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

Percentage Accurate: 83.8% → 97.1%

Time: 8.9s

Alternatives: 10

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: 83.8% 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: 97.1% 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 84.1%

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

   1. associate-/l* 97.2%

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

3. Simplified 97.2%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+109}:\\ \;\;\;\;x - x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e+109)
   (- x (* x (/ y z)))
   (if (<= z 1.1e-165)
     (/ x (/ t (- y z)))
     (if (<= z 1.7e+95) (/ x (/ (- t z) y)) (* x (/ z (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e+109) {
		tmp = x - (x * (y / z));
	} else if (z <= 1.1e-165) {
		tmp = x / (t / (y - z));
	} else if (z <= 1.7e+95) {
		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 (z <= (-3.7d+109)) then
        tmp = x - (x * (y / z))
    else if (z <= 1.1d-165) then
        tmp = x / (t / (y - z))
    else if (z <= 1.7d+95) 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 (z <= -3.7e+109) {
		tmp = x - (x * (y / z));
	} else if (z <= 1.1e-165) {
		tmp = x / (t / (y - z));
	} else if (z <= 1.7e+95) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.7e+109:
		tmp = x - (x * (y / z))
	elif z <= 1.1e-165:
		tmp = x / (t / (y - z))
	elif z <= 1.7e+95:
		tmp = x / ((t - z) / y)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e+109)
		tmp = Float64(x - Float64(x * Float64(y / z)));
	elseif (z <= 1.1e-165)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (z <= 1.7e+95)
		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 (z <= -3.7e+109)
		tmp = x - (x * (y / z));
	elseif (z <= 1.1e-165)
		tmp = x / (t / (y - z));
	elseif (z <= 1.7e+95)
		tmp = x / ((t - z) / y);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e+109], N[(x - N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-165], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+95], 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 4 regimes

