Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.7% → 94.6%

Time: 11.4s

Alternatives: 14

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * 2.0d0) / ((y * z) - (t * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * 2.0d0) / ((y * z) - (t * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - z \cdot t} \leq 0:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* x 2.0) (- (* y z) (* z t))) 0.0)
   (* (/ 2.0 z) (/ x (- y t)))
   (/ (* x 2.0) (* z (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) / ((y * z) - (z * t))) <= 0.0) {
		tmp = (2.0 / z) * (x / (y - t));
	} else {
		tmp = (x * 2.0) / (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) / ((y * z) - (z * t))) <= 0.0d0) then
        tmp = (2.0d0 / z) * (x / (y - t))
    else
        tmp = (x * 2.0d0) / (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) / ((y * z) - (z * t))) <= 0.0) {
		tmp = (2.0 / z) * (x / (y - t));
	} else {
		tmp = (x * 2.0) / (z * (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * 2.0) / ((y * z) - (z * t))) <= 0.0:
		tmp = (2.0 / z) * (x / (y - t))
	else:
		tmp = (x * 2.0) / (z * (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x * 2.0) / Float64(Float64(y * z) - Float64(z * t))) <= 0.0)
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	else
		tmp = Float64(Float64(x * 2.0) / Float64(z * Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * 2.0) / ((y * z) - (z * t))) <= 0.0)
		tmp = (2.0 / z) * (x / (y - t));
	else
		tmp = (x * 2.0) / (z * (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x * 2.0), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z))) < 0.0

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

      2. distribute-rgt-out-- 90.2%

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

      3. times-frac 97.2%

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

   3. Simplified 97.2%

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

   if 0.0 < (/.f64 (*.f64 x 2) (-.f64 (*.f64 y z) (*.f64 t z)))

   1. Initial program 93.0%

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

      1. distribute-rgt-out-- 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - z \cdot t} \leq 0:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 2: 95.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -5 \cdot 10^{-169} \lor \neg \left(x \cdot 2 \leq 2 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* x 2.0) -5e-169) (not (<= (* x 2.0) 2e-32)))
   (* (/ 2.0 z) (/ x (- y t)))
   (* x (/ 2.0 (* z (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x * 2.0) <= -5e-169) || !((x * 2.0) <= 2e-32)) {
		tmp = (2.0 / z) * (x / (y - t));
	} else {
		tmp = x * (2.0 / (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) <= (-5d-169)) .or. (.not. ((x * 2.0d0) <= 2d-32))) then
        tmp = (2.0d0 / z) * (x / (y - t))
    else
        tmp = x * (2.0d0 / (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) <= -5e-169) || !((x * 2.0) <= 2e-32)) {
		tmp = (2.0 / z) * (x / (y - t));
	} else {
		tmp = x * (2.0 / (z * (y - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x * 2.0) <= -5e-169) or not ((x * 2.0) <= 2e-32):
		tmp = (2.0 / z) * (x / (y - t))
	else:
		tmp = x * (2.0 / (z * (y - t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x * 2.0) <= -5e-169) || !(Float64(x * 2.0) <= 2e-32))
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	else
		tmp = Float64(x * Float64(2.0 / Float64(z * Float64(y - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x * 2.0) <= -5e-169) || ~(((x * 2.0) <= 2e-32)))
		tmp = (2.0 / z) * (x / (y - t));
	else
		tmp = x * (2.0 / (z * (y - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x * 2.0), $MachinePrecision], -5e-169], N[Not[LessEqual[N[(x * 2.0), $MachinePrecision], 2e-32]], $MachinePrecision]], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < -5.0000000000000002e-169 or 2.00000000000000011e-32 < (*.f64 x 2)

