Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.4% → 97.4%

Time: 10.1s

Alternatives: 19

Speedup: 0.7×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{t - z} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{t - z} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+119} \lor \neg \left(t_1 \leq 10^{+275}\right):\\ \;\;\;\;\frac{y - z}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y z)) (- t z))))
   (if (or (<= t_1 -5e+119) (not (<= t_1 1e+275)))
     (/ (- y z) (/ (- t z) x))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if ((t_1 <= -5e+119) || !(t_1 <= 1e+275)) {
		tmp = (y - z) / ((t - z) / x);
	} 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 = (x * (y - z)) / (t - z)
    if ((t_1 <= (-5d+119)) .or. (.not. (t_1 <= 1d+275))) then
        tmp = (y - z) / ((t - z) / x)
    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 - z)) / (t - z);
	double tmp;
	if ((t_1 <= -5e+119) || !(t_1 <= 1e+275)) {
		tmp = (y - z) / ((t - z) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * (y - z)) / (t - z)
	tmp = 0
	if (t_1 <= -5e+119) or not (t_1 <= 1e+275):
		tmp = (y - z) / ((t - z) / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if ((t_1 <= -5e+119) || !(t_1 <= 1e+275))
		tmp = Float64(Float64(y - z) / Float64(Float64(t - z) / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (y - z)) / (t - z);
	tmp = 0.0;
	if ((t_1 <= -5e+119) || ~((t_1 <= 1e+275)))
		tmp = (y - z) / ((t - z) / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+119], N[Not[LessEqual[t$95$1, 1e+275]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -4.9999999999999999e119 or 9.9999999999999996e274 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 50.8%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -4.9999999999999999e119 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 9.9999999999999996e274

   1. Initial program 98.4%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -5 \cdot 10^{+119} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \leq 10^{+275}\right):\\ \;\;\;\;\frac{y - z}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array} \]

Alternative 2: 98.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(y - z\right)}{t - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+289} \lor \neg \left(t_1 \leq 10^{+275}\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y z)) (- t z))))
   (if (or (<= t_1 -5e+289) (not (<= t_1 1e+275)))
     (* (- y z) (/ x (- t z)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if ((t_1 <= -5e+289) || !(t_1 <= 1e+275)) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (y - z)) / (t - z)
    if ((t_1 <= (-5d+289)) .or. (.not. (t_1 <= 1d+275))) then
        tmp = (y - z) * (x / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * (y - z)) / (t - z);
	double tmp;
	if ((t_1 <= -5e+289) || !(t_1 <= 1e+275)) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * (y - z)) / (t - z)
	tmp = 0
	if (t_1 <= -5e+289) or not (t_1 <= 1e+275):
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(y - z)) / Float64(t - z))
	tmp = 0.0
	if ((t_1 <= -5e+289) || !(t_1 <= 1e+275))
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (y - z)) / (t - z);
	tmp = 0.0;
	if ((t_1 <= -5e+289) || ~((t_1 <= 1e+275)))
		tmp = (y - z) * (x / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+289], N[Not[LessEqual[t$95$1, 1e+275]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -5.00000000000000031e289 or 9.9999999999999996e274 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 42.5%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   if -5.00000000000000031e289 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 9.9999999999999996e274

   1. Initial program 98.5%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -5 \cdot 10^{+289} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{t - z} \leq 10^{+275}\right):\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t - z}\\ \end{array} \]

Alternative 3: 58.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{\frac{z}{y}}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -115000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (/ z y))))
   (if (<= z -1.2e+102)
     x
     (if (<= z -115000000.0)
       t_1
       (if (<= z -9.2e-16)
         x
         (if (<= z 1.08e-131)
           (/ y (/ t x))
           (if (<= z 5e-61) t_1 (if (<= z 2.6e-32) (/ x (/ t y)) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -x / (z / y);
	double tmp;
	if (z <= -1.2e+102) {
		tmp = x;
	} else if (z <= -115000000.0) {
		tmp = t_1;
	} else if (z <= -9.2e-16) {
		tmp = x;
	} else if (z <= 1.08e-131) {
		tmp = y / (t / x);
	} else if (z <= 5e-61) {
		tmp = t_1;
	} else if (z <= 2.6e-32) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -x / (z / y)
    if (z <= (-1.2d+102)) then
        tmp = x
    else if (z <= (-115000000.0d0)) then
        tmp = t_1
    else if (z <= (-9.2d-16)) then
        tmp = x
    else if (z <= 1.08d-131) then
        tmp = y / (t / x)
    else if (z <= 5d-61) then
        tmp = t_1
    else if (z <= 2.6d-32) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z / y);
	double tmp;
	if (z <= -1.2e+102) {
		tmp = x;
	} else if (z <= -115000000.0) {
		tmp = t_1;
	} else if (z <= -9.2e-16) {
		tmp = x;
	} else if (z <= 1.08e-131) {
		tmp = y / (t / x);
	} else if (z <= 5e-61) {
		tmp = t_1;
	} else if (z <= 2.6e-32) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -x / (z / y)
	tmp = 0
	if z <= -1.2e+102:
		tmp = x
	elif z <= -115000000.0:
		tmp = t_1
	elif z <= -9.2e-16:
		tmp = x
	elif z <= 1.08e-131:
		tmp = y / (t / x)
	elif z <= 5e-61:
		tmp = t_1
	elif z <= 2.6e-32:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z / y))
	tmp = 0.0
	if (z <= -1.2e+102)
		tmp = x;
	elseif (z <= -115000000.0)
		tmp = t_1;
	elseif (z <= -9.2e-16)
		tmp = x;
	elseif (z <= 1.08e-131)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 5e-61)
		tmp = t_1;
	elseif (z <= 2.6e-32)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z / y);
	tmp = 0.0;
	if (z <= -1.2e+102)
		tmp = x;
	elseif (z <= -115000000.0)
		tmp = t_1;
	elseif (z <= -9.2e-16)
		tmp = x;
	elseif (z <= 1.08e-131)
		tmp = y / (t / x);
	elseif (z <= 5e-61)
		tmp = t_1;
	elseif (z <= 2.6e-32)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+102], x, If[LessEqual[z, -115000000.0], t$95$1, If[LessEqual[z, -9.2e-16], x, If[LessEqual[z, 1.08e-131], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-61], t$95$1, If[LessEqual[z, 2.6e-32], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.19999999999999997e102 or -1.15e8 < z < -9.1999999999999996e-16 or 2.5999999999999997e-32 < z

