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

Percentage Accurate: 84.3% → 96.8%

Time: 10.7s

Alternatives: 11

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{t - z} \cdot x\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-123}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- y z) (- t z)) x)))
   (if (<= z -1.35e-146)
     t_1
     (if (<= z 2.1e-123) (/ (* (- y z) x) (- t z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((y - z) / (t - z)) * x;
	double tmp;
	if (z <= -1.35e-146) {
		tmp = t_1;
	} else if (z <= 2.1e-123) {
		tmp = ((y - z) * x) / (t - z);
	} 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 = ((y - z) / (t - z)) * x
    if (z <= (-1.35d-146)) then
        tmp = t_1
    else if (z <= 2.1d-123) then
        tmp = ((y - z) * x) / (t - z)
    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 = ((y - z) / (t - z)) * x;
	double tmp;
	if (z <= -1.35e-146) {
		tmp = t_1;
	} else if (z <= 2.1e-123) {
		tmp = ((y - z) * x) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((y - z) / (t - z)) * x
	tmp = 0
	if z <= -1.35e-146:
		tmp = t_1
	elif z <= 2.1e-123:
		tmp = ((y - z) * x) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(y - z) / Float64(t - z)) * x)
	tmp = 0.0
	if (z <= -1.35e-146)
		tmp = t_1;
	elseif (z <= 2.1e-123)
		tmp = Float64(Float64(Float64(y - z) * x) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((y - z) / (t - z)) * x;
	tmp = 0.0;
	if (z <= -1.35e-146)
		tmp = t_1;
	elseif (z <= 2.1e-123)
		tmp = ((y - z) * x) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -1.35e-146], t$95$1, If[LessEqual[z, 2.1e-123], N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999997e-146 or 2.0999999999999999e-123 < z

   1. Initial program 79.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{t - z}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(t - z\right)\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(t - z\right)\right), x\right) \]

      6. --lowering--.f64 99.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 99.5%

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

   if -1.34999999999999997e-146 < z < 2.0999999999999999e-123

   1. Initial program 98.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-146}:\\ \;\;\;\;\frac{y - z}{t - z} \cdot x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-123}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t - z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(0 - \frac{y}{z}, x, x\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{elif}\;z \leq 350:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.5e-12)
   (fma (- 0.0 (/ y z)) x x)
   (if (<= z 5.2e-169)
     (/ (* (- y z) x) t)
     (if (<= z 350.0) (* y (/ x (- t z))) (* x (- 1.0 (/ y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.5e-12) {
		tmp = fma((0.0 - (y / z)), x, x);
	} else if (z <= 5.2e-169) {
		tmp = ((y - z) * x) / t;
	} else if (z <= 350.0) {
		tmp = y * (x / (t - z));
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.5e-12)
		tmp = fma(Float64(0.0 - Float64(y / z)), x, x);
	elseif (z <= 5.2e-169)
		tmp = Float64(Float64(Float64(y - z) * x) / t);
	elseif (z <= 350.0)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.5e-12], N[(N[(0.0 - N[(y / z), $MachinePrecision]), $MachinePrecision] * x + x), $MachinePrecision], If[LessEqual[z, 5.2e-169], N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 350.0], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.49999999999999981e-12

   1. Initial program 80.5%

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

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 80.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 80.1%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

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

         \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right), \color{blue}{x}, x\right) \]

      6. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\frac{y}{\mathsf{neg}\left(z\right)}\right), x, x\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(z\right)\right)\right), x, x\right) \]

      8. neg-sub0 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \left(0 - z\right)\right), x, x\right) \]

      9. --lowering--.f64 80.1%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(0, z\right)\right), x, x\right) \]

   7. Applied egg-rr 80.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{0 - z}, x, x\right)} \]
   8. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \left(\mathsf{neg}\left(z\right)\right)\right), x, x\right) \]

      2. neg-lowering-neg.f64 80.1%

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{/.f64}\left(y, \mathsf{neg.f64}\left(z\right)\right), x, x\right) \]

   9. Applied egg-rr 80.1%

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

   if -4.49999999999999981e-12 < z < 5.20000000000000028e-169

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - z\right)\right), \color{blue}{t}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - z\right)\right), t\right) \]

      3. --lowering--.f64 86.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right) \]