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

      2. distribute-rgt-out-- 91.1%

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

      3. times-frac 97.5%

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

   3. Simplified 97.5%

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

   if -5.0000000000000002e-169 < (*.f64 x 2) < 2.00000000000000011e-32

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

      2. distribute-rgt-out-- 98.6%

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

      3. times-frac 84.2%

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

   3. Simplified 84.2%

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

   4. Taylor expanded in z around 0 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-*l/ 98.6%

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

      3. associate-*r/ 98.6%

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

   6. Simplified 98.6%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -5 \cdot 10^{-169} \lor \neg \left(x \cdot 2 \leq 2 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 3: 95.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -5 \cdot 10^{-169}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{elif}\;x \cdot 2 \leq 0.0001:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y - t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* x 2.0) -5e-169)
   (* (/ 2.0 z) (/ x (- y t)))
   (if (<= (* x 2.0) 0.0001)
     (* x (/ 2.0 (* z (- y t))))
     (/ 2.0 (* z (/ (- y t) x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x * 2.0) <= -5e-169) {
		tmp = (2.0 / z) * (x / (y - t));
	} else if ((x * 2.0) <= 0.0001) {
		tmp = x * (2.0 / (z * (y - t)));
	} else {
		tmp = 2.0 / (z * ((y - t) / x));
	}
	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) <= (-5d-169)) then
        tmp = (2.0d0 / z) * (x / (y - t))
    else if ((x * 2.0d0) <= 0.0001d0) then
        tmp = x * (2.0d0 / (z * (y - t)))
    else
        tmp = 2.0d0 / (z * ((y - t) / x))
    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) <= -5e-169) {
		tmp = (2.0 / z) * (x / (y - t));
	} else if ((x * 2.0) <= 0.0001) {
		tmp = x * (2.0 / (z * (y - t)));
	} else {
		tmp = 2.0 / (z * ((y - t) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x * 2.0) <= -5e-169:
		tmp = (2.0 / z) * (x / (y - t))
	elif (x * 2.0) <= 0.0001:
		tmp = x * (2.0 / (z * (y - t)))
	else:
		tmp = 2.0 / (z * ((y - t) / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x * 2.0) <= -5e-169)
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	elseif (Float64(x * 2.0) <= 0.0001)
		tmp = Float64(x * Float64(2.0 / Float64(z * Float64(y - t))));
	else
		tmp = Float64(2.0 / Float64(z * Float64(Float64(y - t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x * 2.0) <= -5e-169)
		tmp = (2.0 / z) * (x / (y - t));
	elseif ((x * 2.0) <= 0.0001)
		tmp = x * (2.0 / (z * (y - t)));
	else
		tmp = 2.0 / (z * ((y - t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x * 2.0), $MachinePrecision], -5e-169], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * 2.0), $MachinePrecision], 0.0001], N[(x * N[(2.0 / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 / N[(z * N[(N[(y - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x 2) < -5.0000000000000002e-169

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

      2. distribute-rgt-out-- 93.4%

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

      3. times-frac 97.0%

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

   3. Simplified 97.0%

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

   if -5.0000000000000002e-169 < (*.f64 x 2) < 1.00000000000000005e-4

   1. Initial program 96.5%

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

      1. *-commutative 96.5%

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

      2. distribute-rgt-out-- 98.7%

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

      3. times-frac 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in z around 0 98.7%

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

      1. *-commutative 98.7%

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

      2. associate-*l/ 98.7%

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

      3. associate-*r/ 98.7%

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

   6. Simplified 98.7%

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

   if 1.00000000000000005e-4 < (*.f64 x 2)

   1. Initial program 83.2%

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

      1. *-commutative 83.2%

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

      2. distribute-rgt-out-- 86.4%

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

      3. times-frac 98.0%

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

   3. Simplified 98.0%

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

      1. clear-num 97.9%

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

      2. frac-times 98.2%

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

      3. metadata-eval 98.2%

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

   5. Applied egg-rr 98.2%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -5 \cdot 10^{-169}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \mathbf{elif}\;x \cdot 2 \leq 0.0001:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y - t}{x}}\\ \end{array} \]

Alternative 4: 71.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+47} \lor \neg \left(t \leq -1.22 \cdot 10^{-34}\right) \land \left(t \leq -9 \cdot 10^{-100} \lor \neg \left(t \leq 2.3 \cdot 10^{+54}\right)\right):\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.3e+47)
         (and (not (<= t -1.22e-34)) (or (<= t -9e-100) (not (<= t 2.3e+54)))))
   (* -2.0 (/ (/ x t) z))
   (* (/ 2.0 z) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.3e+47) || (!(t <= -1.22e-34) && ((t <= -9e-100) || !(t <= 2.3e+54)))) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = (2.0 / z) * (x / 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 <= (-2.3d+47)) .or. (.not. (t <= (-1.22d-34))) .and. (t <= (-9d-100)) .or. (.not. (t <= 2.3d+54))) then
        tmp = (-2.0d0) * ((x / t) / z)
    else
        tmp = (2.0d0 / z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.3e+47) || (!(t <= -1.22e-34) && ((t <= -9e-100) || !(t <= 2.3e+54)))) {
		tmp = -2.0 * ((x / t) / z);
	} else {
		tmp = (2.0 / z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.3e+47) or (not (t <= -1.22e-34) and ((t <= -9e-100) or not (t <= 2.3e+54))):
		tmp = -2.0 * ((x / t) / z)
	else:
		tmp = (2.0 / z) * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.3e+47) || (!(t <= -1.22e-34) && ((t <= -9e-100) || !(t <= 2.3e+54))))
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.3e+47) || (~((t <= -1.22e-34)) && ((t <= -9e-100) || ~((t <= 2.3e+54)))))
		tmp = -2.0 * ((x / t) / z);
	else
		tmp = (2.0 / z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.3e+47], And[N[Not[LessEqual[t, -1.22e-34]], $MachinePrecision], Or[LessEqual[t, -9e-100], N[Not[LessEqual[t, 2.3e+54]], $MachinePrecision]]]], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2999999999999999e47 or -1.22e-34 < t < -9.0000000000000002e-100 or 2.29999999999999994e54 < t

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

      2. distribute-rgt-out-- 90.6%

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

      3. times-frac 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around 0 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*l/ 90.6%

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

      3. associate-*r/ 90.6%

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

   6. Simplified 90.6%

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

   7. Taylor expanded in y around 0 83.9%

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

      1. associate-/r* 86.4%

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

   9. Simplified 86.4%

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

   if -2.2999999999999999e47 < t < -1.22e-34 or -9.0000000000000002e-100 < t < 2.29999999999999994e54

