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

Percentage Accurate: 83.9% → 96.8%

Time: 7.7s

Alternatives: 14

Speedup: 1.0×

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: 83.9% 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: 96.8% 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]

Derivation

1. Initial program 85.5%

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

   1. associate-/l* 97.4%

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

3. Simplified 97.4%

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

4. Final simplification 97.4%

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

Alternative 2: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -x \cdot \frac{z}{t}\\ \mathbf{if}\;z \leq -1850000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8500000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* x (/ z t)))))
   (if (<= z -1850000.0)
     x
     (if (<= z -2.3e-39)
       t_1
       (if (<= z -2.5e-92)
         (/ x (/ t y))
         (if (<= z -7.2e-111)
           t_1
           (if (<= z 8500000000.0) (* x (/ y t)) x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -(x * (z / t));
	double tmp;
	if (z <= -1850000.0) {
		tmp = x;
	} else if (z <= -2.3e-39) {
		tmp = t_1;
	} else if (z <= -2.5e-92) {
		tmp = x / (t / y);
	} else if (z <= -7.2e-111) {
		tmp = t_1;
	} else if (z <= 8500000000.0) {
		tmp = x * (y / 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 = -(x * (z / t))
    if (z <= (-1850000.0d0)) then
        tmp = x
    else if (z <= (-2.3d-39)) then
        tmp = t_1
    else if (z <= (-2.5d-92)) then
        tmp = x / (t / y)
    else if (z <= (-7.2d-111)) then
        tmp = t_1
    else if (z <= 8500000000.0d0) then
        tmp = x * (y / 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 = -(x * (z / t));
	double tmp;
	if (z <= -1850000.0) {
		tmp = x;
	} else if (z <= -2.3e-39) {
		tmp = t_1;
	} else if (z <= -2.5e-92) {
		tmp = x / (t / y);
	} else if (z <= -7.2e-111) {
		tmp = t_1;
	} else if (z <= 8500000000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -(x * (z / t))
	tmp = 0
	if z <= -1850000.0:
		tmp = x
	elif z <= -2.3e-39:
		tmp = t_1
	elif z <= -2.5e-92:
		tmp = x / (t / y)
	elif z <= -7.2e-111:
		tmp = t_1
	elif z <= 8500000000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-Float64(x * Float64(z / t)))
	tmp = 0.0
	if (z <= -1850000.0)
		tmp = x;
	elseif (z <= -2.3e-39)
		tmp = t_1;
	elseif (z <= -2.5e-92)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= -7.2e-111)
		tmp = t_1;
	elseif (z <= 8500000000.0)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -(x * (z / t));
	tmp = 0.0;
	if (z <= -1850000.0)
		tmp = x;
	elseif (z <= -2.3e-39)
		tmp = t_1;
	elseif (z <= -2.5e-92)
		tmp = x / (t / y);
	elseif (z <= -7.2e-111)
		tmp = t_1;
	elseif (z <= 8500000000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[z, -1850000.0], x, If[LessEqual[z, -2.3e-39], t$95$1, If[LessEqual[z, -2.5e-92], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e-111], t$95$1, If[LessEqual[z, 8500000000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.85e6 or 8.5e9 < z

   1. Initial program 78.2%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 64.0%

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

   if -1.85e6 < z < -2.30000000000000008e-39 or -2.50000000000000006e-92 < z < -7.20000000000000019e-111