   5. Simplified 86.7%

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

   if 5.20000000000000028e-169 < z < 350

   1. Initial program 88.3%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. flip3-- N/A

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

      4. clear-num N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t \cdot t + \left(z \cdot z + t \cdot z\right)}{{t}^{3} - {z}^{3}}\right), \color{blue}{\left(x \cdot \left(y - z\right)\right)}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{{t}^{3} - {z}^{3}}{t \cdot t + \left(z \cdot z + t \cdot z\right)}}\right), \left(\color{blue}{x} \cdot \left(y - z\right)\right)\right) \]

      7. flip3-- N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{t - z}\right), \left(x \cdot \left(y - z\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(t - z\right)\right), \left(\color{blue}{x} \cdot \left(y - z\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, z\right)\right), \left(x \cdot \left(y - z\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, \color{blue}{\left(y - z\right)}\right)\right) \]

      11. --lowering--.f64 88.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, z\right)\right), \color{blue}{\left(x \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, z\right)\right), \left(y \cdot \color{blue}{x}\right)\right) \]

      2. *-lowering-*.f64 70.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right) \]

   7. Simplified 70.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-/r/ N/A

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

      4. clear-num N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t - z}\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(t - z\right)\right), y\right) \]

      7. --lowering--.f64 74.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), y\right) \]

   9. Applied egg-rr 74.5%

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

   if 350 < z

   1. Initial program 68.7%

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

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 90.3%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 90.3%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-12}:\\ \;\;\;\;\mathsf{fma}\left(0 - \frac{y}{z}, x, x\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{elif}\;z \leq 350:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-167}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{elif}\;z \leq 390:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -4.8e-13)
     t_1
     (if (<= z 1.2e-167)
       (/ (* (- y z) x) t)
       (if (<= z 390.0) (* y (/ x (- t z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -4.8e-13) {
		tmp = t_1;
	} else if (z <= 1.2e-167) {
		tmp = ((y - z) * x) / t;
	} else if (z <= 390.0) {
		tmp = y * (x / (t - z));
	} 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 * (1.0d0 - (y / z))
    if (z <= (-4.8d-13)) then
        tmp = t_1
    else if (z <= 1.2d-167) then
        tmp = ((y - z) * x) / t
    else if (z <= 390.0d0) then
        tmp = y * (x / (t - z))
    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 * (1.0 - (y / z));
	double tmp;
	if (z <= -4.8e-13) {
		tmp = t_1;
	} else if (z <= 1.2e-167) {
		tmp = ((y - z) * x) / t;
	} else if (z <= 390.0) {
		tmp = y * (x / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -4.8e-13:
		tmp = t_1
	elif z <= 1.2e-167:
		tmp = ((y - z) * x) / t
	elif z <= 390.0:
		tmp = y * (x / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -4.8e-13)
		tmp = t_1;
	elseif (z <= 1.2e-167)
		tmp = Float64(Float64(Float64(y - z) * x) / t);
	elseif (z <= 390.0)
		tmp = Float64(y * Float64(x / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -4.8e-13)
		tmp = t_1;
	elseif (z <= 1.2e-167)
		tmp = ((y - z) * x) / t;
	elseif (z <= 390.0)
		tmp = y * (x / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-13], t$95$1, If[LessEqual[z, 1.2e-167], N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 390.0], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7999999999999997e-13 or 390 < z

   1. Initial program 74.4%

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

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 85.4%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 85.4%

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

   if -4.7999999999999997e-13 < z < 1.19999999999999997e-167

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - z\right)\right), \color{blue}{t}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - z\right)\right), t\right) \]

      3. --lowering--.f64 86.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right) \]

   5. Simplified 86.7%

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

   if 1.19999999999999997e-167 < z < 390

   1. Initial program 88.3%

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

      1. div-inv N/A

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

      2. *-commutative N/A

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

      3. flip3-- N/A

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

      4. clear-num N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t \cdot t + \left(z \cdot z + t \cdot z\right)}{{t}^{3} - {z}^{3}}\right), \color{blue}{\left(x \cdot \left(y - z\right)\right)}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{\frac{{t}^{3} - {z}^{3}}{t \cdot t + \left(z \cdot z + t \cdot z\right)}}\right), \left(\color{blue}{x} \cdot \left(y - z\right)\right)\right) \]

