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

Percentage Accurate: 84.3% → 96.9%

Time: 9.2s

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: 84.3% 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/ 80.4%

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

3. Simplified 80.4%

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

   1. associate-/r/ 98.0%

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

5. Applied egg-rr 98.0%

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

6. Final simplification 98.0%

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

Alternative 2: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-13} \lor \neg \left(z \leq 3.8 \cdot 10^{-100} \lor \neg \left(z \leq 1.65 \cdot 10^{+39}\right) \land z \leq 2.3 \cdot 10^{+73}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.6e-13)
         (not (or (<= z 3.8e-100) (and (not (<= z 1.65e+39)) (<= z 2.3e+73)))))
   (* x (/ z (- z t)))
   (* x (/ (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.6e-13) || !((z <= 3.8e-100) || (!(z <= 1.65e+39) && (z <= 2.3e+73)))) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.6d-13)) .or. (.not. (z <= 3.8d-100) .or. (.not. (z <= 1.65d+39)) .and. (z <= 2.3d+73))) then
        tmp = x * (z / (z - t))
    else
        tmp = x * ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.6e-13) || !((z <= 3.8e-100) || (!(z <= 1.65e+39) && (z <= 2.3e+73)))) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.6e-13) or not ((z <= 3.8e-100) or (not (z <= 1.65e+39) and (z <= 2.3e+73))):
		tmp = x * (z / (z - t))
	else:
		tmp = x * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.6e-13) || !((z <= 3.8e-100) || (!(z <= 1.65e+39) && (z <= 2.3e+73))))
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = Float64(x * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.6e-13) || ~(((z <= 3.8e-100) || (~((z <= 1.65e+39)) && (z <= 2.3e+73)))))
		tmp = x * (z / (z - t));
	else
		tmp = x * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.6e-13], N[Not[Or[LessEqual[z, 3.8e-100], And[N[Not[LessEqual[z, 1.65e+39]], $MachinePrecision], LessEqual[z, 2.3e+73]]]], $MachinePrecision]], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6000000000000001e-13 or 3.79999999999999997e-100 < z < 1.6500000000000001e39 or 2.3e73 < z

   1. Initial program 81.8%

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

      1. associate-*l/ 75.9%

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

      2. div-inv 75.8%

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

      3. associate-*l* 99.1%

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

   3. Applied egg-rr 99.1%

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

   4. Taylor expanded in y around 0 78.8%

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

      1. mul-1-neg 78.8%

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

      2. distribute-neg-frac 78.8%

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

   6. Simplified 78.8%

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

      1. frac-2neg 78.8%

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

      2. remove-double-neg 78.8%

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

      3. associate-*r/ 63.8%

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

      4. sub-neg 63.8%

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

      5. distribute-neg-in 63.8%

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

      6. remove-double-neg 63.8%

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

   8. Applied egg-rr 63.8%

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

      1. *-commutative 63.8%

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

      2. associate-/l* 59.0%

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

      3. associate-/r/ 78.8%

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

      4. +-commutative 78.8%

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

      5. unsub-neg 78.8%

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

   10. Simplified 78.8%

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

   if -6.6000000000000001e-13 < z < 3.79999999999999997e-100 or 1.6500000000000001e39 < z < 2.3e73

