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

Percentage Accurate: 84.2% → 96.9%

Time: 9.0s

Alternatives: 13

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: 84.2% 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: 96.9% 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 85.9%

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

   1. associate-/l* 96.0%

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

3. Simplified 96.0%

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

4. Final simplification 96.0%

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

Alternative 2: 75.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.18:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-11} \lor \neg \left(z \leq 135\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z y) z))))
   (if (<= z -1.55e+44)
     t_1
     (if (<= z -0.18)
       (/ x (/ t (- y z)))
       (if (or (<= z -1.02e-11) (not (<= z 135.0)))
         t_1
         (* x (/ y (- t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -1.55e+44) {
		tmp = t_1;
	} else if (z <= -0.18) {
		tmp = x / (t / (y - z));
	} else if ((z <= -1.02e-11) || !(z <= 135.0)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - y) / z)
    if (z <= (-1.55d+44)) then
        tmp = t_1
    else if (z <= (-0.18d0)) then
        tmp = x / (t / (y - z))
    else if ((z <= (-1.02d-11)) .or. (.not. (z <= 135.0d0))) then
        tmp = t_1
    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 t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -1.55e+44) {
		tmp = t_1;
	} else if (z <= -0.18) {
		tmp = x / (t / (y - z));
	} else if ((z <= -1.02e-11) || !(z <= 135.0)) {
		tmp = t_1;
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - y) / z)
	tmp = 0
	if z <= -1.55e+44:
		tmp = t_1
	elif z <= -0.18:
		tmp = x / (t / (y - z))
	elif (z <= -1.02e-11) or not (z <= 135.0):
		tmp = t_1
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -1.55e+44)
		tmp = t_1;
	elseif (z <= -0.18)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif ((z <= -1.02e-11) || !(z <= 135.0))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - y) / z);
	tmp = 0.0;
	if (z <= -1.55e+44)
		tmp = t_1;
	elseif (z <= -0.18)
		tmp = x / (t / (y - z));
	elseif ((z <= -1.02e-11) || ~((z <= 135.0)))
		tmp = t_1;
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+44], t$95$1, If[LessEqual[z, -0.18], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.02e-11], N[Not[LessEqual[z, 135.0]], $MachinePrecision]], t$95$1, N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999998e44 or -0.17999999999999999 < z < -1.01999999999999994e-11 or 135 < z

   1. Initial program 78.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 67.2%

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

      1. mul-1-neg 67.2%

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

      2. associate-/l* 60.5%

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

      3. distribute-neg-frac 60.5%

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

      4. neg-sub0 60.5%

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

      5. associate--r- 60.5%

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

      6. neg-sub0 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in x around 0 67.2%

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

      1. associate-/l* 60.5%

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

      2. associate-/r/ 86.6%

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

   9. Simplified 86.6%

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

   if -1.54999999999999998e44 < z < -0.17999999999999999

   1. Initial program 84.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 99.7%

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

   if -1.01999999999999994e-11 < z < 135

   1. Initial program 91.7%

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

      1. associate-*r/ 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around inf 77.7%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -0.18:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-11} \lor \neg \left(z \leq 135\right):\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 3: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.23:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-12} \lor \neg \left(z \leq 0.7\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z y) z))))
   (if (<= z -1.55e+44)
     t_1
     (if (<= z -0.23)
       (/ x (/ t (- y z)))
       (if (or (<= z -4.1e-12) (not (<= z 0.7))) t_1 (/ x (/ (- t z) y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -1.55e+44) {
		tmp = t_1;
	} else if (z <= -0.23) {
		tmp = x / (t / (y - z));
	} else if ((z <= -4.1e-12) || !(z <= 0.7)) {
		tmp = t_1;
	} else {
		tmp = x / ((t - z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((z - y) / z)
    if (z <= (-1.55d+44)) then
        tmp = t_1
    else if (z <= (-0.23d0)) then
        tmp = x / (t / (y - z))
    else if ((z <= (-4.1d-12)) .or. (.not. (z <= 0.7d0))) then
        tmp = t_1
    else
        tmp = x / ((t - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -1.55e+44) {
		tmp = t_1;
	} else if (z <= -0.23) {
		tmp = x / (t / (y - z));
	} else if ((z <= -4.1e-12) || !(z <= 0.7)) {
		tmp = t_1;
	} else {
		tmp = x / ((t - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - y) / z)
	tmp = 0
	if z <= -1.55e+44:
		tmp = t_1
	elif z <= -0.23:
		tmp = x / (t / (y - z))
	elif (z <= -4.1e-12) or not (z <= 0.7):
		tmp = t_1
	else:
		tmp = x / ((t - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -1.55e+44)
		tmp = t_1;
	elseif (z <= -0.23)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif ((z <= -4.1e-12) || !(z <= 0.7))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(Float64(t - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - y) / z);
	tmp = 0.0;
	if (z <= -1.55e+44)
		tmp = t_1;
	elseif (z <= -0.23)
		tmp = x / (t / (y - z));
	elseif ((z <= -4.1e-12) || ~((z <= 0.7)))
		tmp = t_1;
	else
		tmp = x / ((t - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+44], t$95$1, If[LessEqual[z, -0.23], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.1e-12], N[Not[LessEqual[z, 0.7]], $MachinePrecision]], t$95$1, N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999998e44 or -0.23000000000000001 < z < -4.0999999999999999e-12 or 0.69999999999999996 < z

