Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.8% → 98.3%

Time: 12.6s

Alternatives: 15

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: 89.8% 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: 98.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+223}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+223)))
     (* 2.0 (/ (/ x z) (- y t)))
     (/ (* 2.0 x) (* z (- y t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+223)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = (2.0 * x) / (z * (y - t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - (z * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+223)) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = (2.0 * x) / (z * (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - (z * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+223):
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = (2.0 * x) / (z * (y - t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+223))
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(Float64(2.0 * x) / Float64(z * Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+223)))
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = (2.0 * x) / (z * (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+223]], $MachinePrecision]], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * x), $MachinePrecision] / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 y z) (*.f64 t z)) < -inf.0 or 4.99999999999999985e223 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 56.9%

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

      1. *-commutative 56.9%

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

      2. associate-*r/ 56.9%

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

      3. distribute-rgt-out-- 62.0%

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

      4. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   if -inf.0 < (-.f64 (*.f64 y z) (*.f64 t z)) < 4.99999999999999985e223

   1. Initial program 97.6%

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

      1. distribute-rgt-out-- 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -\infty \lor \neg \left(y \cdot z - z \cdot t \leq 5 \cdot 10^{+223}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 2: 95.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot x \leq -1 \cdot 10^{-133} \lor \neg \left(2 \cdot x \leq 5 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* 2.0 x) -1e-133) (not (<= (* 2.0 x) 5e+16)))
   (* (/ x (- y t)) (/ 2.0 z))
   (* 2.0 (/ (/ x z) (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((2.0 * x) <= -1e-133) || !((2.0 * x) <= 5e+16)) {
		tmp = (x / (y - t)) * (2.0 / z);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((2.0d0 * x) <= (-1d-133)) .or. (.not. ((2.0d0 * x) <= 5d+16))) then
        tmp = (x / (y - t)) * (2.0d0 / z)
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((2.0 * x) <= -1e-133) || !((2.0 * x) <= 5e+16)) {
		tmp = (x / (y - t)) * (2.0 / z);
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((2.0 * x) <= -1e-133) or not ((2.0 * x) <= 5e+16):
		tmp = (x / (y - t)) * (2.0 / z)
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(2.0 * x) <= -1e-133) || !(Float64(2.0 * x) <= 5e+16))
		tmp = Float64(Float64(x / Float64(y - t)) * Float64(2.0 / z));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((2.0 * x) <= -1e-133) || ~(((2.0 * x) <= 5e+16)))
		tmp = (x / (y - t)) * (2.0 / z);
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(2.0 * x), $MachinePrecision], -1e-133], N[Not[LessEqual[N[(2.0 * x), $MachinePrecision], 5e+16]], $MachinePrecision]], N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < -1.0000000000000001e-133 or 5e16 < (*.f64 x 2)

   1. Initial program 79.1%

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

      1. *-commutative 79.1%

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

      2. distribute-rgt-out-- 81.1%

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

      3. times-frac 96.4%

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

   3. Simplified 96.4%

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

   if -1.0000000000000001e-133 < (*.f64 x 2) < 5e16

   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. associate-*r/ 94.7%

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

      3. distribute-rgt-out-- 95.9%

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

      4. associate-/r* 97.4%

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

   3. Simplified 97.4%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x \leq -1 \cdot 10^{-133} \lor \neg \left(2 \cdot x \leq 5 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 3: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -9.6:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-154}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-80}:\\ \;\;\;\;\frac{\frac{x}{t}}{z} \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))))
   (if (<= y -9.6)
     t_1
     (if (<= y -4.7e-120)
       (/ (/ -2.0 t) (/ z x))
       (if (<= y -5e-154)
         (/ (* 2.0 x) (* y z))
         (if (<= y 3.15e-80) (* (/ (/ x t) z) (- 2.0)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (y <= -9.6) {
		tmp = t_1;
	} else if (y <= -4.7e-120) {
		tmp = (-2.0 / t) / (z / x);
	} else if (y <= -5e-154) {
		tmp = (2.0 * x) / (y * z);
	} else if (y <= 3.15e-80) {
		tmp = ((x / t) / z) * -2.0;
	} 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) :: tmp
    t_1 = (2.0d0 / z) * (x / y)
    if (y <= (-9.6d0)) then
        tmp = t_1
    else if (y <= (-4.7d-120)) then
        tmp = ((-2.0d0) / t) / (z / x)
    else if (y <= (-5d-154)) then
        tmp = (2.0d0 * x) / (y * z)
    else if (y <= 3.15d-80) then
        tmp = ((x / t) / z) * -2.0d0
    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 = (2.0 / z) * (x / y);
	double tmp;
	if (y <= -9.6) {
		tmp = t_1;
	} else if (y <= -4.7e-120) {
		tmp = (-2.0 / t) / (z / x);
	} else if (y <= -5e-154) {
		tmp = (2.0 * x) / (y * z);
	} else if (y <= 3.15e-80) {
		tmp = ((x / t) / z) * -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	tmp = 0
	if y <= -9.6:
		tmp = t_1
	elif y <= -4.7e-120:
		tmp = (-2.0 / t) / (z / x)
	elif y <= -5e-154:
		tmp = (2.0 * x) / (y * z)
	elif y <= 3.15e-80:
		tmp = ((x / t) / z) * -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	tmp = 0.0
	if (y <= -9.6)
		tmp = t_1;
	elseif (y <= -4.7e-120)
		tmp = Float64(Float64(-2.0 / t) / Float64(z / x));
	elseif (y <= -5e-154)
		tmp = Float64(Float64(2.0 * x) / Float64(y * z));
	elseif (y <= 3.15e-80)
		tmp = Float64(Float64(Float64(x / t) / z) * Float64(-2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	tmp = 0.0;
	if (y <= -9.6)
		tmp = t_1;
	elseif (y <= -4.7e-120)
		tmp = (-2.0 / t) / (z / x);
	elseif (y <= -5e-154)
		tmp = (2.0 * x) / (y * z);
	elseif (y <= 3.15e-80)
		tmp = ((x / t) / z) * -2.0;
	else
		tmp = t_1;
	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[y, -9.6], t$95$1, If[LessEqual[y, -4.7e-120], N[(N[(-2.0 / t), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-154], N[(N[(2.0 * x), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.15e-80], N[(N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision] * (-2.0)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.59999999999999964 or 3.14999999999999983e-80 < y