   1. Initial program 94.7%

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

      1. *-commutative 94.7%

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

      2. distribute-rgt-out-- 96.2%

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

      3. times-frac 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around inf 76.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+47} \lor \neg \left(t \leq -1.22 \cdot 10^{-34}\right) \land \left(t \leq -9 \cdot 10^{-100} \lor \neg \left(t \leq 2.3 \cdot 10^{+54}\right)\right):\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 71.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+47}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-34} \lor \neg \left(t \leq -2.3 \cdot 10^{-100}\right) \land t \leq 1.08 \cdot 10^{+55}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.35e+47)
   (* -2.0 (/ (/ x t) z))
   (if (or (<= t -3.05e-34) (and (not (<= t -2.3e-100)) (<= t 1.08e+55)))
     (* (/ 2.0 z) (/ x y))
     (* (/ x t) (/ -2.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.35e+47) {
		tmp = -2.0 * ((x / t) / z);
	} else if ((t <= -3.05e-34) || (!(t <= -2.3e-100) && (t <= 1.08e+55))) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = (x / t) * (-2.0 / 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 <= (-1.35d+47)) then
        tmp = (-2.0d0) * ((x / t) / z)
    else if ((t <= (-3.05d-34)) .or. (.not. (t <= (-2.3d-100))) .and. (t <= 1.08d+55)) then
        tmp = (2.0d0 / z) * (x / y)
    else
        tmp = (x / t) * ((-2.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.35e+47) {
		tmp = -2.0 * ((x / t) / z);
	} else if ((t <= -3.05e-34) || (!(t <= -2.3e-100) && (t <= 1.08e+55))) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = (x / t) * (-2.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.35e+47:
		tmp = -2.0 * ((x / t) / z)
	elif (t <= -3.05e-34) or (not (t <= -2.3e-100) and (t <= 1.08e+55)):
		tmp = (2.0 / z) * (x / y)
	else:
		tmp = (x / t) * (-2.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.35e+47)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	elseif ((t <= -3.05e-34) || (!(t <= -2.3e-100) && (t <= 1.08e+55)))
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	else
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.35e+47)
		tmp = -2.0 * ((x / t) / z);
	elseif ((t <= -3.05e-34) || (~((t <= -2.3e-100)) && (t <= 1.08e+55)))
		tmp = (2.0 / z) * (x / y);
	else
		tmp = (x / t) * (-2.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.35e+47], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -3.05e-34], And[N[Not[LessEqual[t, -2.3e-100]], $MachinePrecision], LessEqual[t, 1.08e+55]]], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.34999999999999998e47

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

      2. distribute-rgt-out-- 91.5%

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

      3. times-frac 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*l/ 91.5%

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

      3. associate-*r/ 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in y around 0 82.7%

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

      1. associate-/r* 85.1%

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

   9. Simplified 85.1%

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

   if -1.34999999999999998e47 < t < -3.0499999999999999e-34 or -2.29999999999999994e-100 < t < 1.08000000000000004e55

   1. Initial program 94.7%

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

      1. *-commutative 94.7%

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

      2. distribute-rgt-out-- 96.2%

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

      3. times-frac 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around inf 76.1%

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

   if -3.0499999999999999e-34 < t < -2.29999999999999994e-100 or 1.08000000000000004e55 < t

   1. Initial program 83.8%

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

      1. *-commutative 83.8%

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

      2. distribute-rgt-out-- 89.4%

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

      3. times-frac 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in z around 0 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-*l/ 89.4%

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

      3. associate-*r/ 89.3%

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

   6. Simplified 89.3%

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

   7. Taylor expanded in y around 0 85.5%

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

      1. associate-/r* 88.0%

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

   9. Simplified 88.0%

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

       1. *-commutative 88.0%

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

       2. associate-/l/ 85.5%

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

       3. associate-*l/ 85.5%

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

       4. times-frac 86.6%

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

       5. associate-*l/ 88.1%

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

   11. Applied egg-rr 88.1%

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

       1. associate-*r/ 88.0%

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

       2. associate-/r* 85.5%

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

       3. times-frac 88.0%

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

   13. Applied egg-rr 88.0%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+47}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-34} \lor \neg \left(t \leq -2.3 \cdot 10^{-100}\right) \land t \leq 1.08 \cdot 10^{+55}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \end{array} \]

Alternative 6: 71.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))))
   (if (<= t -1.5e+47)
     (* -2.0 (/ (/ x t) z))
     (if (<= t -1.3e-29)
       t_1
       (if (<= t -4.5e-100)
         (* (/ x t) (/ -2.0 z))
         (if (<= t 1.08e+55) t_1 (* (/ x z) (/ -2.0 t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (t <= -1.5e+47) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= -1.3e-29) {
		tmp = t_1;
	} else if (t <= -4.5e-100) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 1.08e+55) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (-2.0 / 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) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 / z) * (x / y)
    if (t <= (-1.5d+47)) then
        tmp = (-2.0d0) * ((x / t) / z)
    else if (t <= (-1.3d-29)) then
        tmp = t_1
    else if (t <= (-4.5d-100)) then
        tmp = (x / t) * ((-2.0d0) / z)
    else if (t <= 1.08d+55) then
        tmp = t_1
    else
        tmp = (x / z) * ((-2.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (t <= -1.5e+47) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= -1.3e-29) {
		tmp = t_1;
	} else if (t <= -4.5e-100) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 1.08e+55) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (-2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	tmp = 0
	if t <= -1.5e+47:
		tmp = -2.0 * ((x / t) / z)
	elif t <= -1.3e-29:
		tmp = t_1
	elif t <= -4.5e-100:
		tmp = (x / t) * (-2.0 / z)
	elif t <= 1.08e+55:
		tmp = t_1
	else:
		tmp = (x / z) * (-2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	tmp = 0.0
	if (t <= -1.5e+47)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	elseif (t <= -1.3e-29)
		tmp = t_1;
	elseif (t <= -4.5e-100)
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	elseif (t <= 1.08e+55)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	tmp = 0.0;
	if (t <= -1.5e+47)
		tmp = -2.0 * ((x / t) / z);
	elseif (t <= -1.3e-29)
		tmp = t_1;
	elseif (t <= -4.5e-100)
		tmp = (x / t) * (-2.0 / z);
	elseif (t <= 1.08e+55)
		tmp = t_1;
	else
		tmp = (x / z) * (-2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+47], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.3e-29], t$95$1, If[LessEqual[t, -4.5e-100], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.08e+55], t$95$1, N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.5000000000000001e47

