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

Percentage Accurate: 85.0% → 97.1%

Time: 12.2s

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: 85.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (/ (* x (- y z)) (- t z)))

C

double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - z);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x * (y - z)) / (t - z)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x * (y - z)) / (t - z);
}

Python

def code(x, y, z, t):
	return (x * (y - z)) / (t - z)

Julia

function code(x, y, z, t)
	return Float64(Float64(x * Float64(y - z)) / Float64(t - z))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x * (y - z)) / (t - z);
end

Wolfram

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

Alternative 1: 97.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (* x (/ (- y z) (- t z))))

C

double code(double x, double y, double z, double t) {
	return x * ((y - z) / (t - z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x * ((y - z) / (t - z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x * ((y - z) / (t - z));
}

Python

def code(x, y, z, t):
	return x * ((y - z) / (t - z))

Julia

function code(x, y, z, t)
	return Float64(x * Float64(Float64(y - z) / Float64(t - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x * ((y - z) / (t - z));
end

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. associate-/l* 98.4%

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

3. Simplified 98.4%

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

Alternative 2: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-41} \lor \neg \left(y \leq 1.82 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.4e-41) (not (<= y 1.82e+53)))
   (/ x (/ (- t z) y))
   (/ x (/ (- z t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e-41) || !(y <= 1.82e+53)) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x / ((z - t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.4d-41)) .or. (.not. (y <= 1.82d+53))) then
        tmp = x / ((t - z) / y)
    else
        tmp = x / ((z - t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e-41) || !(y <= 1.82e+53)) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x / ((z - t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.4e-41) or not (y <= 1.82e+53):
		tmp = x / ((t - z) / y)
	else:
		tmp = x / ((z - t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.4e-41) || !(y <= 1.82e+53))
		tmp = Float64(x / Float64(Float64(t - z) / y));
	else
		tmp = Float64(x / Float64(Float64(z - t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.4e-41) || ~((y <= 1.82e+53)))
		tmp = x / ((t - z) / y);
	else
		tmp = x / ((z - t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.4e-41], N[Not[LessEqual[y, 1.82e+53]], $MachinePrecision]], N[(x / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4e-41 or 1.81999999999999999e53 < y

   1. Initial program 84.8%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around 0 84.8%

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

      1. *-rgt-identity 84.8%

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

      2. times-frac 89.8%

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

      3. /-rgt-identity 89.8%

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

      4. associate-/r/ 98.9%

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

   7. Simplified 98.9%

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

   8. Taylor expanded in y around inf 81.1%

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

   if -4.4e-41 < y < 1.81999999999999999e53

   1. Initial program 87.4%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in x around 0 87.4%

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

      1. *-rgt-identity 87.4%

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

      2. times-frac 86.3%

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

      3. /-rgt-identity 86.3%

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

      4. associate-/r/ 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in y around 0 82.8%

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

      1. neg-mul-1 82.8%

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

   10. Simplified 82.8%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-41} \lor \neg \left(y \leq 1.82 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-40} \lor \neg \left(y \leq 3.3 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.2e-40) (not (<= y 3.3e+53)))
   (/ x (/ (- t z) y))
   (* x (/ z (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e-40) || !(y <= 3.3e+53)) {
		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 <= (-5.2d-40)) .or. (.not. (y <= 3.3d+53))) 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 <= -5.2e-40) || !(y <= 3.3e+53)) {
		tmp = x / ((t - z) / y);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.2e-40) or not (y <= 3.3e+53):
		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 <= -5.2e-40) || !(y <= 3.3e+53))
		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 <= -5.2e-40) || ~((y <= 3.3e+53)))
		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, -5.2e-40], N[Not[LessEqual[y, 3.3e+53]], $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 < -5.2000000000000003e-40 or 3.3000000000000002e53 < y

