Linear.Projection:infinitePerspective from linear-1.19.1.3, A

Percentage Accurate: 89.6% → 98.5%

Time: 12.5s

Alternatives: 13

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 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

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - z \cdot t\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+298}:\\ \;\;\;\;\frac{\frac{x}{y - t}}{z \cdot 0.5}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+247}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) (* z t))))
   (if (<= t_1 -1e+298)
     (/ (/ x (- y t)) (* z 0.5))
     (if (<= t_1 2e+247)
       (/ (* x 2.0) (* 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+298) {
		tmp = (x / (y - t)) / (z * 0.5);
	} else if (t_1 <= 2e+247) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (y * z) - (z * t)
    if (t_1 <= (-1d+298)) then
        tmp = (x / (y - t)) / (z * 0.5d0)
    else if (t_1 <= 2d+247) 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 t_1 = (y * z) - (z * t);
	double tmp;
	if (t_1 <= -1e+298) {
		tmp = (x / (y - t)) / (z * 0.5);
	} else if (t_1 <= 2e+247) {
		tmp = (x * 2.0) / (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+298:
		tmp = (x / (y - t)) / (z * 0.5)
	elif t_1 <= 2e+247:
		tmp = (x * 2.0) / (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+298)
		tmp = Float64(Float64(x / Float64(y - t)) / Float64(z * 0.5));
	elseif (t_1 <= 2e+247)
		tmp = Float64(Float64(x * 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)
	t_1 = (y * z) - (z * t);
	tmp = 0.0;
	if (t_1 <= -1e+298)
		tmp = (x / (y - t)) / (z * 0.5);
	elseif (t_1 <= 2e+247)
		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_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+298], N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] / N[(z * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+247], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $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 (-.f64 (*.f64 y z) (*.f64 t z)) < -9.9999999999999996e297

   1. Initial program 59.3%

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

      1. *-commutative 59.3%

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

      2. distribute-rgt-out-- 59.3%

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

      3. times-frac 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

      4. div-inv 99.9%

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

      5. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   if -9.9999999999999996e297 < (-.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-- 97.7%

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

   3. Simplified 97.7%

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

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

   1. Initial program 66.0%

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

      1. *-commutative 66.0%

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

      2. associate-*r/ 66.0%

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

      3. distribute-rgt-out-- 74.4%

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

      4. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z - z \cdot t \leq -1 \cdot 10^{+298}:\\ \;\;\;\;\frac{\frac{x}{y - t}}{z \cdot 0.5}\\ \mathbf{elif}\;y \cdot z - z \cdot t \leq 2 \cdot 10^{+247}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 2: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-7} \lor \neg \left(y \leq -2.8 \cdot 10^{-66}\right) \land \left(y \leq -6.5 \cdot 10^{-98} \lor \neg \left(y \leq 6 \cdot 10^{-68}\right)\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.5e-7)
         (and (not (<= y -2.8e-66)) (or (<= y -6.5e-98) (not (<= y 6e-68)))))
   (* (/ 2.0 z) (/ x y))
   (* (/ x t) (/ -2.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.5e-7) || (!(y <= -2.8e-66) && ((y <= -6.5e-98) || !(y <= 6e-68)))) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = (x / t) * (-2.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.5d-7)) .or. (.not. (y <= (-2.8d-66))) .and. (y <= (-6.5d-98)) .or. (.not. (y <= 6d-68))) then
        tmp = (2.0d0 / z) * (x / y)
    else
        tmp = (x / t) * ((-2.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.5e-7) || (!(y <= -2.8e-66) && ((y <= -6.5e-98) || !(y <= 6e-68)))) {
		tmp = (2.0 / z) * (x / y);
	} else {
		tmp = (x / t) * (-2.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.5e-7) or (not (y <= -2.8e-66) and ((y <= -6.5e-98) or not (y <= 6e-68))):
		tmp = (2.0 / z) * (x / y)
	else:
		tmp = (x / t) * (-2.0 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.5e-7) || (!(y <= -2.8e-66) && ((y <= -6.5e-98) || !(y <= 6e-68))))
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	else
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.5e-7) || (~((y <= -2.8e-66)) && ((y <= -6.5e-98) || ~((y <= 6e-68)))))
		tmp = (2.0 / z) * (x / y);
	else
		tmp = (x / t) * (-2.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.5e-7], And[N[Not[LessEqual[y, -2.8e-66]], $MachinePrecision], Or[LessEqual[y, -6.5e-98], N[Not[LessEqual[y, 6e-68]], $MachinePrecision]]]], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4999999999999999e-7 or -2.8e-66 < y < -6.50000000000000017e-98 or 6e-68 < y

