Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.6% → 98.5%

Time: 14.2s

Alternatives: 11

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+263} \lor \neg \left(t_1 \leq 2 \cdot 10^{+247}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (or (<= t_1 -1e+263) (not (<= t_1 2e+247)))
     (* 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 <= -1e+263) || !(t_1 <= 2e+247)) {
		tmp = 2.0 * ((x / 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) :: t_1
    real(8) :: tmp
    t_1 = (y * z) - (z * t)
    if ((t_1 <= (-1d+263)) .or. (.not. (t_1 <= 2d+247))) then
        tmp = 2.0d0 * ((x / 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 t_1 = (y * z) - (z * t);
	double tmp;
	if ((t_1 <= -1e+263) || !(t_1 <= 2e+247)) {
		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 <= -1e+263) or not (t_1 <= 2e+247):
		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 <= -1e+263) || !(t_1 <= 2e+247))
		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 <= -1e+263) || ~((t_1 <= 2e+247)))
		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, -1e+263], N[Not[LessEqual[t$95$1, 2e+247]], $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)) < -1.00000000000000002e263 or 1.9999999999999999e247 < (-.f64 (*.f64 y z) (*.f64 t z))

   1. Initial program 65.3%

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

      1. *-commutative 65.3%

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

      2. associate-*r/ 65.3%

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

      3. distribute-rgt-out-- 70.7%

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

      4. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   if -1.00000000000000002e263 < (-.f64 (*.f64 y z) (*.f64 t z)) < 1.9999999999999999e247

   1. Initial program 96.5%

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

      1. distribute-rgt-out-- 97.6%

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

   3. Simplified 97.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -1 \cdot 10^{+263} \lor \neg \left(y \cdot z - z \cdot t \leq 2 \cdot 10^{+247}\right):\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{z \cdot \left(y - t\right)}\\ \end{array} \]

Alternative 2: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{-2}{z}}{t}\\ t_2 := 2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (/ -2.0 z) t))) (t_2 (* 2.0 (/ (/ x y) z))))
   (if (<= y -1.12e-10)
     t_2
     (if (<= y -2.5e-66)
       t_1
       (if (<= y -6.5e-98)
         (* x (/ 2.0 (* y z)))
         (if (<= y 3.5e-69) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((-2.0 / z) / t);
	double t_2 = 2.0 * ((x / y) / z);
	double tmp;
	if (y <= -1.12e-10) {
		tmp = t_2;
	} else if (y <= -2.5e-66) {
		tmp = t_1;
	} else if (y <= -6.5e-98) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 3.5e-69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 * (((-2.0d0) / z) / t)
    t_2 = 2.0d0 * ((x / y) / z)
    if (y <= (-1.12d-10)) then
        tmp = t_2
    else if (y <= (-2.5d-66)) then
        tmp = t_1
    else if (y <= (-6.5d-98)) then
        tmp = x * (2.0d0 / (y * z))
    else if (y <= 3.5d-69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((-2.0 / z) / t);
	double t_2 = 2.0 * ((x / y) / z);
	double tmp;
	if (y <= -1.12e-10) {
		tmp = t_2;
	} else if (y <= -2.5e-66) {
		tmp = t_1;
	} else if (y <= -6.5e-98) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 3.5e-69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((-2.0 / z) / t)
	t_2 = 2.0 * ((x / y) / z)
	tmp = 0
	if y <= -1.12e-10:
		tmp = t_2
	elif y <= -2.5e-66:
		tmp = t_1
	elif y <= -6.5e-98:
		tmp = x * (2.0 / (y * z))
	elif y <= 3.5e-69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(-2.0 / z) / t))
	t_2 = Float64(2.0 * Float64(Float64(x / y) / z))
	tmp = 0.0
	if (y <= -1.12e-10)
		tmp = t_2;
	elseif (y <= -2.5e-66)
		tmp = t_1;
	elseif (y <= -6.5e-98)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	elseif (y <= 3.5e-69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((-2.0 / z) / t);
	t_2 = 2.0 * ((x / y) / z);
	tmp = 0.0;
	if (y <= -1.12e-10)
		tmp = t_2;
	elseif (y <= -2.5e-66)
		tmp = t_1;
	elseif (y <= -6.5e-98)
		tmp = x * (2.0 / (y * z));
	elseif (y <= 3.5e-69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e-10], t$95$2, If[LessEqual[y, -2.5e-66], t$95$1, If[LessEqual[y, -6.5e-98], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e-10 or 3.5000000000000001e-69 < y