   1. Initial program 70.4%

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

      1. associate-*l/ 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{x} \]

   if -1.19999999999999997e102 < z < -1.15e8 or 1.07999999999999996e-131 < z < 4.9999999999999999e-61

   1. Initial program 92.0%

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

      1. associate-*l/ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in y around inf 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-/l* 60.2%

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

      3. associate-/r/ 60.9%

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

   6. Simplified 60.9%

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

   7. Taylor expanded in t around 0 49.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   8. Step-by-step derivation

      1. mul-1-neg 49.8%

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

      2. associate-/l* 50.2%

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

   9. Simplified 50.2%

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

   if -9.1999999999999996e-16 < z < 1.07999999999999996e-131

   1. Initial program 95.6%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around 0 77.0%

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

      1. associate-/l* 77.7%

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

      2. associate-/r/ 77.7%

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

   6. Simplified 77.7%

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

      1. *-commutative 77.7%

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

      2. clear-num 77.7%

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

      3. un-div-inv 77.8%

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

   8. Applied egg-rr 77.8%

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

   if 4.9999999999999999e-61 < z < 2.5999999999999997e-32

   1. Initial program 99.7%

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

      1. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in z around 0 99.7%

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

      1. associate-/l* 99.7%

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

   6. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{t}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -115000000:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-61}:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 58.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-58}:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e+102)
   x
   (if (<= z -1.4e+74)
     (* x (/ (- z) t))
     (if (<= z -3e+38)
       x
       (if (<= z 1.08e-131)
         (/ y (/ t x))
         (if (<= z 6.6e-58)
           (/ (- x) (/ z y))
           (if (<= z 2e-32) (/ x (/ t y)) x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+102) {
		tmp = x;
	} else if (z <= -1.4e+74) {
		tmp = x * (-z / t);
	} else if (z <= -3e+38) {
		tmp = x;
	} else if (z <= 1.08e-131) {
		tmp = y / (t / x);
	} else if (z <= 6.6e-58) {
		tmp = -x / (z / y);
	} else if (z <= 2e-32) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.2d+102)) then
        tmp = x
    else if (z <= (-1.4d+74)) then
        tmp = x * (-z / t)
    else if (z <= (-3d+38)) then
        tmp = x
    else if (z <= 1.08d-131) then
        tmp = y / (t / x)
    else if (z <= 6.6d-58) then
        tmp = -x / (z / y)
    else if (z <= 2d-32) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+102) {
		tmp = x;
	} else if (z <= -1.4e+74) {
		tmp = x * (-z / t);
	} else if (z <= -3e+38) {
		tmp = x;
	} else if (z <= 1.08e-131) {
		tmp = y / (t / x);
	} else if (z <= 6.6e-58) {
		tmp = -x / (z / y);
	} else if (z <= 2e-32) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e+102:
		tmp = x
	elif z <= -1.4e+74:
		tmp = x * (-z / t)
	elif z <= -3e+38:
		tmp = x
	elif z <= 1.08e-131:
		tmp = y / (t / x)
	elif z <= 6.6e-58:
		tmp = -x / (z / y)
	elif z <= 2e-32:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e+102)
		tmp = x;
	elseif (z <= -1.4e+74)
		tmp = Float64(x * Float64(Float64(-z) / t));
	elseif (z <= -3e+38)
		tmp = x;
	elseif (z <= 1.08e-131)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 6.6e-58)
		tmp = Float64(Float64(-x) / Float64(z / y));
	elseif (z <= 2e-32)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e+102)
		tmp = x;
	elseif (z <= -1.4e+74)
		tmp = x * (-z / t);
	elseif (z <= -3e+38)
		tmp = x;
	elseif (z <= 1.08e-131)
		tmp = y / (t / x);
	elseif (z <= 6.6e-58)
		tmp = -x / (z / y);
	elseif (z <= 2e-32)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e+102], x, If[LessEqual[z, -1.4e+74], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e+38], x, If[LessEqual[z, 1.08e-131], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-58], N[((-x) / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-32], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.19999999999999997e102 or -1.40000000000000001e74 < z < -3.0000000000000001e38 or 2.00000000000000011e-32 < z

   1. Initial program 71.2%

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

      1. associate-*l/ 72.4%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in z around inf 70.1%

      \[\leadsto \color{blue}{x} \]

   if -1.19999999999999997e102 < z < -1.40000000000000001e74

   1. Initial program 81.0%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around inf 41.5%

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

      1. associate-/l* 51.2%

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

      2. associate-/r/ 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in y around 0 61.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 61.6%