   1. Initial program 80.7%

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

      1. *-commutative 80.7%

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

      2. distribute-rgt-out-- 83.6%

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

      3. times-frac 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 72.7%

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

      1. associate-*r/ 72.7%

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

      2. *-commutative 72.7%

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

      3. times-frac 79.2%

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

   6. Simplified 79.2%

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

   if -9.59999999999999964 < y < -4.70000000000000016e-120

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

      2. distribute-rgt-out-- 85.5%

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

      3. times-frac 96.4%

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

   3. Simplified 96.4%

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

      1. frac-times 85.5%

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

      2. *-commutative 85.5%

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

      3. times-frac 92.2%

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

      4. clear-num 92.1%

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

      5. associate-*l/ 93.4%

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

      6. *-un-lft-identity 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in y around 0 71.3%

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

   if -4.70000000000000016e-120 < y < -5.0000000000000002e-154

   1. Initial program 99.8%

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

      1. distribute-rgt-out-- 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 67.2%

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

      1. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   if -5.0000000000000002e-154 < y < 3.14999999999999983e-80

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

      2. associate-*r/ 90.0%

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

      3. distribute-rgt-out-- 90.1%

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

      4. associate-/r* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. distribute-frac-neg 80.5%

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

      3. associate-/r* 80.8%

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

   6. Simplified 80.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-154}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-80}:\\ \;\;\;\;\frac{\frac{x}{t}}{z} \cdot \left(-2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -25 \lor \neg \left(y \leq 7.2 \cdot 10^{-78}\right) \land \left(y \leq 3450000 \lor \neg \left(y \leq 7.8 \cdot 10^{+90}\right)\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -25.0)
         (and (not (<= y 7.2e-78)) (or (<= y 3450000.0) (not (<= y 7.8e+90)))))
   (* (/ x z) (/ 2.0 y))
   (* -2.0 (/ (/ x z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -25.0) || (!(y <= 7.2e-78) && ((y <= 3450000.0) || !(y <= 7.8e+90)))) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = -2.0 * ((x / z) / 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 ((y <= (-25.0d0)) .or. (.not. (y <= 7.2d-78)) .and. (y <= 3450000.0d0) .or. (.not. (y <= 7.8d+90))) then
        tmp = (x / z) * (2.0d0 / y)
    else
        tmp = (-2.0d0) * ((x / z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -25.0) || (!(y <= 7.2e-78) && ((y <= 3450000.0) || !(y <= 7.8e+90)))) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = -2.0 * ((x / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -25.0) or (not (y <= 7.2e-78) and ((y <= 3450000.0) or not (y <= 7.8e+90))):
		tmp = (x / z) * (2.0 / y)
	else:
		tmp = -2.0 * ((x / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -25.0) || (!(y <= 7.2e-78) && ((y <= 3450000.0) || !(y <= 7.8e+90))))
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	else
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -25.0) || (~((y <= 7.2e-78)) && ((y <= 3450000.0) || ~((y <= 7.8e+90)))))
		tmp = (x / z) * (2.0 / y);
	else
		tmp = -2.0 * ((x / z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -25.0], And[N[Not[LessEqual[y, 7.2e-78]], $MachinePrecision], Or[LessEqual[y, 3450000.0], N[Not[LessEqual[y, 7.8e+90]], $MachinePrecision]]]], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -25 or 7.2000000000000005e-78 < y < 3.45e6 or 7.8000000000000004e90 < y

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

      2. distribute-rgt-out-- 83.8%

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

      3. times-frac 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 76.0%

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

      1. associate-*r/ 76.0%

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

      2. *-commutative 76.0%

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

      3. times-frac 83.7%

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

   6. Simplified 83.7%

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

      1. clear-num 83.1%

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

      2. frac-times 82.7%

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

      3. metadata-eval 82.7%

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

   8. Applied egg-rr 82.7%

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

      1. associate-/l/ 83.2%

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

      2. div-inv 83.2%

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

      3. div-inv 83.1%

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

      4. times-frac 79.2%

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

      5. associate-/r* 79.2%

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

      6. div-inv 79.3%

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

      7. clear-num 79.3%

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

   10. Applied egg-rr 79.3%

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

   if -25 < y < 7.2000000000000005e-78 or 3.45e6 < y < 7.8000000000000004e90

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

      2. distribute-rgt-out-- 88.8%

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

      3. times-frac 93.6%

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

   3. Simplified 93.6%

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

      1. frac-times 88.8%

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

      2. *-commutative 88.8%

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

      3. times-frac 91.7%

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

      4. clear-num 90.6%

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

      5. associate-*l/ 91.1%

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

      6. *-un-lft-identity 91.1%

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

   5. Applied egg-rr 91.1%

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

   6. Taylor expanded in y around 0 66.5%

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

      1. *-commutative 66.5%

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

      2. associate-/r* 71.4%

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

   8. Simplified 71.4%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -25 \lor \neg \left(y \leq 7.2 \cdot 10^{-78}\right) \land \left(y \leq 3450000 \lor \neg \left(y \leq 7.8 \cdot 10^{+90}\right)\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \end{array} \]