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-*r/ 87.3%

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

      3. distribute-rgt-out-- 90.2%

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

      4. associate-/r* 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in y around inf 77.3%

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

      1. associate-/r* 78.8%

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

   6. Simplified 78.8%

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

   if -1.12e-10 < y < -2.49999999999999981e-66 or -6.50000000000000017e-98 < y < 3.5000000000000001e-69

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

      2. distribute-rgt-out-- 88.7%

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

      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. Step-by-step derivation

      1. frac-times 88.7%

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

      2. *-commutative 88.7%

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

      3. times-frac 95.2%

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

      4. clear-num 95.1%

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

      5. frac-times 94.7%

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

      6. metadata-eval 94.7%

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

   5. Applied egg-rr 94.7%

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

   6. Taylor expanded in y around 0 76.3%

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

      1. associate-*r/ 76.3%

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

      2. *-commutative 76.3%

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

      3. *-rgt-identity 76.3%

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

      4. *-commutative 76.3%

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

      5. associate-*r/ 76.2%

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

      6. associate-*l* 76.2%

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

      7. associate-/r* 76.2%

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

      8. associate-*r/ 76.3%

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

      9. *-commutative 76.3%

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

      10. associate-*l/ 76.3%

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

      11. metadata-eval 76.3%

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

   8. Simplified 76.3%

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

   if -2.49999999999999981e-66 < y < -6.50000000000000017e-98

   1. Initial program 99.6%

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

      1. distribute-rgt-out-- 99.6%

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

   3. Simplified 99.6%

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

      1. times-frac 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*r/ 88.1%

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

      3. associate-*l/ 88.3%

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

      4. *-commutative 88.3%

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

      5. *-commutative 88.3%

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

   8. Simplified 88.3%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-10}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \end{array} \]

Alternative 3: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{if}\;y \leq -5.1 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-67}:\\ \;\;\;\;\frac{-2}{z} \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (/ (/ x y) z))))
   (if (<= y -5.1e-11)
     t_1
     (if (<= y -2.5e-66)
       (* x (/ (/ -2.0 z) t))
       (if (<= y -6.2e-98)
         (* x (/ 2.0 (* y z)))
         (if (<= y 1.3e-67) (* (/ -2.0 z) (/ x t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / y) / z);
	double tmp;
	if (y <= -5.1e-11) {
		tmp = t_1;
	} else if (y <= -2.5e-66) {
		tmp = x * ((-2.0 / z) / t);
	} else if (y <= -6.2e-98) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 1.3e-67) {
		tmp = (-2.0 / z) * (x / 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) :: tmp
    t_1 = 2.0d0 * ((x / y) / z)
    if (y <= (-5.1d-11)) then
        tmp = t_1
    else if (y <= (-2.5d-66)) then
        tmp = x * (((-2.0d0) / z) / t)
    else if (y <= (-6.2d-98)) then
        tmp = x * (2.0d0 / (y * z))
    else if (y <= 1.3d-67) then
        tmp = ((-2.0d0) / z) * (x / 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 = 2.0 * ((x / y) / z);
	double tmp;
	if (y <= -5.1e-11) {
		tmp = t_1;
	} else if (y <= -2.5e-66) {
		tmp = x * ((-2.0 / z) / t);
	} else if (y <= -6.2e-98) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 1.3e-67) {
		tmp = (-2.0 / z) * (x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * ((x / y) / z)
	tmp = 0
	if y <= -5.1e-11:
		tmp = t_1
	elif y <= -2.5e-66:
		tmp = x * ((-2.0 / z) / t)
	elif y <= -6.2e-98:
		tmp = x * (2.0 / (y * z))
	elif y <= 1.3e-67:
		tmp = (-2.0 / z) * (x / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(Float64(x / y) / z))
	tmp = 0.0
	if (y <= -5.1e-11)
		tmp = t_1;
	elseif (y <= -2.5e-66)
		tmp = Float64(x * Float64(Float64(-2.0 / z) / t));
	elseif (y <= -6.2e-98)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	elseif (y <= 1.3e-67)
		tmp = Float64(Float64(-2.0 / z) * Float64(x / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * ((x / y) / z);
	tmp = 0.0;
	if (y <= -5.1e-11)
		tmp = t_1;
	elseif (y <= -2.5e-66)
		tmp = x * ((-2.0 / z) / t);
	elseif (y <= -6.2e-98)
		tmp = x * (2.0 / (y * z));
	elseif (y <= 1.3e-67)
		tmp = (-2.0 / z) * (x / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.1e-11], t$95$1, If[LessEqual[y, -2.5e-66], N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.2e-98], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-67], N[(N[(-2.0 / z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.09999999999999984e-11 or 1.2999999999999999e-67 < y

