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

Percentage Accurate: 84.7% → 96.9%

Time: 7.6s

Alternatives: 9

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: 84.7% 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

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

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 89.4%

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

   1. associate-*r/ 97.7%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 2: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 75000000:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.25e+50)
     t_1
     (if (<= z -1.05e-7)
       (* x (/ (- y z) t))
       (if (<= z -4.4e-35)
         t_1
         (if (<= z 75000000.0)
           (* x (/ y (- t z)))
           (/ (- x) (+ (/ t z) -1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.25e+50) {
		tmp = t_1;
	} else if (z <= -1.05e-7) {
		tmp = x * ((y - z) / t);
	} else if (z <= -4.4e-35) {
		tmp = t_1;
	} else if (z <= 75000000.0) {
		tmp = x * (y / (t - z));
	} else {
		tmp = -x / ((t / z) + -1.0);
	}
	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 * (1.0d0 - (y / z))
    if (z <= (-1.25d+50)) then
        tmp = t_1
    else if (z <= (-1.05d-7)) then
        tmp = x * ((y - z) / t)
    else if (z <= (-4.4d-35)) then
        tmp = t_1
    else if (z <= 75000000.0d0) then
        tmp = x * (y / (t - z))
    else
        tmp = -x / ((t / z) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.25e+50) {
		tmp = t_1;
	} else if (z <= -1.05e-7) {
		tmp = x * ((y - z) / t);
	} else if (z <= -4.4e-35) {
		tmp = t_1;
	} else if (z <= 75000000.0) {
		tmp = x * (y / (t - z));
	} else {
		tmp = -x / ((t / z) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.25e+50:
		tmp = t_1
	elif z <= -1.05e-7:
		tmp = x * ((y - z) / t)
	elif z <= -4.4e-35:
		tmp = t_1
	elif z <= 75000000.0:
		tmp = x * (y / (t - z))
	else:
		tmp = -x / ((t / z) + -1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.25e+50)
		tmp = t_1;
	elseif (z <= -1.05e-7)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	elseif (z <= -4.4e-35)
		tmp = t_1;
	elseif (z <= 75000000.0)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(Float64(-x) / Float64(Float64(t / z) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.25e+50)
		tmp = t_1;
	elseif (z <= -1.05e-7)
		tmp = x * ((y - z) / t);
	elseif (z <= -4.4e-35)
		tmp = t_1;
	elseif (z <= 75000000.0)
		tmp = x * (y / (t - z));
	else
		tmp = -x / ((t / z) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+50], t$95$1, If[LessEqual[z, -1.05e-7], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-35], t$95$1, If[LessEqual[z, 75000000.0], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(N[(t / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25e50 or -1.05e-7 < z < -4.39999999999999987e-35

   1. Initial program 84.9%

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

      1. associate-*r/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in t around 0 83.8%

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

      1. mul-1-neg 83.8%

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

      2. div-sub 83.8%

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

      3. sub-neg 83.8%

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

      4. *-inverses 83.8%

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

      5. metadata-eval 83.8%

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

   6. Simplified 83.8%

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

   7. Taylor expanded in x around 0 83.8%

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

   if -1.25e50 < z < -1.05e-7

   1. Initial program 85.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 inf 76.9%

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

   if -4.39999999999999987e-35 < z < 7.5e7

   1. Initial program 95.6%

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

      1. associate-*r/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around inf 86.1%

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

   if 7.5e7 < z

   1. Initial program 82.7%

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

      1. associate-*r/ 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. Taylor expanded in y around 0 70.9%

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

      1. mul-1-neg 70.9%

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

      2. associate-/l* 86.4%

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

      3. distribute-neg-frac 86.4%

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

      4. div-sub 86.4%

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

      5. sub-neg 86.4%

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

      6. *-inverses 86.4%

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

      7. metadata-eval 86.4%

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

   6. Simplified 86.4%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 75000000:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{t}{z} + -1}\\ \end{array} \]

