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

Percentage Accurate: 83.6% → 97.3%

Time: 10.8s

Alternatives: 11

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: 83.6% 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: 97.3% 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 83.7%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
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 97.5

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

4. Applied egg-rr 97.5%

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

Alternative 2: 23.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \leq -2 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (* (- y z) x) (- t z)) -2e-179) (* x (/ t z)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((((y - z) * x) / (t - z)) <= -2e-179) {
		tmp = x * (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((((y - z) * x) / (t - z)) <= (-2d-179)) then
        tmp = x * (t / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((((y - z) * x) / (t - z)) <= -2e-179) {
		tmp = x * (t / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (((y - z) * x) / (t - z)) <= -2e-179:
		tmp = x * (t / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(Float64(y - z) * x) / Float64(t - z)) <= -2e-179)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((((y - z) * x) / (t - z)) <= -2e-179)
		tmp = x * (t / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], -2e-179], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -2e-179

   1. Initial program 82.6%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. associate--r+ N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. div-sub N/A

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

      12. --lowering--.f64 52.7

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

   5. Simplified 52.7%

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

   6. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 7.6

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

   8. Simplified 7.6%

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

   if -2e-179 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 84.2%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 38.7%

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

4. Final simplification 28.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot x}{t - z} \leq -2 \cdot 10^{-179}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+175}:\\ \;\;\;\;\mathsf{fma}\left(t - y, \frac{x}{z}, x\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+72}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.65e+175)
   (fma (- t y) (/ x z) x)
   (if (<= z 2.5e+72) (* (- 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 <= -2.65e+175) {
		tmp = fma((t - y), (x / z), x);
	} else if (z <= 2.5e+72) {
		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 <= -2.65e+175)
		tmp = fma(Float64(t - y), Float64(x / z), x);
	elseif (z <= 2.5e+72)
		tmp = Float64(Float64(y - z) * 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, -2.65e+175], N[(N[(t - y), $MachinePrecision] * N[(x / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2.5e+72], 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 < -2.65000000000000006e175

   1. Initial program 52.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

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

      3. associate--l- N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. div-sub N/A

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

      7. *-commutative N/A

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

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

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

      9. unsub-neg N/A

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

      10. *-rgt-identity N/A

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

      11. associate-/l* N/A

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

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

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

      13. mul-1-neg N/A

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

      14. distribute-lft-in N/A

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

      15. +-commutative N/A

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

      16. distribute-rgt-in N/A

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

      17. *-lft-identity N/A

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

   7. Simplified 93.4%

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

   if -2.65000000000000006e175 < z < 2.49999999999999996e72

   1. Initial program 90.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 92.9

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

   4. Applied egg-rr 92.9%

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

   if 2.49999999999999996e72 < z

   1. Initial program 77.5%

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. neg-sub0 N/A

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

      6. div-sub N/A

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

      7. *-inverses N/A

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

      8. associate-+l- N/A

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

      9. neg-sub0 N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

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

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

      15. /-lowering-/.f64 80.3

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

   5. Simplified 80.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+175}:\\ \;\;\;\;\mathsf{fma}\left(t - y, \frac{x}{z}, x\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+72}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -6.3 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.22 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -6.3e-37) t_1 (if (<= z 2.22e+17) (* x (/ y (- 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 <= -6.3e-37) {
		tmp = t_1;
	} else if (z <= 2.22e+17) {
		tmp = x * (y / (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 <= (-6.3d-37)) then
        tmp = t_1
    else if (z <= 2.22d+17) then
        tmp = x * (y / (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 <= -6.3e-37) {
		tmp = t_1;
	} else if (z <= 2.22e+17) {
		tmp = x * (y / (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 <= -6.3e-37:
		tmp = t_1
	elif z <= 2.22e+17:
		tmp = x * (y / (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 <= -6.3e-37)
		tmp = t_1;
	elseif (z <= 2.22e+17)
		tmp = Float64(x * Float64(y / 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 <= -6.3e-37)
		tmp = t_1;
	elseif (z <= 2.22e+17)
		tmp = x * (y / (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, -6.3e-37], t$95$1, If[LessEqual[z, 2.22e+17], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.30000000000000023e-37 or 2.22e17 < z