   1. Initial program 99.7%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 62.0%

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

      1. neg-mul-1 62.0%

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

      2. distribute-neg-frac 62.0%

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

   6. Simplified 62.0%

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

   7. Taylor expanded in z around 0 61.6%

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

      1. neg-mul-1 61.6%

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

      2. distribute-neg-frac 61.6%

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

   9. Simplified 61.6%

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

   if -2.30000000000000008e-39 < z < -2.50000000000000006e-92

   1. Initial program 86.6%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 57.8%

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

   if -7.20000000000000019e-111 < z < 8.5e9

   1. Initial program 94.0%

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

      1. associate-*r/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around 0 65.1%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1850000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-39}:\\ \;\;\;\;-x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-111}:\\ \;\;\;\;-x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 8500000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -440000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-108}:\\ \;\;\;\;-x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 122000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -440000.0)
   x
   (if (<= z -2.3e-39)
     (/ (* x z) (- t))
     (if (<= z -2e-93)
       (/ x (/ t y))
       (if (<= z -3.1e-108)
         (- (* x (/ z t)))
         (if (<= z 122000000.0) (* x (/ y t)) x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -440000.0) {
		tmp = x;
	} else if (z <= -2.3e-39) {
		tmp = (x * z) / -t;
	} else if (z <= -2e-93) {
		tmp = x / (t / y);
	} else if (z <= -3.1e-108) {
		tmp = -(x * (z / t));
	} else if (z <= 122000000.0) {
		tmp = x * (y / 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 <= (-440000.0d0)) then
        tmp = x
    else if (z <= (-2.3d-39)) then
        tmp = (x * z) / -t
    else if (z <= (-2d-93)) then
        tmp = x / (t / y)
    else if (z <= (-3.1d-108)) then
        tmp = -(x * (z / t))
    else if (z <= 122000000.0d0) then
        tmp = x * (y / 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 <= -440000.0) {
		tmp = x;
	} else if (z <= -2.3e-39) {
		tmp = (x * z) / -t;
	} else if (z <= -2e-93) {
		tmp = x / (t / y);
	} else if (z <= -3.1e-108) {
		tmp = -(x * (z / t));
	} else if (z <= 122000000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -440000.0:
		tmp = x
	elif z <= -2.3e-39:
		tmp = (x * z) / -t
	elif z <= -2e-93:
		tmp = x / (t / y)
	elif z <= -3.1e-108:
		tmp = -(x * (z / t))
	elif z <= 122000000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -440000.0)
		tmp = x;
	elseif (z <= -2.3e-39)
		tmp = Float64(Float64(x * z) / Float64(-t));
	elseif (z <= -2e-93)
		tmp = Float64(x / Float64(t / y));
	elseif (z <= -3.1e-108)
		tmp = Float64(-Float64(x * Float64(z / t)));
	elseif (z <= 122000000.0)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -440000.0)
		tmp = x;
	elseif (z <= -2.3e-39)
		tmp = (x * z) / -t;
	elseif (z <= -2e-93)
		tmp = x / (t / y);
	elseif (z <= -3.1e-108)
		tmp = -(x * (z / t));
	elseif (z <= 122000000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -440000.0], x, If[LessEqual[z, -2.3e-39], N[(N[(x * z), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, -2e-93], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-108], (-N[(x * N[(z / t), $MachinePrecision]), $MachinePrecision]), If[LessEqual[z, 122000000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.4e5 or 1.22e8 < z

   1. Initial program 78.2%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 64.0%

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

   if -4.4e5 < z < -2.30000000000000008e-39

   1. Initial program 99.7%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 60.9%

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

      1. neg-mul-1 60.9%

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

      2. distribute-neg-frac 60.9%

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

   6. Simplified 60.9%

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

   7. Taylor expanded in z around 0 52.0%

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

      1. neg-mul-1 52.0%

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

      2. distribute-neg-frac 52.0%

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

   9. Simplified 52.0%

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

       1. *-commutative 52.0%

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

       2. frac-2neg 52.0%

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

       3. remove-double-neg 52.0%

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

       4. associate-*l/ 52.1%

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

   11. Applied egg-rr 52.1%

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

   if -2.30000000000000008e-39 < z < -1.9999999999999998e-93

   1. Initial program 86.6%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 57.8%

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

   if -1.9999999999999998e-93 < z < -3.10000000000000014e-108

   1. Initial program 99.5%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 66.7%

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

      1. neg-mul-1 66.7%

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

      2. distribute-neg-frac 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in z around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-neg-frac 100.0%

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

   9. Simplified 100.0%

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

   if -3.10000000000000014e-108 < z < 1.22e8

   1. Initial program 94.0%

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

      1. associate-*r/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around 0 65.1%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -440000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{x \cdot z}{-t}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-108}:\\ \;\;\;\;-x \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq 122000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-14} \lor \neg \left(z \leq 16000000\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.2e-14) (not (<= z 16000000.0)))
   (* x (/ z (- z t)))
   (* x (/ (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-14) || !(z <= 16000000.0)) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.2d-14)) .or. (.not. (z <= 16000000.0d0))) then
        tmp = x * (z / (z - t))
    else
        tmp = x * ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-14) || !(z <= 16000000.0)) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.2e-14) or not (z <= 16000000.0):
		tmp = x * (z / (z - t))
	else:
		tmp = x * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.2e-14) || !(z <= 16000000.0))
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = Float64(x * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.2e-14) || ~((z <= 16000000.0)))
		tmp = x * (z / (z - t));
	else
		tmp = x * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.2e-14], N[Not[LessEqual[z, 16000000.0]], $MachinePrecision]], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.1999999999999996e-14 or 1.6e7 < z

