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

Percentage Accurate: 84.2% → 97.0%

Time: 7.6s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% 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 86.2%

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

   1. associate-*r/ 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 2: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+139}:\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t - z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.6e+139)
   (- x (/ x (/ z y)))
   (if (<= z -4.8e+19)
     (/ (* x (- z)) (- t z))
     (if (<= z 3e+32) (* x (/ y (- t z))) (* x (/ (- z y) z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e+139) {
		tmp = x - (x / (z / y));
	} else if (z <= -4.8e+19) {
		tmp = (x * -z) / (t - z);
	} else if (z <= 3e+32) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * ((z - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.6d+139)) then
        tmp = x - (x / (z / y))
    else if (z <= (-4.8d+19)) then
        tmp = (x * -z) / (t - z)
    else if (z <= 3d+32) then
        tmp = x * (y / (t - z))
    else
        tmp = x * ((z - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.6e+139) {
		tmp = x - (x / (z / y));
	} else if (z <= -4.8e+19) {
		tmp = (x * -z) / (t - z);
	} else if (z <= 3e+32) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * ((z - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.6e+139:
		tmp = x - (x / (z / y))
	elif z <= -4.8e+19:
		tmp = (x * -z) / (t - z)
	elif z <= 3e+32:
		tmp = x * (y / (t - z))
	else:
		tmp = x * ((z - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.6e+139)
		tmp = Float64(x - Float64(x / Float64(z / y)));
	elseif (z <= -4.8e+19)
		tmp = Float64(Float64(x * Float64(-z)) / Float64(t - z));
	elseif (z <= 3e+32)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x * Float64(Float64(z - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.6e+139)
		tmp = x - (x / (z / y));
	elseif (z <= -4.8e+19)
		tmp = (x * -z) / (t - z);
	elseif (z <= 3e+32)
		tmp = x * (y / (t - z));
	else
		tmp = x * ((z - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.6e+139], N[(x - N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e+19], N[(N[(x * (-z)), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+32], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.6e139

   1. Initial program 70.6%

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

      1. associate-*r/ 70.6%

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

      2. clear-num 67.5%

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

   5. Applied egg-rr 67.5%

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

   6. Taylor expanded in t around 0 61.6%

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

      1. mul-1-neg 61.6%

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

      2. neg-sub0 61.6%

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

      3. associate-/l* 49.8%

         \[\leadsto 0 - \color{blue}{\frac{y - z}{\frac{z}{x}}} \]

      4. div-sub 49.8%

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

      5. associate-/l* 46.6%

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

      6. associate-*r/ 50.7%

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

      7. *-commutative 50.7%

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

      8. associate-/r/ 82.0%

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

      9. *-inverses 82.0%

         \[\leadsto 0 - \left(\frac{x}{z} \cdot y - \color{blue}{1} \cdot x\right) \]

      10. *-lft-identity 82.0%

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

      11. associate-+l- 82.0%

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

      12. neg-sub0 82.0%

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

      13. associate-*l/ 79.8%

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

      14. *-commutative 79.8%

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

      15. mul-1-neg 79.8%

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

      16. +-commutative 79.8%

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

      17. mul-1-neg 79.8%

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

      18. associate-*r/ 82.0%

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

      19. *-commutative 82.0%

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

      20. unsub-neg 82.0%

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

      21. *-commutative 82.0%

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

   8. Simplified 82.0%

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

      1. associate-*r/ 79.8%

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

      2. *-commutative 79.8%

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

      3. associate-/l* 88.7%

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

   10. Applied egg-rr 88.7%

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

   if -4.6e139 < z < -4.8e19

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 87.3%

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

      1. mul-1-neg 87.3%

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

      2. distribute-rgt-neg-in 87.3%

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

   4. Simplified 87.3%

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

   if -4.8e19 < z < 3e32

   1. Initial program 92.9%

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

      1. associate-*r/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around inf 78.3%