2. if z < -3.7000000000000002e109

   1. Initial program 65.2%

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

      1. remove-double-neg 65.2%

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

      2. distribute-lft-neg-out 65.2%

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

      3. distribute-neg-frac 65.2%

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

      4. distribute-neg-frac2 65.2%

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

      5. distribute-lft-neg-out 65.2%

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

      6. distribute-rgt-neg-in 65.2%

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

      7. sub-neg 65.2%

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

      8. distribute-neg-in 65.2%

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

      9. remove-double-neg 65.2%

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

      10. +-commutative 65.2%

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

      11. sub-neg 65.2%

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

      12. sub-neg 65.2%

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

      13. distribute-neg-in 65.2%

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

      14. remove-double-neg 65.2%

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

      15. +-commutative 65.2%

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

      16. sub-neg 65.2%

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

   3. Simplified 65.2%

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

   5. Taylor expanded in t around 0 60.4%

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

   6. Taylor expanded in z around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

      3. associate-/l* 94.1%

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

   8. Simplified 94.1%

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

   if -3.7000000000000002e109 < z < 1.0999999999999999e-165

   1. Initial program 92.3%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in x around 0 92.3%

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

      1. *-rgt-identity 92.3%

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

      2. times-frac 93.2%

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

      3. /-rgt-identity 93.2%

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

      4. associate-/r/ 98.0%

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

   7. Simplified 98.0%

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

   8. Taylor expanded in t around inf 79.0%

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

   if 1.0999999999999999e-165 < z < 1.70000000000000011e95

   1. Initial program 93.6%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 93.6%

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

      1. *-rgt-identity 93.6%

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

      2. times-frac 95.3%

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

      3. /-rgt-identity 95.3%

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

      4. associate-/r/ 92.1%

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

   7. Simplified 92.1%

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

   8. Taylor expanded in y around inf 66.0%

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

   if 1.70000000000000011e95 < z

   1. Initial program 72.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. distribute-neg-frac2 63.8%

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

      3. sub-neg 63.8%

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

      4. distribute-neg-in 63.8%

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

      5. remove-double-neg 63.8%

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

      6. +-commutative 63.8%

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

      7. sub-neg 63.8%

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

      8. associate-/l* 88.4%

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

   7. Simplified 88.4%

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

Alternative 3: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+107}:\\ \;\;\;\;x - x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.6e+107)
   (- x (* x (/ y z)))
   (if (<= z 1.95e-165)
     (/ x (/ t (- y z)))
     (if (<= z 1.25e+98) (* x (/ y (- t z))) (* x (/ z (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.6e+107) {
		tmp = x - (x * (y / z));
	} else if (z <= 1.95e-165) {
		tmp = x / (t / (y - z));
	} else if (z <= 1.25e+98) {
		tmp = x * (y / (t - z));
	} 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 (z <= (-3.6d+107)) then
        tmp = x - (x * (y / z))
    else if (z <= 1.95d-165) then
        tmp = x / (t / (y - z))
    else if (z <= 1.25d+98) then
        tmp = x * (y / (t - z))
    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 (z <= -3.6e+107) {
		tmp = x - (x * (y / z));
	} else if (z <= 1.95e-165) {
		tmp = x / (t / (y - z));
	} else if (z <= 1.25e+98) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.6e+107:
		tmp = x - (x * (y / z))
	elif z <= 1.95e-165:
		tmp = x / (t / (y - z))
	elif z <= 1.25e+98:
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.6e+107)
		tmp = Float64(x - Float64(x * Float64(y / z)));
	elseif (z <= 1.95e-165)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (z <= 1.25e+98)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	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 (z <= -3.6e+107)
		tmp = x - (x * (y / z));
	elseif (z <= 1.95e-165)
		tmp = x / (t / (y - z));
	elseif (z <= 1.25e+98)
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.6e+107], N[(x - N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e-165], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+98], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5999999999999998e107