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

      2. distribute-rgt-out-- 90.7%

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

      3. times-frac 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around inf 79.2%

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

   if -1.4999999999999999e-7 < y < -2.8e-66 or -6.50000000000000017e-98 < y < 6e-68

   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. Taylor expanded in y around 0 76.3%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   5. 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. *-commutative 76.3%

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

   6. Simplified 76.3%

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

      1. *-commutative 76.3%

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

      2. times-frac 78.4%

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

   8. Applied egg-rr 78.4%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-7} \lor \neg \left(y \leq -2.8 \cdot 10^{-66}\right) \land \left(y \leq -6.5 \cdot 10^{-98} \lor \neg \left(y \leq 6 \cdot 10^{-68}\right)\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \end{array} \]

Alternative 3: 73.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-98} \lor \neg \left(y \leq 1.4 \cdot 10^{-67}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ 2.0 z) (/ x y))))
   (if (<= y -4.5e-5)
     t_1
     (if (<= y -2.9e-66)
       (* (/ x t) (/ -2.0 z))
       (if (or (<= y -6.5e-98) (not (<= y 1.4e-67)))
         t_1
         (* (/ x z) (/ -2.0 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (y <= -4.5e-5) {
		tmp = t_1;
	} else if (y <= -2.9e-66) {
		tmp = (x / t) * (-2.0 / z);
	} else if ((y <= -6.5e-98) || !(y <= 1.4e-67)) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (-2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 / z) * (x / y)
    if (y <= (-4.5d-5)) then
        tmp = t_1
    else if (y <= (-2.9d-66)) then
        tmp = (x / t) * ((-2.0d0) / z)
    else if ((y <= (-6.5d-98)) .or. (.not. (y <= 1.4d-67))) then
        tmp = t_1
    else
        tmp = (x / z) * ((-2.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / z) * (x / y);
	double tmp;
	if (y <= -4.5e-5) {
		tmp = t_1;
	} else if (y <= -2.9e-66) {
		tmp = (x / t) * (-2.0 / z);
	} else if ((y <= -6.5e-98) || !(y <= 1.4e-67)) {
		tmp = t_1;
	} else {
		tmp = (x / z) * (-2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / z) * (x / y)
	tmp = 0
	if y <= -4.5e-5:
		tmp = t_1
	elif y <= -2.9e-66:
		tmp = (x / t) * (-2.0 / z)
	elif (y <= -6.5e-98) or not (y <= 1.4e-67):
		tmp = t_1
	else:
		tmp = (x / z) * (-2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / z) * Float64(x / y))
	tmp = 0.0
	if (y <= -4.5e-5)
		tmp = t_1;
	elseif (y <= -2.9e-66)
		tmp = Float64(Float64(x / t) * Float64(-2.0 / z));
	elseif ((y <= -6.5e-98) || !(y <= 1.4e-67))
		tmp = t_1;
	else
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / z) * (x / y);
	tmp = 0.0;
	if (y <= -4.5e-5)
		tmp = t_1;
	elseif (y <= -2.9e-66)
		tmp = (x / t) * (-2.0 / z);
	elseif ((y <= -6.5e-98) || ~((y <= 1.4e-67)))
		tmp = t_1;
	else
		tmp = (x / z) * (-2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e-5], t$95$1, If[LessEqual[y, -2.9e-66], N[(N[(x / t), $MachinePrecision] * N[(-2.0 / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -6.5e-98], N[Not[LessEqual[y, 1.4e-67]], $MachinePrecision]], t$95$1, N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.50000000000000028e-5 or -2.90000000000000011e-66 < y < -6.50000000000000017e-98 or 1.40000000000000005e-67 < y