Alternative 5: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{if}\;y \leq -0.88:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;y \leq 1.82 \lor \neg \left(y \leq 7 \cdot 10^{+90}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 2.0 y))))
   (if (<= y -0.88)
     t_1
     (if (<= y 3e-78)
       (* (/ x t) (/ -2.0 z))
       (if (or (<= y 1.82) (not (<= y 7e+90))) t_1 (* -2.0 (/ (/ x z) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (2.0 / y);
	double tmp;
	if (y <= -0.88) {
		tmp = t_1;
	} else if (y <= 3e-78) {
		tmp = (x / t) * (-2.0 / z);
	} else if ((y <= 1.82) || !(y <= 7e+90)) {
		tmp = t_1;
	} else {
		tmp = -2.0 * ((x / z) / 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 (y <= (-0.88d0)) then
        tmp = t_1
    else if (y <= 3d-78) then
        tmp = (x / t) * ((-2.0d0) / z)
    else if ((y <= 1.82d0) .or. (.not. (y <= 7d+90))) then
        tmp = t_1
    else
        tmp = (-2.0d0) * ((x / z) / 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 (y <= -0.88) {
		tmp = t_1;
	} else if (y <= 3e-78) {
		tmp = (x / t) * (-2.0 / z);
	} else if ((y <= 1.82) || !(y <= 7e+90)) {
		tmp = t_1;
	} else {
		tmp = -2.0 * ((x / z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / z) * (2.0 / y)
	tmp = 0
	if y <= -0.88:
		tmp = t_1
	elif y <= 3e-78:
		tmp = (x / t) * (-2.0 / z)
	elif (y <= 1.82) or not (y <= 7e+90):
		tmp = t_1
	else:
		tmp = -2.0 * ((x / z) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(2.0 / y))
	tmp = 0.0
	if (y <= -0.88)
		tmp = t_1;
	elseif (y <= 3e-78)
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	elseif ((y <= 1.82) || !(y <= 7e+90))
		tmp = t_1;
	else
		tmp = Float64(-2.0 * Float64(Float64(x / z) / 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 (y <= -0.88)
		tmp = t_1;
	elseif (y <= 3e-78)
		tmp = (x / t) * (-2.0 / z);
	elseif ((y <= 1.82) || ~((y <= 7e+90)))
		tmp = t_1;
	else
		tmp = -2.0 * ((x / z) / 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[y, -0.88], t$95$1, If[LessEqual[y, 3e-78], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.82], N[Not[LessEqual[y, 7e+90]], $MachinePrecision]], t$95$1, N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.880000000000000004 or 2.99999999999999988e-78 < y < 1.82000000000000006 or 6.9999999999999997e90 < y

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

      2. distribute-rgt-out-- 83.8%

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

      3. times-frac 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 76.0%

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

      1. associate-*r/ 76.0%

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

      2. *-commutative 76.0%

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

      3. times-frac 83.7%

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

   6. Simplified 83.7%

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

      1. clear-num 83.1%

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

      2. frac-times 82.7%

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

      3. metadata-eval 82.7%

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

   8. Applied egg-rr 82.7%

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

      1. associate-/l/ 83.2%

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

      2. div-inv 83.2%

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

      3. div-inv 83.1%

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

      4. times-frac 79.2%

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

      5. associate-/r* 79.2%

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

      6. div-inv 79.3%

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

      7. clear-num 79.3%

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

   10. Applied egg-rr 79.3%

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

   if -0.880000000000000004 < y < 2.99999999999999988e-78

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. distribute-rgt-out-- 89.9%

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

      3. times-frac 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around 0 69.8%

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

      1. associate-*r/ 69.8%

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

      2. *-commutative 69.8%

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

      3. *-commutative 69.8%

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

   6. Simplified 69.8%

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

      1. *-commutative 69.8%

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

      2. times-frac 73.2%

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

   8. Applied egg-rr 73.2%

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

   if 1.82000000000000006 < y < 6.9999999999999997e90

   1. Initial program 73.3%

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

      1. *-commutative 73.3%

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

      2. distribute-rgt-out-- 82.7%

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

      3. times-frac 93.2%

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

   3. Simplified 93.2%

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

      1. frac-times 82.7%

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

      2. *-commutative 82.7%

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

      3. times-frac 95.7%

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

      4. clear-num 95.6%

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

      5. associate-*l/ 95.8%

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

      6. *-un-lft-identity 95.8%

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

   5. Applied egg-rr 95.8%

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

   6. Taylor expanded in y around 0 49.6%

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

      1. *-commutative 49.6%

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

      2. associate-/r* 66.6%

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

   8. Simplified 66.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.88:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;y \leq 1.82 \lor \neg \left(y \leq 7 \cdot 10^{+90}\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \end{array} \]