   1. Initial program 78.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 67.2%

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

      1. mul-1-neg 67.2%

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

      2. associate-/l* 60.5%

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

      3. distribute-neg-frac 60.5%

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

      4. neg-sub0 60.5%

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

      5. associate--r- 60.5%

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

      6. neg-sub0 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in x around 0 67.2%

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

      1. associate-/l* 60.5%

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

      2. associate-/r/ 86.6%

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

   9. Simplified 86.6%

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

   if -1.54999999999999998e44 < z < -0.23000000000000001

   1. Initial program 84.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 99.7%

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

   if -4.0999999999999999e-12 < z < 0.69999999999999996

   1. Initial program 91.7%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   4. Taylor expanded in y around inf 79.1%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -0.23:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-12} \lor \neg \left(z \leq 0.7\right):\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \]

Alternative 4: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{t - z}{x}}\\ \mathbf{if}\;z \leq -3800000:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-62}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 400:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (/ (- t z) x))))
   (if (<= z -3800000.0)
     (/ x (/ (- z t) z))
     (if (<= z 5e-216)
       t_1
       (if (<= z 3.3e-62)
         (/ (- y z) (/ t x))
         (if (<= z 400.0) t_1 (* x (/ (- z y) z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / ((t - z) / x);
	double tmp;
	if (z <= -3800000.0) {
		tmp = x / ((z - t) / z);
	} else if (z <= 5e-216) {
		tmp = t_1;
	} else if (z <= 3.3e-62) {
		tmp = (y - z) / (t / x);
	} else if (z <= 400.0) {
		tmp = t_1;
	} else {
		tmp = x * ((z - y) / 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) :: t_1
    real(8) :: tmp
    t_1 = y / ((t - z) / x)
    if (z <= (-3800000.0d0)) then
        tmp = x / ((z - t) / z)
    else if (z <= 5d-216) then
        tmp = t_1
    else if (z <= 3.3d-62) then
        tmp = (y - z) / (t / x)
    else if (z <= 400.0d0) then
        tmp = t_1
    else
        tmp = x * ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / ((t - z) / x);
	double tmp;
	if (z <= -3800000.0) {
		tmp = x / ((z - t) / z);
	} else if (z <= 5e-216) {
		tmp = t_1;
	} else if (z <= 3.3e-62) {
		tmp = (y - z) / (t / x);
	} else if (z <= 400.0) {
		tmp = t_1;
	} else {
		tmp = x * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / ((t - z) / x)
	tmp = 0
	if z <= -3800000.0:
		tmp = x / ((z - t) / z)
	elif z <= 5e-216:
		tmp = t_1
	elif z <= 3.3e-62:
		tmp = (y - z) / (t / x)
	elif z <= 400.0:
		tmp = t_1
	else:
		tmp = x * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(Float64(t - z) / x))
	tmp = 0.0
	if (z <= -3800000.0)
		tmp = Float64(x / Float64(Float64(z - t) / z));
	elseif (z <= 5e-216)
		tmp = t_1;
	elseif (z <= 3.3e-62)
		tmp = Float64(Float64(y - z) / Float64(t / x));
	elseif (z <= 400.0)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / ((t - z) / x);
	tmp = 0.0;
	if (z <= -3800000.0)
		tmp = x / ((z - t) / z);
	elseif (z <= 5e-216)
		tmp = t_1;
	elseif (z <= 3.3e-62)
		tmp = (y - z) / (t / x);
	elseif (z <= 400.0)
		tmp = t_1;
	else
		tmp = x * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3800000.0], N[(x / N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-216], t$95$1, If[LessEqual[z, 3.3e-62], N[(N[(y - z), $MachinePrecision] / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 400.0], t$95$1, N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.8e6