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

   if 3e32 < z

   1. Initial program 77.5%

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

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

      1. associate-*r/ 76.9%

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

      2. neg-mul-1 76.9%

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

      3. neg-sub0 76.9%

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

      4. associate--r- 76.9%

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

      5. neg-sub0 76.9%

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

   6. Simplified 76.9%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+139}:\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{x \cdot \left(-z\right)}{t - z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \]

Alternative 3: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+22} \lor \neg \left(t \leq 1.75 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.1e+22) (not (<= t 1.75e-25)))
   (* x (/ (- y z) t))
   (- x (* y (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.1e+22) || !(t <= 1.75e-25)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x - (y * (x / 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 <= (-3.1d+22)) .or. (.not. (t <= 1.75d-25))) then
        tmp = x * ((y - z) / t)
    else
        tmp = x - (y * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.1e+22) || !(t <= 1.75e-25)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x - (y * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.1e+22) or not (t <= 1.75e-25):
		tmp = x * ((y - z) / t)
	else:
		tmp = x - (y * (x / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.1e+22) || !(t <= 1.75e-25))
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x - Float64(y * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.1e+22) || ~((t <= 1.75e-25)))
		tmp = x * ((y - z) / t);
	else
		tmp = x - (y * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.1e+22], N[Not[LessEqual[t, 1.75e-25]], $MachinePrecision]], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1000000000000002e22 or 1.7500000000000001e-25 < t

   1. Initial program 86.1%

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

      1. associate-*r/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around inf 77.3%

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

   if -3.1000000000000002e22 < t < 1.7500000000000001e-25

   1. Initial program 86.4%

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

      1. associate-*r/ 86.4%

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

      2. clear-num 86.3%

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

   5. Applied egg-rr 86.3%

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

   6. Taylor expanded in t around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. neg-sub0 68.3%

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

      3. associate-/l* 62.2%

         \[\leadsto 0 - \color{blue}{\frac{y - z}{\frac{z}{x}}} \]

      4. div-sub 61.3%

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

      5. associate-/l* 61.6%

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

      6. associate-*r/ 62.7%

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

      7. *-commutative 62.7%

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

      8. associate-/r/ 76.8%

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

      9. *-inverses 76.8%

         \[\leadsto 0 - \left(\frac{x}{z} \cdot y - \color{blue}{1} \cdot x\right) \]

      10. *-lft-identity 76.8%

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

      11. associate-+l- 76.8%

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

      12. neg-sub0 76.8%

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

      13. associate-*l/ 76.6%

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

      14. *-commutative 76.6%

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

      15. mul-1-neg 76.6%

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

      16. +-commutative 76.6%

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

      17. mul-1-neg 76.6%

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

      18. associate-*r/ 76.8%

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

      19. *-commutative 76.8%

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

      20. unsub-neg 76.8%

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

      21. *-commutative 76.8%

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

   8. Simplified 76.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+22} \lor \neg \left(t \leq 1.75 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+22} \lor \neg \left(t \leq 1.25 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.3e+22) (not (<= t 1.25e-25)))
   (* x (/ (- y z) t))
   (- x (/ x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.3e+22) || !(t <= 1.25e-25)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x - (x / (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) :: tmp
    if ((t <= (-2.3d+22)) .or. (.not. (t <= 1.25d-25))) then
        tmp = x * ((y - z) / t)
    else
        tmp = x - (x / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.3e+22) || !(t <= 1.25e-25)) {
		tmp = x * ((y - z) / t);
	} else {
		tmp = x - (x / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.3e+22) or not (t <= 1.25e-25):
		tmp = x * ((y - z) / t)
	else:
		tmp = x - (x / (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.3e+22) || !(t <= 1.25e-25))
		tmp = Float64(x * Float64(Float64(y - z) / t));
	else
		tmp = Float64(x - Float64(x / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.3e+22) || ~((t <= 1.25e-25)))
		tmp = x * ((y - z) / t);
	else
		tmp = x - (x / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.3e+22], N[Not[LessEqual[t, 1.25e-25]], $MachinePrecision]], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3000000000000002e22 or 1.2499999999999999e-25 < t