   1. Initial program 84.8%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around 0 84.8%

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

      1. *-rgt-identity 84.8%

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

      2. times-frac 89.8%

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

      3. /-rgt-identity 89.8%

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

      4. associate-/r/ 98.9%

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

   7. Simplified 98.9%

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

   8. Taylor expanded in y around inf 81.1%

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

   if -5.2000000000000003e-40 < y < 3.3000000000000002e53

   1. Initial program 87.4%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. distribute-neg-frac2 70.3%

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

      3. sub-neg 70.3%

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

      4. distribute-neg-in 70.3%

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

      5. remove-double-neg 70.3%

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

      6. +-commutative 70.3%

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

      7. sub-neg 70.3%

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

      8. associate-/l* 82.8%

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

   7. Simplified 82.8%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-40} \lor \neg \left(y \leq 3.3 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1250 \lor \neg \left(t \leq 5.4 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1250.0) (not (<= t 5.4e+23)))
   (/ x (/ t (- y z)))
   (* x (- 1.0 (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1250.0) || !(t <= 5.4e+23)) {
		tmp = x / (t / (y - z));
	} else {
		tmp = x * (1.0 - (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 ((t <= (-1250.0d0)) .or. (.not. (t <= 5.4d+23))) then
        tmp = x / (t / (y - z))
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1250.0) || !(t <= 5.4e+23)) {
		tmp = x / (t / (y - z));
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1250.0) or not (t <= 5.4e+23):
		tmp = x / (t / (y - z))
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1250.0) || !(t <= 5.4e+23))
		tmp = Float64(x / Float64(t / Float64(y - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1250.0) || ~((t <= 5.4e+23)))
		tmp = x / (t / (y - z));
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1250.0], N[Not[LessEqual[t, 5.4e+23]], $MachinePrecision]], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1250 or 5.3999999999999997e23 < t

   1. Initial program 83.0%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in x around 0 83.0%

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

      1. *-rgt-identity 83.0%

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

      2. times-frac 89.1%

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

      3. /-rgt-identity 89.1%

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

      4. associate-/r/ 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in t around inf 77.9%

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

   if -1250 < t < 5.3999999999999997e23

   1. Initial program 88.8%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in t around 0 73.0%

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

      1. mul-1-neg 73.0%

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

      2. associate-/l* 82.9%

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

      3. distribute-rgt-neg-in 82.9%

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

      4. distribute-frac-neg 82.9%

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

      5. sub-neg 82.9%

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

      6. distribute-neg-in 82.9%

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

      7. remove-double-neg 82.9%

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

      8. +-commutative 82.9%

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

      9. sub-neg 82.9%

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

      10. div-sub 82.9%

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

      11. *-inverses 82.9%

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

   7. Simplified 82.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1250 \lor \neg \left(t \leq 5.4 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-40} \lor \neg \left(y \leq 4.1 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6e-40) (not (<= y 4.1e+53)))
   (* y (/ x (- t z)))
   (* x (/ z (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e-40) || !(y <= 4.1e+53)) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6d-40)) .or. (.not. (y <= 4.1d+53))) then
        tmp = y * (x / (t - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e-40) || !(y <= 4.1e+53)) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6e-40) or not (y <= 4.1e+53):
		tmp = y * (x / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6e-40) || !(y <= 4.1e+53))
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6e-40) || ~((y <= 4.1e+53)))
		tmp = y * (x / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6e-40], N[Not[LessEqual[y, 4.1e+53]], $MachinePrecision]], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.00000000000000039e-40 or 4.10000000000000018e53 < y

   1. Initial program 84.8%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around 0 84.8%

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

      1. *-rgt-identity 84.8%

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

      2. times-frac 89.8%

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

      3. /-rgt-identity 89.8%

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

      4. associate-/r/ 98.9%

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

   7. Simplified 98.9%

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

      1. associate-/r/ 89.8%

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

   9. Applied egg-rr 89.8%

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

   10. Taylor expanded in y around inf 76.8%

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

   if -6.00000000000000039e-40 < y < 4.10000000000000018e53

   1. Initial program 87.4%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. distribute-neg-frac2 70.3%

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

      3. sub-neg 70.3%

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

      4. distribute-neg-in 70.3%

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

      5. remove-double-neg 70.3%

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

      6. +-commutative 70.3%

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

      7. sub-neg 70.3%

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

      8. associate-/l* 82.8%

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

   7. Simplified 82.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-40} \lor \neg \left(y \leq 4.1 \cdot 10^{+53}\right):\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-142} \lor \neg \left(z \leq 1.75 \cdot 10^{-127}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.8e-142) (not (<= z 1.75e-127)))
   (* x (- 1.0 (/ y z)))
   (/ x (/ t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-142) || !(z <= 1.75e-127)) {
		tmp = x * (1.0 - (y / z));
	} 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) :: tmp
    if ((z <= (-8.8d-142)) .or. (.not. (z <= 1.75d-127))) then
        tmp = x * (1.0d0 - (y / z))
    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 tmp;
	if ((z <= -8.8e-142) || !(z <= 1.75e-127)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.8e-142) or not (z <= 1.75e-127):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.8e-142) || !(z <= 1.75e-127))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.8e-142) || ~((z <= 1.75e-127)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.8e-142], N[Not[LessEqual[z, 1.75e-127]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000066e-142 or 1.74999999999999995e-127 < z