   1. Initial program 80.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. div-inv 99.9%

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

      2. add-cube-cbrt 98.1%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \frac{1}{\frac{t - z}{y - z}} \]

      3. clear-num 98.1%

         \[\leadsto \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right) \cdot \color{blue}{\frac{y - z}{t - z}} \]

      4. associate-*l* 98.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{y - z}{t - z}\right)} \]

      5. pow2 98.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}} \cdot \left(\sqrt[3]{x} \cdot \frac{y - z}{t - z}\right) \]

   5. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2} \cdot \left(\sqrt[3]{x} \cdot \frac{y - z}{t - z}\right)} \]

   6. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 71.7%

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

      2. mul-1-neg 71.7%

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

      3. distribute-lft-neg-out 71.7%

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

      4. *-commutative 71.7%

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

      5. associate-/l* 85.9%

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

   8. Simplified 85.9%

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

      1. frac-2neg 85.9%

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

      2. div-inv 85.7%

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

      3. sub-neg 85.7%

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

      4. distribute-neg-in 85.7%

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

      5. remove-double-neg 85.7%

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

      6. remove-double-neg 85.7%

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

   10. Applied egg-rr 85.7%

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

       1. associate-*r/ 85.9%

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

       2. *-rgt-identity 85.9%

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

       3. +-commutative 85.9%

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

       4. unsub-neg 85.9%

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

   12. Simplified 85.9%

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

   if -3.8e6 < z < 5.00000000000000021e-216 or 3.30000000000000004e-62 < z < 400

   1. Initial program 92.6%

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

      1. associate-*r/ 90.4%

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

   3. Simplified 90.4%

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

      1. associate-*r/ 92.6%

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

      2. associate-/l* 92.3%

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

      3. div-inv 92.2%

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

      4. associate-/r* 95.0%

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

   5. Applied egg-rr 95.0%

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

   6. Taylor expanded in y around inf 81.7%

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

      1. associate-/l* 84.7%

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

   8. Simplified 84.7%

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

   if 5.00000000000000021e-216 < z < 3.30000000000000004e-62

   1. Initial program 90.4%

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

      1. associate-*r/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in t around inf 75.3%

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

      1. associate-/l* 82.5%

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

   6. Simplified 82.5%

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

   if 400 < z

   1. Initial program 76.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.7%

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

      1. mul-1-neg 66.7%

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

      2. associate-/l* 59.3%

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

      3. distribute-neg-frac 59.3%

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

      4. neg-sub0 59.3%

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

      5. associate--r- 59.3%

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

      6. neg-sub0 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in x around 0 66.7%

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

      1. associate-/l* 59.3%

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

      2. associate-/r/ 86.9%

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

   9. Simplified 86.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3800000:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-216}:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-62}:\\ \;\;\;\;\frac{y - z}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 400:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 5: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{elif}\;z \leq 1.3:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.85e+83)
   x
   (if (<= z -4.6e-105) (* y (/ (- x) z)) (if (<= z 1.3) (* y (/ x t)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85e+83) {
		tmp = x;
	} else if (z <= -4.6e-105) {
		tmp = y * (-x / z);
	} else if (z <= 1.3) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.85d+83)) then
        tmp = x
    else if (z <= (-4.6d-105)) then
        tmp = y * (-x / z)
    else if (z <= 1.3d0) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85e+83) {
		tmp = x;
	} else if (z <= -4.6e-105) {
		tmp = y * (-x / z);
	} else if (z <= 1.3) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.85e+83:
		tmp = x
	elif z <= -4.6e-105:
		tmp = y * (-x / z)
	elif z <= 1.3:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.85e+83)
		tmp = x;
	elseif (z <= -4.6e-105)
		tmp = Float64(y * Float64(Float64(-x) / z));
	elseif (z <= 1.3)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.85e+83)
		tmp = x;
	elseif (z <= -4.6e-105)
		tmp = y * (-x / z);
	elseif (z <= 1.3)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.85e+83], x, If[LessEqual[z, -4.6e-105], N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8500000000000001e83 or 1.30000000000000004 < z