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-*r/ 87.3%

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

      3. distribute-rgt-out-- 90.2%

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

      4. associate-/r* 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in y around inf 77.3%

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

      1. associate-/r* 78.8%

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

   6. Simplified 78.8%

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

   if -5.09999999999999984e-11 < y < -2.49999999999999981e-66

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. distribute-rgt-out-- 93.8%

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

      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. Step-by-step derivation

      1. frac-times 93.8%

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

      2. *-commutative 93.8%

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

      3. times-frac 93.7%

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

      4. clear-num 93.8%

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

      5. frac-times 94.0%

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

      6. metadata-eval 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in y around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. *-commutative 70.6%

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

      3. *-rgt-identity 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-*r/ 70.5%

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

      6. associate-*l* 70.5%

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

      7. associate-/r* 70.5%

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

      8. associate-*r/ 70.5%

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

      9. *-commutative 70.5%

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

      10. associate-*l/ 70.5%

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

      11. metadata-eval 70.5%

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

   8. Simplified 70.5%

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

   if -2.49999999999999981e-66 < y < -6.2e-98

   1. Initial program 99.6%

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

      1. distribute-rgt-out-- 99.6%

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

   3. Simplified 99.6%

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

      1. times-frac 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*r/ 88.1%

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

      3. associate-*l/ 88.3%

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

      4. *-commutative 88.3%

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

      5. *-commutative 88.3%

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

   8. Simplified 88.3%

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

   if -6.2e-98 < y < 1.2999999999999999e-67

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

      2. distribute-rgt-out-- 87.9%

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

      3. times-frac 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around 0 77.2%

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

      1. *-commutative 77.2%

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

   6. Simplified 77.2%

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

      1. associate-*l/ 77.2%

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

      2. metadata-eval 77.2%

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

      3. distribute-rgt-neg-in 77.2%

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

      4. associate-/r* 80.5%

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

      5. distribute-rgt-neg-in 80.5%

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

      6. metadata-eval 80.5%

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

   8. Applied egg-rr 80.5%

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

      1. associate-/l/ 77.2%

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

      2. *-commutative 77.2%

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

      3. times-frac 80.5%

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

   10. Applied egg-rr 80.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{-11}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-67}:\\ \;\;\;\;\frac{-2}{z} \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \end{array} \]

Alternative 4: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{if}\;y \leq -4 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 2.0 (/ (/ x y) z))))
   (if (<= y -4e-7)
     t_1
     (if (<= y -3.3e-66)
       (* x (/ (/ -2.0 z) t))
       (if (<= y -6.2e-98)
         (* x (/ 2.0 (* y z)))
         (if (<= y 6e-68) (* (/ x z) (/ -2.0 t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 * ((x / y) / z);
	double tmp;
	if (y <= -4e-7) {
		tmp = t_1;
	} else if (y <= -3.3e-66) {
		tmp = x * ((-2.0 / z) / t);
	} else if (y <= -6.2e-98) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 6e-68) {
		tmp = (x / z) * (-2.0 / 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) :: tmp
    t_1 = 2.0d0 * ((x / y) / z)
    if (y <= (-4d-7)) then
        tmp = t_1
    else if (y <= (-3.3d-66)) then
        tmp = x * (((-2.0d0) / z) / t)
    else if (y <= (-6.2d-98)) then
        tmp = x * (2.0d0 / (y * z))
    else if (y <= 6d-68) then
        tmp = (x / z) * ((-2.0d0) / 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 = 2.0 * ((x / y) / z);
	double tmp;
	if (y <= -4e-7) {
		tmp = t_1;
	} else if (y <= -3.3e-66) {
		tmp = x * ((-2.0 / z) / t);
	} else if (y <= -6.2e-98) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 6e-68) {
		tmp = (x / z) * (-2.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 * ((x / y) / z)
	tmp = 0
	if y <= -4e-7:
		tmp = t_1
	elif y <= -3.3e-66:
		tmp = x * ((-2.0 / z) / t)
	elif y <= -6.2e-98:
		tmp = x * (2.0 / (y * z))
	elif y <= 6e-68:
		tmp = (x / z) * (-2.0 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 * Float64(Float64(x / y) / z))
	tmp = 0.0
	if (y <= -4e-7)
		tmp = t_1;
	elseif (y <= -3.3e-66)
		tmp = Float64(x * Float64(Float64(-2.0 / z) / t));
	elseif (y <= -6.2e-98)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	elseif (y <= 6e-68)
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 * ((x / y) / z);
	tmp = 0.0;
	if (y <= -4e-7)
		tmp = t_1;
	elseif (y <= -3.3e-66)
		tmp = x * ((-2.0 / z) / t);
	elseif (y <= -6.2e-98)
		tmp = x * (2.0 / (y * z));
	elseif (y <= 6e-68)
		tmp = (x / z) * (-2.0 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 * N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e-7], t$95$1, If[LessEqual[y, -3.3e-66], N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.2e-98], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-68], N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.9999999999999998e-7 or 6e-68 < y