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

      2. distribute-rgt-out-- 90.7%

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

      3. times-frac 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around inf 79.2%

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

   if -4.50000000000000028e-5 < y < -2.90000000000000011e-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. 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. *-commutative 70.6%

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

   6. Simplified 70.6%

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

      1. *-commutative 70.6%

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

      2. times-frac 66.1%

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

   8. Applied egg-rr 66.1%

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

   if -6.50000000000000017e-98 < y < 1.40000000000000005e-67

   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 3 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{-2}{z}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-98} \lor \neg \left(y \leq 1.4 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \end{array} \]

Alternative 4: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-5}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-98}:\\ \;\;\;\;\frac{2}{\frac{y \cdot z}{x}}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.85e-5)
   (* (/ 2.0 z) (/ x y))
   (if (<= y -2.5e-66)
     (/ (* x -2.0) (* z t))
     (if (<= y -2.7e-98)
       (/ 2.0 (/ (* y z) x))
       (if (<= y 1.16e+24) (/ (* (/ 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 <= -1.85e-5) {
		tmp = (2.0 / z) * (x / y);
	} else if (y <= -2.5e-66) {
		tmp = (x * -2.0) / (z * t);
	} else if (y <= -2.7e-98) {
		tmp = 2.0 / ((y * z) / x);
	} else if (y <= 1.16e+24) {
		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 <= (-1.85d-5)) then
        tmp = (2.0d0 / z) * (x / y)
    else if (y <= (-2.5d-66)) then
        tmp = (x * (-2.0d0)) / (z * t)
    else if (y <= (-2.7d-98)) then
        tmp = 2.0d0 / ((y * z) / x)
    else if (y <= 1.16d+24) 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 <= -1.85e-5) {
		tmp = (2.0 / z) * (x / y);
	} else if (y <= -2.5e-66) {
		tmp = (x * -2.0) / (z * t);
	} else if (y <= -2.7e-98) {
		tmp = 2.0 / ((y * z) / x);
	} else if (y <= 1.16e+24) {
		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 <= -1.85e-5:
		tmp = (2.0 / z) * (x / y)
	elif y <= -2.5e-66:
		tmp = (x * -2.0) / (z * t)
	elif y <= -2.7e-98:
		tmp = 2.0 / ((y * z) / x)
	elif y <= 1.16e+24:
		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 <= -1.85e-5)
		tmp = Float64(Float64(2.0 / z) * Float64(x / y));
	elseif (y <= -2.5e-66)
		tmp = Float64(Float64(x * -2.0) / Float64(z * t));
	elseif (y <= -2.7e-98)
		tmp = Float64(2.0 / Float64(Float64(y * z) / x));
	elseif (y <= 1.16e+24)
		tmp = Float64(Float64(Float64(x / z) * -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 <= -1.85e-5)
		tmp = (2.0 / z) * (x / y);
	elseif (y <= -2.5e-66)
		tmp = (x * -2.0) / (z * t);
	elseif (y <= -2.7e-98)
		tmp = 2.0 / ((y * z) / x);
	elseif (y <= 1.16e+24)
		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, -1.85e-5], N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-66], N[(N[(x * -2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e-98], N[(2.0 / N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.16e+24], N[(N[(N[(x / z), $MachinePrecision] * -2.0), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.84999999999999991e-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. distribute-rgt-out-- 91.9%

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

      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 inf 87.0%

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

   if -1.84999999999999991e-5 < 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. Taylor expanded in y around 0 70.6%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   5. 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. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -2.49999999999999981e-66 < y < -2.6999999999999999e-98