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

      2. associate-*r/ 61.5%

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

      3. distribute-rgt-neg-in 61.5%

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

   9. Simplified 61.5%

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

   if -3.0000000000000001e38 < z < 1.07999999999999996e-131

   1. Initial program 95.9%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around 0 74.2%

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

      1. associate-/l* 74.8%

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

      2. associate-/r/ 74.8%

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

   6. Simplified 74.8%

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

      1. *-commutative 74.8%

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

      2. clear-num 74.8%

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

      3. un-div-inv 74.9%

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

   8. Applied egg-rr 74.9%

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

   if 1.07999999999999996e-131 < z < 6.60000000000000052e-58

   1. Initial program 94.1%

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

      1. associate-*l/ 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

      2. associate-/l* 58.8%

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

      3. associate-/r/ 60.6%

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

   6. Simplified 60.6%

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

   7. Taylor expanded in t around 0 54.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   8. Step-by-step derivation

      1. mul-1-neg 54.5%

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

      2. associate-/l* 54.9%

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

   9. Simplified 54.9%

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

   if 6.60000000000000052e-58 < z < 2.00000000000000011e-32

   1. Initial program 99.7%

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

      1. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in z around 0 99.7%

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

      1. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-58}:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 58.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-60}:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.3e+104)
   x
   (if (<= z -6e+73)
     (/ x (/ (- t) z))
     (if (<= z -7.6e+37)
       x
       (if (<= z 1.08e-131)
         (/ y (/ t x))
         (if (<= z 1.2e-60)
           (/ (- x) (/ z y))
           (if (<= z 1.06e-32) (/ x (/ t y)) x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e+104) {
		tmp = x;
	} else if (z <= -6e+73) {
		tmp = x / (-t / z);
	} else if (z <= -7.6e+37) {
		tmp = x;
	} else if (z <= 1.08e-131) {
		tmp = y / (t / x);
	} else if (z <= 1.2e-60) {
		tmp = -x / (z / y);
	} else if (z <= 1.06e-32) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.3d+104)) then
        tmp = x
    else if (z <= (-6d+73)) then
        tmp = x / (-t / z)
    else if (z <= (-7.6d+37)) then
        tmp = x
    else if (z <= 1.08d-131) then
        tmp = y / (t / x)
    else if (z <= 1.2d-60) then
        tmp = -x / (z / y)
    else if (z <= 1.06d-32) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e+104) {
		tmp = x;
	} else if (z <= -6e+73) {
		tmp = x / (-t / z);
	} else if (z <= -7.6e+37) {
		tmp = x;
	} else if (z <= 1.08e-131) {
		tmp = y / (t / x);
	} else if (z <= 1.2e-60) {
		tmp = -x / (z / y);
	} else if (z <= 1.06e-32) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.3e+104:
		tmp = x
	elif z <= -6e+73:
		tmp = x / (-t / z)
	elif z <= -7.6e+37:
		tmp = x
	elif z <= 1.08e-131:
		tmp = y / (t / x)
	elif z <= 1.2e-60:
		tmp = -x / (z / y)
	elif z <= 1.06e-32:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.3e+104)
		tmp = x;
	elseif (z <= -6e+73)
		tmp = Float64(x / Float64(Float64(-t) / z));
	elseif (z <= -7.6e+37)
		tmp = x;
	elseif (z <= 1.08e-131)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 1.2e-60)
		tmp = Float64(Float64(-x) / Float64(z / y));
	elseif (z <= 1.06e-32)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.3e+104)
		tmp = x;
	elseif (z <= -6e+73)
		tmp = x / (-t / z);
	elseif (z <= -7.6e+37)
		tmp = x;
	elseif (z <= 1.08e-131)
		tmp = y / (t / x);
	elseif (z <= 1.2e-60)
		tmp = -x / (z / y);
	elseif (z <= 1.06e-32)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.3e+104], x, If[LessEqual[z, -6e+73], N[(x / N[((-t) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e+37], x, If[LessEqual[z, 1.08e-131], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-60], N[((-x) / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-32], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.3e104 or -6.00000000000000021e73 < z < -7.59999999999999979e37 or 1.05999999999999994e-32 < z

   1. Initial program 71.2%

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

      1. associate-*l/ 72.4%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in z around inf 70.1%

      \[\leadsto \color{blue}{x} \]

   if -1.3e104 < z < -6.00000000000000021e73

   1. Initial program 81.0%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around 0 32.3%

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

      1. associate-*r/ 32.3%

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

      2. mul-1-neg 32.3%

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

      3. distribute-rgt-neg-out 32.3%

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

      4. associate-/l* 25.8%

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

   6. Simplified 25.8%

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

   7. Taylor expanded in t around inf 61.6%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \frac{t}{z}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 61.6%

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

      2. neg-mul-1 61.6%

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

   9. Simplified 61.6%

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

   if -7.59999999999999979e37 < z < 1.07999999999999996e-131

   1. Initial program 95.9%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around 0 74.2%

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

      1. associate-/l* 74.8%

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

      2. associate-/r/ 74.8%

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

   6. Simplified 74.8%

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

      1. *-commutative 74.8%

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

      2. clear-num 74.8%

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

      3. un-div-inv 74.9%

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

   8. Applied egg-rr 74.9%

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

   if 1.07999999999999996e-131 < z < 1.20000000000000005e-60

   1. Initial program 94.1%

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

      1. associate-*l/ 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

      2. associate-/l* 58.8%

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

      3. associate-/r/ 60.6%

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

   6. Simplified 60.6%

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

   7. Taylor expanded in t around 0 54.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   8. Step-by-step derivation

      1. mul-1-neg 54.5%

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

      2. associate-/l* 54.9%

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

   9. Simplified 54.9%

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

   if 1.20000000000000005e-60 < z < 1.05999999999999994e-32

   1. Initial program 99.7%

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

      1. associate-*l/ 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in z around 0 99.7%

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

      1. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{\frac{-t}{z}}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-131}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-60}:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{t - z}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-161}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 0.0039:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x (- t z)))))
   (if (<= z -1.25e+102)
     x
     (if (<= z -1.12e+17)
       t_1
       (if (<= z 1.5e-161)
         (* (- y z) (/ x t))
         (if (<= z 0.0039) t_1 (if (<= z 1.2e+15) (* x (/ (- z) t)) x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / (t - z));
	double tmp;
	if (z <= -1.25e+102) {
		tmp = x;
	} else if (z <= -1.12e+17) {
		tmp = t_1;
	} else if (z <= 1.5e-161) {
		tmp = (y - z) * (x / t);
	} else if (z <= 0.0039) {
		tmp = t_1;
	} else if (z <= 1.2e+15) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x / (t - z))
    if (z <= (-1.25d+102)) then
        tmp = x
    else if (z <= (-1.12d+17)) then
        tmp = t_1
    else if (z <= 1.5d-161) then
        tmp = (y - z) * (x / t)
    else if (z <= 0.0039d0) then
        tmp = t_1
    else if (z <= 1.2d+15) then
        tmp = x * (-z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / (t - z));
	double tmp;
	if (z <= -1.25e+102) {
		tmp = x;
	} else if (z <= -1.12e+17) {
		tmp = t_1;
	} else if (z <= 1.5e-161) {
		tmp = (y - z) * (x / t);
	} else if (z <= 0.0039) {
		tmp = t_1;
	} else if (z <= 1.2e+15) {
		tmp = x * (-z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / (t - z))
	tmp = 0
	if z <= -1.25e+102:
		tmp = x
	elif z <= -1.12e+17:
		tmp = t_1
	elif z <= 1.5e-161:
		tmp = (y - z) * (x / t)
	elif z <= 0.0039:
		tmp = t_1
	elif z <= 1.2e+15:
		tmp = x * (-z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / Float64(t - z)))
	tmp = 0.0
	if (z <= -1.25e+102)
		tmp = x;
	elseif (z <= -1.12e+17)
		tmp = t_1;
	elseif (z <= 1.5e-161)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 0.0039)
		tmp = t_1;
	elseif (z <= 1.2e+15)
		tmp = Float64(x * Float64(Float64(-z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / (t - z));
	tmp = 0.0;
	if (z <= -1.25e+102)
		tmp = x;
	elseif (z <= -1.12e+17)
		tmp = t_1;
	elseif (z <= 1.5e-161)
		tmp = (y - z) * (x / t);
	elseif (z <= 0.0039)
		tmp = t_1;
	elseif (z <= 1.2e+15)
		tmp = x * (-z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+102], x, If[LessEqual[z, -1.12e+17], t$95$1, If[LessEqual[z, 1.5e-161], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0039], t$95$1, If[LessEqual[z, 1.2e+15], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25e102 or 1.2e15 < z