Alternative 6: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -2.1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-120}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-154} \lor \neg \left(y \leq 6.5 \cdot 10^{-78}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))))
   (if (<= y -2.1)
     t_1
     (if (<= y -4.7e-120)
       (* -2.0 (/ (/ x z) t))
       (if (or (<= y -5e-154) (not (<= y 6.5e-78)))
         t_1
         (* (/ x t) (/ -2.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (y <= -2.1) {
		tmp = t_1;
	} else if (y <= -4.7e-120) {
		tmp = -2.0 * ((x / z) / t);
	} else if ((y <= -5e-154) || !(y <= 6.5e-78)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 / z) * (x / y)
    if (y <= (-2.1d0)) then
        tmp = t_1
    else if (y <= (-4.7d-120)) then
        tmp = (-2.0d0) * ((x / z) / t)
    else if ((y <= (-5d-154)) .or. (.not. (y <= 6.5d-78))) then
        tmp = t_1
    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 t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (y <= -2.1) {
		tmp = t_1;
	} else if (y <= -4.7e-120) {
		tmp = -2.0 * ((x / z) / t);
	} else if ((y <= -5e-154) || !(y <= 6.5e-78)) {
		tmp = t_1;
	} else {
		tmp = (x / t) * (-2.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	tmp = 0
	if y <= -2.1:
		tmp = t_1
	elif y <= -4.7e-120:
		tmp = -2.0 * ((x / z) / t)
	elif (y <= -5e-154) or not (y <= 6.5e-78):
		tmp = t_1
	else:
		tmp = (x / t) * (-2.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	tmp = 0.0
	if (y <= -2.1)
		tmp = t_1;
	elseif (y <= -4.7e-120)
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	elseif ((y <= -5e-154) || !(y <= 6.5e-78))
		tmp = t_1;
	else
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	tmp = 0.0;
	if (y <= -2.1)
		tmp = t_1;
	elseif (y <= -4.7e-120)
		tmp = -2.0 * ((x / z) / t);
	elseif ((y <= -5e-154) || ~((y <= 6.5e-78)))
		tmp = t_1;
	else
		tmp = (x / t) * (-2.0 / z);
	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[y, -2.1], t$95$1, If[LessEqual[y, -4.7e-120], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5e-154], N[Not[LessEqual[y, 6.5e-78]], $MachinePrecision]], t$95$1, N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.10000000000000009 or -4.70000000000000016e-120 < y < -5.0000000000000002e-154 or 6.5000000000000003e-78 < y

   1. Initial program 81.9%

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

      1. *-commutative 81.9%

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

      2. distribute-rgt-out-- 84.7%

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

      3. times-frac 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 72.4%

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

      1. associate-*r/ 72.4%

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

      2. *-commutative 72.4%

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

      3. times-frac 78.4%

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

   6. Simplified 78.4%

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

   if -2.10000000000000009 < y < -4.70000000000000016e-120

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

      2. distribute-rgt-out-- 85.5%

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

      3. times-frac 96.4%

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

   3. Simplified 96.4%

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

      1. frac-times 85.5%

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

      2. *-commutative 85.5%

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

      3. times-frac 92.2%

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

      4. clear-num 92.1%

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

      5. associate-*l/ 93.4%

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

      6. *-un-lft-identity 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in y around 0 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-/r* 70.3%

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

   8. Simplified 70.3%

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

   if -5.0000000000000002e-154 < y < 6.5000000000000003e-78

   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-- 90.1%

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

      3. times-frac 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in y around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. *-commutative 80.5%

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

      3. *-commutative 80.5%

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

   6. Simplified 80.5%

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

      1. *-commutative 80.5%

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

      2. times-frac 80.7%

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

   8. Applied egg-rr 80.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-120}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-154} \lor \neg \left(y \leq 6.5 \cdot 10^{-78}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \end{array} \]

Alternative 7: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -0.62:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-120}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-154}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))))
   (if (<= y -0.62)
     t_1
     (if (<= y -4.7e-120)
       (* -2.0 (/ (/ x z) t))
       (if (<= y -5e-154)
         (/ 2.0 (* z (/ y x)))
         (if (<= y 4.5e-78) (* (/ x t) (/ -2.0 z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (y <= -0.62) {
		tmp = t_1;
	} else if (y <= -4.7e-120) {
		tmp = -2.0 * ((x / z) / t);
	} else if (y <= -5e-154) {
		tmp = 2.0 / (z * (y / x));
	} else if (y <= 4.5e-78) {
		tmp = (x / t) * (-2.0 / z);
	} 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) :: tmp
    t_1 = (2.0d0 / z) * (x / y)
    if (y <= (-0.62d0)) then
        tmp = t_1
    else if (y <= (-4.7d-120)) then
        tmp = (-2.0d0) * ((x / z) / t)
    else if (y <= (-5d-154)) then
        tmp = 2.0d0 / (z * (y / x))
    else if (y <= 4.5d-78) then
        tmp = (x / t) * ((-2.0d0) / z)
    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 = (2.0 / z) * (x / y);
	double tmp;
	if (y <= -0.62) {
		tmp = t_1;
	} else if (y <= -4.7e-120) {
		tmp = -2.0 * ((x / z) / t);
	} else if (y <= -5e-154) {
		tmp = 2.0 / (z * (y / x));
	} else if (y <= 4.5e-78) {
		tmp = (x / t) * (-2.0 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	tmp = 0
	if y <= -0.62:
		tmp = t_1
	elif y <= -4.7e-120:
		tmp = -2.0 * ((x / z) / t)
	elif y <= -5e-154:
		tmp = 2.0 / (z * (y / x))
	elif y <= 4.5e-78:
		tmp = (x / t) * (-2.0 / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	tmp = 0.0
	if (y <= -0.62)
		tmp = t_1;
	elseif (y <= -4.7e-120)
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	elseif (y <= -5e-154)
		tmp = Float64(2.0 / Float64(z * Float64(y / x)));
	elseif (y <= 4.5e-78)
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	tmp = 0.0;
	if (y <= -0.62)
		tmp = t_1;
	elseif (y <= -4.7e-120)
		tmp = -2.0 * ((x / z) / t);
	elseif (y <= -5e-154)
		tmp = 2.0 / (z * (y / x));
	elseif (y <= 4.5e-78)
		tmp = (x / t) * (-2.0 / z);
	else
		tmp = t_1;
	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[y, -0.62], t$95$1, If[LessEqual[y, -4.7e-120], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-154], N[(2.0 / N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-78], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.619999999999999996 or 4.5e-78 < y