   1. Initial program 78.8%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 77.9%

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

      1. neg-mul-1 77.9%

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

      2. distribute-neg-frac 77.9%

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

   6. Simplified 77.9%

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

      1. distribute-frac-neg 77.9%

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

      2. frac-2neg 77.9%

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

      3. distribute-frac-neg 77.9%

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

      4. remove-double-neg 77.9%

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

      5. associate-*r/ 60.2%

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

      6. sub-neg 60.2%

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

      7. distribute-neg-in 60.2%

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

      8. remove-double-neg 60.2%

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

   8. Applied egg-rr 60.2%

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

      1. *-commutative 60.2%

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

      2. associate-/l* 58.4%

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

      3. associate-/r/ 77.9%

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

      4. +-commutative 77.9%

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

      5. unsub-neg 77.9%

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

   10. Simplified 77.9%

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

   if -7.1999999999999996e-14 < z < 1.6e7

   1. Initial program 93.9%

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

      1. associate-*r/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in t around inf 76.3%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-14} \lor \neg \left(z \leq 16000000\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 5: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+32} \lor \neg \left(y \leq 4.2 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.8e+32) (not (<= y 4.2e+70)))
   (/ x (/ (- t z) y))
   (* x (/ z (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.8e+32) || !(y <= 4.2e+70)) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-8.8d+32)) .or. (.not. (y <= 4.2d+70))) then
        tmp = x / ((t - z) / y)
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.8e+32) || !(y <= 4.2e+70)) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8.8e+32) or not (y <= 4.2e+70):
		tmp = x / ((t - z) / y)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.8e+32) || !(y <= 4.2e+70))
		tmp = Float64(x / Float64(Float64(t - z) / y));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8.8e+32) || ~((y <= 4.2e+70)))
		tmp = x / ((t - z) / y);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.8e+32], N[Not[LessEqual[y, 4.2e+70]], $MachinePrecision]], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.80000000000000004e32 or 4.20000000000000015e70 < y

   1. Initial program 86.7%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around inf 75.6%

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

   if -8.80000000000000004e32 < y < 4.20000000000000015e70

   1. Initial program 84.9%

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

      1. associate-*r/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around 0 82.2%

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

      1. neg-mul-1 82.2%

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

      2. distribute-neg-frac 82.2%

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

   6. Simplified 82.2%

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

      1. distribute-frac-neg 82.2%

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

      2. frac-2neg 82.2%

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

      3. distribute-frac-neg 82.2%

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

      4. remove-double-neg 82.2%

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

      5. associate-*r/ 68.4%

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

      6. sub-neg 68.4%

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

      7. distribute-neg-in 68.4%

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

      8. remove-double-neg 68.4%

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

   8. Applied egg-rr 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-/l* 70.7%

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

      3. associate-/r/ 82.2%

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

      4. +-commutative 82.2%

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

      5. unsub-neg 82.2%

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

   10. Simplified 82.2%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+32} \lor \neg \left(y \leq 4.2 \cdot 10^{+70}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 6: 66.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -44000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 28500000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -44000000.0) x (if (<= z 28500000000.0) (* x (/ (- y z) t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -44000000.0) {
		tmp = x;
	} else if (z <= 28500000000.0) {
		tmp = x * ((y - 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 <= (-44000000.0d0)) then
        tmp = x
    else if (z <= 28500000000.0d0) then
        tmp = x * ((y - 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 <= -44000000.0) {
		tmp = x;
	} else if (z <= 28500000000.0) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -44000000.0:
		tmp = x
	elif z <= 28500000000.0:
		tmp = x * ((y - z) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -44000000.0)
		tmp = x;
	elseif (z <= 28500000000.0)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -44000000.0)
		tmp = x;
	elseif (z <= 28500000000.0)
		tmp = x * ((y - z) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -44000000.0], x, If[LessEqual[z, 28500000000.0], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4e7 or 2.85e10 < z