   1. Initial program 67.8%

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

      1. associate-*l/ 70.1%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in z around inf 73.2%

      \[\leadsto \color{blue}{x} \]

   if -1.25e102 < z < -1.12e17 or 1.49999999999999994e-161 < z < 0.0038999999999999998

   1. Initial program 94.1%

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

      1. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in y around inf 67.1%

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

      1. associate-*l/ 66.8%

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

      2. *-commutative 66.8%

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

   6. Simplified 66.8%

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

   if -1.12e17 < z < 1.49999999999999994e-161

   1. Initial program 95.6%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in t around inf 84.9%

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

      1. associate-/l* 83.5%

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

      2. associate-/r/ 85.3%

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

   6. Simplified 85.3%

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

   if 0.0038999999999999998 < z < 1.2e15

   1. Initial program 99.5%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 99.5%

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

      1. associate-/l* 99.5%

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

      2. associate-/r/ 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 99.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   8. Step-by-step derivation

      1. mul-1-neg 99.5%

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

      2. associate-*r/ 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-161}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 0.0039:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 68.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-161}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= z -1.55e+108)
     x
     (if (<= z -5e-103)
       t_1
       (if (<= z 1.4e-161) (* (- y z) (/ x t)) (if (<= z 1.42e-8) t_1 x))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (z <= -1.55e+108) {
		tmp = x;
	} else if (z <= -5e-103) {
		tmp = t_1;
	} else if (z <= 1.4e-161) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.42e-8) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (z <= (-1.55d+108)) then
        tmp = x
    else if (z <= (-5d-103)) then
        tmp = t_1
    else if (z <= 1.4d-161) then
        tmp = (y - z) * (x / t)
    else if (z <= 1.42d-8) then
        tmp = t_1
    else
        tmp = x
    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));
	double tmp;
	if (z <= -1.55e+108) {
		tmp = x;
	} else if (z <= -5e-103) {
		tmp = t_1;
	} else if (z <= 1.4e-161) {
		tmp = (y - z) * (x / t);
	} else if (z <= 1.42e-8) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if z <= -1.55e+108:
		tmp = x
	elif z <= -5e-103:
		tmp = t_1
	elif z <= 1.4e-161:
		tmp = (y - z) * (x / t)
	elif z <= 1.42e-8:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (z <= -1.55e+108)
		tmp = x;
	elseif (z <= -5e-103)
		tmp = t_1;
	elseif (z <= 1.4e-161)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 1.42e-8)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (z <= -1.55e+108)
		tmp = x;
	elseif (z <= -5e-103)
		tmp = t_1;
	elseif (z <= 1.4e-161)
		tmp = (y - z) * (x / t);
	elseif (z <= 1.42e-8)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+108], x, If[LessEqual[z, -5e-103], t$95$1, If[LessEqual[z, 1.4e-161], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e-8], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5500000000000001e108 or 1.41999999999999998e-8 < z

   1. Initial program 69.0%

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

      1. associate-*l/ 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in z around inf 71.5%

      \[\leadsto \color{blue}{x} \]

   if -1.5500000000000001e108 < z < -4.99999999999999966e-103 or 1.39999999999999996e-161 < z < 1.41999999999999998e-8

   1. Initial program 95.9%

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

      1. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in y around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. associate-/l* 64.8%

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

      3. associate-/r/ 67.7%

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

   6. Simplified 67.7%

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

   if -4.99999999999999966e-103 < z < 1.39999999999999996e-161

   1. Initial program 94.2%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in t around inf 91.1%

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

      1. associate-/l* 89.3%

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

      2. associate-/r/ 92.9%

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

   6. Simplified 92.9%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-161}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-249}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-10}:\\ \;\;\;\;\frac{1}{t - z} \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.8e-17)
   (- x (/ x (/ z y)))
   (if (<= z 6e-249)
     (/ (- y z) (/ t x))
     (if (<= z 1.55e-10) (* (/ 1.0 (- t z)) (* x y)) (/ x (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e-17) {
		tmp = x - (x / (z / y));
	} else if (z <= 6e-249) {
		tmp = (y - z) / (t / x);
	} else if (z <= 1.55e-10) {
		tmp = (1.0 / (t - z)) * (x * y);
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.8d-17)) then
        tmp = x - (x / (z / y))
    else if (z <= 6d-249) then
        tmp = (y - z) / (t / x)
    else if (z <= 1.55d-10) then
        tmp = (1.0d0 / (t - z)) * (x * y)
    else
        tmp = x / (1.0d0 - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e-17) {
		tmp = x - (x / (z / y));
	} else if (z <= 6e-249) {
		tmp = (y - z) / (t / x);
	} else if (z <= 1.55e-10) {
		tmp = (1.0 / (t - z)) * (x * y);
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.8e-17:
		tmp = x - (x / (z / y))
	elif z <= 6e-249:
		tmp = (y - z) / (t / x)
	elif z <= 1.55e-10:
		tmp = (1.0 / (t - z)) * (x * y)
	else:
		tmp = x / (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.8e-17)
		tmp = Float64(x - Float64(x / Float64(z / y)));
	elseif (z <= 6e-249)
		tmp = Float64(Float64(y - z) / Float64(t / x));
	elseif (z <= 1.55e-10)
		tmp = Float64(Float64(1.0 / Float64(t - z)) * Float64(x * y));
	else
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.8e-17)
		tmp = x - (x / (z / y));
	elseif (z <= 6e-249)
		tmp = (y - z) / (t / x);
	elseif (z <= 1.55e-10)
		tmp = (1.0 / (t - z)) * (x * y);
	else
		tmp = x / (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.8e-17], N[(x - N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-249], N[(N[(y - z), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e-10], N[(N[(1.0 / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.7999999999999996e-17

   1. Initial program 80.9%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

      1. *-commutative 73.0%

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

      2. clear-num 70.5%

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

      3. un-div-inv 70.6%

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

   5. Applied egg-rr 70.6%

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

   6. Taylor expanded in t around 0 55.9%

      \[\leadsto \frac{y - z}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   7. Step-by-step derivation

      1. neg-mul-1 55.9%

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

      2. distribute-neg-frac 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in y around 0 70.7%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 70.7%