Alternative 3: 68.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.017:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-78} \lor \neg \left(z \leq 2.05 \cdot 10^{-83}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.7e+49)
     t_1
     (if (<= z -0.017)
       (* x (/ y t))
       (if (or (<= z -2.1e-78) (not (<= z 2.05e-83))) t_1 (/ x (/ t y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.7e+49) {
		tmp = t_1;
	} else if (z <= -0.017) {
		tmp = x * (y / t);
	} else if ((z <= -2.1e-78) || !(z <= 2.05e-83)) {
		tmp = t_1;
	} else {
		tmp = x / (t / 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 * (1.0d0 - (y / z))
    if (z <= (-1.7d+49)) then
        tmp = t_1
    else if (z <= (-0.017d0)) then
        tmp = x * (y / t)
    else if ((z <= (-2.1d-78)) .or. (.not. (z <= 2.05d-83))) then
        tmp = t_1
    else
        tmp = x / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.7e+49) {
		tmp = t_1;
	} else if (z <= -0.017) {
		tmp = x * (y / t);
	} else if ((z <= -2.1e-78) || !(z <= 2.05e-83)) {
		tmp = t_1;
	} else {
		tmp = x / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.7e+49:
		tmp = t_1
	elif z <= -0.017:
		tmp = x * (y / t)
	elif (z <= -2.1e-78) or not (z <= 2.05e-83):
		tmp = t_1
	else:
		tmp = x / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.7e+49)
		tmp = t_1;
	elseif (z <= -0.017)
		tmp = Float64(x * Float64(y / t));
	elseif ((z <= -2.1e-78) || !(z <= 2.05e-83))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.7e+49)
		tmp = t_1;
	elseif (z <= -0.017)
		tmp = x * (y / t);
	elseif ((z <= -2.1e-78) || ~((z <= 2.05e-83)))
		tmp = t_1;
	else
		tmp = x / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+49], t$95$1, If[LessEqual[z, -0.017], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.1e-78], N[Not[LessEqual[z, 2.05e-83]], $MachinePrecision]], t$95$1, N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e49 or -0.017000000000000001 < z < -2.1000000000000001e-78 or 2.05e-83 < z

   1. Initial program 85.6%

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

      1. associate-*r/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in t around 0 79.6%

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

      1. mul-1-neg 79.6%

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

      2. div-sub 79.6%

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

      3. sub-neg 79.6%

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

      4. *-inverses 79.6%

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

      5. metadata-eval 79.6%

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

   6. Simplified 79.6%

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

   7. Taylor expanded in x around 0 79.6%

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

   if -1.7e49 < z < -0.017000000000000001

   1. Initial program 85.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 0 59.6%

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

   if -2.1000000000000001e-78 < z < 2.05e-83

   1. Initial program 95.7%

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

      1. associate-*r/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in z around 0 72.9%

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

      1. associate-/l* 73.2%

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

   6. Simplified 73.2%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -0.017:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-78} \lor \neg \left(z \leq 2.05 \cdot 10^{-83}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \]

Alternative 4: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.3:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-35} \lor \neg \left(z \leq 7000000000000\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -4.3e+54)
     t_1
     (if (<= z -2.3)
       (* x (/ (- y z) t))
       (if (or (<= z -2.6e-35) (not (<= z 7000000000000.0)))
         t_1
         (* x (/ y (- t z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -4.3e+54) {
		tmp = t_1;
	} else if (z <= -2.3) {
		tmp = x * ((y - z) / t);
	} else if ((z <= -2.6e-35) || !(z <= 7000000000000.0)) {
		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 * (1.0d0 - (y / z))
    if (z <= (-4.3d+54)) then
        tmp = t_1
    else if (z <= (-2.3d0)) then
        tmp = x * ((y - z) / t)
    else if ((z <= (-2.6d-35)) .or. (.not. (z <= 7000000000000.0d0))) 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 * (1.0 - (y / z));
	double tmp;
	if (z <= -4.3e+54) {
		tmp = t_1;
	} else if (z <= -2.3) {
		tmp = x * ((y - z) / t);
	} else if ((z <= -2.6e-35) || !(z <= 7000000000000.0)) {
		tmp = t_1;
	} else {
		tmp = x * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -4.3e+54:
		tmp = t_1
	elif z <= -2.3:
		tmp = x * ((y - z) / t)
	elif (z <= -2.6e-35) or not (z <= 7000000000000.0):
		tmp = t_1
	else:
		tmp = x * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -4.3e+54)
		tmp = t_1;
	elseif (z <= -2.3)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	elseif ((z <= -2.6e-35) || !(z <= 7000000000000.0))
		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 * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -4.3e+54)
		tmp = t_1;
	elseif (z <= -2.3)
		tmp = x * ((y - z) / t);
	elseif ((z <= -2.6e-35) || ~((z <= 7000000000000.0)))
		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[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+54], t$95$1, If[LessEqual[z, -2.3], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.6e-35], N[Not[LessEqual[z, 7000000000000.0]], $MachinePrecision]], t$95$1, N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.29999999999999976e54 or -2.2999999999999998 < z < -2.60000000000000005e-35 or 7e12 < z