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

      2. distribute-rgt-out-- 91.5%

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

      3. times-frac 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*l/ 91.5%

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

      3. associate-*r/ 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in y around 0 82.7%

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

      1. associate-/r* 85.1%

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

   9. Simplified 85.1%

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

   if -1.5000000000000001e47 < t < -1.3000000000000001e-29 or -4.5000000000000001e-100 < t < 1.08000000000000004e55

   1. Initial program 94.7%

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

      1. *-commutative 94.7%

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

      2. distribute-rgt-out-- 96.2%

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

      3. times-frac 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around inf 76.1%

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

   if -1.3000000000000001e-29 < t < -4.5000000000000001e-100

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

      3. times-frac 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.6%

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

      3. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around 0 99.6%

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

      1. associate-/r* 99.7%

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

   9. Simplified 99.7%

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

       1. *-commutative 99.7%

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

       2. associate-/l/ 99.6%

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

       3. associate-*l/ 99.6%

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

       4. times-frac 91.4%

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

       5. associate-*l/ 99.9%

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

   11. Applied egg-rr 99.9%

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

       1. associate-*r/ 99.7%

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

       2. associate-/r* 99.6%

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

       3. times-frac 99.9%

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

   13. Applied egg-rr 99.9%

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

   if 1.08000000000000004e55 < t

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. distribute-rgt-out-- 86.8%

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

      3. times-frac 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around 0 81.9%

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

      1. associate-*r/ 81.9%

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

      2. *-commutative 81.9%

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

      3. *-commutative 81.9%

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

   6. Simplified 81.9%

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

      1. times-frac 85.4%

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

   8. Applied egg-rr 85.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-29}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{+55}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \end{array} \]

Alternative 7: 72.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+47}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 2.0 y))))
   (if (<= t -2.5e+47)
     (* -2.0 (/ (/ x t) z))
     (if (<= t -1.25e-35)
       t_1
       (if (<= t -8.5e-100)
         (* (/ x t) (/ -2.0 z))
         (if (<= t 8.5e+53) t_1 (* (/ x z) (/ -2.0 t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (2.0 / y);
	double tmp;
	if (t <= -2.5e+47) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= -1.25e-35) {
		tmp = t_1;
	} else if (t <= -8.5e-100) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 8.5e+53) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (-2.0 / 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) :: t_1
    real(8) :: tmp
    t_1 = (x / z) * (2.0d0 / y)
    if (t <= (-2.5d+47)) then
        tmp = (-2.0d0) * ((x / t) / z)
    else if (t <= (-1.25d-35)) then
        tmp = t_1
    else if (t <= (-8.5d-100)) then
        tmp = (x / t) * ((-2.0d0) / z)
    else if (t <= 8.5d+53) then
        tmp = t_1
    else
        tmp = (x / z) * ((-2.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (2.0 / y);
	double tmp;
	if (t <= -2.5e+47) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= -1.25e-35) {
		tmp = t_1;
	} else if (t <= -8.5e-100) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 8.5e+53) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (-2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * (2.0 / y)
	tmp = 0
	if t <= -2.5e+47:
		tmp = -2.0 * ((x / t) / z)
	elif t <= -1.25e-35:
		tmp = t_1
	elif t <= -8.5e-100:
		tmp = (x / t) * (-2.0 / z)
	elif t <= 8.5e+53:
		tmp = t_1
	else:
		tmp = (x / z) * (-2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(2.0 / y))
	tmp = 0.0
	if (t <= -2.5e+47)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	elseif (t <= -1.25e-35)
		tmp = t_1;
	elseif (t <= -8.5e-100)
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	elseif (t <= 8.5e+53)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (2.0 / y);
	tmp = 0.0;
	if (t <= -2.5e+47)
		tmp = -2.0 * ((x / t) / z);
	elseif (t <= -1.25e-35)
		tmp = t_1;
	elseif (t <= -8.5e-100)
		tmp = (x / t) * (-2.0 / z);
	elseif (t <= 8.5e+53)
		tmp = t_1;
	else
		tmp = (x / z) * (-2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+47], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.25e-35], t$95$1, If[LessEqual[t, -8.5e-100], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+53], t$95$1, N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.50000000000000011e47

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

      2. distribute-rgt-out-- 91.5%

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

      3. times-frac 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*l/ 91.5%

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

      3. associate-*r/ 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in y around 0 82.7%

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

      1. associate-/r* 85.1%

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

   9. Simplified 85.1%

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

   if -2.50000000000000011e47 < t < -1.24999999999999991e-35 or -8.50000000000000017e-100 < t < 8.5000000000000002e53