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

       2. associate-/l* 79.4%

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

   11. Simplified 79.4%

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

   if -6.7999999999999996e-17 < z < 6.00000000000000008e-249

   1. Initial program 94.8%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

      1. *-commutative 96.0%

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

      2. clear-num 96.0%

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

      3. un-div-inv 96.0%

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

   5. Applied egg-rr 96.0%

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

   6. Taylor expanded in t around inf 88.2%

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

   if 6.00000000000000008e-249 < z < 1.55000000000000008e-10

   1. Initial program 97.0%

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

      1. clear-num 96.8%

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

      2. associate-/r/ 96.8%

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

   3. Applied egg-rr 96.8%

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

   4. Taylor expanded in y around inf 79.4%

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

   if 1.55000000000000008e-10 < z

   1. Initial program 65.3%

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

      1. associate-*l/ 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in y around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. mul-1-neg 59.2%

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

      3. distribute-rgt-neg-out 59.2%

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

      4. associate-/l* 90.9%

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

   6. Simplified 90.9%

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

   7. Taylor expanded in t around 0 90.9%

      \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot \frac{t}{z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 90.9%

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

      2. unsub-neg 90.9%

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

   9. Simplified 90.9%

      \[\leadsto \frac{x}{\color{blue}{1 - \frac{t}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-249}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-10}:\\ \;\;\;\;\frac{1}{t - z} \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]

Alternative 9: 72.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-160}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* y (/ x z)))))
   (if (<= z -7.8e-16)
     t_1
     (if (<= z 1.5e-160)
       (* (- y z) (/ x t))
       (if (<= z 2.35e-32) (* x (/ y (- t z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y * (x / z));
	double tmp;
	if (z <= -7.8e-16) {
		tmp = t_1;
	} else if (z <= 1.5e-160) {
		tmp = (y - z) * (x / t);
	} else if (z <= 2.35e-32) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (x / z))
    if (z <= (-7.8d-16)) then
        tmp = t_1
    else if (z <= 1.5d-160) then
        tmp = (y - z) * (x / t)
    else if (z <= 2.35d-32) then
        tmp = x * (y / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y * (x / z));
	double tmp;
	if (z <= -7.8e-16) {
		tmp = t_1;
	} else if (z <= 1.5e-160) {
		tmp = (y - z) * (x / t);
	} else if (z <= 2.35e-32) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y * (x / z))
	tmp = 0
	if z <= -7.8e-16:
		tmp = t_1
	elif z <= 1.5e-160:
		tmp = (y - z) * (x / t)
	elif z <= 2.35e-32:
		tmp = x * (y / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y * Float64(x / z)))
	tmp = 0.0
	if (z <= -7.8e-16)
		tmp = t_1;
	elseif (z <= 1.5e-160)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 2.35e-32)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y * (x / z));
	tmp = 0.0;
	if (z <= -7.8e-16)
		tmp = t_1;
	elseif (z <= 1.5e-160)
		tmp = (y - z) * (x / t);
	elseif (z <= 2.35e-32)
		tmp = x * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e-16], t$95$1, If[LessEqual[z, 1.5e-160], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e-32], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.79999999999999954e-16 or 2.3500000000000001e-32 < z

   1. Initial program 73.4%

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

      1. associate-*l/ 75.3%

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

   3. Simplified 75.3%

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

      1. *-commutative 75.3%

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

      2. clear-num 73.2%

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

      3. un-div-inv 73.3%

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

   5. Applied egg-rr 73.3%

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

   6. Taylor expanded in t around 0 58.9%

      \[\leadsto \frac{y - z}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   7. Step-by-step derivation

      1. neg-mul-1 58.9%

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

      2. distribute-neg-frac 58.9%

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

   8. Simplified 58.9%

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

   9. Taylor expanded in y around 0 70.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 70.0%

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

       2. unsub-neg 70.0%

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

       3. *-commutative 70.0%

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

       4. associate-*r/ 77.9%

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

   11. Simplified 77.9%

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

   if -7.79999999999999954e-16 < z < 1.49999999999999998e-160

   1. Initial program 95.4%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in t around inf 87.0%

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

      1. associate-/l* 85.6%

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

      2. associate-/r/ 87.4%

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

   6. Simplified 87.4%

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

   if 1.49999999999999998e-160 < z < 2.3500000000000001e-32

   1. Initial program 96.3%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in y around inf 76.3%

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

      1. *-commutative 76.3%

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

      2. associate-/l* 72.1%

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

      3. associate-/r/ 76.5%

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

   6. Simplified 76.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-160}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 10: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-159}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2e-16)
   (- x (* y (/ x z)))
   (if (<= z 1.4e-159)
     (* (- y z) (/ x t))
     (if (<= z 2.8e-12) (* x (/ y (- t z))) (/ x (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e-16) {
		tmp = x - (y * (x / z));
	} else if (z <= 1.4e-159) {
		tmp = (y - z) * (x / t);
	} else if (z <= 2.8e-12) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.2d-16)) then
        tmp = x - (y * (x / z))
    else if (z <= 1.4d-159) then
        tmp = (y - z) * (x / t)
    else if (z <= 2.8d-12) then
        tmp = x * (y / (t - z))
    else
        tmp = x / (1.0d0 - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e-16) {
		tmp = x - (y * (x / z));
	} else if (z <= 1.4e-159) {
		tmp = (y - z) * (x / t);
	} else if (z <= 2.8e-12) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.2e-16:
		tmp = x - (y * (x / z))
	elif z <= 1.4e-159:
		tmp = (y - z) * (x / t)
	elif z <= 2.8e-12:
		tmp = x * (y / (t - z))
	else:
		tmp = x / (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2e-16)
		tmp = Float64(x - Float64(y * Float64(x / z)));
	elseif (z <= 1.4e-159)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 2.8e-12)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.2e-16)
		tmp = x - (y * (x / z));
	elseif (z <= 1.4e-159)
		tmp = (y - z) * (x / t);
	elseif (z <= 2.8e-12)
		tmp = x * (y / (t - z));
	else
		tmp = x / (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.2e-16], N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-159], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-12], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2e-16

   1. Initial program 80.9%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

      1. *-commutative 73.0%

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

      2. clear-num 70.5%

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

      3. un-div-inv 70.6%

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

   5. Applied egg-rr 70.6%

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

   6. Taylor expanded in t around 0 55.9%

      \[\leadsto \frac{y - z}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   7. Step-by-step derivation

      1. neg-mul-1 55.9%

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

      2. distribute-neg-frac 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in y around 0 70.7%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 70.7%