   1. Initial program 86.1%

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

      1. associate-*r/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around inf 77.3%

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

   if -2.3000000000000002e22 < t < 1.2499999999999999e-25

   1. Initial program 86.4%

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

      1. associate-*r/ 86.4%

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

      2. clear-num 86.3%

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

   5. Applied egg-rr 86.3%

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

   6. Taylor expanded in t around 0 68.3%

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

      1. mul-1-neg 68.3%

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

      2. neg-sub0 68.3%

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

      3. associate-/l* 62.2%

         \[\leadsto 0 - \color{blue}{\frac{y - z}{\frac{z}{x}}} \]

      4. div-sub 61.3%

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

      5. associate-/l* 61.6%

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

      6. associate-*r/ 62.7%

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

      7. *-commutative 62.7%

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

      8. associate-/r/ 76.8%

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

      9. *-inverses 76.8%

         \[\leadsto 0 - \left(\frac{x}{z} \cdot y - \color{blue}{1} \cdot x\right) \]

      10. *-lft-identity 76.8%

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

      11. associate-+l- 76.8%

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

      12. neg-sub0 76.8%

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

      13. associate-*l/ 76.6%

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

      14. *-commutative 76.6%

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

      15. mul-1-neg 76.6%

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

      16. +-commutative 76.6%

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

      17. mul-1-neg 76.6%

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

      18. associate-*r/ 76.8%

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

      19. *-commutative 76.8%

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

      20. unsub-neg 76.8%

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

      21. *-commutative 76.8%

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

   8. Simplified 76.8%

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

      1. associate-*r/ 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-/l* 80.2%

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

   10. Applied egg-rr 80.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+22} \lor \neg \left(t \leq 1.25 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{z}{y}}\\ \end{array} \]

Alternative 5: 69.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.2e+31) x (if (<= z 1.1e+103) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+31) {
		tmp = x;
	} else if (z <= 1.1e+103) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.2d+31)) then
        tmp = x
    else if (z <= 1.1d+103) then
        tmp = x * (y / (t - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+31) {
		tmp = x;
	} else if (z <= 1.1e+103) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e+31:
		tmp = x
	elif z <= 1.1e+103:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.2e+31)
		tmp = x;
	elseif (z <= 1.1e+103)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.2e+31)
		tmp = x;
	elseif (z <= 1.1e+103)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.2e+31], x, If[LessEqual[z, 1.1e+103], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999958e31 or 1.09999999999999996e103 < z

   1. Initial program 76.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 69.8%

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

   if -4.19999999999999958e31 < z < 1.09999999999999996e103

   1. Initial program 92.5%

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

      1. associate-*r/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around inf 75.1%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -50:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -50.0) x (if (<= z 2.8e+31) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -50.0) {
		tmp = x;
	} else if (z <= 2.8e+31) {
		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 <= (-50.0d0)) then
        tmp = x
    else if (z <= 2.8d+31) 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 <= -50.0) {
		tmp = x;
	} else if (z <= 2.8e+31) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -50.0:
		tmp = x
	elif z <= 2.8e+31:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -50.0)
		tmp = x;
	elseif (z <= 2.8e+31)
		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 <= -50.0)
		tmp = x;
	elseif (z <= 2.8e+31)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -50.0], x, If[LessEqual[z, 2.8e+31], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -50 or 2.80000000000000017e31 < z

   1. Initial program 78.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 63.5%

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

   if -50 < z < 2.80000000000000017e31

   1. Initial program 93.3%

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

      1. associate-*r/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around 0 65.6%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -50:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 36.2% 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 86.2%

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

   1. associate-*r/ 98.3%

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

3. Simplified 98.3%

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

4. Taylor expanded in z around inf 36.0%

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

5. Final simplification 36.0%

   \[\leadsto x \]

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 2023230 
(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)))