   1. Initial program 80.7%

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

      1. *-commutative 80.7%

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

      2. distribute-rgt-out-- 83.6%

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

      3. times-frac 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 72.7%

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

      1. associate-*r/ 72.7%

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

      2. *-commutative 72.7%

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

      3. times-frac 79.2%

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

   6. Simplified 79.2%

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

   if -0.619999999999999996 < y < -4.70000000000000016e-120

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

      2. distribute-rgt-out-- 85.5%

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

      3. times-frac 96.4%

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

   3. Simplified 96.4%

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

      1. frac-times 85.5%

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

      2. *-commutative 85.5%

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

      3. times-frac 92.2%

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

      4. clear-num 92.1%

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

      5. associate-*l/ 93.4%

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

      6. *-un-lft-identity 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in y around 0 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-/r* 70.3%

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

   8. Simplified 70.3%

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

   if -4.70000000000000016e-120 < y < -5.0000000000000002e-154

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. distribute-rgt-out-- 99.8%

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

      3. times-frac 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around inf 67.2%

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

      1. associate-*r/ 67.2%

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

      2. *-commutative 67.2%

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

      3. times-frac 66.6%

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

   6. Simplified 66.6%

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

      1. clear-num 66.8%

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

      2. frac-times 66.9%

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

      3. metadata-eval 66.9%

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

   8. Applied egg-rr 66.9%

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

   if -5.0000000000000002e-154 < y < 4.5e-78

   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-- 90.1%

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

      3. times-frac 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in y around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. *-commutative 80.5%

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

      3. *-commutative 80.5%

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

   6. Simplified 80.5%

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

      1. *-commutative 80.5%

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

      2. times-frac 80.7%

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

   8. Applied egg-rr 80.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.62:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-120}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-154}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y}{x}}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 8: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -1.15:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-120}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-154}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))))
   (if (<= y -1.15)
     t_1
     (if (<= y -4.9e-120)
       (* -2.0 (/ (/ x z) t))
       (if (<= y -5e-154)
         (/ (* 2.0 x) (* y z))
         (if (<= y 7.2e-78) (* (/ x t) (/ -2.0 z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (y <= -1.15) {
		tmp = t_1;
	} else if (y <= -4.9e-120) {
		tmp = -2.0 * ((x / z) / t);
	} else if (y <= -5e-154) {
		tmp = (2.0 * x) / (y * z);
	} else if (y <= 7.2e-78) {
		tmp = (x / t) * (-2.0 / z);
	} 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) :: tmp
    t_1 = (2.0d0 / z) * (x / y)
    if (y <= (-1.15d0)) then
        tmp = t_1
    else if (y <= (-4.9d-120)) then
        tmp = (-2.0d0) * ((x / z) / t)
    else if (y <= (-5d-154)) then
        tmp = (2.0d0 * x) / (y * z)
    else if (y <= 7.2d-78) then
        tmp = (x / t) * ((-2.0d0) / z)
    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 = (2.0 / z) * (x / y);
	double tmp;
	if (y <= -1.15) {
		tmp = t_1;
	} else if (y <= -4.9e-120) {
		tmp = -2.0 * ((x / z) / t);
	} else if (y <= -5e-154) {
		tmp = (2.0 * x) / (y * z);
	} else if (y <= 7.2e-78) {
		tmp = (x / t) * (-2.0 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	tmp = 0
	if y <= -1.15:
		tmp = t_1
	elif y <= -4.9e-120:
		tmp = -2.0 * ((x / z) / t)
	elif y <= -5e-154:
		tmp = (2.0 * x) / (y * z)
	elif y <= 7.2e-78:
		tmp = (x / t) * (-2.0 / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	tmp = 0.0
	if (y <= -1.15)
		tmp = t_1;
	elseif (y <= -4.9e-120)
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	elseif (y <= -5e-154)
		tmp = Float64(Float64(2.0 * x) / Float64(y * z));
	elseif (y <= 7.2e-78)
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	tmp = 0.0;
	if (y <= -1.15)
		tmp = t_1;
	elseif (y <= -4.9e-120)
		tmp = -2.0 * ((x / z) / t);
	elseif (y <= -5e-154)
		tmp = (2.0 * x) / (y * z);
	elseif (y <= 7.2e-78)
		tmp = (x / t) * (-2.0 / z);
	else
		tmp = t_1;
	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[y, -1.15], t$95$1, If[LessEqual[y, -4.9e-120], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-154], N[(N[(2.0 * x), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-78], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1499999999999999 or 7.2000000000000005e-78 < y

   1. Initial program 80.7%

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

      1. *-commutative 80.7%

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

      2. distribute-rgt-out-- 83.6%

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

      3. times-frac 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 72.7%

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

      1. associate-*r/ 72.7%

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

      2. *-commutative 72.7%

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

      3. times-frac 79.2%

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

   6. Simplified 79.2%

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

   if -1.1499999999999999 < y < -4.9000000000000003e-120

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

      2. distribute-rgt-out-- 85.5%

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

      3. times-frac 96.4%

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

   3. Simplified 96.4%

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

      1. frac-times 85.5%

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

      2. *-commutative 85.5%

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

      3. times-frac 92.2%

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

      4. clear-num 92.1%

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

      5. associate-*l/ 93.4%

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

      6. *-un-lft-identity 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in y around 0 56.0%