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 80.4%

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

      1. *-commutative 80.4%

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

   4. Simplified 80.4%

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

      1. times-frac 78.8%

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

   6. Applied egg-rr 78.8%

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

   if -1.24999999999999991e-35 < t < -8.50000000000000017e-100

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

      3. times-frac 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.6%

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

      3. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around 0 99.6%

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

      1. associate-/r* 99.7%

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

   9. Simplified 99.7%

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

       1. *-commutative 99.7%

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

       2. associate-/l/ 99.6%

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

       3. associate-*l/ 99.6%

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

       4. times-frac 91.4%

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

       5. associate-*l/ 99.9%

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

   11. Applied egg-rr 99.9%

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

       1. associate-*r/ 99.7%

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

       2. associate-/r* 99.6%

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

       3. times-frac 99.9%

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

   13. Applied egg-rr 99.9%

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

   if 8.5000000000000002e53 < t

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. distribute-rgt-out-- 86.8%

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

      3. times-frac 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around 0 81.9%

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

      1. associate-*r/ 81.9%

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

      2. *-commutative 81.9%

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

      3. *-commutative 81.9%

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

   6. Simplified 81.9%

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

      1. times-frac 85.4%

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

   8. Applied egg-rr 85.4%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+47}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \end{array} \]

Alternative 8: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 2.0 y))))
   (if (<= t -4.2e+48)
     (* -2.0 (/ (/ x t) z))
     (if (<= t -4.9e-26)
       t_1
       (if (<= t -9e-100)
         (* (/ x t) (/ -2.0 z))
         (if (<= t 1.12e+54) t_1 (/ -2.0 (* t (/ z x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (2.0 / y);
	double tmp;
	if (t <= -4.2e+48) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= -4.9e-26) {
		tmp = t_1;
	} else if (t <= -9e-100) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 1.12e+54) {
		tmp = t_1;
	} else {
		tmp = -2.0 / (t * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) * (2.0d0 / y)
    if (t <= (-4.2d+48)) then
        tmp = (-2.0d0) * ((x / t) / z)
    else if (t <= (-4.9d-26)) then
        tmp = t_1
    else if (t <= (-9d-100)) then
        tmp = (x / t) * ((-2.0d0) / z)
    else if (t <= 1.12d+54) then
        tmp = t_1
    else
        tmp = (-2.0d0) / (t * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (2.0 / y);
	double tmp;
	if (t <= -4.2e+48) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= -4.9e-26) {
		tmp = t_1;
	} else if (t <= -9e-100) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 1.12e+54) {
		tmp = t_1;
	} else {
		tmp = -2.0 / (t * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * (2.0 / y)
	tmp = 0
	if t <= -4.2e+48:
		tmp = -2.0 * ((x / t) / z)
	elif t <= -4.9e-26:
		tmp = t_1
	elif t <= -9e-100:
		tmp = (x / t) * (-2.0 / z)
	elif t <= 1.12e+54:
		tmp = t_1
	else:
		tmp = -2.0 / (t * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(2.0 / y))
	tmp = 0.0
	if (t <= -4.2e+48)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	elseif (t <= -4.9e-26)
		tmp = t_1;
	elseif (t <= -9e-100)
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	elseif (t <= 1.12e+54)
		tmp = t_1;
	else
		tmp = Float64(-2.0 / Float64(t * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (2.0 / y);
	tmp = 0.0;
	if (t <= -4.2e+48)
		tmp = -2.0 * ((x / t) / z);
	elseif (t <= -4.9e-26)
		tmp = t_1;
	elseif (t <= -9e-100)
		tmp = (x / t) * (-2.0 / z);
	elseif (t <= 1.12e+54)
		tmp = t_1;
	else
		tmp = -2.0 / (t * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+48], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.9e-26], t$95$1, If[LessEqual[t, -9e-100], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e+54], t$95$1, N[(-2.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.1999999999999997e48

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

      2. distribute-rgt-out-- 91.5%

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

      3. times-frac 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*l/ 91.5%

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

      3. associate-*r/ 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in y around 0 82.7%

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

      1. associate-/r* 85.1%

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

   9. Simplified 85.1%

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

   if -4.1999999999999997e48 < t < -4.8999999999999999e-26 or -9.0000000000000002e-100 < t < 1.12e54

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 80.4%

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

      1. *-commutative 80.4%

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

   4. Simplified 80.4%

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

      1. times-frac 78.8%

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

   6. Applied egg-rr 78.8%

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

   if -4.8999999999999999e-26 < t < -9.0000000000000002e-100

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

      3. times-frac 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.6%

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

      3. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around 0 99.6%

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

      1. associate-/r* 99.7%

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

   9. Simplified 99.7%

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

       1. *-commutative 99.7%

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

       2. associate-/l/ 99.6%

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

       3. associate-*l/ 99.6%

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

       4. times-frac 91.4%

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

       5. associate-*l/ 99.9%

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

   11. Applied egg-rr 99.9%

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

       1. associate-*r/ 99.7%

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

       2. associate-/r* 99.6%

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

       3. times-frac 99.9%

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

   13. Applied egg-rr 99.9%

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

   if 1.12e54 < t

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. distribute-rgt-out-- 86.8%

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

      3. times-frac 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around 0 81.9%