   1. Initial program 78.2%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 64.0%

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

   if -4.4e7 < z < 2.85e10

   1. Initial program 94.1%

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

      1. associate-*r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around inf 74.8%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -44000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 28500000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 1200000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.5e-14)
   (* x (/ z (- z t)))
   (if (<= z 1200000000.0) (* x (/ (- y z) t)) (- x (* y (/ x z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e-14) {
		tmp = x * (z / (z - t));
	} else if (z <= 1200000000.0) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x - (y * (x / 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 <= (-3.5d-14)) then
        tmp = x * (z / (z - t))
    else if (z <= 1200000000.0d0) then
        tmp = x * ((y - z) / t)
    else
        tmp = x - (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e-14) {
		tmp = x * (z / (z - t));
	} else if (z <= 1200000000.0) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x - (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.5e-14:
		tmp = x * (z / (z - t))
	elif z <= 1200000000.0:
		tmp = x * ((y - z) / t)
	else:
		tmp = x - (y * (x / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.5e-14)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 1200000000.0)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x - Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.5e-14)
		tmp = x * (z / (z - t));
	elseif (z <= 1200000000.0)
		tmp = x * ((y - z) / t);
	else
		tmp = x - (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.5e-14], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1200000000.0], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000002e-14

   1. Initial program 82.9%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 83.8%

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

      1. neg-mul-1 83.8%

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

      2. distribute-neg-frac 83.8%

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

   6. Simplified 83.8%

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

      1. distribute-frac-neg 83.8%

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

      2. frac-2neg 83.8%

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

      3. distribute-frac-neg 83.8%

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

      4. remove-double-neg 83.8%

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

      5. associate-*r/ 68.2%

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

      6. sub-neg 68.2%

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

      7. distribute-neg-in 68.2%

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

      8. remove-double-neg 68.2%

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

   8. Applied egg-rr 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-/l* 58.9%

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

      3. associate-/r/ 83.8%

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

      4. +-commutative 83.8%

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

      5. unsub-neg 83.8%

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

   10. Simplified 83.8%

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

   if -3.5000000000000002e-14 < z < 1.2e9

   1. Initial program 94.0%

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

      1. associate-*r/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in t around inf 75.8%

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

   if 1.2e9 < z

   1. Initial program 74.8%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. associate-/l* 65.3%

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

      3. distribute-neg-frac 65.3%

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

      4. neg-sub0 65.3%

         \[\leadsto \frac{\color{blue}{0 - \left(y - z\right)}}{\frac{z}{x}} \]

      5. associate--r- 65.3%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right) + z}}{\frac{z}{x}} \]

      6. neg-sub0 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in y around 0 70.1%

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

      1. +-commutative 70.1%

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

      2. mul-1-neg 70.1%

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

      3. unsub-neg 70.1%

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

      4. associate-*r/ 76.2%

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

   9. Simplified 76.2%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 1200000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 8: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 1400000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.2e-14)
   (* x (/ z (- z t)))
   (if (<= z 1400000000.0) (* x (/ (- y z) t)) (- x (/ y (/ z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e-14) {
		tmp = x * (z / (z - t));
	} else if (z <= 1400000000.0) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x - (y / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.2d-14)) then
        tmp = x * (z / (z - t))
    else if (z <= 1400000000.0d0) then
        tmp = x * ((y - z) / t)
    else
        tmp = x - (y / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e-14) {
		tmp = x * (z / (z - t));
	} else if (z <= 1400000000.0) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x - (y / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.2e-14:
		tmp = x * (z / (z - t))
	elif z <= 1400000000.0:
		tmp = x * ((y - z) / t)
	else:
		tmp = x - (y / (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.2e-14)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 1400000000.0)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x - Float64(y / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.2e-14)
		tmp = x * (z / (z - t));
	elseif (z <= 1400000000.0)
		tmp = x * ((y - z) / t);
	else
		tmp = x - (y / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.2e-14], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1400000000.0], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.19999999999999993e-14

   1. Initial program 82.9%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 83.8%

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

      1. neg-mul-1 83.8%

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

      2. distribute-neg-frac 83.8%

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

   6. Simplified 83.8%

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

      1. distribute-frac-neg 83.8%

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

      2. frac-2neg 83.8%

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

      3. distribute-frac-neg 83.8%

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

      4. remove-double-neg 83.8%

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

      5. associate-*r/ 68.2%

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

      6. sub-neg 68.2%

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

      7. distribute-neg-in 68.2%

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

      8. remove-double-neg 68.2%

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

   8. Applied egg-rr 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-/l* 58.9%

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

      3. associate-/r/ 83.8%

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

      4. +-commutative 83.8%

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

      5. unsub-neg 83.8%

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

   10. Simplified 83.8%

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

   if -5.19999999999999993e-14 < z < 1.4e9

   1. Initial program 94.0%

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

      1. associate-*r/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in t around inf 75.8%