      7. flip3-- N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{t - z}\right), \left(x \cdot \left(y - z\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \left(t - z\right)\right), \left(\color{blue}{x} \cdot \left(y - z\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, z\right)\right), \left(x \cdot \left(y - z\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, \color{blue}{\left(y - z\right)}\right)\right) \]

      11. --lowering--.f64 88.2%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, z\right)\right), \color{blue}{\left(x \cdot y\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, z\right)\right), \left(y \cdot \color{blue}{x}\right)\right) \]

      2. *-lowering-*.f64 70.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(y, \color{blue}{x}\right)\right) \]

   7. Simplified 70.0%

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. associate-/r/ N/A

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

      4. clear-num N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t - z}\right), \color{blue}{y}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(t - z\right)\right), y\right) \]

      7. --lowering--.f64 74.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), y\right) \]

   9. Applied egg-rr 74.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-167}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{elif}\;z \leq 390:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(1 + \frac{t - y}{z}\right)\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+88}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.2e+121)
   (* x (+ 1.0 (/ (- t y) z)))
   (if (<= z 1.18e+88) (* (- y z) (/ x (- t z))) (* x (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.2e+121) {
		tmp = x * (1.0 + ((t - y) / z));
	} else if (z <= 1.18e+88) {
		tmp = (y - z) * (x / (t - 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 (z <= (-4.2d+121)) then
        tmp = x * (1.0d0 + ((t - y) / z))
    else if (z <= 1.18d+88) then
        tmp = (y - z) * (x / (t - 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 (z <= -4.2e+121) {
		tmp = x * (1.0 + ((t - y) / z));
	} else if (z <= 1.18e+88) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.2e+121:
		tmp = x * (1.0 + ((t - y) / z))
	elif z <= 1.18e+88:
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.2e+121)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(t - y) / z)));
	elseif (z <= 1.18e+88)
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - 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 (z <= -4.2e+121)
		tmp = x * (1.0 + ((t - y) / z));
	elseif (z <= 1.18e+88)
		tmp = (y - z) * (x / (t - z));
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.2e+121], N[(x * N[(1.0 + N[(N[(t - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.18e+88], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2000000000000003e121

   1. Initial program 64.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{t - z}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(t - z\right)\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(t - z\right)\right), x\right) \]

      6. --lowering--.f64 99.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\left(1 + -1 \cdot \frac{y}{z}\right) - -1 \cdot \frac{t}{z}\right)}, x\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right) - -1 \cdot \frac{t}{z}\right), x\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\left(1 - \frac{y}{z}\right) - -1 \cdot \frac{t}{z}\right), x\right) \]

      3. associate--l- N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 - \left(\frac{y}{z} + -1 \cdot \frac{t}{z}\right)\right), x\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 - \left(\frac{y}{z} + \left(\mathsf{neg}\left(\frac{t}{z}\right)\right)\right)\right), x\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 - \left(\frac{y}{z} - \frac{t}{z}\right)\right), x\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 - \frac{y - t}{z}\right), x\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 + \left(\mathsf{neg}\left(\frac{y - t}{z}\right)\right)\right), x\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\left(1 + -1 \cdot \frac{y - t}{z}\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \left(-1 \cdot \frac{y - t}{z}\right)\right), x\right) \]

      10. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{-1 \cdot \left(y - t\right)}{z}\right)\right), x\right) \]

      11. distribute-lft-out-- N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{-1 \cdot y - -1 \cdot t}{z}\right)\right), x\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot y - -1 \cdot t\right), z\right)\right), x\right) \]

      13. cancel-sign-sub-inv N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot y + \left(\mathsf{neg}\left(-1\right)\right) \cdot t\right), z\right)\right), x\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot y + 1 \cdot t\right), z\right)\right), x\right) \]

      15. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(-1 \cdot y + t\right), z\right)\right), x\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(t + -1 \cdot y\right), z\right)\right), x\right) \]

      17. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(t + \left(\mathsf{neg}\left(y\right)\right)\right), z\right)\right), x\right) \]

      18. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(t - y\right), z\right)\right), x\right) \]

      19. --lowering--.f64 95.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, y\right), z\right)\right), x\right) \]

   7. Simplified 95.8%

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

   if -4.2000000000000003e121 < z < 1.1799999999999999e88

   1. Initial program 95.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t - z}\right), \color{blue}{\left(y - z\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(t - z\right)\right), \left(\color{blue}{y} - z\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), \left(y - z\right)\right) \]