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

      3. times-frac 99.4%

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

   3. Simplified 99.4%

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

      1. frac-times 99.6%

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

      2. *-commutative 99.6%

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

      3. times-frac 99.6%

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

      4. clear-num 99.6%

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

      5. frac-times 99.6%

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

      6. metadata-eval 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 88.3%

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

   if -2.6999999999999999e-98 < y < 1.16000000000000005e24

   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 76.9%

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

      1. associate-*r/ 76.9%

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

      2. neg-mul-1 76.9%

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

   6. Simplified 76.9%

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

      1. frac-times 72.6%

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

      2. neg-mul-1 72.6%

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

      3. associate-*r* 72.6%

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

      4. metadata-eval 72.6%

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

      5. *-commutative 72.6%

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

      6. associate-/r* 78.3%

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

      7. *-commutative 78.3%

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

      8. *-un-lft-identity 78.3%

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

      9. times-frac 78.3%

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

      10. metadata-eval 78.3%

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

   8. Applied egg-rr 78.3%

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

   if 1.16000000000000005e24 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-5}:\\ \;\;\;\;\frac{2}{z} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-98}:\\ \;\;\;\;\frac{2}{\frac{y \cdot z}{x}}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 5: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y}}{z}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-98}:\\ \;\;\;\;\frac{2}{\frac{y \cdot z}{x}}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+30}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e-6)
   (/ (* x (/ 2.0 y)) z)
   (if (<= y -2.5e-66)
     (/ (* x -2.0) (* z t))
     (if (<= y -6.5e-98)
       (/ 2.0 (/ (* y z) x))
       (if (<= y 2.15e+30) (/ (* (/ 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 <= -9e-6) {
		tmp = (x * (2.0 / y)) / z;
	} else if (y <= -2.5e-66) {
		tmp = (x * -2.0) / (z * t);
	} else if (y <= -6.5e-98) {
		tmp = 2.0 / ((y * z) / x);
	} else if (y <= 2.15e+30) {
		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 <= (-9d-6)) then
        tmp = (x * (2.0d0 / y)) / z
    else if (y <= (-2.5d-66)) then
        tmp = (x * (-2.0d0)) / (z * t)
    else if (y <= (-6.5d-98)) then
        tmp = 2.0d0 / ((y * z) / x)
    else if (y <= 2.15d+30) 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 <= -9e-6) {
		tmp = (x * (2.0 / y)) / z;
	} else if (y <= -2.5e-66) {
		tmp = (x * -2.0) / (z * t);
	} else if (y <= -6.5e-98) {
		tmp = 2.0 / ((y * z) / x);
	} else if (y <= 2.15e+30) {
		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 <= -9e-6:
		tmp = (x * (2.0 / y)) / z
	elif y <= -2.5e-66:
		tmp = (x * -2.0) / (z * t)
	elif y <= -6.5e-98:
		tmp = 2.0 / ((y * z) / x)
	elif y <= 2.15e+30:
		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 <= -9e-6)
		tmp = Float64(Float64(x * Float64(2.0 / y)) / z);
	elseif (y <= -2.5e-66)
		tmp = Float64(Float64(x * -2.0) / Float64(z * t));
	elseif (y <= -6.5e-98)
		tmp = Float64(2.0 / Float64(Float64(y * z) / x));
	elseif (y <= 2.15e+30)
		tmp = Float64(Float64(Float64(x / z) * -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 <= -9e-6)
		tmp = (x * (2.0 / y)) / z;
	elseif (y <= -2.5e-66)
		tmp = (x * -2.0) / (z * t);
	elseif (y <= -6.5e-98)
		tmp = 2.0 / ((y * z) / x);
	elseif (y <= 2.15e+30)
		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, -9e-6], N[(N[(x * N[(2.0 / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -2.5e-66], N[(N[(x * -2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-98], N[(2.0 / N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+30], N[(N[(N[(x / z), $MachinePrecision] * -2.0), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.00000000000000023e-6

   1. Initial program 86.8%

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

      1. distribute-rgt-out-- 91.9%

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

   3. Simplified 91.9%

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

      1. times-frac 91.8%

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

   5. Applied egg-rr 91.8%

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

   6. Taylor expanded in y around inf 86.6%

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

      1. associate-*l/ 87.1%

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

   8. Applied egg-rr 87.1%

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

   if -9.00000000000000023e-6 < 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. Taylor expanded in y around 0 70.6%

      \[\leadsto \color{blue}{-2 \cdot \frac{x}{t \cdot z}} \]
   5. 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. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   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. *-commutative 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