   1. Initial program 76.2%

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

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

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

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

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

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

      5. neg-sub0 N/A

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

      6. div-sub N/A

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

      7. *-inverses N/A

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

      8. associate-+l- N/A

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

      9. neg-sub0 N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

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

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

      15. /-lowering-/.f64 74.3

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

   5. Simplified 74.3%

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

   if -6.30000000000000023e-37 < z < 2.22e17

   1. Initial program 92.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 94.9

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 82.9

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

   7. Simplified 82.9%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2.22 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -5.1e-37) t_1 (if (<= z 4.6e+19) (* 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 <= -5.1e-37) {
		tmp = t_1;
	} else if (z <= 4.6e+19) {
		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 <= (-5.1d-37)) then
        tmp = t_1
    else if (z <= 4.6d+19) 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 <= -5.1e-37) {
		tmp = t_1;
	} else if (z <= 4.6e+19) {
		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 <= -5.1e-37:
		tmp = t_1
	elif z <= 4.6e+19:
		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 <= -5.1e-37)
		tmp = t_1;
	elseif (z <= 4.6e+19)
		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 <= -5.1e-37)
		tmp = t_1;
	elseif (z <= 4.6e+19)
		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, -5.1e-37], t$95$1, If[LessEqual[z, 4.6e+19], N[(y * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1000000000000001e-37 or 4.6e19 < z

   1. Initial program 76.2%

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

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

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

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

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

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

      5. neg-sub0 N/A

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

      6. div-sub N/A

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

      7. *-inverses N/A

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

      8. associate-+l- N/A

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

      9. neg-sub0 N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

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

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

      15. /-lowering-/.f64 74.3

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

   5. Simplified 74.3%

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

   if -5.1000000000000001e-37 < z < 4.6e19

   1. Initial program 92.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 94.3

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

   4. Applied egg-rr 94.3%

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

   5. Taylor expanded in y around inf

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

   7. Simplified 80.7%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+66}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.1e-90) t_1 (if (<= z 1.65e+66) (* (- 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 <= -1.1e-90) {
		tmp = t_1;
	} else if (z <= 1.65e+66) {
		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 <= (-1.1d-90)) then
        tmp = t_1
    else if (z <= 1.65d+66) 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 <= -1.1e-90) {
		tmp = t_1;
	} else if (z <= 1.65e+66) {
		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 <= -1.1e-90:
		tmp = t_1
	elif z <= 1.65e+66:
		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 <= -1.1e-90)
		tmp = t_1;
	elseif (z <= 1.65e+66)
		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 <= -1.1e-90)
		tmp = t_1;
	elseif (z <= 1.65e+66)
		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, -1.1e-90], t$95$1, If[LessEqual[z, 1.65e+66], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.09999999999999993e-90 or 1.6500000000000001e66 < z

   1. Initial program 76.2%

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

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

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

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

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

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

      5. neg-sub0 N/A

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

      6. div-sub N/A

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

      7. *-inverses N/A

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

      8. associate-+l- N/A

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

      9. neg-sub0 N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

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

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

      15. /-lowering-/.f64 75.7

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

   5. Simplified 75.7%

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

   if -1.09999999999999993e-90 < z < 1.6500000000000001e66

   1. Initial program 91.8%

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

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

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

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

      3. --lowering--.f64 75.8

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

   5. Simplified 75.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 78.2

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

   7. Applied egg-rr 78.2%

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

Alternative 7: 70.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{-90}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{+17}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.1e-90) t_1 (if (<= z 1e+17) (* x (/ y 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 <= -1.1e-90) {
		tmp = t_1;
	} else if (z <= 1e+17) {
		tmp = x * (y / 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 <= (-1.1d-90)) then
        tmp = t_1
    else if (z <= 1d+17) then
        tmp = x * (y / 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 <= -1.1e-90) {
		tmp = t_1;
	} else if (z <= 1e+17) {
		tmp = x * (y / 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 <= -1.1e-90:
		tmp = t_1
	elif z <= 1e+17:
		tmp = x * (y / 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 <= -1.1e-90)
		tmp = t_1;
	elseif (z <= 1e+17)
		tmp = Float64(x * Float64(y / 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 <= -1.1e-90)
		tmp = t_1;
	elseif (z <= 1e+17)
		tmp = x * (y / 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, -1.1e-90], t$95$1, If[LessEqual[z, 1e+17], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.09999999999999993e-90 or 1e17 < z