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

       2. unsub-neg 70.7%

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

       3. *-commutative 70.7%

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

       4. associate-*r/ 74.9%

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

   11. Simplified 74.9%

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

   if -2.2e-16 < z < 1.4000000000000001e-159

   1. Initial program 95.4%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in t around inf 87.0%

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

      1. associate-/l* 85.6%

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

      2. associate-/r/ 87.4%

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

   6. Simplified 87.4%

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

   if 1.4000000000000001e-159 < z < 2.8000000000000002e-12

   1. Initial program 96.6%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in y around inf 74.7%

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

      1. *-commutative 74.7%

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

      2. associate-/l* 70.7%

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

      3. associate-/r/ 74.8%

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

   6. Simplified 74.8%

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

   if 2.8000000000000002e-12 < z

   1. Initial program 65.3%

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

      1. associate-*l/ 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in y around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. mul-1-neg 59.2%

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

      3. distribute-rgt-neg-out 59.2%

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

      4. associate-/l* 90.9%

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

   6. Simplified 90.9%

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

   7. Taylor expanded in t around 0 90.9%

      \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot \frac{t}{z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 90.9%

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

      2. unsub-neg 90.9%

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

   9. Simplified 90.9%

      \[\leadsto \frac{x}{\color{blue}{1 - \frac{t}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-159}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]

Alternative 11: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.5e-16)
   (- x (* y (/ x z)))
   (if (<= z 1.25e-203)
     (/ (* x (- y z)) t)
     (if (<= z 5.6e-8) (* x (/ y (- t z))) (/ x (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e-16) {
		tmp = x - (y * (x / z));
	} else if (z <= 1.25e-203) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 5.6e-8) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.5d-16)) then
        tmp = x - (y * (x / z))
    else if (z <= 1.25d-203) then
        tmp = (x * (y - z)) / t
    else if (z <= 5.6d-8) then
        tmp = x * (y / (t - z))
    else
        tmp = x / (1.0d0 - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e-16) {
		tmp = x - (y * (x / z));
	} else if (z <= 1.25e-203) {
		tmp = (x * (y - z)) / t;
	} else if (z <= 5.6e-8) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.5e-16:
		tmp = x - (y * (x / z))
	elif z <= 1.25e-203:
		tmp = (x * (y - z)) / t
	elif z <= 5.6e-8:
		tmp = x * (y / (t - z))
	else:
		tmp = x / (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.5e-16)
		tmp = Float64(x - Float64(y * Float64(x / z)));
	elseif (z <= 1.25e-203)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	elseif (z <= 5.6e-8)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.5e-16)
		tmp = x - (y * (x / z));
	elseif (z <= 1.25e-203)
		tmp = (x * (y - z)) / t;
	elseif (z <= 5.6e-8)
		tmp = x * (y / (t - z));
	else
		tmp = x / (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.5e-16], N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-203], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 5.6e-8], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.5000000000000002e-16

   1. Initial program 80.9%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

      1. *-commutative 73.0%

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

      2. clear-num 70.5%

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

      3. un-div-inv 70.6%

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

   5. Applied egg-rr 70.6%

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

   6. Taylor expanded in t around 0 55.9%

      \[\leadsto \frac{y - z}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   7. Step-by-step derivation

      1. neg-mul-1 55.9%

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

      2. distribute-neg-frac 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in y around 0 70.7%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 70.7%

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

       2. unsub-neg 70.7%

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

       3. *-commutative 70.7%

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

       4. associate-*r/ 74.9%

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

   11. Simplified 74.9%

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

   if -2.5000000000000002e-16 < z < 1.25e-203

   1. Initial program 95.4%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around inf 87.9%

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

   if 1.25e-203 < z < 5.5999999999999999e-8

   1. Initial program 96.3%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around inf 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-/l* 74.5%

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

      3. associate-/r/ 77.5%

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

   6. Simplified 77.5%

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

   if 5.5999999999999999e-8 < z

   1. Initial program 65.3%

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

      1. associate-*l/ 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in y around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. mul-1-neg 59.2%

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

      3. distribute-rgt-neg-out 59.2%

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

      4. associate-/l* 90.9%

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

   6. Simplified 90.9%

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

   7. Taylor expanded in t around 0 90.9%

      \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot \frac{t}{z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 90.9%

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

      2. unsub-neg 90.9%

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

   9. Simplified 90.9%

      \[\leadsto \frac{x}{\color{blue}{1 - \frac{t}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-203}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]

Alternative 12: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-17}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-158}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e-17)
   (- x (* y (/ x z)))
   (if (<= z 5.6e-158)
     (/ (- y z) (/ t x))
     (if (<= z 2.05e-10) (* x (/ y (- t z))) (/ x (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-17) {
		tmp = x - (y * (x / z));
	} else if (z <= 5.6e-158) {
		tmp = (y - z) / (t / x);
	} else if (z <= 2.05e-10) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.8d-17)) then
        tmp = x - (y * (x / z))
    else if (z <= 5.6d-158) then
        tmp = (y - z) / (t / x)
    else if (z <= 2.05d-10) then
        tmp = x * (y / (t - z))
    else
        tmp = x / (1.0d0 - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e-17) {
		tmp = x - (y * (x / z));
	} else if (z <= 5.6e-158) {
		tmp = (y - z) / (t / x);
	} else if (z <= 2.05e-10) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e-17:
		tmp = x - (y * (x / z))
	elif z <= 5.6e-158:
		tmp = (y - z) / (t / x)
	elif z <= 2.05e-10:
		tmp = x * (y / (t - z))
	else:
		tmp = x / (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e-17)
		tmp = Float64(x - Float64(y * Float64(x / z)));
	elseif (z <= 5.6e-158)
		tmp = Float64(Float64(y - z) / Float64(t / x));
	elseif (z <= 2.05e-10)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e-17)
		tmp = x - (y * (x / z));
	elseif (z <= 5.6e-158)
		tmp = (y - z) / (t / x);
	elseif (z <= 2.05e-10)
		tmp = x * (y / (t - z));
	else
		tmp = x / (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e-17], N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e-158], N[(N[(y - z), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-10], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.79999999999999973e-17

   1. Initial program 80.9%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

      1. *-commutative 73.0%

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

      2. clear-num 70.5%

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

      3. un-div-inv 70.6%

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

   5. Applied egg-rr 70.6%

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

   6. Taylor expanded in t around 0 55.9%

      \[\leadsto \frac{y - z}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   7. Step-by-step derivation

      1. neg-mul-1 55.9%

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

      2. distribute-neg-frac 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in y around 0 70.7%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 70.7%

