x / y) / (z * 0.5);
	} else {
		tmp = ((x * -2.0) / t) / z;
	}
	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) :: tmp
    if (t <= (-2.1d+89)) then
        tmp = (2.0d0 / z) * (-x / t)
    else if (t <= 1.05d+35) then
        tmp = (x / y) / (z * 0.5d0)
    else
        tmp = ((x * (-2.0d0)) / t) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.1e+89) {
		tmp = (2.0 / z) * (-x / t);
	} else if (t <= 1.05e+35) {
		tmp = (x / y) / (z * 0.5);
	} else {
		tmp = ((x * -2.0) / t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.1e+89:
		tmp = (2.0 / z) * (-x / t)
	elif t <= 1.05e+35:
		tmp = (x / y) / (z * 0.5)
	else:
		tmp = ((x * -2.0) / t) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.1e+89)
		tmp = Float64(Float64(2.0 / z) * Float64(Float64(-x) / t));
	elseif (t <= 1.05e+35)
		tmp = Float64(Float64(x / y) / Float64(z * 0.5));
	else
		tmp = Float64(Float64(Float64(x * -2.0) / t) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.1e+89)
		tmp = (2.0 / z) * (-x / t);
	elseif (t <= 1.05e+35)
		tmp = (x / y) / (z * 0.5);
	else
		tmp = ((x * -2.0) / t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.1e+89], N[(N[(2.0 / z), $MachinePrecision] * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+35], N[(N[(x / y), $MachinePrecision] / N[(z * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * -2.0), $MachinePrecision] / t), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.09999999999999986e89

   1. Initial program 82.9%

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

      1. *-commutative 87.5%

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

      2. times-frac 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in y around 0 82.5%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{t}\right)} \cdot \frac{2}{z} \]
   7. Step-by-step derivation

      1. associate-*r/ 82.5%

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

      2. neg-mul-1 82.5%

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

   8. Simplified 82.5%

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

   if -2.09999999999999986e89 < t < 1.0499999999999999e35

   1. Initial program 90.4%

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

      1. associate-*r/ 90.4%

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

      2. distribute-rgt-out-- 91.7%

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

      3. associate-/l/ 91.7%

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

      4. sub-neg 91.7%

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

      5. +-commutative 91.7%

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

      6. neg-sub0 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 91.7%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 91.7%

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

      9. neg-mul-1 91.7%

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

      10. associate-/r* 91.7%

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

      11. metadata-eval 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around 0 70.2%

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

      1. associate-*r/ 70.2%

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

      2. times-frac 73.1%

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

      3. clear-num 73.1%

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

      4. un-div-inv 73.2%

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

      5. div-inv 73.2%

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

      6. metadata-eval 73.2%

         \[\leadsto \frac{\frac{x}{y}}{z \cdot \color{blue}{0.5}} \]

   6. Applied egg-rr 73.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{z \cdot 0.5}} \]

   if 1.0499999999999999e35 < t

   1. Initial program 84.7%

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

      1. associate-*r/ 84.5%

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

      2. distribute-rgt-out-- 89.8%

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

      3. associate-/l/ 89.8%

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

      4. sub-neg 89.8%

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

      5. +-commutative 89.8%

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

      6. neg-sub0 89.8%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

      7. associate-+l- 89.8%

         \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

      8. sub0-neg 89.8%

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

      9. neg-mul-1 89.8%

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

      10. associate-/r* 89.8%

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

      11. metadata-eval 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in t around inf 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 77.9%

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

   6. Applied egg-rr 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*r/ 78.1%

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

   8. Applied egg-rr 78.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+89}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{-x}{t}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{x}{y}}{z \cdot 0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{t}}{z}\\ \end{array} \]

Alternative 11: 91.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 = 2.0d0 * ((x / z) / (y - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

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

   1. associate-*l/ 87.8%

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

   2. *-commutative 87.8%

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

   3. distribute-rgt-out-- 90.6%

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

   4. associate-/r* 91.3%

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

3. Simplified 91.3%

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

4. Final simplification 91.3%

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

Alternative 12: 23.0% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

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 = (-2.0d0) * ((x / z) / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

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

   1. distribute-rgt-out-- 90.6%

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

3. Simplified 90.6%

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

4. Taylor expanded in y around inf 53.6%

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

   1. *-commutative 53.6%

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

   2. times-frac 53.6%

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

6. Applied egg-rr 53.6%

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

   1. *-commutative 53.6%

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

   2. clear-num 53.6%

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

   3. frac-2neg 53.6%

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

   4. frac-times 53.6%

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

   5. *-un-lft-identity 53.6%

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

   6. add-sqr-sqrt 27.4%

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

   7. sqrt-unprod 33.3%

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

   8. sqr-neg 33.3%

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

   9. sqrt-unprod 8.4%

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

   10. add-sqr-sqrt 21.1%

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

   11. div-inv 21.1%

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

   12. metadata-eval 21.1%

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

8. Applied egg-rr 21.1%

   \[\leadsto \color{blue}{\frac{x}{\left(y \cdot 0.5\right) \cdot \left(-z\right)}} \]
9. Step-by-step derivation

   1. *-commutative 21.1%

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

   2. /-rgt-identity 21.1%

      \[\leadsto \frac{x}{\color{blue}{\frac{\left(-z\right) \cdot \left(y \cdot 0.5\right)}{1}}} \]

   3. associate-*r* 21.1%

      \[\leadsto \frac{x}{\frac{\color{blue}{\left(\left(-z\right) \cdot y\right) \cdot 0.5}}{1}} \]

   4. distribute-lft-neg-in 21.1%

      \[\leadsto \frac{x}{\frac{\color{blue}{\left(-z \cdot y\right)} \cdot 0.5}{1}} \]

   5. associate-/l* 21.1%

      \[\leadsto \frac{x}{\color{blue}{\frac{-z \cdot y}{\frac{1}{0.5}}}} \]

   6. metadata-eval 21.1%

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

   7. associate-/l* 21.1%

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

   8. distribute-rgt-neg-in 21.1%

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

   9. associate-/r* 21.9%

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

   10. *-commutative 21.9%

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

   11. associate-*r/ 21.9%

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

   12. neg-mul-1 21.9%

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

   13. times-frac 21.9%

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

   14. metadata-eval 21.9%

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

10. Simplified 21.9%

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

11. Final simplification 21.9%

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

Alternative 13: 53.7% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

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

   1. associate-*r/ 87.7%

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

   2. distribute-rgt-out-- 90.5%

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

   3. associate-/l/ 90.5%

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

   4. sub-neg 90.5%

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

   5. +-commutative 90.5%

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

   6. neg-sub0 90.5%

      \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{\left(0 - t\right)} + y}}{z} \]

   7. associate-+l- 90.5%

      \[\leadsto x \cdot \frac{\frac{2}{\color{blue}{0 - \left(t - y\right)}}}{z} \]

   8. sub0-neg 90.5%

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

   9. neg-mul-1 90.5%

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

   10. associate-/r* 90.5%

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

   11. metadata-eval 90.5%

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

3. Simplified 90.5%

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

4. Taylor expanded in t around 0 53.6%

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

5. Final simplification 53.6%

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

Developer target: 96.8% 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 2023200 
(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))))