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

      2. associate-*r/ 87.3%

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

      3. distribute-rgt-out-- 90.2%

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

      4. associate-/r* 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in y around inf 77.3%

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

      1. associate-/r* 78.8%

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

   6. Simplified 78.8%

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

   if -3.9999999999999998e-7 < y < -3.2999999999999999e-66

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. distribute-rgt-out-- 93.8%

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

      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. Step-by-step derivation

      1. frac-times 93.8%

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

      2. *-commutative 93.8%

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

      3. times-frac 93.7%

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

      4. clear-num 93.8%

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

      5. frac-times 94.0%

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

      6. metadata-eval 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in y around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. *-commutative 70.6%

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

      3. *-rgt-identity 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-*r/ 70.5%

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

      6. associate-*l* 70.5%

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

      7. associate-/r* 70.5%

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

      8. associate-*r/ 70.5%

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

      9. *-commutative 70.5%

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

      10. associate-*l/ 70.5%

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

      11. metadata-eval 70.5%

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

   8. Simplified 70.5%

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

   if -3.2999999999999999e-66 < y < -6.2e-98

   1. Initial program 99.6%

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

      1. distribute-rgt-out-- 99.6%

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

   3. Simplified 99.6%

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

      1. times-frac 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*r/ 88.1%

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

      3. associate-*l/ 88.3%

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

      4. *-commutative 88.3%

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

      5. *-commutative 88.3%

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

   8. Simplified 88.3%

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

   if -6.2e-98 < y < 6e-68

   1. Initial program 85.6%

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

      1. distribute-rgt-out-- 87.9%

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

   3. Simplified 87.9%

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

      1. times-frac 95.5%

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

   5. Applied egg-rr 95.5%

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

   6. Taylor expanded in y around 0 82.0%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-7}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \end{array} \]