   1. Initial program 83.9%

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

      1. associate-*r/ 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in t around 0 83.0%

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

      1. mul-1-neg 83.0%

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

      2. div-sub 83.0%

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

      3. sub-neg 83.0%

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

      4. *-inverses 83.0%

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

      5. metadata-eval 83.0%

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

   6. Simplified 83.0%

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

   7. Taylor expanded in x around 0 83.0%

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

   if -4.29999999999999976e54 < z < -2.2999999999999998

   1. Initial program 85.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 inf 76.9%

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

   if -2.60000000000000005e-35 < z < 7e12

   1. Initial program 95.7%

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

      1. associate-*r/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around inf 86.3%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.3:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-35} \lor \neg \left(z \leq 7000000000000\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 5: 59.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 60000000000000:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.3e+49)
   x
   (if (<= z 2.15e-82)
     (* x (/ y t))
     (if (<= z 60000000000000.0) (/ (- x) (/ z y)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.3e+49) {
		tmp = x;
	} else if (z <= 2.15e-82) {
		tmp = x * (y / t);
	} else if (z <= 60000000000000.0) {
		tmp = -x / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.3d+49)) then
        tmp = x
    else if (z <= 2.15d-82) then
        tmp = x * (y / t)
    else if (z <= 60000000000000.0d0) then
        tmp = -x / (z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.3e+49) {
		tmp = x;
	} else if (z <= 2.15e-82) {
		tmp = x * (y / t);
	} else if (z <= 60000000000000.0) {
		tmp = -x / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.3e+49:
		tmp = x
	elif z <= 2.15e-82:
		tmp = x * (y / t)
	elif z <= 60000000000000.0:
		tmp = -x / (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.3e+49)
		tmp = x;
	elseif (z <= 2.15e-82)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 60000000000000.0)
		tmp = Float64(Float64(-x) / Float64(z / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.3e+49)
		tmp = x;
	elseif (z <= 2.15e-82)
		tmp = x * (y / t);
	elseif (z <= 60000000000000.0)
		tmp = -x / (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.3e+49], x, If[LessEqual[z, 2.15e-82], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 60000000000000.0], N[((-x) / N[(z / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2999999999999999e49 or 6e13 < z

   1. Initial program 82.6%

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

      1. associate-*r/ 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. Taylor expanded in z around inf 72.4%

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

   if -4.2999999999999999e49 < z < 2.15000000000000009e-82

   1. Initial program 95.2%

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

      1. associate-*r/ 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. Taylor expanded in z around 0 65.2%