   1. Initial program 91.0%

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

      1. associate-*l/ 85.9%

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

      2. div-inv 85.8%

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

      3. associate-*l* 95.8%

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

   3. Applied egg-rr 95.8%

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

   4. Taylor expanded in t around inf 85.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-13} \lor \neg \left(z \leq 3.8 \cdot 10^{-100} \lor \neg \left(z \leq 1.65 \cdot 10^{+39}\right) \land z \leq 2.3 \cdot 10^{+73}\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 3: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-13} \lor \neg \left(z \leq 1.95 \cdot 10^{-100}\right) \land \left(z \leq 5.2 \cdot 10^{+39} \lor \neg \left(z \leq 8.5 \cdot 10^{+72}\right)\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.35e-13)
         (and (not (<= z 1.95e-100)) (or (<= z 5.2e+39) (not (<= z 8.5e+72)))))
   (* x (/ z (- z t)))
   (/ x (/ t (- y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.35e-13) || (!(z <= 1.95e-100) && ((z <= 5.2e+39) || !(z <= 8.5e+72)))) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x / (t / (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 <= (-2.35d-13)) .or. (.not. (z <= 1.95d-100)) .and. (z <= 5.2d+39) .or. (.not. (z <= 8.5d+72))) then
        tmp = x * (z / (z - t))
    else
        tmp = x / (t / (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 <= -2.35e-13) || (!(z <= 1.95e-100) && ((z <= 5.2e+39) || !(z <= 8.5e+72)))) {
		tmp = x * (z / (z - t));
	} else {
		tmp = x / (t / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.35e-13) or (not (z <= 1.95e-100) and ((z <= 5.2e+39) or not (z <= 8.5e+72))):
		tmp = x * (z / (z - t))
	else:
		tmp = x / (t / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.35e-13) || (!(z <= 1.95e-100) && ((z <= 5.2e+39) || !(z <= 8.5e+72))))
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = Float64(x / Float64(t / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.35e-13) || (~((z <= 1.95e-100)) && ((z <= 5.2e+39) || ~((z <= 8.5e+72)))))
		tmp = x * (z / (z - t));
	else
		tmp = x / (t / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.35e-13], And[N[Not[LessEqual[z, 1.95e-100]], $MachinePrecision], Or[LessEqual[z, 5.2e+39], N[Not[LessEqual[z, 8.5e+72]], $MachinePrecision]]]], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3500000000000001e-13 or 1.94999999999999989e-100 < z < 5.2e39 or 8.5000000000000004e72 < z

   1. Initial program 81.8%

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

      1. associate-*l/ 75.9%

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

      2. div-inv 75.8%

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

      3. associate-*l* 99.1%

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

   3. Applied egg-rr 99.1%

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

   4. Taylor expanded in y around 0 78.8%

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

      1. mul-1-neg 78.8%

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

      2. distribute-neg-frac 78.8%

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

   6. Simplified 78.8%

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

      1. frac-2neg 78.8%

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

      2. remove-double-neg 78.8%

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

      3. associate-*r/ 63.8%

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

      4. sub-neg 63.8%

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

      5. distribute-neg-in 63.8%

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

      6. remove-double-neg 63.8%

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

   8. Applied egg-rr 63.8%

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

      1. *-commutative 63.8%

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

      2. associate-/l* 59.0%

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

      3. associate-/r/ 78.8%

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

      4. +-commutative 78.8%

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

      5. unsub-neg 78.8%

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

   10. Simplified 78.8%

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

   if -2.3500000000000001e-13 < z < 1.94999999999999989e-100 or 5.2e39 < z < 8.5000000000000004e72

   1. Initial program 91.0%

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

      1. associate-*l/ 85.9%

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

   3. Simplified 85.9%

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

      1. associate-/r/ 96.6%

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

   5. Applied egg-rr 96.6%

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

   6. Taylor expanded in t around inf 86.4%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-13} \lor \neg \left(z \leq 1.95 \cdot 10^{-100}\right) \land \left(z \leq 5.2 \cdot 10^{+39} \lor \neg \left(z \leq 8.5 \cdot 10^{+72}\right)\right):\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \end{array} \]

Alternative 4: 84.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ x (- t z)))))
   (if (<= y -4.8e-90)
     t_1
     (if (<= y 2.35e-144)
       (* x (/ z (- z t)))
       (if (<= y 2.6e+108) t_1 (/ x (/ (- t z) y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / (t - z));
	double tmp;
	if (y <= -4.8e-90) {
		tmp = t_1;
	} else if (y <= 2.35e-144) {
		tmp = x * (z / (z - t));
	} else if (y <= 2.6e+108) {
		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 = (y - z) * (x / (t - z))
    if (y <= (-4.8d-90)) then
        tmp = t_1
    else if (y <= 2.35d-144) then
        tmp = x * (z / (z - t))
    else if (y <= 2.6d+108) 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 = (y - z) * (x / (t - z));
	double tmp;
	if (y <= -4.8e-90) {
		tmp = t_1;
	} else if (y <= 2.35e-144) {
		tmp = x * (z / (z - t));
	} else if (y <= 2.6e+108) {
		tmp = t_1;
	} else {
		tmp = x / ((t - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (x / (t - z))
	tmp = 0
	if y <= -4.8e-90:
		tmp = t_1
	elif y <= 2.35e-144:
		tmp = x * (z / (z - t))
	elif y <= 2.6e+108:
		tmp = t_1
	else:
		tmp = x / ((t - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(x / Float64(t - z)))
	tmp = 0.0
	if (y <= -4.8e-90)
		tmp = t_1;
	elseif (y <= 2.35e-144)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	elseif (y <= 2.6e+108)
		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 = (y - z) * (x / (t - z));
	tmp = 0.0;
	if (y <= -4.8e-90)
		tmp = t_1;
	elseif (y <= 2.35e-144)
		tmp = x * (z / (z - t));
	elseif (y <= 2.6e+108)
		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[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e-90], t$95$1, If[LessEqual[y, 2.35e-144], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+108], t$95$1, N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8000000000000003e-90 or 2.3500000000000001e-144 < y < 2.6000000000000002e108