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

      1. *-commutative 56.0%

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

      2. associate-/r* 70.3%

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

   8. Simplified 70.3%

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

   if -4.9000000000000003e-120 < y < -5.0000000000000002e-154

   1. Initial program 99.8%

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

      1. distribute-rgt-out-- 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 67.2%

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

      1. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   if -5.0000000000000002e-154 < y < 7.2000000000000005e-78

   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-- 90.1%

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

      3. times-frac 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in y around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. *-commutative 80.5%

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

      3. *-commutative 80.5%

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

   6. Simplified 80.5%

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

      1. *-commutative 80.5%

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

      2. times-frac 80.7%

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

   8. Applied egg-rr 80.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-120}:\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-154}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 9: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.6:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-154}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))))
   (if (<= y -3.6)
     t_1
     (if (<= y -4.7e-120)
       (/ (/ -2.0 t) (/ z x))
       (if (<= y -5e-154)
         (/ (* 2.0 x) (* y z))
         (if (<= y 7.2e-78) (* (/ x t) (/ -2.0 z)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (y <= -3.6) {
		tmp = t_1;
	} else if (y <= -4.7e-120) {
		tmp = (-2.0 / t) / (z / x);
	} else if (y <= -5e-154) {
		tmp = (2.0 * x) / (y * z);
	} else if (y <= 7.2e-78) {
		tmp = (x / t) * (-2.0 / z);
	} 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) :: tmp
    t_1 = (2.0d0 / z) * (x / y)
    if (y <= (-3.6d0)) then
        tmp = t_1
    else if (y <= (-4.7d-120)) then
        tmp = ((-2.0d0) / t) / (z / x)
    else if (y <= (-5d-154)) then
        tmp = (2.0d0 * x) / (y * z)
    else if (y <= 7.2d-78) then
        tmp = (x / t) * ((-2.0d0) / z)
    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 = (2.0 / z) * (x / y);
	double tmp;
	if (y <= -3.6) {
		tmp = t_1;
	} else if (y <= -4.7e-120) {
		tmp = (-2.0 / t) / (z / x);
	} else if (y <= -5e-154) {
		tmp = (2.0 * x) / (y * z);
	} else if (y <= 7.2e-78) {
		tmp = (x / t) * (-2.0 / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	tmp = 0
	if y <= -3.6:
		tmp = t_1
	elif y <= -4.7e-120:
		tmp = (-2.0 / t) / (z / x)
	elif y <= -5e-154:
		tmp = (2.0 * x) / (y * z)
	elif y <= 7.2e-78:
		tmp = (x / t) * (-2.0 / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	tmp = 0.0
	if (y <= -3.6)
		tmp = t_1;
	elseif (y <= -4.7e-120)
		tmp = Float64(Float64(-2.0 / t) / Float64(z / x));
	elseif (y <= -5e-154)
		tmp = Float64(Float64(2.0 * x) / Float64(y * z));
	elseif (y <= 7.2e-78)
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	tmp = 0.0;
	if (y <= -3.6)
		tmp = t_1;
	elseif (y <= -4.7e-120)
		tmp = (-2.0 / t) / (z / x);
	elseif (y <= -5e-154)
		tmp = (2.0 * x) / (y * z);
	elseif (y <= 7.2e-78)
		tmp = (x / t) * (-2.0 / z);
	else
		tmp = t_1;
	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[y, -3.6], t$95$1, If[LessEqual[y, -4.7e-120], N[(N[(-2.0 / t), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-154], N[(N[(2.0 * x), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-78], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.60000000000000009 or 7.2000000000000005e-78 < y

   1. Initial program 80.7%

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

      1. *-commutative 80.7%

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

      2. distribute-rgt-out-- 83.6%

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

      3. times-frac 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around inf 72.7%

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

      1. associate-*r/ 72.7%

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

      2. *-commutative 72.7%

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

      3. times-frac 79.2%

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

   6. Simplified 79.2%

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

   if -3.60000000000000009 < y < -4.70000000000000016e-120

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

      2. distribute-rgt-out-- 85.5%

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

      3. times-frac 96.4%

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

   3. Simplified 96.4%

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

      1. frac-times 85.5%

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

      2. *-commutative 85.5%

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

      3. times-frac 92.2%

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

      4. clear-num 92.1%

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

      5. associate-*l/ 93.4%

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

      6. *-un-lft-identity 93.4%

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

   5. Applied egg-rr 93.4%

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

   6. Taylor expanded in y around 0 71.3%

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

   if -4.70000000000000016e-120 < y < -5.0000000000000002e-154

   1. Initial program 99.8%

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

      1. distribute-rgt-out-- 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 67.2%

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

      1. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   if -5.0000000000000002e-154 < y < 7.2000000000000005e-78