Alternative 5: 73.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e-9)
   (* 2.0 (/ (/ x y) z))
   (if (<= y -2.3e-66)
     (* x (/ (/ -2.0 z) t))
     (if (<= y -6.5e-98)
       (* x (/ 2.0 (* y z)))
       (if (<= y 1.55e+27) (* (/ x z) (/ -2.0 t)) (* (/ x z) (/ 2.0 y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-9) {
		tmp = 2.0 * ((x / y) / z);
	} else if (y <= -2.3e-66) {
		tmp = x * ((-2.0 / z) / t);
	} else if (y <= -6.5e-98) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 1.55e+27) {
		tmp = (x / z) * (-2.0 / t);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.7d-9)) then
        tmp = 2.0d0 * ((x / y) / z)
    else if (y <= (-2.3d-66)) then
        tmp = x * (((-2.0d0) / z) / t)
    else if (y <= (-6.5d-98)) then
        tmp = x * (2.0d0 / (y * z))
    else if (y <= 1.55d+27) then
        tmp = (x / z) * ((-2.0d0) / t)
    else
        tmp = (x / z) * (2.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-9) {
		tmp = 2.0 * ((x / y) / z);
	} else if (y <= -2.3e-66) {
		tmp = x * ((-2.0 / z) / t);
	} else if (y <= -6.5e-98) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 1.55e+27) {
		tmp = (x / z) * (-2.0 / t);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e-9:
		tmp = 2.0 * ((x / y) / z)
	elif y <= -2.3e-66:
		tmp = x * ((-2.0 / z) / t)
	elif y <= -6.5e-98:
		tmp = x * (2.0 / (y * z))
	elif y <= 1.55e+27:
		tmp = (x / z) * (-2.0 / t)
	else:
		tmp = (x / z) * (2.0 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e-9)
		tmp = Float64(2.0 * Float64(Float64(x / y) / z));
	elseif (y <= -2.3e-66)
		tmp = Float64(x * Float64(Float64(-2.0 / z) / t));
	elseif (y <= -6.5e-98)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	elseif (y <= 1.55e+27)
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	else
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e-9)
		tmp = 2.0 * ((x / y) / z);
	elseif (y <= -2.3e-66)
		tmp = x * ((-2.0 / z) / t);
	elseif (y <= -6.5e-98)
		tmp = x * (2.0 / (y * z));
	elseif (y <= 1.55e+27)
		tmp = (x / z) * (-2.0 / t);
	else
		tmp = (x / z) * (2.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e-9], N[(2.0 * N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-66], N[(x * N[(N[(-2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-98], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+27], N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.6999999999999999e-9

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-*r/ 86.8%

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

      3. distribute-rgt-out-- 91.9%

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

      4. associate-/r* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around inf 83.6%

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

      1. associate-/r* 87.1%

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

   6. Simplified 87.1%

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

   if -1.6999999999999999e-9 < y < -2.29999999999999992e-66

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. distribute-rgt-out-- 93.8%

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

      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. Step-by-step derivation

      1. frac-times 93.8%

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

      2. *-commutative 93.8%

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

      3. times-frac 93.7%

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

      4. clear-num 93.8%

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

      5. frac-times 94.0%

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

      6. metadata-eval 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in y around 0 70.6%

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

      1. associate-*r/ 70.6%

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

      2. *-commutative 70.6%

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

      3. *-rgt-identity 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-*r/ 70.5%