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

       2. unsub-neg 70.7%

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

       3. *-commutative 70.7%

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

       4. associate-*r/ 74.9%

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

   11. Simplified 74.9%

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

   if -4.79999999999999973e-17 < z < 5.60000000000000004e-158

   1. Initial program 95.4%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

      1. *-commutative 95.9%

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

      2. clear-num 95.9%

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

      3. un-div-inv 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in t around inf 87.5%

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

   if 5.60000000000000004e-158 < z < 2.0499999999999999e-10

   1. Initial program 96.6%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in y around inf 74.7%

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

      1. *-commutative 74.7%

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

      2. associate-/l* 70.7%

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

      3. associate-/r/ 74.8%

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

   6. Simplified 74.8%

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

   if 2.0499999999999999e-10 < z

   1. Initial program 65.3%

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

      1. associate-*l/ 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in y around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. mul-1-neg 59.2%

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

      3. distribute-rgt-neg-out 59.2%

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

      4. associate-/l* 90.9%

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

   6. Simplified 90.9%

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

   7. Taylor expanded in t around 0 90.9%

      \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot \frac{t}{z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 90.9%

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

      2. unsub-neg 90.9%

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

   9. Simplified 90.9%

      \[\leadsto \frac{x}{\color{blue}{1 - \frac{t}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-17}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-158}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]

Alternative 13: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-16}:\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-159}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 4.25 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.3e-16)
   (- x (/ x (/ z y)))
   (if (<= z 2.15e-159)
     (/ (- y z) (/ t x))
     (if (<= z 4.25e-10) (* x (/ y (- t z))) (/ x (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.3e-16) {
		tmp = x - (x / (z / y));
	} else if (z <= 2.15e-159) {
		tmp = (y - z) / (t / x);
	} else if (z <= 4.25e-10) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.3d-16)) then
        tmp = x - (x / (z / y))
    else if (z <= 2.15d-159) then
        tmp = (y - z) / (t / x)
    else if (z <= 4.25d-10) then
        tmp = x * (y / (t - z))
    else
        tmp = x / (1.0d0 - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.3e-16) {
		tmp = x - (x / (z / y));
	} else if (z <= 2.15e-159) {
		tmp = (y - z) / (t / x);
	} else if (z <= 4.25e-10) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.3e-16:
		tmp = x - (x / (z / y))
	elif z <= 2.15e-159:
		tmp = (y - z) / (t / x)
	elif z <= 4.25e-10:
		tmp = x * (y / (t - z))
	else:
		tmp = x / (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.3e-16)
		tmp = Float64(x - Float64(x / Float64(z / y)));
	elseif (z <= 2.15e-159)
		tmp = Float64(Float64(y - z) / Float64(t / x));
	elseif (z <= 4.25e-10)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.3e-16)
		tmp = x - (x / (z / y));
	elseif (z <= 2.15e-159)
		tmp = (y - z) / (t / x);
	elseif (z <= 4.25e-10)
		tmp = x * (y / (t - z));
	else
		tmp = x / (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.3e-16], N[(x - N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-159], N[(N[(y - z), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.25e-10], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.2999999999999999e-16

   1. Initial program 80.9%

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

      1. associate-*l/ 73.0%

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

   3. Simplified 73.0%

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

      1. *-commutative 73.0%

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

      2. clear-num 70.5%

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

      3. un-div-inv 70.6%

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

   5. Applied egg-rr 70.6%

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

   6. Taylor expanded in t around 0 55.9%

      \[\leadsto \frac{y - z}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   7. Step-by-step derivation

      1. neg-mul-1 55.9%

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

      2. distribute-neg-frac 55.9%

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

   8. Simplified 55.9%

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

   9. Taylor expanded in y around 0 70.7%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 70.7%

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

       2. associate-/l* 79.4%

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

   11. Simplified 79.4%

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

   if -4.2999999999999999e-16 < z < 2.15e-159

   1. Initial program 95.4%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

      1. *-commutative 95.9%

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

      2. clear-num 95.9%

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

      3. un-div-inv 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in t around inf 87.5%

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

   if 2.15e-159 < z < 4.2499999999999998e-10

   1. Initial program 96.6%

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

      1. associate-*l/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in y around inf 74.7%

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

      1. *-commutative 74.7%

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

      2. associate-/l* 70.7%

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

      3. associate-/r/ 74.8%

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

   6. Simplified 74.8%

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

   if 4.2499999999999998e-10 < z

   1. Initial program 65.3%

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

      1. associate-*l/ 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in y around 0 59.2%

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

      1. associate-*r/ 59.2%

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

      2. mul-1-neg 59.2%

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

      3. distribute-rgt-neg-out 59.2%

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

      4. associate-/l* 90.9%

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

   6. Simplified 90.9%

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

   7. Taylor expanded in t around 0 90.9%

      \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot \frac{t}{z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 90.9%

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

      2. unsub-neg 90.9%

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

   9. Simplified 90.9%

      \[\leadsto \frac{x}{\color{blue}{1 - \frac{t}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-16}:\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-159}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 4.25 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]

Alternative 14: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+148}:\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+175}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e+148)
   (- x (/ x (/ z y)))
   (if (<= z 9.5e+175) (* (- y z) (/ x (- t z))) (/ x (- 1.0 (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+148) {
		tmp = x - (x / (z / y));
	} else if (z <= 9.5e+175) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.2d+148)) then
        tmp = x - (x / (z / y))
    else if (z <= 9.5d+175) then
        tmp = (y - z) * (x / (t - z))
    else
        tmp = x / (1.0d0 - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+148) {
		tmp = x - (x / (z / y));
	} else if (z <= 9.5e+175) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x / (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e+148:
		tmp = x - (x / (z / y))
	elif z <= 9.5e+175:
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = x / (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e+148)
		tmp = Float64(x - Float64(x / Float64(z / y)));
	elseif (z <= 9.5e+175)
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e+148)
		tmp = x - (x / (z / y));
	elseif (z <= 9.5e+175)
		tmp = (y - z) * (x / (t - z));
	else
		tmp = x / (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e+148], N[(x - N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+175], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999997e148

   1. Initial program 71.4%

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

      1. associate-*l/ 53.2%

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

   3. Simplified 53.2%

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

      1. *-commutative 53.2%

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

      2. clear-num 48.5%

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

      3. un-div-inv 48.6%

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

   5. Applied egg-rr 48.6%

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

   6. Taylor expanded in t around 0 45.5%

      \[\leadsto \frac{y - z}{\color{blue}{-1 \cdot \frac{z}{x}}} \]
   7. Step-by-step derivation