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

      1. associate-*r/ 81.9%

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

      2. *-commutative 81.9%

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

      3. *-commutative 81.9%

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

   6. Simplified 81.9%

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

      1. times-frac 85.4%

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

   8. Applied egg-rr 85.4%

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

      1. *-commutative 85.4%

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

      2. clear-num 85.4%

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

      3. frac-times 87.2%

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

      4. metadata-eval 87.2%

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

   10. Applied egg-rr 87.2%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 9: 72.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 2}{y \cdot z}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+48}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x 2.0) (* y z))))
   (if (<= t -1.2e+48)
     (* -2.0 (/ (/ x t) z))
     (if (<= t -1.02e-35)
       t_1
       (if (<= t -2.4e-100)
         (* (/ x t) (/ -2.0 z))
         (if (<= t 9e+53) t_1 (/ -2.0 (* t (/ z x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * 2.0) / (y * z);
	double tmp;
	if (t <= -1.2e+48) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= -1.02e-35) {
		tmp = t_1;
	} else if (t <= -2.4e-100) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 9e+53) {
		tmp = t_1;
	} else {
		tmp = -2.0 / (t * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) / (y * z)
    if (t <= (-1.2d+48)) then
        tmp = (-2.0d0) * ((x / t) / z)
    else if (t <= (-1.02d-35)) then
        tmp = t_1
    else if (t <= (-2.4d-100)) then
        tmp = (x / t) * ((-2.0d0) / z)
    else if (t <= 9d+53) then
        tmp = t_1
    else
        tmp = (-2.0d0) / (t * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * 2.0) / (y * z);
	double tmp;
	if (t <= -1.2e+48) {
		tmp = -2.0 * ((x / t) / z);
	} else if (t <= -1.02e-35) {
		tmp = t_1;
	} else if (t <= -2.4e-100) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 9e+53) {
		tmp = t_1;
	} else {
		tmp = -2.0 / (t * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * 2.0) / (y * z)
	tmp = 0
	if t <= -1.2e+48:
		tmp = -2.0 * ((x / t) / z)
	elif t <= -1.02e-35:
		tmp = t_1
	elif t <= -2.4e-100:
		tmp = (x / t) * (-2.0 / z)
	elif t <= 9e+53:
		tmp = t_1
	else:
		tmp = -2.0 / (t * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * 2.0) / Float64(y * z))
	tmp = 0.0
	if (t <= -1.2e+48)
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	elseif (t <= -1.02e-35)
		tmp = t_1;
	elseif (t <= -2.4e-100)
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	elseif (t <= 9e+53)
		tmp = t_1;
	else
		tmp = Float64(-2.0 / Float64(t * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * 2.0) / (y * z);
	tmp = 0.0;
	if (t <= -1.2e+48)
		tmp = -2.0 * ((x / t) / z);
	elseif (t <= -1.02e-35)
		tmp = t_1;
	elseif (t <= -2.4e-100)
		tmp = (x / t) * (-2.0 / z);
	elseif (t <= 9e+53)
		tmp = t_1;
	else
		tmp = -2.0 / (t * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+48], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.02e-35], t$95$1, If[LessEqual[t, -2.4e-100], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e+53], t$95$1, N[(-2.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2000000000000001e48

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

      2. distribute-rgt-out-- 91.5%

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

      3. times-frac 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*l/ 91.5%

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

      3. associate-*r/ 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in y around 0 82.7%

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

      1. associate-/r* 85.1%

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

   9. Simplified 85.1%

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

   if -1.2000000000000001e48 < t < -1.01999999999999995e-35 or -2.4000000000000003e-100 < t < 9.0000000000000004e53

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 80.4%

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

      1. *-commutative 80.4%

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

   4. Simplified 80.4%

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

   if -1.01999999999999995e-35 < t < -2.4000000000000003e-100

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

      3. times-frac 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.6%

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

      3. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around 0 99.6%

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

      1. associate-/r* 99.7%

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

   9. Simplified 99.7%

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

       1. *-commutative 99.7%

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

       2. associate-/l/ 99.6%

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

       3. associate-*l/ 99.6%

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

       4. times-frac 91.4%

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

       5. associate-*l/ 99.9%

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

   11. Applied egg-rr 99.9%

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

       1. associate-*r/ 99.7%

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

       2. associate-/r* 99.6%

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

       3. times-frac 99.9%

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

   13. Applied egg-rr 99.9%

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

   if 9.0000000000000004e53 < t

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. distribute-rgt-out-- 86.8%

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

      3. times-frac 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around 0 81.9%