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

      6. associate-*l* 70.5%

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

      7. associate-/r* 70.5%

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

      8. associate-*r/ 70.5%

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

      9. *-commutative 70.5%

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

      10. associate-*l/ 70.5%

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

      11. metadata-eval 70.5%

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

   8. Simplified 70.5%

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

   if -2.29999999999999992e-66 < y < -6.50000000000000017e-98

   1. Initial program 99.6%

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

      1. distribute-rgt-out-- 99.6%

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

   3. Simplified 99.6%

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

      1. times-frac 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*r/ 88.1%

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

      3. associate-*l/ 88.3%

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

      4. *-commutative 88.3%

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

      5. *-commutative 88.3%

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

   8. Simplified 88.3%

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

   if -6.50000000000000017e-98 < y < 1.54999999999999998e27

   1. Initial program 86.4%

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

      1. distribute-rgt-out-- 88.2%

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

   3. Simplified 88.2%

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

      1. times-frac 95.3%

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

   5. Applied egg-rr 95.3%

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

   6. Taylor expanded in y around 0 78.3%

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

   if 1.54999999999999998e27 < y

   1. Initial program 86.9%

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

      1. distribute-rgt-out-- 88.7%

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

   3. Simplified 88.7%

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

      1. times-frac 88.6%

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

   5. Applied egg-rr 88.6%

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

   6. Taylor expanded in y around inf 79.6%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-9}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{\frac{-2}{z}}{t}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 6: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{z \cdot t} \cdot -2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.1e-8)
   (* 2.0 (/ (/ x y) z))
   (if (<= y -2.8e-66)
     (* (/ x (* z t)) -2.0)
     (if (<= y -6.5e-98)
       (* x (/ 2.0 (* y z)))
       (if (<= y 3.5e+26) (* (/ x z) (/ -2.0 t)) (* (/ x z) (/ 2.0 y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e-8) {
		tmp = 2.0 * ((x / y) / z);
	} else if (y <= -2.8e-66) {
		tmp = (x / (z * t)) * -2.0;
	} else if (y <= -6.5e-98) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 3.5e+26) {
		tmp = (x / z) * (-2.0 / t);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.1d-8)) then
        tmp = 2.0d0 * ((x / y) / z)
    else if (y <= (-2.8d-66)) then
        tmp = (x / (z * t)) * (-2.0d0)
    else if (y <= (-6.5d-98)) then
        tmp = x * (2.0d0 / (y * z))
    else if (y <= 3.5d+26) then
        tmp = (x / z) * ((-2.0d0) / t)
    else
        tmp = (x / z) * (2.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e-8) {
		tmp = 2.0 * ((x / y) / z);
	} else if (y <= -2.8e-66) {
		tmp = (x / (z * t)) * -2.0;
	} else if (y <= -6.5e-98) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 3.5e+26) {
		tmp = (x / z) * (-2.0 / t);
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.1e-8:
		tmp = 2.0 * ((x / y) / z)
	elif y <= -2.8e-66:
		tmp = (x / (z * t)) * -2.0
	elif y <= -6.5e-98:
		tmp = x * (2.0 / (y * z))
	elif y <= 3.5e+26:
		tmp = (x / z) * (-2.0 / t)
	else:
		tmp = (x / z) * (2.0 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.1e-8)
		tmp = Float64(2.0 * Float64(Float64(x / y) / z));
	elseif (y <= -2.8e-66)
		tmp = Float64(Float64(x / Float64(z * t)) * -2.0);
	elseif (y <= -6.5e-98)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	elseif (y <= 3.5e+26)
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	else
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.1e-8)
		tmp = 2.0 * ((x / y) / z);
	elseif (y <= -2.8e-66)
		tmp = (x / (z * t)) * -2.0;
	elseif (y <= -6.5e-98)
		tmp = x * (2.0 / (y * z));
	elseif (y <= 3.5e+26)
		tmp = (x / z) * (-2.0 / t);
	else
		tmp = (x / z) * (2.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.1e-8], N[(2.0 * N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-66], N[(N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[y, -6.5e-98], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+26], N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.09999999999999994e-8

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-*r/ 86.8%

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

      3. distribute-rgt-out-- 91.9%

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

      4. associate-/r* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around inf 83.6%

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

      1. associate-/r* 87.1%

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

   6. Simplified 87.1%

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

   if -2.09999999999999994e-8 < y < -2.8e-66

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. distribute-rgt-out-- 93.8%

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

      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 70.6%

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

      1. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -2.8e-66 < y < -6.50000000000000017e-98