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

   if 1.4e9 < z

   1. Initial program 74.8%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. associate-/l* 65.3%

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

      3. distribute-neg-frac 65.3%

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

      4. neg-sub0 65.3%

         \[\leadsto \frac{\color{blue}{0 - \left(y - z\right)}}{\frac{z}{x}} \]

      5. associate--r- 65.3%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right) + z}}{\frac{z}{x}} \]

      6. neg-sub0 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in y around 0 70.1%

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

      1. +-commutative 70.1%

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

      2. mul-1-neg 70.1%

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

      3. unsub-neg 70.1%

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

      4. associate-*r/ 76.2%

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

   9. Simplified 76.2%

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

       1. clear-num 76.2%

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

       2. un-div-inv 76.2%

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

   11. Applied egg-rr 76.2%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 1400000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 9: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 920000000:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6e-14)
   (* x (/ z (- z t)))
   (if (<= z 920000000.0) (/ x (/ t (- y z))) (- x (/ y (/ z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e-14) {
		tmp = x * (z / (z - t));
	} else if (z <= 920000000.0) {
		tmp = x / (t / (y - z));
	} else {
		tmp = x - (y / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6d-14)) then
        tmp = x * (z / (z - t))
    else if (z <= 920000000.0d0) then
        tmp = x / (t / (y - z))
    else
        tmp = x - (y / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e-14) {
		tmp = x * (z / (z - t));
	} else if (z <= 920000000.0) {
		tmp = x / (t / (y - z));
	} else {
		tmp = x - (y / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6e-14:
		tmp = x * (z / (z - t))
	elif z <= 920000000.0:
		tmp = x / (t / (y - z))
	else:
		tmp = x - (y / (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6e-14)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (z <= 920000000.0)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	else
		tmp = Float64(x - Float64(y / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6e-14)
		tmp = x * (z / (z - t));
	elseif (z <= 920000000.0)
		tmp = x / (t / (y - z));
	else
		tmp = x - (y / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6e-14], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 920000000.0], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.9999999999999997e-14

   1. Initial program 82.9%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 83.8%

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

      1. neg-mul-1 83.8%

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

      2. distribute-neg-frac 83.8%

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

   6. Simplified 83.8%

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

      1. distribute-frac-neg 83.8%

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

      2. frac-2neg 83.8%

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

      3. distribute-frac-neg 83.8%

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

      4. remove-double-neg 83.8%

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

      5. associate-*r/ 68.2%

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

      6. sub-neg 68.2%

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

      7. distribute-neg-in 68.2%

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

      8. remove-double-neg 68.2%

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

   8. Applied egg-rr 68.2%

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

      1. *-commutative 68.2%

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

      2. associate-/l* 58.9%

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

      3. associate-/r/ 83.8%

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

      4. +-commutative 83.8%

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

      5. unsub-neg 83.8%

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

   10. Simplified 83.8%

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

   if -5.9999999999999997e-14 < z < 9.2e8

   1. Initial program 94.0%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in t around inf 75.8%

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

   if 9.2e8 < z

   1. Initial program 74.8%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 56.9%

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

      1. mul-1-neg 56.9%

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

      2. associate-/l* 65.3%

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

      3. distribute-neg-frac 65.3%

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

      4. neg-sub0 65.3%

         \[\leadsto \frac{\color{blue}{0 - \left(y - z\right)}}{\frac{z}{x}} \]

      5. associate--r- 65.3%

         \[\leadsto \frac{\color{blue}{\left(0 - y\right) + z}}{\frac{z}{x}} \]

      6. neg-sub0 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in y around 0 70.1%