   1. Initial program 78.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 71.0%

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

   if -1.8500000000000001e83 < z < -4.6000000000000002e-105

   1. Initial program 89.6%

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

      1. associate-*r/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in y around inf 62.6%

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

   5. Taylor expanded in t around 0 42.0%

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

      1. associate-*r/ 42.0%

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

      2. mul-1-neg 42.0%

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

      3. *-commutative 42.0%

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

      4. distribute-rgt-neg-in 42.0%

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

   7. Simplified 42.0%

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

   8. Taylor expanded in x around 0 42.0%

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

      1. mul-1-neg 42.0%

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

      2. associate-*r/ 46.4%

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

      3. *-commutative 46.4%

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

      4. distribute-rgt-neg-in 46.4%

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

   10. Simplified 46.4%

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

   if -4.6000000000000002e-105 < z < 1.30000000000000004

   1. Initial program 91.8%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in z around 0 71.8%

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

      1. associate-/r/ 73.5%

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

   6. Applied egg-rr 73.5%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-105}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{elif}\;z \leq 1.3:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+44} \lor \neg \left(z \leq 470\right):\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e+44) (not (<= z 470.0)))
   (* x (/ (- z y) z))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e+44) || !(z <= 470.0)) {
		tmp = x * ((z - 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 <= (-1.65d+44)) .or. (.not. (z <= 470.0d0))) then
        tmp = x * ((z - 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 <= -1.65e+44) || !(z <= 470.0)) {
		tmp = x * ((z - y) / z);
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.65e+44) or not (z <= 470.0):
		tmp = x * ((z - y) / z)
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e+44) || !(z <= 470.0))
		tmp = Float64(x * Float64(Float64(z - 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 <= -1.65e+44) || ~((z <= 470.0)))
		tmp = x * ((z - y) / z);
	else
		tmp = x * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e+44], N[Not[LessEqual[z, 470.0]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65000000000000007e44 or 470 < z

   1. Initial program 78.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.0%

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

      1. mul-1-neg 66.0%

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

      2. associate-/l* 59.1%

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

      3. distribute-neg-frac 59.1%

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

      4. neg-sub0 59.1%

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

      5. associate--r- 59.1%

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

      6. neg-sub0 59.1%

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

   6. Simplified 59.1%

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

   7. Taylor expanded in x around 0 66.0%

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

      1. associate-/l* 59.1%

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

      2. associate-/r/ 86.1%

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

   9. Simplified 86.1%

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

   if -1.65000000000000007e44 < z < 470

   1. Initial program 91.6%

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

      1. associate-*r/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in y around inf 76.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+44} \lor \neg \left(z \leq 470\right):\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 7: 69.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4800:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.5e+81) x (if (<= z 4800.0) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e+81) {
		tmp = x;
	} else if (z <= 4800.0) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.5d+81)) then
        tmp = x
    else if (z <= 4800.0d0) then
        tmp = x * (y / (t - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.5e+81) {
		tmp = x;
	} else if (z <= 4800.0) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.5e+81:
		tmp = x
	elif z <= 4800.0:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.5e+81)
		tmp = x;
	elseif (z <= 4800.0)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.5e+81)
		tmp = x;
	elseif (z <= 4800.0)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.5e+81], x, If[LessEqual[z, 4800.0], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999996e81 or 4800 < z