      7. --lowering--.f64 92.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   4. Applied egg-rr 92.1%

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

   if 1.1799999999999999e88 < z

   1. Initial program 56.7%

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

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 91.5%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 91.5%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(1 + \frac{t - y}{z}\right)\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+88}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 360:\\ \;\;\;\;\frac{y \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -7.5e-9) t_1 (if (<= z 360.0) (/ (* y x) (- t z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -7.5e-9) {
		tmp = t_1;
	} else if (z <= 360.0) {
		tmp = (y * x) / (t - z);
	} 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 * (1.0d0 - (y / z))
    if (z <= (-7.5d-9)) then
        tmp = t_1
    else if (z <= 360.0d0) then
        tmp = (y * x) / (t - z)
    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 * (1.0 - (y / z));
	double tmp;
	if (z <= -7.5e-9) {
		tmp = t_1;
	} else if (z <= 360.0) {
		tmp = (y * x) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -7.5e-9:
		tmp = t_1
	elif z <= 360.0:
		tmp = (y * x) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -7.5e-9)
		tmp = t_1;
	elseif (z <= 360.0)
		tmp = Float64(Float64(y * x) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -7.5e-9)
		tmp = t_1;
	elseif (z <= 360.0)
		tmp = (y * x) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e-9], t$95$1, If[LessEqual[z, 360.0], N[(N[(y * x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999933e-9 or 360 < z

   1. Initial program 74.0%

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

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 86.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 86.0%

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

   if -7.49999999999999933e-9 < z < 360

   1. Initial program 95.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t - z\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} - z\right)\right) \]

      3. --lowering--.f64 77.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   5. Simplified 77.1%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 360:\\ \;\;\;\;\frac{y \cdot x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 280:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -4.8e-12) t_1 (if (<= z 280.0) (* (- y z) (/ x t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -4.8e-12) {
		tmp = t_1;
	} else if (z <= 280.0) {
		tmp = (y - z) * (x / 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 * (1.0d0 - (y / z))
    if (z <= (-4.8d-12)) then
        tmp = t_1
    else if (z <= 280.0d0) then
        tmp = (y - z) * (x / 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 * (1.0 - (y / z));
	double tmp;
	if (z <= -4.8e-12) {
		tmp = t_1;
	} else if (z <= 280.0) {
		tmp = (y - z) * (x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -4.8e-12:
		tmp = t_1
	elif z <= 280.0:
		tmp = (y - z) * (x / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -4.8e-12)
		tmp = t_1;
	elseif (z <= 280.0)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -4.8e-12)
		tmp = t_1;
	elseif (z <= 280.0)
		tmp = (y - z) * (x / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-12], t$95$1, If[LessEqual[z, 280.0], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999974e-12 or 280 < z

   1. Initial program 74.4%

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

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 85.4%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 85.4%

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

   if -4.79999999999999974e-12 < z < 280

   1. Initial program 95.3%

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

   3. Taylor expanded in t around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(y - z\right)\right), \color{blue}{t}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(y - z\right)\right), t\right) \]

      3. --lowering--.f64 79.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), t\right) \]

   5. Simplified 79.3%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(y - z\right), \color{blue}{\left(\frac{x}{t}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{\color{blue}{x}}{t}\right)\right) \]

      5. /-lowering-/.f64 76.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(x, \color{blue}{t}\right)\right) \]

   7. Applied egg-rr 76.3%

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

Alternative 7: 69.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -6.3 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-66}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -6.3e-21) t_1 (if (<= z 1.12e-66) (/ (* y x) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -6.3e-21) {
		tmp = t_1;
	} else if (z <= 1.12e-66) {
		tmp = (y * x) / 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 * (1.0d0 - (y / z))
    if (z <= (-6.3d-21)) then
        tmp = t_1
    else if (z <= 1.12d-66) then
        tmp = (y * x) / 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 * (1.0 - (y / z));
	double tmp;
	if (z <= -6.3e-21) {
		tmp = t_1;
	} else if (z <= 1.12e-66) {
		tmp = (y * x) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -6.3e-21:
		tmp = t_1
	elif z <= 1.12e-66:
		tmp = (y * x) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -6.3e-21)
		tmp = t_1;
	elseif (z <= 1.12e-66)
		tmp = Float64(Float64(y * x) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -6.3e-21)
		tmp = t_1;
	elseif (z <= 1.12e-66)
		tmp = (y * x) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.3e-21], t$95$1, If[LessEqual[z, 1.12e-66], N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.3e-21 or 1.12000000000000004e-66 < z