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

      1. +-commutative 70.1%

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

      2. mul-1-neg 70.1%

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

      3. unsub-neg 70.1%

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

      4. associate-*r/ 76.2%

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

   9. Simplified 76.2%

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

       1. clear-num 76.2%

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

       2. un-div-inv 76.2%

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

   11. Applied egg-rr 76.2%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 920000000:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 10: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.35e+33)
   (/ x (/ (- t z) y))
   (if (<= y 6.8e+76) (* x (/ z (- z t))) (/ (* x y) (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.35e+33) {
		tmp = x / ((t - z) / y);
	} else if (y <= 6.8e+76) {
		tmp = x * (z / (z - t));
	} else {
		tmp = (x * y) / (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.35d+33)) then
        tmp = x / ((t - z) / y)
    else if (y <= 6.8d+76) then
        tmp = x * (z / (z - t))
    else
        tmp = (x * y) / (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.35e+33) {
		tmp = x / ((t - z) / y);
	} else if (y <= 6.8e+76) {
		tmp = x * (z / (z - t));
	} else {
		tmp = (x * y) / (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.35e+33:
		tmp = x / ((t - z) / y)
	elif y <= 6.8e+76:
		tmp = x * (z / (z - t))
	else:
		tmp = (x * y) / (t - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.35e+33)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	elseif (y <= 6.8e+76)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = Float64(Float64(x * y) / Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.35e+33)
		tmp = x / ((t - z) / y);
	elseif (y <= 6.8e+76)
		tmp = x * (z / (z - t));
	else
		tmp = (x * y) / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.35e+33], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+76], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3499999999999999e33

   1. Initial program 83.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 80.1%

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

   if -2.3499999999999999e33 < y < 6.7999999999999994e76

   1. Initial program 84.9%

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

      1. associate-*r/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around 0 82.2%

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

      1. neg-mul-1 82.2%

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

      2. distribute-neg-frac 82.2%

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

   6. Simplified 82.2%

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

      1. distribute-frac-neg 82.2%

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

      2. frac-2neg 82.2%

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

      3. distribute-frac-neg 82.2%

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

      4. remove-double-neg 82.2%

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

      5. associate-*r/ 68.4%

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

      6. sub-neg 68.4%

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

      7. distribute-neg-in 68.4%

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

      8. remove-double-neg 68.4%

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

   8. Applied egg-rr 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-/l* 70.7%

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

      3. associate-/r/ 82.2%

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

      4. +-commutative 82.2%

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

      5. unsub-neg 82.2%

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

   10. Simplified 82.2%

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

   if 6.7999999999999994e76 < y

   1. Initial program 90.1%

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

      1. associate-*r/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in y around inf 73.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \end{array} \]

Alternative 11: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4200000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.5e-14) x (if (<= z 4200000000.0) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e-14) {
		tmp = x;
	} else if (z <= 4200000000.0) {
		tmp = x * (y / 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 <= (-9.5d-14)) then
        tmp = x
    else if (z <= 4200000000.0d0) then
        tmp = x * (y / 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 <= -9.5e-14) {
		tmp = x;
	} else if (z <= 4200000000.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.5e-14:
		tmp = x
	elif z <= 4200000000.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.5e-14)
		tmp = x;
	elseif (z <= 4200000000.0)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.5e-14)
		tmp = x;
	elseif (z <= 4200000000.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.5e-14], x, If[LessEqual[z, 4200000000.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999999e-14 or 4.2e9 < z

   1. Initial program 78.6%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 62.9%

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

   if -9.4999999999999999e-14 < z < 4.2e9

   1. Initial program 94.0%

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

      1. associate-*r/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in z around 0 61.5%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4200000000:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 550000000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.5e-14) x (if (<= z 550000000.0) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e-14) {
		tmp = x;
	} else if (z <= 550000000.0) {
		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 <= (-6.5d-14)) then
        tmp = x
    else if (z <= 550000000.0d0) 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 <= -6.5e-14) {
		tmp = x;
	} else if (z <= 550000000.0) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.5e-14:
		tmp = x
	elif z <= 550000000.0:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.5e-14)
		tmp = x;
	elseif (z <= 550000000.0)
		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 <= -6.5e-14)
		tmp = x;
	elseif (z <= 550000000.0)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.5e-14], x, If[LessEqual[z, 550000000.0], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5000000000000001e-14 or 5.5e8 < z

   1. Initial program 78.6%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 62.9%

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

   if -6.5000000000000001e-14 < z < 5.5e8

   1. Initial program 94.0%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in z around 0 61.5%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 550000000:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 96.8% accurate, 1.0× speedup

Math

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

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(x * Float64(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[(x * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 85.5%

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

   1. associate-*r/ 97.4%

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

3. Simplified 97.4%

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

4. Final simplification 97.4%

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

Alternative 14: 34.3% 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 85.5%

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

   1. associate-*r/ 97.4%

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

3. Simplified 97.4%

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

4. Taylor expanded in z around inf 39.4%

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

5. Final simplification 39.4%

   \[\leadsto x \]

Developer target: 96.8% 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 2023176 
(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)))