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

Percentage Accurate: 83.5% → 97.1%

Time: 10.5s

Alternatives: 10

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: 83.5% 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

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((y - z) / (t - z)) * 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 = ((y - z) / (t - z)) * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.3%

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

   1. associate-/l* N/A

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

   2. *-commutative N/A

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

   3. *-lowering-*.f64 N/A

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

   4. /-lowering-/.f64 N/A

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

   5. --lowering--.f64 N/A

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

   6. --lowering--.f64 97.3

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

4. Applied egg-rr 97.3%

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

Alternative 2: 61.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.1e+42)
   (fma x (/ t z) x)
   (if (<= z 2.55e+23)
     (* x (/ y t))
     (if (<= z 8.2e+101) (* y (/ x (- z))) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.1e+42) {
		tmp = fma(x, (t / z), x);
	} else if (z <= 2.55e+23) {
		tmp = x * (y / t);
	} else if (z <= 8.2e+101) {
		tmp = y * (x / -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.1e+42)
		tmp = fma(x, Float64(t / z), x);
	elseif (z <= 2.55e+23)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 8.2e+101)
		tmp = Float64(y * Float64(x / Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.1e+42], N[(x * N[(t / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2.55e+23], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+101], N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.1e42

   1. Initial program 72.2%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 58.5

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

   5. Simplified 58.5%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 69.6

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

   8. Simplified 69.6%

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

   if -4.1e42 < z < 2.5500000000000001e23

   1. Initial program 93.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 95.3

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 61.4

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

   7. Simplified 61.4%

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

   if 2.5500000000000001e23 < z < 8.1999999999999999e101

   1. Initial program 84.4%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. associate-/l* N/A

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

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. *-inverses N/A

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

      7. metadata-eval N/A

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

      8. distribute-rgt-in N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. mul-1-neg N/A

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

      12. unsub-neg N/A

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

      13. associate-+l- N/A

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

      14. neg-sub0 N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. unsub-neg N/A

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

      19. --lowering--.f64 N/A

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

      20. *-commutative N/A

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

      21. associate-/l* N/A

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

      22. *-lowering-*.f64 N/A

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

      23. /-lowering-/.f64 73.3

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

   5. Simplified 73.3%

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

   6. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. *-lowering-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. distribute-neg-frac2 N/A

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

      9. mul-1-neg N/A

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

      10. /-lowering-/.f64 N/A

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

      11. mul-1-neg N/A

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

      12. neg-lowering-neg.f64 62.4

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

   8. Simplified 62.4%

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

   if 8.1999999999999999e101 < z

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 56.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+101}:\\ \;\;\;\;\frac{y \cdot x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.7e+43)
   (fma x (/ t z) x)
   (if (<= z 3.6e+21) (* x (/ y t)) (if (<= z 7.5e+101) (/ (* y x) (- z)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.7e+43) {
		tmp = fma(x, (t / z), x);
	} else if (z <= 3.6e+21) {
		tmp = x * (y / t);
	} else if (z <= 7.5e+101) {
		tmp = (y * x) / -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.7e+43)
		tmp = fma(x, Float64(t / z), x);
	elseif (z <= 3.6e+21)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= 7.5e+101)
		tmp = Float64(Float64(y * x) / Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.7e+43], N[(x * N[(t / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.6e+21], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+101], N[(N[(y * x), $MachinePrecision] / (-z)), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.6999999999999999e43

   1. Initial program 72.2%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 58.5

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

   5. Simplified 58.5%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 69.6

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

   8. Simplified 69.6%

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

   if -5.6999999999999999e43 < z < 3.6e21

   1. Initial program 93.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 95.3

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 61.4

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

   7. Simplified 61.4%

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

   if 3.6e21 < z < 7.4999999999999995e101

   1. Initial program 84.4%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. flip3-- N/A

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

      4. clear-num N/A

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

      5. *-lowering-*.f64 N/A

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

      6. clear-num N/A

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

      7. flip3-- N/A

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

      8. /-lowering-/.f64 N/A

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

      9. --lowering--.f64 N/A

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

      10. *-lowering-*.f64 N/A

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

      11. --lowering--.f64 84.2

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

   4. Applied egg-rr 84.2%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 63.0%

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

   8. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. *-lowering-*.f64 52.3

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

   10. Simplified 52.3%

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

   if 7.4999999999999995e101 < z

   1. Initial program 71.2%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 56.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.7 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+21}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+101}:\\ \;\;\;\;\frac{y \cdot x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -3600:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= y -3600.0) t_1 (if (<= y 7e+100) (* x (/ z (- z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -3600.0) {
		tmp = t_1;
	} else if (y <= 7e+100) {
		tmp = x * (z / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (y <= (-3600.0d0)) then
        tmp = t_1
    else if (y <= 7d+100) then
        tmp = x * (z / (z - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -3600.0) {
		tmp = t_1;
	} else if (y <= 7e+100) {
		tmp = x * (z / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if y <= -3600.0:
		tmp = t_1
	elif y <= 7e+100:
		tmp = x * (z / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -3600.0)
		tmp = t_1;
	elseif (y <= 7e+100)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (y <= -3600.0)
		tmp = t_1;
	elseif (y <= 7e+100)
		tmp = x * (z / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3600.0], t$95$1, If[LessEqual[y, 7e+100], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3600 or 6.99999999999999953e100 < y