   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-- 90.1%

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

      3. times-frac 92.1%

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

   3. Simplified 92.1%

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

   4. Taylor expanded in y around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. *-commutative 80.5%

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

      3. *-commutative 80.5%

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

   6. Simplified 80.5%

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

      1. *-commutative 80.5%

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

      2. times-frac 80.7%

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

   8. Applied egg-rr 80.7%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-120}:\\ \;\;\;\;\frac{\frac{-2}{t}}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-154}:\\ \;\;\;\;\frac{2 \cdot x}{y \cdot z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 10: 96.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.75e+59)
   (* (/ x (- y t)) (/ 2.0 z))
   (if (<= z 6.1e-47)
     (* x (/ 2.0 (* z (- y t))))
     (* 2.0 (/ (/ x z) (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e+59) {
		tmp = (x / (y - t)) * (2.0 / z);
	} else if (z <= 6.1e-47) {
		tmp = x * (2.0 / (z * (y - t)));
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.75d+59)) then
        tmp = (x / (y - t)) * (2.0d0 / z)
    else if (z <= 6.1d-47) then
        tmp = x * (2.0d0 / (z * (y - t)))
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.75e+59) {
		tmp = (x / (y - t)) * (2.0 / z);
	} else if (z <= 6.1e-47) {
		tmp = x * (2.0 / (z * (y - t)));
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.75e+59:
		tmp = (x / (y - t)) * (2.0 / z)
	elif z <= 6.1e-47:
		tmp = x * (2.0 / (z * (y - t)))
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.75e+59)
		tmp = Float64(Float64(x / Float64(y - t)) * Float64(2.0 / z));
	elseif (z <= 6.1e-47)
		tmp = Float64(x * Float64(2.0 / Float64(z * Float64(y - t))));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.75e+59)
		tmp = (x / (y - t)) * (2.0 / z);
	elseif (z <= 6.1e-47)
		tmp = x * (2.0 / (z * (y - t)));
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.75e+59], N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.1e-47], N[(x * N[(2.0 / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75e59

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

      2. distribute-rgt-out-- 78.5%

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

      3. times-frac 96.0%

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

   3. Simplified 96.0%

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

   if -1.75e59 < z < 6.1e-47

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

      2. distribute-rgt-out-- 96.7%

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

      3. times-frac 90.3%

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

   3. Simplified 90.3%

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

      1. associate-*l/ 90.5%

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

      2. associate-/l* 89.6%

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

   5. Applied egg-rr 89.6%

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

      1. associate-/l* 95.8%

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

      2. associate-/r/ 96.6%

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

   7. Applied egg-rr 96.6%

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

   if 6.1e-47 < z

   1. Initial program 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-*r/ 75.1%

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

      3. distribute-rgt-out-- 76.5%

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

      4. associate-/r* 98.6%

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

   3. Simplified 98.6%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 11: 96.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+65}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y - t}{x}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7e+65)
   (/ 2.0 (* z (/ (- y t) x)))
   (if (<= z 2.5e-53)
     (* x (/ 2.0 (* z (- y t))))
     (* 2.0 (/ (/ x z) (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7e+65) {
		tmp = 2.0 / (z * ((y - t) / x));
	} else if (z <= 2.5e-53) {
		tmp = x * (2.0 / (z * (y - t)));
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7d+65)) then
        tmp = 2.0d0 / (z * ((y - t) / x))
    else if (z <= 2.5d-53) then
        tmp = x * (2.0d0 / (z * (y - t)))
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7e+65) {
		tmp = 2.0 / (z * ((y - t) / x));
	} else if (z <= 2.5e-53) {
		tmp = x * (2.0 / (z * (y - t)));
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7e+65:
		tmp = 2.0 / (z * ((y - t) / x))
	elif z <= 2.5e-53:
		tmp = x * (2.0 / (z * (y - t)))
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7e+65)
		tmp = Float64(2.0 / Float64(z * Float64(Float64(y - t) / x)));
	elseif (z <= 2.5e-53)
		tmp = Float64(x * Float64(2.0 / Float64(z * Float64(y - t))));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7e+65)
		tmp = 2.0 / (z * ((y - t) / x));
	elseif (z <= 2.5e-53)
		tmp = x * (2.0 / (z * (y - t)));
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7e+65], N[(2.0 / N[(z * N[(N[(y - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-53], N[(x * N[(2.0 / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0000000000000002e65

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

      2. distribute-rgt-out-- 78.5%

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

      3. times-frac 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 96.0%

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

      2. frac-times 96.1%

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

      3. metadata-eval 96.1%

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

   5. Applied egg-rr 96.1%

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

   if -7.0000000000000002e65 < z < 2.5e-53

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

      2. distribute-rgt-out-- 96.7%

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

      3. times-frac 90.3%

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

   3. Simplified 90.3%

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

      1. associate-*l/ 90.5%

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

      2. associate-/l* 89.6%

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

   5. Applied egg-rr 89.6%

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

      1. associate-/l* 95.8%

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

      2. associate-/r/ 96.6%

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

   7. Applied egg-rr 96.6%

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

   if 2.5e-53 < z

   1. Initial program 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-*r/ 75.1%

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

      3. distribute-rgt-out-- 76.5%

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

      4. associate-/r* 98.6%

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

   3. Simplified 98.6%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+65}:\\ \;\;\;\;\frac{2}{z \cdot \frac{y - t}{x}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-53}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 12: 96.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+66}:\\ \;\;\;\;\frac{2}{\frac{z}{\frac{x}{y - t}}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e+66)
   (/ 2.0 (/ z (/ x (- y t))))
   (if (<= z 9e-48) (* x (/ 2.0 (* z (- y t)))) (* 2.0 (/ (/ x z) (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+66) {
		tmp = 2.0 / (z / (x / (y - t)));
	} else if (z <= 9e-48) {
		tmp = x * (2.0 / (z * (y - t)));
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1d+66)) then
        tmp = 2.0d0 / (z / (x / (y - t)))
    else if (z <= 9d-48) then
        tmp = x * (2.0d0 / (z * (y - t)))
    else
        tmp = 2.0d0 * ((x / z) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+66) {
		tmp = 2.0 / (z / (x / (y - t)));
	} else if (z <= 9e-48) {
		tmp = x * (2.0 / (z * (y - t)));
	} else {
		tmp = 2.0 * ((x / z) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1e+66:
		tmp = 2.0 / (z / (x / (y - t)))
	elif z <= 9e-48:
		tmp = x * (2.0 / (z * (y - t)))
	else:
		tmp = 2.0 * ((x / z) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e+66)
		tmp = Float64(2.0 / Float64(z / Float64(x / Float64(y - t))));
	elseif (z <= 9e-48)
		tmp = Float64(x * Float64(2.0 / Float64(z * Float64(y - t))));
	else
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1e+66)
		tmp = 2.0 / (z / (x / (y - t)));
	elseif (z <= 9e-48)
		tmp = x * (2.0 / (z * (y - t)));
	else
		tmp = 2.0 * ((x / z) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e+66], N[(2.0 / N[(z / N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-48], N[(x * N[(2.0 / N[(z * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.99999999999999945e65