   1. Initial program 85.7%

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

      1. associate-*l/ 84.3%

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

   3. Simplified 84.3%

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

   if -4.8000000000000003e-90 < y < 2.3500000000000001e-144

   1. Initial program 85.7%

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

      1. associate-*l/ 78.3%

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

      2. div-inv 78.2%

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

      3. associate-*l* 97.9%

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

   3. Applied egg-rr 97.9%

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

   4. Taylor expanded in y around 0 92.3%

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

      1. mul-1-neg 92.3%

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

      2. distribute-neg-frac 92.3%

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

   6. Simplified 92.3%

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

      1. frac-2neg 92.3%

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

      2. remove-double-neg 92.3%

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

      3. associate-*r/ 81.0%

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

      4. sub-neg 81.0%

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

      5. distribute-neg-in 81.0%

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

      6. remove-double-neg 81.0%

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

   8. Applied egg-rr 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-/l* 72.7%

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

      3. associate-/r/ 92.3%

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

      4. +-commutative 92.3%

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

      5. unsub-neg 92.3%

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

   10. Simplified 92.3%

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

   if 2.6000000000000002e108 < y

   1. Initial program 86.9%

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

      1. associate-*l/ 72.4%

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

   3. Simplified 72.4%

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

      1. associate-/r/ 97.5%

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

   5. Applied egg-rr 97.5%

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

   6. Taylor expanded in y around inf 85.7%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-90}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+108}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \end{array} \]

Alternative 5: 76.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+17} \lor \neg \left(y \leq 8.2 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.5e+17) (not (<= y 8.2e-40)))
   (/ x (/ (- t z) y))
   (* x (/ z (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e+17) || !(y <= 8.2e-40)) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.5d+17)) .or. (.not. (y <= 8.2d-40))) then
        tmp = x / ((t - z) / y)
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e+17) || !(y <= 8.2e-40)) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.5e+17) or not (y <= 8.2e-40):
		tmp = x / ((t - z) / y)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.5e+17) || !(y <= 8.2e-40))
		tmp = Float64(x / Float64(Float64(t - z) / y));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.5e+17) || ~((y <= 8.2e-40)))
		tmp = x / ((t - z) / y);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.5e+17], N[Not[LessEqual[y, 8.2e-40]], $MachinePrecision]], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e17 or 8.19999999999999926e-40 < y

   1. Initial program 88.1%

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

      1. associate-*l/ 79.6%

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

   3. Simplified 79.6%

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

      1. associate-/r/ 98.9%

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

   5. Applied egg-rr 98.9%

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

   6. Taylor expanded in y around inf 78.0%

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

   if -6.5e17 < y < 8.19999999999999926e-40

   1. Initial program 83.4%

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

      1. associate-*l/ 81.2%

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

      2. div-inv 81.0%

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

      3. associate-*l* 96.9%

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

   3. Applied egg-rr 96.9%

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

   4. Taylor expanded in y around 0 86.3%

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

      1. mul-1-neg 86.3%

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

      2. distribute-neg-frac 86.3%

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

   6. Simplified 86.3%

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

      1. frac-2neg 86.3%

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

      2. remove-double-neg 86.3%

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

      3. associate-*r/ 73.1%

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

      4. sub-neg 73.1%

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

      5. distribute-neg-in 73.1%

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

      6. remove-double-neg 73.1%

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

   8. Applied egg-rr 73.1%

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

      1. *-commutative 73.1%

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

      2. associate-/l* 69.4%

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

      3. associate-/r/ 86.3%

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

      4. +-commutative 86.3%

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

      5. unsub-neg 86.3%

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

   10. Simplified 86.3%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+17} \lor \neg \left(y \leq 8.2 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]