   1. Initial program 65.2%

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

      1. remove-double-neg 65.2%

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

      2. distribute-lft-neg-out 65.2%

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

      3. distribute-neg-frac 65.2%

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

      4. distribute-neg-frac2 65.2%

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

      5. distribute-lft-neg-out 65.2%

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

      6. distribute-rgt-neg-in 65.2%

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

      7. sub-neg 65.2%

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

      8. distribute-neg-in 65.2%

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

      9. remove-double-neg 65.2%

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

      10. +-commutative 65.2%

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

      11. sub-neg 65.2%

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

      12. sub-neg 65.2%

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

      13. distribute-neg-in 65.2%

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

      14. remove-double-neg 65.2%

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

      15. +-commutative 65.2%

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

      16. sub-neg 65.2%

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

   3. Simplified 65.2%

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

   5. Taylor expanded in t around 0 60.4%

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

   6. Taylor expanded in z around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

      3. associate-/l* 94.1%

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

   8. Simplified 94.1%

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

   if -3.5999999999999998e107 < z < 1.9499999999999999e-165

   1. Initial program 92.3%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in x around 0 92.3%

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

      1. *-rgt-identity 92.3%

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

      2. times-frac 93.2%

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

      3. /-rgt-identity 93.2%

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

      4. associate-/r/ 98.0%

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

   7. Simplified 98.0%

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

   8. Taylor expanded in t around inf 79.0%

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

   if 1.9499999999999999e-165 < z < 1.25e98

   1. Initial program 93.6%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.3%

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

      1. associate-/l* 65.9%

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

   7. Simplified 65.9%

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

   if 1.25e98 < z

   1. Initial program 72.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. distribute-neg-frac2 63.8%

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

      3. sub-neg 63.8%

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

      4. distribute-neg-in 63.8%

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

      5. remove-double-neg 63.8%

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

      6. +-commutative 63.8%

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

      7. sub-neg 63.8%

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

      8. associate-/l* 88.4%

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

   7. Simplified 88.4%

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

Alternative 4: 72.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+109}:\\ \;\;\;\;x - x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.1e+109)
   (- x (* x (/ y z)))
   (if (<= z 2.65e-166)
     (* x (/ (- y z) t))
     (if (<= z 2e+98) (* x (/ y (- t z))) (* x (/ z (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.1e+109) {
		tmp = x - (x * (y / z));
	} else if (z <= 2.65e-166) {
		tmp = x * ((y - z) / t);
	} else if (z <= 2e+98) {
		tmp = x * (y / (t - z));
	} 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 (z <= (-3.1d+109)) then
        tmp = x - (x * (y / z))
    else if (z <= 2.65d-166) then
        tmp = x * ((y - z) / t)
    else if (z <= 2d+98) then
        tmp = x * (y / (t - z))
    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 (z <= -3.1e+109) {
		tmp = x - (x * (y / z));
	} else if (z <= 2.65e-166) {
		tmp = x * ((y - z) / t);
	} else if (z <= 2e+98) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.1e+109:
		tmp = x - (x * (y / z))
	elif z <= 2.65e-166:
		tmp = x * ((y - z) / t)
	elif z <= 2e+98:
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.1e+109)
		tmp = Float64(x - Float64(x * Float64(y / z)));
	elseif (z <= 2.65e-166)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	elseif (z <= 2e+98)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	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 (z <= -3.1e+109)
		tmp = x - (x * (y / z));
	elseif (z <= 2.65e-166)
		tmp = x * ((y - z) / t);
	elseif (z <= 2e+98)
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.1e+109], N[(x - N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.65e-166], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+98], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.09999999999999992e109

   1. Initial program 65.2%

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

      1. remove-double-neg 65.2%

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

      2. distribute-lft-neg-out 65.2%

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

      3. distribute-neg-frac 65.2%

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

      4. distribute-neg-frac2 65.2%

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

      5. distribute-lft-neg-out 65.2%

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

      6. distribute-rgt-neg-in 65.2%

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

      7. sub-neg 65.2%

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

      8. distribute-neg-in 65.2%

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

      9. remove-double-neg 65.2%

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

      10. +-commutative 65.2%

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

      11. sub-neg 65.2%

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

      12. sub-neg 65.2%

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

      13. distribute-neg-in 65.2%

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

      14. remove-double-neg 65.2%

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

      15. +-commutative 65.2%

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

      16. sub-neg 65.2%

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

   3. Simplified 65.2%

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

   5. Taylor expanded in t around 0 60.4%

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

   6. Taylor expanded in z around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

      3. associate-/l* 94.1%

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

   8. Simplified 94.1%

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

   if -3.09999999999999992e109 < z < 2.64999999999999998e-166

   1. Initial program 92.3%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in t around inf 72.8%

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

      1. associate-/l* 79.0%

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

   7. Simplified 79.0%

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

   if 2.64999999999999998e-166 < z < 2e98

   1. Initial program 93.6%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.3%

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

      1. associate-/l* 65.9%

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

   7. Simplified 65.9%

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

   if 2e98 < z

   1. Initial program 72.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. distribute-neg-frac2 63.8%

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

      3. sub-neg 63.8%

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

      4. distribute-neg-in 63.8%

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

      5. remove-double-neg 63.8%

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

      6. +-commutative 63.8%

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

      7. sub-neg 63.8%

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

      8. associate-/l* 88.4%

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

   7. Simplified 88.4%

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

Alternative 5: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-165}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.6e+107)
   (* x (- 1.0 (/ y z)))
   (if (<= z 2.8e-165)
     (* x (/ (- y z) t))
     (if (<= z 7.5e+95) (* x (/ y (- t z))) (* x (/ z (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.6e+107) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 2.8e-165) {
		tmp = x * ((y - z) / t);
	} else if (z <= 7.5e+95) {
		tmp = x * (y / (t - z));
	} 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 (z <= (-3.6d+107)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= 2.8d-165) then
        tmp = x * ((y - z) / t)
    else if (z <= 7.5d+95) then
        tmp = x * (y / (t - z))
    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 (z <= -3.6e+107) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 2.8e-165) {
		tmp = x * ((y - z) / t);
	} else if (z <= 7.5e+95) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.6e+107:
		tmp = x * (1.0 - (y / z))
	elif z <= 2.8e-165:
		tmp = x * ((y - z) / t)
	elif z <= 7.5e+95:
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.6e+107)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= 2.8e-165)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	elseif (z <= 7.5e+95)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	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 (z <= -3.6e+107)
		tmp = x * (1.0 - (y / z));
	elseif (z <= 2.8e-165)
		tmp = x * ((y - z) / t);
	elseif (z <= 7.5e+95)
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.6e+107], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-165], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+95], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5999999999999998e107