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

      2. distribute-rgt-out-- 78.5%

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

      3. times-frac 96.0%

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

   3. Simplified 96.0%

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

      1. associate-*l/ 96.2%

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

      2. associate-/l* 96.1%

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

   5. Applied egg-rr 96.1%

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

   if -9.99999999999999945e65 < z < 8.99999999999999977e-48

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

      2. distribute-rgt-out-- 96.7%

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

      3. times-frac 90.3%

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

   3. Simplified 90.3%

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

      1. associate-*l/ 90.5%

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

      2. associate-/l* 89.6%

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

   5. Applied egg-rr 89.6%

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

      1. associate-/l* 95.8%

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

      2. associate-/r/ 96.6%

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

   7. Applied egg-rr 96.6%

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

   if 8.99999999999999977e-48 < z

   1. Initial program 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-*r/ 75.1%

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

      3. distribute-rgt-out-- 76.5%

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

      4. associate-/r* 98.6%

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

   3. Simplified 98.6%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+66}:\\ \;\;\;\;\frac{2}{\frac{z}{\frac{x}{y - t}}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \frac{2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 13: 57.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+116} \lor \neg \left(z \leq 10^{+84}\right):\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.56e+116) (not (<= z 1e+84)))
   (* -2.0 (/ (/ x z) t))
   (* x (/ -2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.56e+116) || !(z <= 1e+84)) {
		tmp = -2.0 * ((x / z) / t);
	} else {
		tmp = x * (-2.0 / (z * 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 <= (-1.56d+116)) .or. (.not. (z <= 1d+84))) then
        tmp = (-2.0d0) * ((x / z) / t)
    else
        tmp = x * ((-2.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.56e+116) || !(z <= 1e+84)) {
		tmp = -2.0 * ((x / z) / t);
	} else {
		tmp = x * (-2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.56e+116) or not (z <= 1e+84):
		tmp = -2.0 * ((x / z) / t)
	else:
		tmp = x * (-2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.56e+116) || !(z <= 1e+84))
		tmp = Float64(-2.0 * Float64(Float64(x / z) / t));
	else
		tmp = Float64(x * Float64(-2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.56e+116) || ~((z <= 1e+84)))
		tmp = -2.0 * ((x / z) / t);
	else
		tmp = x * (-2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.56e+116], N[Not[LessEqual[z, 1e+84]], $MachinePrecision]], N[(-2.0 * N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.56000000000000002e116 or 1.00000000000000006e84 < z

   1. Initial program 69.8%

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

      1. *-commutative 69.8%

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

      2. distribute-rgt-out-- 73.8%

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

      3. times-frac 95.9%

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

   3. Simplified 95.9%

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

      1. frac-times 73.8%

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

      2. *-commutative 73.8%

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

      3. times-frac 95.7%

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

      4. clear-num 94.2%

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

      5. associate-*l/ 94.3%

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

      6. *-un-lft-identity 94.3%

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

   5. Applied egg-rr 94.3%

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

   6. Taylor expanded in y around 0 49.0%

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

      1. *-commutative 49.0%

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

      2. associate-/r* 66.1%

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

   8. Simplified 66.1%

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

   if -1.56000000000000002e116 < z < 1.00000000000000006e84

   1. Initial program 94.8%

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

      1. *-commutative 94.8%

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

      2. distribute-rgt-out-- 94.9%

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

      3. times-frac 91.7%

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

   3. Simplified 91.7%

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

      1. associate-*l/ 91.9%

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

      2. associate-/l* 91.2%

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

   5. Applied egg-rr 91.2%

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

      1. associate-/l* 94.2%

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

      2. associate-/r/ 94.8%

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

   7. Applied egg-rr 94.8%

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

   8. Taylor expanded in y around 0 46.6%

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

      1. *-commutative 46.6%

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

   10. Simplified 46.6%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+116} \lor \neg \left(z \leq 10^{+84}\right):\\ \;\;\;\;-2 \cdot \frac{\frac{x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-2}{z \cdot t}\\ \end{array} \]

Alternative 14: 92.2% 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 84.7%

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

   1. *-commutative 84.7%

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

   2. associate-*r/ 84.7%

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

   3. distribute-rgt-out-- 86.4%

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

   4. associate-/r* 90.1%

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

3. Simplified 90.1%

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

4. Final simplification 90.1%

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

Alternative 15: 55.8% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.7%

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

   1. *-commutative 84.7%

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

   2. distribute-rgt-out-- 86.4%

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

   3. times-frac 93.4%

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

3. Simplified 93.4%

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

   1. frac-times 86.4%

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

   2. *-commutative 86.4%

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

   3. times-frac 90.0%

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

   4. clear-num 89.3%

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

   5. associate-*l/ 90.2%

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

   6. *-un-lft-identity 90.2%

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

5. Applied egg-rr 90.2%

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

6. Taylor expanded in y around 0 47.6%

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

   1. *-commutative 47.6%

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

   2. associate-/r* 51.1%

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

8. Simplified 51.1%

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

9. Final simplification 51.1%

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

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 2023308 
(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))))