Alternative 6: 67.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.06e+71) x (if (<= z 5.2e+77) (* x (/ (- y z) t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.06e+71) {
		tmp = x;
	} else if (z <= 5.2e+77) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.06d+71)) then
        tmp = x
    else if (z <= 5.2d+77) then
        tmp = x * ((y - z) / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.06e+71) {
		tmp = x;
	} else if (z <= 5.2e+77) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.06e+71:
		tmp = x
	elif z <= 5.2e+77:
		tmp = x * ((y - z) / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.06e+71)
		tmp = x;
	elseif (z <= 5.2e+77)
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.06e+71)
		tmp = x;
	elseif (z <= 5.2e+77)
		tmp = x * ((y - z) / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.06e+71], x, If[LessEqual[z, 5.2e+77], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.06e71 or 5.2000000000000004e77 < z

   1. Initial program 77.0%

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

      1. associate-*l/ 68.9%

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

   3. Simplified 68.9%

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

   4. Taylor expanded in z around inf 67.3%

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

   if -1.06e71 < z < 5.2000000000000004e77

   1. Initial program 91.5%

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

      1. associate-*l/ 87.5%

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

      2. div-inv 87.5%

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

      3. associate-*l* 96.3%

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

   3. Applied egg-rr 96.3%

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

   4. Taylor expanded in t around inf 74.8%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{+73}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.85e+21) x (if (<= z 1e+73) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.85e+21) {
		tmp = x;
	} else if (z <= 1e+73) {
		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 <= (-2.85d+21)) then
        tmp = x
    else if (z <= 1d+73) 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 <= -2.85e+21) {
		tmp = x;
	} else if (z <= 1e+73) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.85e+21:
		tmp = x
	elif z <= 1e+73:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.85e+21)
		tmp = x;
	elseif (z <= 1e+73)
		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 <= -2.85e+21)
		tmp = x;
	elseif (z <= 1e+73)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.85e+21], x, If[LessEqual[z, 1e+73], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.85e21 or 9.99999999999999983e72 < z

   1. Initial program 77.8%

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

      1. associate-*l/ 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in z around inf 62.2%

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

   if -2.85e21 < z < 9.99999999999999983e72

   1. Initial program 92.0%

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

      1. associate-*l/ 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around 0 64.9%

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

      1. associate-/l* 60.1%

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

      2. associate-/r/ 67.8%

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

   6. Simplified 67.8%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{+73}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.7e+19) x (if (<= z 2.15e+73) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.7e+19) {
		tmp = x;
	} else if (z <= 2.15e+73) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.7d+19)) then
        tmp = x
    else if (z <= 2.15d+73) then
        tmp = x / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.7e+19) {
		tmp = x;
	} else if (z <= 2.15e+73) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.7e+19:
		tmp = x
	elif z <= 2.15e+73:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.7e+19)
		tmp = x;
	elseif (z <= 2.15e+73)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.7e+19)
		tmp = x;
	elseif (z <= 2.15e+73)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.7e+19], x, If[LessEqual[z, 2.15e+73], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7e19 or 2.15000000000000007e73 < z

   1. Initial program 77.8%

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

      1. associate-*l/ 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in z around inf 62.2%

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

   if -4.7e19 < z < 2.15000000000000007e73

   1. Initial program 92.0%

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

      1. associate-*l/ 87.2%

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

   3. Simplified 87.2%

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

      1. associate-/r/ 96.6%

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

   5. Applied egg-rr 96.6%

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

   6. Taylor expanded in z around 0 68.2%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 34.6% 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-*l/ 80.4%

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

3. Simplified 80.4%

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

4. Taylor expanded in z around inf 34.0%

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

5. Final simplification 34.0%

   \[\leadsto x \]

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 2023274 
(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)))