   1. Initial program 65.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. associate-/l* 94.0%

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

      3. distribute-rgt-neg-in 94.0%

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

      4. distribute-frac-neg 94.0%

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

      5. sub-neg 94.0%

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

      6. distribute-neg-in 94.0%

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

      7. remove-double-neg 94.0%

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

      8. +-commutative 94.0%

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

      9. sub-neg 94.0%

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

      10. div-sub 94.0%

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

      11. *-inverses 94.0%

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

   7. Simplified 94.0%

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

   if -3.5999999999999998e107 < z < 2.7999999999999999e-165

   1. Initial program 92.3%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in t around inf 72.8%

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

      1. associate-/l* 79.0%

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

   7. Simplified 79.0%

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

   if 2.7999999999999999e-165 < z < 7.5000000000000001e95

   1. Initial program 93.6%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 64.3%

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

      1. associate-/l* 65.9%

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

   7. Simplified 65.9%

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

   if 7.5000000000000001e95 < z

   1. Initial program 72.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. distribute-neg-frac2 63.8%

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

      3. sub-neg 63.8%

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

      4. distribute-neg-in 63.8%

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

      5. remove-double-neg 63.8%

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

      6. +-commutative 63.8%

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

      7. sub-neg 63.8%

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

      8. associate-/l* 88.4%

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

   7. Simplified 88.4%

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

Alternative 6: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+107} \lor \neg \left(z \leq 1.45 \cdot 10^{+59}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.2e+107) (not (<= z 1.45e+59)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e+107) || !(z <= 1.45e+59)) {
		tmp = x * (1.0 - (y / z));
	} 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 ((z <= (-4.2d+107)) .or. (.not. (z <= 1.45d+59))) then
        tmp = x * (1.0d0 - (y / z))
    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 ((z <= -4.2e+107) || !(z <= 1.45e+59)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.2e+107) or not (z <= 1.45e+59):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.2e+107) || !(z <= 1.45e+59))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.2e+107) || ~((z <= 1.45e+59)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.2e+107], N[Not[LessEqual[z, 1.45e+59]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1999999999999999e107 or 1.44999999999999995e59 < z

   1. Initial program 72.2%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in t around 0 60.0%

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

      1. mul-1-neg 60.0%

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

      2. associate-/l* 85.5%

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

      3. distribute-rgt-neg-in 85.5%

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

      4. distribute-frac-neg 85.5%

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

      5. sub-neg 85.5%

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

      6. distribute-neg-in 85.5%

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

      7. remove-double-neg 85.5%

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

      8. +-commutative 85.5%

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

      9. sub-neg 85.5%

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

      10. div-sub 85.5%

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

      11. *-inverses 85.5%

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

   7. Simplified 85.5%

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

   if -4.1999999999999999e107 < z < 1.44999999999999995e59

   1. Initial program 92.3%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.9%

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

      1. associate-/l* 71.4%

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

   7. Simplified 71.4%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+107} \lor \neg \left(z \leq 1.45 \cdot 10^{+59}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-88} \lor \neg \left(z \leq 3.05 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.55e-88) (not (<= z 3.05e-37)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55e-88) || !(z <= 3.05e-37)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.55d-88)) .or. (.not. (z <= 3.05d-37))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.55e-88) || !(z <= 3.05e-37)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.55e-88) or not (z <= 3.05e-37):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.55e-88) || !(z <= 3.05e-37))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.55e-88) || ~((z <= 3.05e-37)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.55e-88], N[Not[LessEqual[z, 3.05e-37]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5499999999999999e-88 or 3.0500000000000002e-37 < z