   1. Initial program 99.6%

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

      1. distribute-rgt-out-- 99.6%

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

   3. Simplified 99.6%

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

      1. times-frac 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*r/ 88.1%

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

      3. associate-*l/ 88.3%

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

      4. *-commutative 88.3%

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

      5. *-commutative 88.3%

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

   8. Simplified 88.3%

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

   if -6.50000000000000017e-98 < y < 3.4999999999999999e26

   1. Initial program 86.4%

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

      1. distribute-rgt-out-- 88.2%

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

   3. Simplified 88.2%

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

      1. times-frac 95.3%

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

   5. Applied egg-rr 95.3%

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

   6. Taylor expanded in y around 0 78.3%

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

   if 3.4999999999999999e26 < y

   1. Initial program 86.9%

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

      1. distribute-rgt-out-- 88.7%

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

   3. Simplified 88.7%

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

      1. times-frac 88.6%

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

   5. Applied egg-rr 88.6%

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

   6. Taylor expanded in y around inf 79.6%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-8}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{z \cdot t} \cdot -2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 7: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{z \cdot t} \cdot -2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+25}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e-5)
   (* 2.0 (/ (/ x y) z))
   (if (<= y -2.3e-66)
     (* (/ x (* z t)) -2.0)
     (if (<= y -6.5e-98)
       (* x (/ 2.0 (* y z)))
       (if (<= y 3.9e+25) (/ (/ (* x -2.0) z) t) (* (/ x z) (/ 2.0 y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e-5) {
		tmp = 2.0 * ((x / y) / z);
	} else if (y <= -2.3e-66) {
		tmp = (x / (z * t)) * -2.0;
	} else if (y <= -6.5e-98) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 3.9e+25) {
		tmp = ((x * -2.0) / z) / t;
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.8d-5)) then
        tmp = 2.0d0 * ((x / y) / z)
    else if (y <= (-2.3d-66)) then
        tmp = (x / (z * t)) * (-2.0d0)
    else if (y <= (-6.5d-98)) then
        tmp = x * (2.0d0 / (y * z))
    else if (y <= 3.9d+25) then
        tmp = ((x * (-2.0d0)) / z) / t
    else
        tmp = (x / z) * (2.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e-5) {
		tmp = 2.0 * ((x / y) / z);
	} else if (y <= -2.3e-66) {
		tmp = (x / (z * t)) * -2.0;
	} else if (y <= -6.5e-98) {
		tmp = x * (2.0 / (y * z));
	} else if (y <= 3.9e+25) {
		tmp = ((x * -2.0) / z) / t;
	} else {
		tmp = (x / z) * (2.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e-5:
		tmp = 2.0 * ((x / y) / z)
	elif y <= -2.3e-66:
		tmp = (x / (z * t)) * -2.0
	elif y <= -6.5e-98:
		tmp = x * (2.0 / (y * z))
	elif y <= 3.9e+25:
		tmp = ((x * -2.0) / z) / t
	else:
		tmp = (x / z) * (2.0 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e-5)
		tmp = Float64(2.0 * Float64(Float64(x / y) / z));
	elseif (y <= -2.3e-66)
		tmp = Float64(Float64(x / Float64(z * t)) * -2.0);
	elseif (y <= -6.5e-98)
		tmp = Float64(x * Float64(2.0 / Float64(y * z)));
	elseif (y <= 3.9e+25)
		tmp = Float64(Float64(Float64(x * -2.0) / z) / t);
	else
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.8e-5)
		tmp = 2.0 * ((x / y) / z);
	elseif (y <= -2.3e-66)
		tmp = (x / (z * t)) * -2.0;
	elseif (y <= -6.5e-98)
		tmp = x * (2.0 / (y * z));
	elseif (y <= 3.9e+25)
		tmp = ((x * -2.0) / z) / t;
	else
		tmp = (x / z) * (2.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e-5], N[(2.0 * N[(N[(x / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-66], N[(N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision] * -2.0), $MachinePrecision], If[LessEqual[y, -6.5e-98], N[(x * N[(2.0 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+25], N[(N[(N[(x * -2.0), $MachinePrecision] / z), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.80000000000000005e-5

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-*r/ 86.8%

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

      3. distribute-rgt-out-- 91.9%

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

      4. associate-/r* 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around inf 83.6%

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

      1. associate-/r* 87.1%

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

   6. Simplified 87.1%

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

   if -1.80000000000000005e-5 < y < -2.29999999999999992e-66

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. distribute-rgt-out-- 93.8%

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

      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 70.6%

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

      1. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -2.29999999999999992e-66 < y < -6.50000000000000017e-98

   1. Initial program 99.6%

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

      1. distribute-rgt-out-- 99.6%

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

   3. Simplified 99.6%

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

      1. times-frac 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-*r/ 88.1%

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

      3. associate-*l/ 88.3%

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

      4. *-commutative 88.3%

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

      5. *-commutative 88.3%

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

   8. Simplified 88.3%

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

   if -6.50000000000000017e-98 < y < 3.9000000000000002e25

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

      2. distribute-rgt-out-- 88.2%

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

      3. times-frac 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in y around 0 72.6%