   1. Initial program 82.0%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. associate-/l* 71.5%

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

      3. distribute-rgt-neg-in 71.5%

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

      4. distribute-frac-neg 71.5%

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

      5. sub-neg 71.5%

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

      6. distribute-neg-in 71.5%

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

      7. remove-double-neg 71.5%

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

      8. +-commutative 71.5%

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

      9. sub-neg 71.5%

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

      10. div-sub 71.5%

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

      11. *-inverses 71.5%

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

   7. Simplified 71.5%

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

   if -8.80000000000000066e-142 < z < 1.74999999999999995e-127

   1. Initial program 95.3%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around 0 95.3%

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

      1. *-rgt-identity 95.3%

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

      2. times-frac 89.4%

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

      3. /-rgt-identity 89.4%

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

      4. associate-/r/ 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in z around 0 84.7%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-142} \lor \neg \left(z \leq 1.75 \cdot 10^{-127}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -410000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -410000.0) x (if (<= z 2.5e-23) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -410000.0) {
		tmp = x;
	} else if (z <= 2.5e-23) {
		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 <= (-410000.0d0)) then
        tmp = x
    else if (z <= 2.5d-23) 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 <= -410000.0) {
		tmp = x;
	} else if (z <= 2.5e-23) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -410000.0:
		tmp = x
	elif z <= 2.5e-23:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -410000.0)
		tmp = x;
	elseif (z <= 2.5e-23)
		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 <= -410000.0)
		tmp = x;
	elseif (z <= 2.5e-23)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -410000.0], x, If[LessEqual[z, 2.5e-23], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1e5 or 2.5000000000000001e-23 < z

   1. Initial program 75.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 62.6%

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

   if -4.1e5 < z < 2.5000000000000001e-23

   1. Initial program 95.7%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in x around 0 95.7%

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

      1. *-rgt-identity 95.7%

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

      2. times-frac 92.9%

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

      3. /-rgt-identity 92.9%

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

      4. associate-/r/ 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in z around 0 66.5%

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

Alternative 8: 61.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -20000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -20000000.0) x (if (<= z 6.6e-23) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -20000000.0) {
		tmp = x;
	} else if (z <= 6.6e-23) {
		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 <= (-20000000.0d0)) then
        tmp = x
    else if (z <= 6.6d-23) 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 <= -20000000.0) {
		tmp = x;
	} else if (z <= 6.6e-23) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -20000000.0:
		tmp = x
	elif z <= 6.6e-23:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -20000000.0)
		tmp = x;
	elseif (z <= 6.6e-23)
		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 <= -20000000.0)
		tmp = x;
	elseif (z <= 6.6e-23)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -20000000.0], x, If[LessEqual[z, 6.6e-23], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2e7 or 6.60000000000000041e-23 < z

   1. Initial program 75.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 62.6%

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

   if -2e7 < z < 6.60000000000000041e-23

   1. Initial program 95.7%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around 0 63.7%

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

      1. associate-/l* 66.5%

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

   7. Simplified 66.5%

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

Alternative 9: 34.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 86.3%

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

   1. associate-/l* 98.4%

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

3. Simplified 98.4%

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

5. Taylor expanded in z around inf 35.4%

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

Developer Target 1: 97.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t) :precision binary64 (/ x (/ (- t z) (- y z))))

C

double code(double x, double y, double z, double t) {
	return x / ((t - z) / (y - z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / ((t - z) / (y - z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x / ((t - z) / (y - z));
}

Python

def code(x, y, z, t):
	return x / ((t - z) / (y - z))

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(t - z) / Float64(y - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((t - z) / (y - z));
end

Wolfram

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

Reproduce

herbie shell --seed 2024172 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

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