      3. times-frac 99.4%

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

   3. Simplified 99.4%

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

      1. frac-times 99.6%

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

      2. *-commutative 99.6%

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

      3. times-frac 99.6%

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

      4. clear-num 99.6%

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

      5. frac-times 99.6%

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

      6. metadata-eval 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 88.3%

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

   if -6.50000000000000017e-98 < y < 2.15e30

   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 76.9%

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

      1. associate-*r/ 76.9%

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

      2. neg-mul-1 76.9%

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

   6. Simplified 76.9%

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

      1. frac-times 72.6%

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

      2. neg-mul-1 72.6%

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

      3. associate-*r* 72.6%

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

      4. metadata-eval 72.6%

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

      5. *-commutative 72.6%

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

      6. associate-/r* 78.3%

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

      7. *-commutative 78.3%

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

      8. *-un-lft-identity 78.3%

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

      9. times-frac 78.3%

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

      10. metadata-eval 78.3%

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

   8. Applied egg-rr 78.3%

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

   if 2.15e30 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot \frac{2}{y}}{z}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-98}:\\ \;\;\;\;\frac{2}{\frac{y \cdot z}{x}}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+30}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 6: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{y}}{\frac{z}{x}}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-98}:\\ \;\;\;\;\frac{2}{\frac{y \cdot z}{x}}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot -2}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ 2.0 y) (/ z x))))
   (if (<= y -6.5e-10)
     t_1
     (if (<= y -3e-66)
       (/ (* x -2.0) (* z t))
       (if (<= y -6e-98)
         (/ 2.0 (/ (* y z) x))
         (if (<= y 4.7e+27) (/ (* (/ x z) -2.0) t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / y) / (z / x);
	double tmp;
	if (y <= -6.5e-10) {
		tmp = t_1;
	} else if (y <= -3e-66) {
		tmp = (x * -2.0) / (z * t);
	} else if (y <= -6e-98) {
		tmp = 2.0 / ((y * z) / x);
	} else if (y <= 4.7e+27) {
		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 / y) / (z / x)
    if (y <= (-6.5d-10)) then
        tmp = t_1
    else if (y <= (-3d-66)) then
        tmp = (x * (-2.0d0)) / (z * t)
    else if (y <= (-6d-98)) then
        tmp = 2.0d0 / ((y * z) / x)
    else if (y <= 4.7d+27) 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 / y) / (z / x);
	double tmp;
	if (y <= -6.5e-10) {
		tmp = t_1;
	} else if (y <= -3e-66) {
		tmp = (x * -2.0) / (z * t);
	} else if (y <= -6e-98) {
		tmp = 2.0 / ((y * z) / x);
	} else if (y <= 4.7e+27) {
		tmp = ((x / z) * -2.0) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / y) / (z / x)
	tmp = 0
	if y <= -6.5e-10:
		tmp = t_1
	elif y <= -3e-66:
		tmp = (x * -2.0) / (z * t)
	elif y <= -6e-98:
		tmp = 2.0 / ((y * z) / x)
	elif y <= 4.7e+27:
		tmp = ((x / z) * -2.0) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / y) / Float64(z / x))
	tmp = 0.0
	if (y <= -6.5e-10)
		tmp = t_1;
	elseif (y <= -3e-66)
		tmp = Float64(Float64(x * -2.0) / Float64(z * t));
	elseif (y <= -6e-98)
		tmp = Float64(2.0 / Float64(Float64(y * z) / x));
	elseif (y <= 4.7e+27)
		tmp = Float64(Float64(Float64(x / z) * -2.0) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / y) / (z / x);
	tmp = 0.0;
	if (y <= -6.5e-10)
		tmp = t_1;
	elseif (y <= -3e-66)
		tmp = (x * -2.0) / (z * t);
	elseif (y <= -6e-98)
		tmp = 2.0 / ((y * z) / x);
	elseif (y <= 4.7e+27)
		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[(N[(2.0 / y), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e-10], t$95$1, If[LessEqual[y, -3e-66], N[(N[(x * -2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-98], N[(2.0 / N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+27], N[(N[(N[(x / z), $MachinePrecision] * -2.0), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.5000000000000003e-10 or 4.69999999999999976e27 < y