   1. Initial program 77.0%

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

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 81.2%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 81.2%

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

   if -6.3e-21 < z < 1.12000000000000004e-66

   1. Initial program 95.4%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 70.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), t\right) \]

   5. Simplified 70.6%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-66}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-9}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e-8) x (if (<= z 1.15e-9) (/ (* y x) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e-8) {
		tmp = x;
	} else if (z <= 1.15e-9) {
		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 <= (-2.8d-8)) then
        tmp = x
    else if (z <= 1.15d-9) 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 <= -2.8e-8) {
		tmp = x;
	} else if (z <= 1.15e-9) {
		tmp = (y * x) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e-8:
		tmp = x
	elif z <= 1.15e-9:
		tmp = (y * x) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e-8)
		tmp = x;
	elseif (z <= 1.15e-9)
		tmp = Float64(Float64(y * x) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e-8)
		tmp = x;
	elseif (z <= 1.15e-9)
		tmp = (y * x) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e-8], x, If[LessEqual[z, 1.15e-9], N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999999e-8 or 1.15e-9 < z

   1. Initial program 74.4%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 61.9%

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

   if -2.7999999999999999e-8 < z < 1.15e-9

   1. Initial program 95.3%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 68.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), t\right) \]

   5. Simplified 68.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-9}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -130000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 340:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -130000000.0) x (if (<= z 340.0) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -130000000.0) {
		tmp = x;
	} else if (z <= 340.0) {
		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 <= (-130000000.0d0)) then
        tmp = x
    else if (z <= 340.0d0) 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 <= -130000000.0) {
		tmp = x;
	} else if (z <= 340.0) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -130000000.0:
		tmp = x
	elif z <= 340.0:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -130000000.0)
		tmp = x;
	elseif (z <= 340.0)
		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 <= -130000000.0)
		tmp = x;
	elseif (z <= 340.0)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -130000000.0], x, If[LessEqual[z, 340.0], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e8 or 340 < z

   1. Initial program 73.7%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 63.7%

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

   if -1.3e8 < z < 340

   1. Initial program 94.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{t - z}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(t - z\right)\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(t - z\right)\right), x\right) \]

      6. --lowering--.f64 89.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 89.8%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{t}\right)}, x\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 62.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right) \]

   7. Simplified 62.0%

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

      1. associate-*l/ N/A

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

      2. *-commutative N/A

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

      3. associate-*l/ N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t}\right), \color{blue}{y}\right) \]

      5. /-lowering-/.f64 63.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), y\right) \]

   9. Applied egg-rr 63.2%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -130000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 340:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 96.5% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 1e+17) (* (/ (- y z) (- t z)) x) (* (- y z) (/ x (- t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 1e+17) {
		tmp = ((y - z) / (t - z)) * x;
	} 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 <= 1d+17) then
        tmp = ((y - z) / (t - z)) * x
    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 <= 1e+17) {
		tmp = ((y - z) / (t - z)) * x;
	} else {
		tmp = (y - z) * (x / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 1e+17:
		tmp = ((y - z) / (t - z)) * x
	else:
		tmp = (y - z) * (x / (t - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 1e+17)
		tmp = Float64(Float64(Float64(y - z) / Float64(t - z)) * x);
	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 <= 1e+17)
		tmp = ((y - z) / (t - z)) * x;
	else
		tmp = (y - z) * (x / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 1e+17], N[(N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1e17

   1. Initial program 88.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{t - z}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(t - z\right)\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(t - z\right)\right), x\right) \]

      6. --lowering--.f64 95.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 95.6%

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

   if 1e17 < x

   1. Initial program 77.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t - z}\right), \color{blue}{\left(y - z\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(t - z\right)\right), \left(\color{blue}{y} - z\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), \left(y - z\right)\right) \]

      7. --lowering--.f64 97.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   4. Applied egg-rr 97.0%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+17}:\\ \;\;\;\;\frac{y - z}{t - z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.3% 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 35.6%

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

Developer Target 1: 96.5% 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 2024193 
(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)))