   1. Initial program 77.8%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in t around 0 54.9%

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

      1. mul-1-neg 54.9%

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

      2. associate-/l* 73.0%

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

      3. distribute-rgt-neg-in 73.0%

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

      4. distribute-frac-neg 73.0%

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

      5. sub-neg 73.0%

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

      6. distribute-neg-in 73.0%

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

      7. remove-double-neg 73.0%

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

      8. +-commutative 73.0%

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

      9. sub-neg 73.0%

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

      10. div-sub 73.0%

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

      11. *-inverses 73.0%

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

   7. Simplified 73.0%

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

   if -1.5499999999999999e-88 < z < 3.0500000000000002e-37

   1. Initial program 93.4%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 60.8%

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

      1. associate-/l* 64.4%

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

   7. Simplified 64.4%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-88} \lor \neg \left(z \leq 3.05 \cdot 10^{-37}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.6e+107)
   (* x (- 1.0 (/ y z)))
   (if (<= z 4.05e+96) (* x (/ y (- t z))) (* x (/ z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.6e+107) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 4.05e+96) {
		tmp = x * (y / (t - z));
	} 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 (z <= (-3.6d+107)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= 4.05d+96) then
        tmp = x * (y / (t - z))
    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 (z <= -3.6e+107) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 4.05e+96) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.6e+107:
		tmp = x * (1.0 - (y / z))
	elif z <= 4.05e+96:
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.6e+107)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= 4.05e+96)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	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 (z <= -3.6e+107)
		tmp = x * (1.0 - (y / z));
	elseif (z <= 4.05e+96)
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.6e+107], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.05e+96], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5999999999999998e107

   1. Initial program 65.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. associate-/l* 94.0%

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

      3. distribute-rgt-neg-in 94.0%

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

      4. distribute-frac-neg 94.0%

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

      5. sub-neg 94.0%

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

      6. distribute-neg-in 94.0%

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

      7. remove-double-neg 94.0%

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

      8. +-commutative 94.0%

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

      9. sub-neg 94.0%

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

      10. div-sub 94.0%

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

      11. *-inverses 94.0%

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

   7. Simplified 94.0%

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

   if -3.5999999999999998e107 < z < 4.0500000000000001e96

   1. Initial program 92.8%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.3%

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

      1. associate-/l* 70.8%

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

   7. Simplified 70.8%

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

   if 4.0500000000000001e96 < z

   1. Initial program 72.0%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in y around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. distribute-neg-frac2 63.8%

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

      3. sub-neg 63.8%

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

      4. distribute-neg-in 63.8%

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

      5. remove-double-neg 63.8%

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

      6. +-commutative 63.8%

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

      7. sub-neg 63.8%

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

      8. associate-/l* 88.4%

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

   7. Simplified 88.4%

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

Alternative 9: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+107}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.7e+107) x (if (<= z 2.65e+66) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.7e+107) {
		tmp = x;
	} else if (z <= 2.65e+66) {
		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 <= (-4.7d+107)) then
        tmp = x
    else if (z <= 2.65d+66) 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 <= -4.7e+107) {
		tmp = x;
	} else if (z <= 2.65e+66) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.7e+107:
		tmp = x
	elif z <= 2.65e+66:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.7e+107)
		tmp = x;
	elseif (z <= 2.65e+66)
		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 <= -4.7e+107)
		tmp = x;
	elseif (z <= 2.65e+66)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.7e+107], x, If[LessEqual[z, 2.65e+66], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7000000000000001e107 or 2.6499999999999998e66 < z

   1. Initial program 71.4%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in z around inf 71.2%

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

   if -4.7000000000000001e107 < z < 2.6499999999999998e66

   1. Initial program 92.5%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 52.9%

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

      1. associate-/l* 56.2%

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

   7. Simplified 56.2%

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

Alternative 10: 34.9% 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 84.1%

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

   1. associate-/l* 97.2%

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

3. Simplified 97.2%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 35.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 97.1% 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 2024181 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (/ x (/ (- t z) (- y z))))

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