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

   if 2.15000000000000009e-82 < z < 6e13

   1. Initial program 92.9%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 83.9%

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

   5. Taylor expanded in t around 0 61.7%

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

      1. associate-*r/ 61.7%

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

      2. neg-mul-1 61.7%

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

   7. Simplified 61.7%

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

      1. distribute-frac-neg 61.7%

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

      2. distribute-rgt-neg-out 61.7%

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

      3. add-sqr-sqrt 25.1%

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

      4. sqrt-unprod 19.5%

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

      5. sqr-neg 19.5%

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

      6. sqrt-unprod 1.3%

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

      7. add-sqr-sqrt 9.5%

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

      8. clear-num 9.5%

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

      9. un-div-inv 9.5%

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

      10. add-sqr-sqrt 1.3%

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

      11. sqrt-unprod 19.6%

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

      12. sqr-neg 19.6%

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

      13. sqrt-unprod 25.2%

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

      14. add-sqr-sqrt 61.7%

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

   9. Applied egg-rr 61.7%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-82}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 60000000000000:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 59.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 10^{+14}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e+49)
   x
   (if (<= z 9.5e-88) (* x (/ y t)) (if (<= z 1e+14) (/ y (/ z (- x))) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+49) {
		tmp = x;
	} else if (z <= 9.5e-88) {
		tmp = x * (y / t);
	} else if (z <= 1e+14) {
		tmp = y / (z / -x);
	} 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 <= (-1.6d+49)) then
        tmp = x
    else if (z <= 9.5d-88) then
        tmp = x * (y / t)
    else if (z <= 1d+14) then
        tmp = y / (z / -x)
    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 <= -1.6e+49) {
		tmp = x;
	} else if (z <= 9.5e-88) {
		tmp = x * (y / t);
	} else if (z <= 1e+14) {
		tmp = y / (z / -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e+49:
		tmp = x
	elif z <= 9.5e-88:
		tmp = x * (y / t)
	elif z <= 1e+14:
		tmp = y / (z / -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e+49)
		tmp = x;
	elseif (z <= 9.5e-88)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 1e+14)
		tmp = Float64(y / Float64(z / Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e+49)
		tmp = x;
	elseif (z <= 9.5e-88)
		tmp = x * (y / t);
	elseif (z <= 1e+14)
		tmp = y / (z / -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e+49], x, If[LessEqual[z, 9.5e-88], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+14], N[(y / N[(z / (-x)), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000007e49 or 1e14 < z

   1. Initial program 82.6%

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

      1. associate-*r/ 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. Taylor expanded in z around inf 72.4%

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

   if -1.60000000000000007e49 < z < 9.5e-88

   1. Initial program 95.2%

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

      1. associate-*r/ 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. Taylor expanded in z around 0 65.2%

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

   if 9.5e-88 < z < 1e14

   1. Initial program 92.9%

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

      1. associate-*r/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 83.9%

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

   5. Taylor expanded in t around 0 61.7%

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

      1. associate-*r/ 61.7%

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

      2. associate-*r* 61.7%

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

      3. neg-mul-1 61.7%

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

      4. *-commutative 61.7%

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

      5. associate-/l* 61.7%

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

   7. Simplified 61.7%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 10^{+14}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+49} \lor \neg \left(z \leq 1300000000000\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e+49) (not (<= z 1300000000000.0)))
   (* x (- 1.0 (/ y z)))
   (* x (/ y (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e+49) || !(z <= 1300000000000.0)) {
		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 <= (-2d+49)) .or. (.not. (z <= 1300000000000.0d0))) 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 <= -2e+49) || !(z <= 1300000000000.0)) {
		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 <= -2e+49) or not (z <= 1300000000000.0):
		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 <= -2e+49) || !(z <= 1300000000000.0))
		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 <= -2e+49) || ~((z <= 1300000000000.0)))
		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, -2e+49], N[Not[LessEqual[z, 1300000000000.0]], $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 < -1.99999999999999989e49 or 1.3e12 < z

   1. Initial program 82.6%

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

      1. associate-*r/ 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. Taylor expanded in t around 0 83.9%

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

      1. mul-1-neg 83.9%

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

      2. div-sub 83.9%

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

      3. sub-neg 83.9%

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

      4. *-inverses 83.9%

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

      5. metadata-eval 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in x around 0 83.9%

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

   if -1.99999999999999989e49 < z < 1.3e12

   1. Initial program 95.0%

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

      1. associate-*r/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around inf 80.7%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+49} \lor \neg \left(z \leq 1300000000000\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]

Alternative 8: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.6e+52) x (if (<= z 3.7e+14) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.6e+52) {
		tmp = x;
	} else if (z <= 3.7e+14) {
		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 <= (-6.6d+52)) then
        tmp = x
    else if (z <= 3.7d+14) 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 <= -6.6e+52) {
		tmp = x;
	} else if (z <= 3.7e+14) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.6e+52:
		tmp = x
	elif z <= 3.7e+14:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.6e+52)
		tmp = x;
	elseif (z <= 3.7e+14)
		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 <= -6.6e+52)
		tmp = x;
	elseif (z <= 3.7e+14)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.6e+52], x, If[LessEqual[z, 3.7e+14], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6e52 or 3.7e14 < z

   1. Initial program 82.6%

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

      1. associate-*r/ 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. Taylor expanded in z around inf 72.4%

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

   if -6.6e52 < z < 3.7e14

   1. Initial program 95.0%

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

      1. associate-*r/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in z around 0 61.8%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+14}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 35.0% 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 89.4%

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

   1. associate-*r/ 97.7%

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

3. Simplified 97.7%

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

4. Taylor expanded in z around inf 38.9%

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

5. Final simplification 38.9%

   \[\leadsto x \]

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 2023310 
(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)))