   1. Initial program 78.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 71.0%

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

   if -6.4999999999999996e81 < z < 4800

   1. Initial program 91.2%

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

      1. associate-*r/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in y around inf 75.2%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4800:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2300000000:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2300000000.0)
   (/ x (/ (- z t) z))
   (if (<= z 1.05) (/ x (/ (- t z) y)) (* x (/ (- z y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2300000000.0) {
		tmp = x / ((z - t) / z);
	} else if (z <= 1.05) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x * ((z - y) / 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 <= (-2300000000.0d0)) then
        tmp = x / ((z - t) / z)
    else if (z <= 1.05d0) then
        tmp = x / ((t - z) / y)
    else
        tmp = x * ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2300000000.0) {
		tmp = x / ((z - t) / z);
	} else if (z <= 1.05) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2300000000.0:
		tmp = x / ((z - t) / z)
	elif z <= 1.05:
		tmp = x / ((t - z) / y)
	else:
		tmp = x * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2300000000.0)
		tmp = Float64(x / Float64(Float64(z - t) / z));
	elseif (z <= 1.05)
		tmp = Float64(x / Float64(Float64(t - z) / y));
	else
		tmp = Float64(x * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2300000000.0)
		tmp = x / ((z - t) / z);
	elseif (z <= 1.05)
		tmp = x / ((t - z) / y);
	else
		tmp = x * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2300000000.0], N[(x / N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e9

   1. Initial program 80.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. div-inv 99.9%

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

      2. add-cube-cbrt 98.1%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \frac{1}{\frac{t - z}{y - z}} \]

      3. clear-num 98.1%

         \[\leadsto \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right) \cdot \color{blue}{\frac{y - z}{t - z}} \]

      4. associate-*l* 98.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{y - z}{t - z}\right)} \]

      5. pow2 98.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}} \cdot \left(\sqrt[3]{x} \cdot \frac{y - z}{t - z}\right) \]

   5. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2} \cdot \left(\sqrt[3]{x} \cdot \frac{y - z}{t - z}\right)} \]

   6. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 71.7%

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

      2. mul-1-neg 71.7%

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

      3. distribute-lft-neg-out 71.7%

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

      4. *-commutative 71.7%

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

      5. associate-/l* 85.9%

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

   8. Simplified 85.9%

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

      1. frac-2neg 85.9%

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

      2. div-inv 85.7%

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

      3. sub-neg 85.7%

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

      4. distribute-neg-in 85.7%

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

      5. remove-double-neg 85.7%

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

      6. remove-double-neg 85.7%

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

   10. Applied egg-rr 85.7%

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

       1. associate-*r/ 85.9%

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

       2. *-rgt-identity 85.9%

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

       3. +-commutative 85.9%

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

       4. unsub-neg 85.9%

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

   12. Simplified 85.9%

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

   if -2.3e9 < z < 1.05000000000000004

   1. Initial program 92.0%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around inf 78.5%

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

   if 1.05000000000000004 < z

   1. Initial program 76.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.7%

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

      1. mul-1-neg 66.7%

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

      2. associate-/l* 59.3%

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

      3. distribute-neg-frac 59.3%

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

      4. neg-sub0 59.3%

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

      5. associate--r- 59.3%

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

      6. neg-sub0 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in x around 0 66.7%

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

      1. associate-/l* 59.3%

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

      2. associate-/r/ 86.9%

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

   9. Simplified 86.9%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2300000000:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 9: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \mathbf{elif}\;z \leq 25:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.85)
   (/ x (/ (- z t) z))
   (if (<= z 25.0) (/ y (/ (- t z) x)) (* x (/ (- z y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85) {
		tmp = x / ((z - t) / z);
	} else if (z <= 25.0) {
		tmp = y / ((t - z) / x);
	} else {
		tmp = x * ((z - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.85d0)) then
        tmp = x / ((z - t) / z)
    else if (z <= 25.0d0) then
        tmp = y / ((t - z) / x)
    else
        tmp = x * ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.85) {
		tmp = x / ((z - t) / z);
	} else if (z <= 25.0) {
		tmp = y / ((t - z) / x);
	} else {
		tmp = x * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.85:
		tmp = x / ((z - t) / z)
	elif z <= 25.0:
		tmp = y / ((t - z) / x)
	else:
		tmp = x * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.85)
		tmp = Float64(x / Float64(Float64(z - t) / z));
	elseif (z <= 25.0)
		tmp = Float64(y / Float64(Float64(t - z) / x));
	else
		tmp = Float64(x * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.85)
		tmp = x / ((z - t) / z);
	elseif (z <= 25.0)
		tmp = y / ((t - z) / x);
	else
		tmp = x * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.85], N[(x / N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 25.0], N[(y / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8500000000000001

   1. Initial program 80.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. div-inv 99.9%

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

      2. add-cube-cbrt 98.1%

         \[\leadsto \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \frac{1}{\frac{t - z}{y - z}} \]