   1. Initial program 85.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. --lowering--.f64 84.9

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

   5. Simplified 84.9%

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

   if -3600 < y < 6.99999999999999953e100

   1. Initial program 84.9%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 65.8

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

   5. Simplified 65.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. distribute-frac-neg N/A

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

      5. distribute-frac-neg2 N/A

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

      6. /-lowering-/.f64 N/A

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

      7. neg-sub0 N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. associate--r+ N/A

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

      11. neg-sub0 N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 78.3

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

   7. Applied egg-rr 78.3%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3600:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.45e+45)
   (fma x (/ t z) x)
   (if (<= z 7.5e+137) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+45) {
		tmp = fma(x, (t / z), x);
	} else if (z <= 7.5e+137) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.45e+45)
		tmp = fma(x, Float64(t / z), x);
	elseif (z <= 7.5e+137)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.45e+45], N[(x * N[(t / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 7.5e+137], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e45

   1. Initial program 72.2%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 58.5

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

   5. Simplified 58.5%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 69.6

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

   8. Simplified 69.6%

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

   if -1.4499999999999999e45 < z < 7.50000000000000025e137

   1. Initial program 92.2%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-lowering-*.f64 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. --lowering--.f64 73.4

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

   5. Simplified 73.4%

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

   if 7.50000000000000025e137 < z

   1. Initial program 64.1%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 68.3%

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

Alternative 6: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e+43) (fma x (/ t z) x) (if (<= z 5.7e+72) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+43) {
		tmp = fma(x, (t / z), x);
	} else if (z <= 5.7e+72) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e+43)
		tmp = fma(x, Float64(t / z), x);
	elseif (z <= 5.7e+72)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+43], N[(x * N[(t / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 5.7e+72], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000001e43

   1. Initial program 72.2%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 58.5

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

   5. Simplified 58.5%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

      5. /-lowering-/.f64 69.6

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

   8. Simplified 69.6%

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

   if -1.05000000000000001e43 < z < 5.6999999999999997e72

   1. Initial program 93.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 95.6

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

   4. Applied egg-rr 95.6%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 59.9

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

   7. Simplified 59.9%

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

   if 5.6999999999999997e72 < z

   1. Initial program 72.6%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 49.3%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+72}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.35e+43) x (if (<= z 1.15e+73) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.35e+43) {
		tmp = x;
	} else if (z <= 1.15e+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 <= (-1.35d+43)) then
        tmp = x
    else if (z <= 1.15d+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 <= -1.35e+43) {
		tmp = x;
	} else if (z <= 1.15e+73) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.35e+43:
		tmp = x
	elif z <= 1.15e+73:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.35e+43)
		tmp = x;
	elseif (z <= 1.15e+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 <= -1.35e+43)
		tmp = x;
	elseif (z <= 1.15e+73)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.35e+43], x, If[LessEqual[z, 1.15e+73], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001e43 or 1.15e73 < z

   1. Initial program 72.4%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 58.9%

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

   if -1.3500000000000001e43 < z < 1.15e73

   1. Initial program 93.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 95.6

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

   4. Applied egg-rr 95.6%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 59.9

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

   7. Simplified 59.9%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+73}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.8e+42) x (if (<= z 2.45e+76) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e+42) {
		tmp = x;
	} else if (z <= 2.45e+76) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.8d+42)) then
        tmp = x
    else if (z <= 2.45d+76) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e+42) {
		tmp = x;
	} else if (z <= 2.45e+76) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.8e+42:
		tmp = x
	elif z <= 2.45e+76:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.8e+42)
		tmp = x;
	elseif (z <= 2.45e+76)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.8e+42)
		tmp = x;
	elseif (z <= 2.45e+76)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.8e+42], x, If[LessEqual[z, 2.45e+76], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999961e42 or 2.45000000000000013e76 < z

   1. Initial program 71.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 60.1%

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

   if -5.79999999999999961e42 < z < 2.45000000000000013e76

   1. Initial program 93.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 95.6

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

   4. Applied egg-rr 95.6%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 59.2

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

   7. Simplified 59.2%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. associate-*r* N/A

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

      5. div-inv N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 55.9

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

   9. Applied egg-rr 55.9%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+76}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{-270}:\\ \;\;\;\;\frac{x \cdot \left(z - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 2.8e-270) (/ (* x (- z y)) z) (* (- y z) (/ x (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 2.8e-270) {
		tmp = (x * (z - y)) / z;
	} else {
		tmp = (y - z) * (x / (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 (x <= 2.8d-270) then
        tmp = (x * (z - y)) / z
    else
        tmp = (y - z) * (x / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 2.8e-270) {
		tmp = (x * (z - y)) / z;
	} else {
		tmp = (y - z) * (x / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 2.8e-270:
		tmp = (x * (z - y)) / z
	else:
		tmp = (y - z) * (x / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 2.8e-270)
		tmp = Float64(Float64(x * Float64(z - y)) / z);
	else
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 2.8e-270)
		tmp = (x * (z - y)) / z;
	else
		tmp = (y - z) * (x / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 2.8e-270], N[(N[(x * N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.7999999999999999e-270

   1. Initial program 84.7%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 43.8

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

   5. Simplified 43.8%

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

   if 2.7999999999999999e-270 < x

   1. Initial program 85.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

      6. --lowering--.f64 N/A

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

      7. --lowering--.f64 91.4

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

   4. Applied egg-rr 91.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{-270}:\\ \;\;\;\;\frac{x \cdot \left(z - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.9% accurate, 23.0× 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 85.3%

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

3. Taylor expanded in z around inf

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

5. Simplified 29.8%

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

Developer Target 1: 97.0% accurate, 0.8× 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 2024205 
(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)))