   1. Initial program 86.8%

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

      1. distribute-rgt-out-- 90.3%

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

   3. Simplified 90.3%

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

      1. times-frac 90.2%

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

   5. Applied egg-rr 90.2%

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

   6. Taylor expanded in y around inf 83.1%

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

      1. *-commutative 83.1%

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

      2. clear-num 83.0%

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

      3. un-div-inv 84.2%

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

   8. Applied egg-rr 84.2%

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

   if -6.5000000000000003e-10 < y < -3.0000000000000002e-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. 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. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   if -3.0000000000000002e-66 < y < -6e-98

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. distribute-rgt-out-- 99.6%

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

      3. times-frac 99.4%

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

   3. Simplified 99.4%

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

      1. frac-times 99.6%

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

      2. *-commutative 99.6%

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

      3. times-frac 99.6%

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

      4. clear-num 99.6%

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

      5. frac-times 99.6%

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

      6. metadata-eval 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 88.3%

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

   if -6e-98 < y < 4.69999999999999976e27

   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 76.9%

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

      1. associate-*r/ 76.9%

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

      2. neg-mul-1 76.9%

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

   6. Simplified 76.9%

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

      1. frac-times 72.6%

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

      2. neg-mul-1 72.6%

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

      3. associate-*r* 72.6%

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

      4. metadata-eval 72.6%

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

      5. *-commutative 72.6%

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

      6. associate-/r* 78.3%

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

      7. *-commutative 78.3%

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

      8. *-un-lft-identity 78.3%

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

      9. times-frac 78.3%

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

      10. metadata-eval 78.3%

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

   8. Applied egg-rr 78.3%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{2}{y}}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot -2}{z \cdot t}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-98}:\\ \;\;\;\;\frac{2}{\frac{y \cdot z}{x}}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{y}}{\frac{z}{x}}\\ \end{array} \]

Alternative 7: 96.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \mathbf{elif}\;z \leq 3000:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.5e+145)
   (* (/ x (- y t)) (/ 2.0 z))
   (if (<= z 3000.0) (/ (* 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 <= -1.5e+145) {
		tmp = (x / (y - t)) * (2.0 / z);
	} else if (z <= 3000.0) {
		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 <= (-1.5d+145)) then
        tmp = (x / (y - t)) * (2.0d0 / z)
    else if (z <= 3000.0d0) 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 <= -1.5e+145) {
		tmp = (x / (y - t)) * (2.0 / z);
	} else if (z <= 3000.0) {
		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 <= -1.5e+145:
		tmp = (x / (y - t)) * (2.0 / z)
	elif z <= 3000.0:
		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 <= -1.5e+145)
		tmp = Float64(Float64(x / Float64(y - t)) * Float64(2.0 / z));
	elseif (z <= 3000.0)
		tmp = Float64(Float64(x * 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 <= -1.5e+145)
		tmp = (x / (y - t)) * (2.0 / z);
	elseif (z <= 3000.0)
		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, -1.5e+145], N[(N[(x / N[(y - t), $MachinePrecision]), $MachinePrecision] * N[(2.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3000.0], N[(N[(x * 2.0), $MachinePrecision] / N[(z * N[(y - t), $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 < -1.5000000000000001e145

   1. Initial program 69.1%

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

      1. *-commutative 69.1%

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

      2. distribute-rgt-out-- 72.2%

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

      3. times-frac 99.8%

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

   3. Simplified 99.8%

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

   if -1.5000000000000001e145 < z < 3e3

   1. Initial program 95.5%

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

      1. distribute-rgt-out-- 96.8%

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

   3. Simplified 96.8%

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

   if 3e3 < z

   1. Initial program 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-*r/ 77.2%

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

      3. distribute-rgt-out-- 82.0%

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

      4. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+145}:\\ \;\;\;\;\frac{x}{y - t} \cdot \frac{2}{z}\\ \mathbf{elif}\;z \leq 3000:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{x}{z}}{y - t}\\ \end{array} \]