      1. neg-mul-1 45.5%

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

      2. distribute-neg-frac 45.5%

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

   8. Simplified 45.5%

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

   9. Taylor expanded in y around 0 77.0%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{x \cdot y}{z}} \]
   10. Step-by-step derivation

       1. mul-1-neg 77.0%

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

       2. associate-/l* 91.0%

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

   11. Simplified 91.0%

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

   if -1.19999999999999997e148 < z < 9.5000000000000006e175

   1. Initial program 91.8%

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

      1. associate-*l/ 93.0%

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

   3. Simplified 93.0%

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

   if 9.5000000000000006e175 < z

   1. Initial program 52.7%

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

      1. associate-*l/ 67.3%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in y around 0 52.7%

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

      1. associate-*r/ 52.7%

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

      2. mul-1-neg 52.7%

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

      3. distribute-rgt-neg-out 52.7%

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

      4. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in t around 0 99.8%

      \[\leadsto \frac{x}{\color{blue}{1 + -1 \cdot \frac{t}{z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

   9. Simplified 99.8%

      \[\leadsto \frac{x}{\color{blue}{1 - \frac{t}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+148}:\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+175}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \end{array} \]

Alternative 15: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.4e+105) x (if (<= z 9.5e-33) (* y (/ x (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e+105) {
		tmp = x;
	} else if (z <= 9.5e-33) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.4d+105)) then
        tmp = x
    else if (z <= 9.5d-33) then
        tmp = y * (x / (t - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.4e+105) {
		tmp = x;
	} else if (z <= 9.5e-33) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.4e+105:
		tmp = x
	elif z <= 9.5e-33:
		tmp = y * (x / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.4e+105)
		tmp = x;
	elseif (z <= 9.5e-33)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.4e+105)
		tmp = x;
	elseif (z <= 9.5e-33)
		tmp = y * (x / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.4e+105], x, If[LessEqual[z, 9.5e-33], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4000000000000001e105 or 9.50000000000000019e-33 < z

   1. Initial program 69.8%

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

      1. associate-*l/ 71.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in z around inf 70.6%

      \[\leadsto \color{blue}{x} \]

   if -1.4000000000000001e105 < z < 9.50000000000000019e-33

   1. Initial program 94.9%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around inf 75.1%

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

      1. associate-*l/ 76.1%

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

      2. *-commutative 76.1%

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

   6. Simplified 76.1%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-33}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 38.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.1e-17) x (if (<= z 3.7e-122) (* x (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e-17) {
		tmp = x;
	} else if (z <= 3.7e-122) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.1d-17)) then
        tmp = x
    else if (z <= 3.7d-122) then
        tmp = x * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e-17) {
		tmp = x;
	} else if (z <= 3.7e-122) {
		tmp = x * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.1e-17:
		tmp = x
	elif z <= 3.7e-122:
		tmp = x * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.1e-17)
		tmp = x;
	elseif (z <= 3.7e-122)
		tmp = Float64(x * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.1e-17)
		tmp = x;
	elseif (z <= 3.7e-122)
		tmp = x * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.1e-17], x, If[LessEqual[z, 3.7e-122], N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999992e-17 or 3.6999999999999997e-122 < z

   1. Initial program 76.2%

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

      1. associate-*l/ 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in z around inf 57.7%

      \[\leadsto \color{blue}{x} \]

   if -2.09999999999999992e-17 < z < 3.6999999999999997e-122

   1. Initial program 95.7%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in y around 0 32.1%

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

      1. associate-*r/ 32.1%

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

      2. mul-1-neg 32.1%

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

      3. distribute-rgt-neg-out 32.1%

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

      4. associate-/l* 29.5%

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

   6. Simplified 29.5%

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

   7. Taylor expanded in t around inf 24.9%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \frac{t}{z}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 24.9%

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

      2. neg-mul-1 24.9%

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

   9. Simplified 24.9%

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

       1. div-inv 24.9%

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

       2. clear-num 24.9%

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

       3. add-sqr-sqrt 14.7%

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

       4. sqrt-unprod 26.2%

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

       5. sqr-neg 26.2%

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

       6. sqrt-unprod 10.7%

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

       7. add-sqr-sqrt 20.8%

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

   11. Applied egg-rr 20.8%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 59.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.4e+94) x (if (<= z 4.1e-39) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.4e+94) {
		tmp = x;
	} else if (z <= 4.1e-39) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.4d+94)) then
        tmp = x
    else if (z <= 4.1d-39) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.4e+94) {
		tmp = x;
	} else if (z <= 4.1e-39) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.4e+94:
		tmp = x
	elif z <= 4.1e-39:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.4e+94)
		tmp = x;
	elseif (z <= 4.1e-39)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.4e+94)
		tmp = x;
	elseif (z <= 4.1e-39)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.4e+94], x, If[LessEqual[z, 4.1e-39], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.40000000000000028e94 or 4.1e-39 < z

   1. Initial program 70.1%

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

      1. associate-*l/ 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in z around inf 68.4%

      \[\leadsto \color{blue}{x} \]

   if -6.40000000000000028e94 < z < 4.1e-39

   1. Initial program 95.5%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around 0 65.9%

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

      1. associate-/l* 67.1%

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

      2. associate-/r/ 67.0%

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

   6. Simplified 67.0%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-39}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.4e+94) x (if (<= z 1.85e-32) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.4e+94) {
		tmp = x;
	} else if (z <= 1.85e-32) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.4d+94)) then
        tmp = x
    else if (z <= 1.85d-32) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.4e+94) {
		tmp = x;
	} else if (z <= 1.85e-32) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.4e+94:
		tmp = x
	elif z <= 1.85e-32:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.4e+94)
		tmp = x;
	elseif (z <= 1.85e-32)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.4e+94)
		tmp = x;
	elseif (z <= 1.85e-32)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.4e+94], x, If[LessEqual[z, 1.85e-32], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.40000000000000028e94 or 1.85e-32 < z

   1. Initial program 69.8%

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

      1. associate-*l/ 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in z around inf 68.9%

      \[\leadsto \color{blue}{x} \]

   if -6.40000000000000028e94 < z < 1.85e-32

   1. Initial program 95.5%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in z around 0 66.1%

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

      1. associate-/l* 67.3%

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

   6. Simplified 67.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 35.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

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

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
end function

Java

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

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 84.3%

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

   1. associate-*l/ 84.6%

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

3. Simplified 84.6%

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

4. Taylor expanded in z around inf 37.4%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 37.4%

   \[\leadsto x \]

Developer target: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))