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

      1. *-commutative 72.6%

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

   6. Simplified 72.6%

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

      1. associate-*l/ 72.6%

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

      2. *-commutative 72.6%

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

      3. metadata-eval 72.6%

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

      4. distribute-rgt-neg-in 72.6%

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

      5. associate-/r* 78.3%

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

      6. distribute-rgt-neg-in 78.3%

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

      7. metadata-eval 78.3%

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

   8. Applied egg-rr 78.3%

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

   if 3.9000000000000002e25 < y

   1. Initial program 86.9%

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

      1. distribute-rgt-out-- 88.7%

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

   3. Simplified 88.7%

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

      1. times-frac 88.6%

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

   5. Applied egg-rr 88.6%

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

   6. Taylor expanded in y around inf 79.6%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{y}}{z}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{z \cdot t} \cdot -2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \frac{2}{y \cdot z}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+25}:\\ \;\;\;\;\frac{\frac{x \cdot -2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 8: 94.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot x \leq 2 \cdot 10^{-77}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* 2.0 x) 2e-77)
   (* 2.0 (/ (/ x z) (- y t)))
   (* (/ 2.0 z) (/ x (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((2.0 * x) <= 2e-77) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = (2.0 / z) * (x / (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) <= 2d-77) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else
        tmp = (2.0d0 / z) * (x / (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) <= 2e-77) {
		tmp = 2.0 * ((x / z) / (y - t));
	} else {
		tmp = (2.0 / z) * (x / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (2.0 * x) <= 2e-77:
		tmp = 2.0 * ((x / z) / (y - t))
	else:
		tmp = (2.0 / z) * (x / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(2.0 * x) <= 2e-77)
		tmp = Float64(2.0 * Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((2.0 * x) <= 2e-77)
		tmp = 2.0 * ((x / z) / (y - t));
	else
		tmp = (2.0 / z) * (x / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(2.0 * x), $MachinePrecision], 2e-77], N[(2.0 * N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < 1.9999999999999999e-77

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

      2. associate-*r/ 89.1%

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

      3. distribute-rgt-out-- 92.1%

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

      4. associate-/r* 94.2%

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

   3. Simplified 94.2%

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

   if 1.9999999999999999e-77 < (*.f64 x 2)

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

      2. distribute-rgt-out-- 85.2%

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

      3. times-frac 98.5%

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

   3. Simplified 98.5%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x \leq 2 \cdot 10^{-77}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \end{array} \]

Alternative 9: 93.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot x \leq 5 \cdot 10^{-23}:\\ \;\;\;\;\frac{2}{\left(y - t\right) \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* 2.0 x) 5e-23)
   (/ 2.0 (* (- y t) (/ z x)))
   (* (/ 2.0 z) (/ x (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((2.0 * x) <= 5e-23) {
		tmp = 2.0 / ((y - t) * (z / x));
	} else {
		tmp = (2.0 / z) * (x / (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) <= 5d-23) then
        tmp = 2.0d0 / ((y - t) * (z / x))
    else
        tmp = (2.0d0 / z) * (x / (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) <= 5e-23) {
		tmp = 2.0 / ((y - t) * (z / x));
	} else {
		tmp = (2.0 / z) * (x / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (2.0 * x) <= 5e-23:
		tmp = 2.0 / ((y - t) * (z / x))
	else:
		tmp = (2.0 / z) * (x / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(2.0 * x) <= 5e-23)
		tmp = Float64(2.0 / Float64(Float64(y - t) * Float64(z / x)));
	else
		tmp = Float64(Float64(2.0 / z) * Float64(x / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((2.0 * x) <= 5e-23)
		tmp = 2.0 / ((y - t) * (z / x));
	else
		tmp = (2.0 / z) * (x / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(2.0 * x), $MachinePrecision], 5e-23], N[(2.0 / N[(N[(y - t), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] * N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 2) < 5.0000000000000002e-23

   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-- 92.6%

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

      3. times-frac 90.5%

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

   3. Simplified 90.5%

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

      1. frac-times 92.6%

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

      2. *-commutative 92.6%

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

      3. times-frac 94.5%

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

      4. clear-num 94.4%

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

      5. frac-times 94.8%

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

      6. metadata-eval 94.8%

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

   5. Applied egg-rr 94.8%

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

   if 5.0000000000000002e-23 < (*.f64 x 2)

   1. Initial program 81.7%

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

      1. *-commutative 81.7%

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

      2. distribute-rgt-out-- 83.1%

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

      3. times-frac 98.3%

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

   3. Simplified 98.3%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x \leq 5 \cdot 10^{-23}:\\ \;\;\;\;\frac{2}{\left(y - t\right) \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y - t}\\ \end{array} \]

Alternative 10: 92.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

   1. *-commutative 87.5%

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

   2. associate-*r/ 87.5%

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

   3. distribute-rgt-out-- 89.9%

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

   4. associate-/r* 93.0%

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

3. Simplified 93.0%

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

4. Final simplification 93.0%

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

Alternative 11: 52.8% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

   1. *-commutative 87.5%

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

   2. associate-*r/ 87.5%

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

   3. distribute-rgt-out-- 89.9%

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

   4. associate-/r* 93.0%

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

3. Simplified 93.0%

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

4. Taylor expanded in y around inf 53.8%

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

   1. associate-/r* 55.0%

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

6. Simplified 55.0%

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

7. Final simplification 55.0%

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

Developer target: 97.0% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(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))))