Alternative 8: 94.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x * 2.0d0) <= 2d-77) then
        tmp = 2.0d0 * ((x / z) / (y - t))
    else
        tmp = (x / (y - t)) * (2.0d0 / z)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 9: 93.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x * 2.0d0) <= 5d-23) then
        tmp = 2.0d0 / ((y - t) * (z / x))
    else
        tmp = (x / (y - t)) * (2.0d0 / z)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 10: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{-98} \lor \neg \left(y \leq 1.4 \cdot 10^{+24}\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.7e-98) (not (<= y 1.4e+24)))
   (* (/ x z) (/ 2.0 y))
   (* (/ x z) (/ -2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.7e-98) || !(y <= 1.4e+24)) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = (x / z) * (-2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.7d-98)) .or. (.not. (y <= 1.4d+24))) then
        tmp = (x / z) * (2.0d0 / y)
    else
        tmp = (x / z) * ((-2.0d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.7e-98) || !(y <= 1.4e+24)) {
		tmp = (x / z) * (2.0 / y);
	} else {
		tmp = (x / z) * (-2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.7e-98) or not (y <= 1.4e+24):
		tmp = (x / z) * (2.0 / y)
	else:
		tmp = (x / z) * (-2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.7e-98) || !(y <= 1.4e+24))
		tmp = Float64(Float64(x / z) * Float64(2.0 / y));
	else
		tmp = Float64(Float64(x / z) * Float64(-2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.7e-98) || ~((y <= 1.4e+24)))
		tmp = (x / z) * (2.0 / y);
	else
		tmp = (x / z) * (-2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.7e-98], N[Not[LessEqual[y, 1.4e+24]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6999999999999998e-98 or 1.4000000000000001e24 < y

   1. Initial program 88.4%

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

      1. distribute-rgt-out-- 91.2%

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

   3. Simplified 91.2%

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

      1. times-frac 91.1%

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

   5. Applied egg-rr 91.1%

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

   6. Taylor expanded in y around inf 79.1%

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

   if -5.6999999999999998e-98 < y < 1.4000000000000001e24

   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%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{-98} \lor \neg \left(y \leq 1.4 \cdot 10^{+24}\right):\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-2}{t}\\ \end{array} \]

Alternative 11: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\neg \left(y \leq -6.5 \cdot 10^{-98}\right) \land y \leq 2 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (and (not (<= y -6.5e-98)) (<= y 2e+24))
   (/ (* (/ 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 <= -6.5e-98) && (y <= 2e+24)) {
		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 ((.not. (y <= (-6.5d-98))) .and. (y <= 2d+24)) 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 <= -6.5e-98) && (y <= 2e+24)) {
		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 not (y <= -6.5e-98) and (y <= 2e+24):
		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 <= -6.5e-98) && (y <= 2e+24))
		tmp = Float64(Float64(Float64(x / z) * -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 <= -6.5e-98)) && (y <= 2e+24))
		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[And[N[Not[LessEqual[y, -6.5e-98]], $MachinePrecision], LessEqual[y, 2e+24]], N[(N[(N[(x / z), $MachinePrecision] * -2.0), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000017e-98 or 2e24 < y

   1. Initial program 88.4%

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

      1. distribute-rgt-out-- 91.2%

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

   3. Simplified 91.2%

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

      1. times-frac 91.1%

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

   5. Applied egg-rr 91.1%

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

   6. Taylor expanded in y around inf 79.1%

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

   if -6.50000000000000017e-98 < y < 2e24

   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 76.9%

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

      1. associate-*r/ 76.9%

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

      2. neg-mul-1 76.9%

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

   6. Simplified 76.9%

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

      1. frac-times 72.6%

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

      2. neg-mul-1 72.6%

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

      3. associate-*r* 72.6%

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

      4. metadata-eval 72.6%

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

      5. *-commutative 72.6%

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

      6. associate-/r* 78.3%

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

      7. *-commutative 78.3%

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

      8. *-un-lft-identity 78.3%

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

      9. times-frac 78.3%

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

      10. metadata-eval 78.3%

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

   8. Applied egg-rr 78.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\neg \left(y \leq -6.5 \cdot 10^{-98}\right) \land y \leq 2 \cdot 10^{+24}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{2}{y}\\ \end{array} \]

Alternative 12: 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 13: 52.8% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(2.0 / z), $MachinePrecision] * N[(x / y), $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. distribute-rgt-out-- 89.9%

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

   3. times-frac 92.8%

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

3. Simplified 92.8%

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

4. Taylor expanded in y around inf 54.9%

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

5. Final simplification 54.9%

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

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))))