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

      1. associate-*r/ 81.9%

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

      2. *-commutative 81.9%

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

      3. *-commutative 81.9%

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

   6. Simplified 81.9%

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

      1. times-frac 85.4%

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

   8. Applied egg-rr 85.4%

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

      1. *-commutative 85.4%

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

      2. clear-num 85.4%

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

      3. frac-times 87.2%

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

      4. metadata-eval 87.2%

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

   10. Applied egg-rr 87.2%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+48}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-35}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 10: 71.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot 2}{y \cdot z}\\ \mathbf{if}\;t \leq -1.36 \cdot 10^{+47}:\\ \;\;\;\;\frac{x \cdot \frac{-2}{t}}{z}\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x 2.0) (* y z))))
   (if (<= t -1.36e+47)
     (/ (* x (/ -2.0 t)) z)
     (if (<= t -5.9e-25)
       t_1
       (if (<= t -9e-100)
         (* (/ x t) (/ -2.0 z))
         (if (<= t 8e+53) t_1 (/ -2.0 (* t (/ z x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * 2.0) / (y * z);
	double tmp;
	if (t <= -1.36e+47) {
		tmp = (x * (-2.0 / t)) / z;
	} else if (t <= -5.9e-25) {
		tmp = t_1;
	} else if (t <= -9e-100) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 8e+53) {
		tmp = t_1;
	} else {
		tmp = -2.0 / (t * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 2.0d0) / (y * z)
    if (t <= (-1.36d+47)) then
        tmp = (x * ((-2.0d0) / t)) / z
    else if (t <= (-5.9d-25)) then
        tmp = t_1
    else if (t <= (-9d-100)) then
        tmp = (x / t) * ((-2.0d0) / z)
    else if (t <= 8d+53) then
        tmp = t_1
    else
        tmp = (-2.0d0) / (t * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * 2.0) / (y * z);
	double tmp;
	if (t <= -1.36e+47) {
		tmp = (x * (-2.0 / t)) / z;
	} else if (t <= -5.9e-25) {
		tmp = t_1;
	} else if (t <= -9e-100) {
		tmp = (x / t) * (-2.0 / z);
	} else if (t <= 8e+53) {
		tmp = t_1;
	} else {
		tmp = -2.0 / (t * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * 2.0) / (y * z)
	tmp = 0
	if t <= -1.36e+47:
		tmp = (x * (-2.0 / t)) / z
	elif t <= -5.9e-25:
		tmp = t_1
	elif t <= -9e-100:
		tmp = (x / t) * (-2.0 / z)
	elif t <= 8e+53:
		tmp = t_1
	else:
		tmp = -2.0 / (t * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * 2.0) / Float64(y * z))
	tmp = 0.0
	if (t <= -1.36e+47)
		tmp = Float64(Float64(x * Float64(-2.0 / t)) / z);
	elseif (t <= -5.9e-25)
		tmp = t_1;
	elseif (t <= -9e-100)
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	elseif (t <= 8e+53)
		tmp = t_1;
	else
		tmp = Float64(-2.0 / Float64(t * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * 2.0) / (y * z);
	tmp = 0.0;
	if (t <= -1.36e+47)
		tmp = (x * (-2.0 / t)) / z;
	elseif (t <= -5.9e-25)
		tmp = t_1;
	elseif (t <= -9e-100)
		tmp = (x / t) * (-2.0 / z);
	elseif (t <= 8e+53)
		tmp = t_1;
	else
		tmp = -2.0 / (t * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.36e+47], N[(N[(x * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t, -5.9e-25], t$95$1, If[LessEqual[t, -9e-100], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+53], t$95$1, N[(-2.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.3599999999999999e47

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

      2. distribute-rgt-out-- 91.5%

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

      3. times-frac 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in z around 0 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*l/ 91.5%

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

      3. associate-*r/ 91.5%

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

   6. Simplified 91.5%

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

   7. Taylor expanded in y around 0 82.7%

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

      1. associate-/r* 85.1%

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

   9. Simplified 85.1%

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

       1. *-commutative 85.1%

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

       2. associate-/l/ 82.7%

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

       3. associate-*l/ 82.7%

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

       4. times-frac 80.7%

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

       5. associate-*l/ 85.3%

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

   11. Applied egg-rr 85.3%

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

   if -1.3599999999999999e47 < t < -5.8999999999999998e-25 or -9.0000000000000002e-100 < t < 7.9999999999999999e53

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 80.4%

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

      1. *-commutative 80.4%

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

   4. Simplified 80.4%

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

   if -5.8999999999999998e-25 < t < -9.0000000000000002e-100

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

      3. times-frac 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.6%

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

      3. associate-*r/ 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around 0 99.6%

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

      1. associate-/r* 99.7%

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

   9. Simplified 99.7%

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

       1. *-commutative 99.7%

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

       2. associate-/l/ 99.6%

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

       3. associate-*l/ 99.6%

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

       4. times-frac 91.4%

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

       5. associate-*l/ 99.9%

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

   11. Applied egg-rr 99.9%

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

       1. associate-*r/ 99.7%

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

       2. associate-/r* 99.6%

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

       3. times-frac 99.9%

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

   13. Applied egg-rr 99.9%

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

   if 7.9999999999999999e53 < t

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. distribute-rgt-out-- 86.8%

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

      3. times-frac 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around 0 81.9%

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

      1. associate-*r/ 81.9%

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

      2. *-commutative 81.9%

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

      3. *-commutative 81.9%

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

   6. Simplified 81.9%

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

      1. times-frac 85.4%

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

   8. Applied egg-rr 85.4%

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

      1. *-commutative 85.4%

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

      2. clear-num 85.4%

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

      3. frac-times 87.2%

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

      4. metadata-eval 87.2%

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

   10. Applied egg-rr 87.2%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+47}:\\ \;\;\;\;\frac{x \cdot \frac{-2}{t}}{z}\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-25}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot 2}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-2}{t \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 11: 96.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+42} \lor \neg \left(z \leq 7 \cdot 10^{+93}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6e+42) (not (<= z 7e+93)))
   (* 2.0 (/ (/ x z) (- y t)))
   (* x (/ 2.0 (* z (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e+42) || !(z <= 7e+93)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * (2.0 / (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 ((z <= (-6d+42)) .or. (.not. (z <= 7d+93))) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else
        tmp = x * (2.0d0 / (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 ((z <= -6e+42) || !(z <= 7e+93)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = x * (2.0 / (z * (y - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6e+42) or not (z <= 7e+93):
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = x * (2.0 / (z * (y - t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e+42) || !(z <= 7e+93))
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(x * Float64(2.0 / Float64(z * Float64(y - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6e+42) || ~((z <= 7e+93)))
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = x * (2.0 / (z * (y - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6e+42], N[Not[LessEqual[z, 7e+93]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(2.0 / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000058e42 or 6.99999999999999996e93 < z