      3. clear-num 98.1%

         \[\leadsto \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right) \cdot \color{blue}{\frac{y - z}{t - z}} \]

      4. associate-*l* 98.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{y - z}{t - z}\right)} \]

      5. pow2 98.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2}} \cdot \left(\sqrt[3]{x} \cdot \frac{y - z}{t - z}\right) \]

   5. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x}\right)}^{2} \cdot \left(\sqrt[3]{x} \cdot \frac{y - z}{t - z}\right)} \]

   6. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 71.7%

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

      2. mul-1-neg 71.7%

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

      3. distribute-lft-neg-out 71.7%

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

      4. *-commutative 71.7%

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

      5. associate-/l* 85.9%

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

   8. Simplified 85.9%

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

      1. frac-2neg 85.9%

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

      2. div-inv 85.7%

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

      3. sub-neg 85.7%

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

      4. distribute-neg-in 85.7%

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

      5. remove-double-neg 85.7%

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

      6. remove-double-neg 85.7%

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

   10. Applied egg-rr 85.7%

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

       1. associate-*r/ 85.9%

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

       2. *-rgt-identity 85.9%

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

       3. +-commutative 85.9%

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

       4. unsub-neg 85.9%

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

   12. Simplified 85.9%

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

   if -1.8500000000000001 < z < 25

   1. Initial program 92.0%

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

      1. associate-*r/ 92.1%

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

   3. Simplified 92.1%

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

      1. associate-*r/ 92.0%

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

      2. associate-/l* 93.0%

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

      3. div-inv 92.9%

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

      4. associate-/r* 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in y around inf 78.1%

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

      1. associate-/l* 80.9%

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

   8. Simplified 80.9%

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

   if 25 < z

   1. Initial program 76.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 66.7%

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

      1. mul-1-neg 66.7%

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

      2. associate-/l* 59.3%

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

      3. distribute-neg-frac 59.3%

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

      4. neg-sub0 59.3%

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

      5. associate--r- 59.3%

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

      6. neg-sub0 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in x around 0 66.7%

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

      1. associate-/l* 59.3%

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

      2. associate-/r/ 86.9%

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

   9. Simplified 86.9%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \mathbf{elif}\;z \leq 25:\\ \;\;\;\;\frac{y}{\frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 10: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4200:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.55e+44) x (if (<= z 4200.0) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e+44) {
		tmp = x;
	} else if (z <= 4200.0) {
		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 <= (-1.55d+44)) then
        tmp = x
    else if (z <= 4200.0d0) 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 <= -1.55e+44) {
		tmp = x;
	} else if (z <= 4200.0) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.55e+44:
		tmp = x
	elif z <= 4200.0:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.55e+44)
		tmp = x;
	elseif (z <= 4200.0)
		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 <= -1.55e+44)
		tmp = x;
	elseif (z <= 4200.0)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.55e+44], x, If[LessEqual[z, 4200.0], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999998e44 or 4200 < z

   1. Initial program 78.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 69.4%

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

   if -1.54999999999999998e44 < z < 4200

   1. Initial program 91.6%

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

      1. associate-*r/ 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around 0 63.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4200:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 60.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 290:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.55e+44) x (if (<= z 290.0) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e+44) {
		tmp = x;
	} else if (z <= 290.0) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.55d+44)) then
        tmp = x
    else if (z <= 290.0d0) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.55e+44) {
		tmp = x;
	} else if (z <= 290.0) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.55e+44:
		tmp = x
	elif z <= 290.0:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.55e+44)
		tmp = x;
	elseif (z <= 290.0)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.55e+44)
		tmp = x;
	elseif (z <= 290.0)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.55e+44], x, If[LessEqual[z, 290.0], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.54999999999999998e44 or 290 < z

   1. Initial program 78.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 69.4%

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

   if -1.54999999999999998e44 < z < 290

   1. Initial program 91.6%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in z around 0 64.1%

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

      1. associate-/r/ 64.8%

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

   6. Applied egg-rr 64.8%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 290:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 96.9% 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 85.9%

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

   1. associate-*r/ 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. Final simplification 95.5%

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

Alternative 13: 35.1% 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 85.9%

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

   1. associate-*r/ 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. Taylor expanded in z around inf 35.7%

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

5. Final simplification 35.7%

   \[\leadsto x \]

Developer target: 96.9% 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 2023185 
(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)))