   1. Initial program 79.7%

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

      1. *-commutative 79.7%

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

      2. associate-*r/ 79.7%

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

      3. distribute-rgt-out-- 85.7%

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

      4. associate-/r* 96.1%

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

   3. Simplified 96.1%

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

   if -6.00000000000000058e42 < z < 6.99999999999999996e93

   1. Initial program 97.9%

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

      1. *-commutative 97.9%

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

      2. distribute-rgt-out-- 98.5%

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

      3. times-frac 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around 0 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*l/ 98.5%

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

      3. associate-*r/ 98.4%

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

   6. Simplified 98.4%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+42} \lor \neg \left(z \leq 7 \cdot 10^{+93}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 12: 55.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+213} \lor \neg \left(y \leq 1.36 \cdot 10^{+143}\right):\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.3e+213) (not (<= y 1.36e+143)))
   (* -2.0 (/ (/ x z) y))
   (* -2.0 (/ (/ x t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e+213) || !(y <= 1.36e+143)) {
		tmp = -2.0 * ((x / z) / y);
	} else {
		tmp = -2.0 * ((x / 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 ((y <= (-1.3d+213)) .or. (.not. (y <= 1.36d+143))) then
        tmp = (-2.0d0) * ((x / z) / y)
    else
        tmp = (-2.0d0) * ((x / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e+213) || !(y <= 1.36e+143)) {
		tmp = -2.0 * ((x / z) / y);
	} else {
		tmp = -2.0 * ((x / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.3e+213) or not (y <= 1.36e+143):
		tmp = -2.0 * ((x / z) / y)
	else:
		tmp = -2.0 * ((x / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.3e+213) || !(y <= 1.36e+143))
		tmp = Float64(-2.0 * Float64(Float64(x / z) / y));
	else
		tmp = Float64(-2.0 * Float64(Float64(x / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.3e+213) || ~((y <= 1.36e+143)))
		tmp = -2.0 * ((x / z) / y);
	else
		tmp = -2.0 * ((x / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.3e+213], N[Not[LessEqual[y, 1.36e+143]], $MachinePrecision]], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999999e213 or 1.3599999999999999e143 < y

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

      2. distribute-rgt-out-- 96.1%

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

      3. times-frac 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in y around inf 95.2%

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

      1. frac-times 95.7%

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

      2. *-commutative 95.7%

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

      3. frac-2neg 95.7%

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

      4. distribute-lft-neg-in 95.7%

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

      5. add-sqr-sqrt 59.4%

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

      6. sqrt-unprod 75.9%

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

      7. sqr-neg 75.9%

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

      8. sqrt-unprod 24.1%

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

      9. add-sqr-sqrt 60.8%

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

      10. distribute-rgt-neg-in 60.8%

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

   6. Applied egg-rr 60.8%

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

      1. associate-/r* 60.7%

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

      2. associate-*l/ 60.7%

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

      3. *-commutative 60.7%

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

      4. neg-mul-1 60.7%

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

      5. times-frac 60.7%

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

      6. metadata-eval 60.7%

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

   8. Simplified 60.7%

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

   if -1.29999999999999999e213 < y < 1.3599999999999999e143

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

      2. distribute-rgt-out-- 92.9%

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

      3. times-frac 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in z around 0 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-*l/ 92.9%

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

      3. associate-*r/ 92.8%

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

   6. Simplified 92.8%

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

   7. Taylor expanded in y around 0 61.0%

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

      1. associate-/r* 63.1%

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

   9. Simplified 63.1%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+213} \lor \neg \left(y \leq 1.36 \cdot 10^{+143}\right):\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{t}}{z}\\ \end{array} \]

Alternative 13: 92.0% 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 90.8%

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

   1. *-commutative 90.8%

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

   2. associate-*r/ 90.8%

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

   3. distribute-rgt-out-- 93.5%

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

   4. associate-/r* 91.6%

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

3. Simplified 91.6%

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

4. Final simplification 91.6%

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

Alternative 14: 52.5% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

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

   1. *-commutative 90.8%

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

   2. distribute-rgt-out-- 93.5%

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

   3. times-frac 93.3%

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

3. Simplified 93.3%

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

4. Taylor expanded in z around 0 93.5%

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

   1. *-commutative 93.5%

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

   2. associate-*l/ 93.5%

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

   3. associate-*r/ 93.4%

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

6. Simplified 93.4%

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

7. Taylor expanded in y around 0 53.8%

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

   1. associate-/r* 54.9%

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

9. Simplified 54.9%

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

10. Final simplification 54.9%

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

Developer target: 97.0% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023318 
(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))))