   1. Initial program 77.2%

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

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

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

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

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

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

      5. neg-sub0 N/A

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

      6. div-sub N/A

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

      7. *-inverses N/A

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

      8. associate-+l- N/A

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

      9. neg-sub0 N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. mul-1-neg N/A

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

      13. unsub-neg N/A

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

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

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

      15. /-lowering-/.f64 74.0

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

   5. Simplified 74.0%

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

   if -1.09999999999999993e-90 < z < 1e17

   1. Initial program 91.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 94.7

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

   4. Applied egg-rr 94.7%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 72.0

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

   7. Simplified 72.0%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-90}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 10^{+17}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \mathbf{if}\;z \leq -6.3 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma x (/ t z) x)))
   (if (<= z -6.3e-37) t_1 (if (<= z 4.1e+63) (* x (/ y t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(x, (t / z), x);
	double tmp;
	if (z <= -6.3e-37) {
		tmp = t_1;
	} else if (z <= 4.1e+63) {
		tmp = x * (y / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(x, Float64(t / z), x)
	tmp = 0.0
	if (z <= -6.3e-37)
		tmp = t_1;
	elseif (z <= 4.1e+63)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -6.3e-37], t$95$1, If[LessEqual[z, 4.1e+63], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.30000000000000023e-37 or 4.09999999999999993e63 < z

   1. Initial program 75.5%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. associate--r+ N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. div-sub N/A

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

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

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

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

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

      9. *-commutative N/A

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

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

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

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

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

      12. --lowering--.f64 68.5

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

   5. Simplified 68.5%

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

   6. Taylor expanded in y around 0

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

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

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

      8. /-lowering-/.f64 61.8

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

   8. Simplified 61.8%

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

   if -6.30000000000000023e-37 < z < 4.09999999999999993e63

   1. Initial program 92.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 95.2

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

   4. Applied egg-rr 95.2%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 68.7

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

   7. Simplified 68.7%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.3 \cdot 10^{-37}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e-62) x (if (<= z 2.8e+63) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e-62) {
		tmp = x;
	} else if (z <= 2.8e+63) {
		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 <= (-3.7d-62)) then
        tmp = x
    else if (z <= 2.8d+63) 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 <= -3.7e-62) {
		tmp = x;
	} else if (z <= 2.8e+63) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.7e-62:
		tmp = x
	elif z <= 2.8e+63:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e-62)
		tmp = x;
	elseif (z <= 2.8e+63)
		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 <= -3.7e-62)
		tmp = x;
	elseif (z <= 2.8e+63)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e-62], x, If[LessEqual[z, 2.8e+63], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6999999999999998e-62 or 2.79999999999999987e63 < z

   1. Initial program 75.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 61.1%

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

   if -3.6999999999999998e-62 < z < 2.79999999999999987e63

   1. Initial program 91.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 95.2

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

   4. Applied egg-rr 95.2%

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

   5. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 69.0

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

   7. Simplified 69.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e-62) x (if (<= z 2.9e+63) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e-62) {
		tmp = x;
	} else if (z <= 2.9e+63) {
		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 <= (-3.7d-62)) then
        tmp = x
    else if (z <= 2.9d+63) 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 <= -3.7e-62) {
		tmp = x;
	} else if (z <= 2.9e+63) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.7e-62:
		tmp = x
	elif z <= 2.9e+63:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e-62)
		tmp = x;
	elseif (z <= 2.9e+63)
		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 <= -3.7e-62)
		tmp = x;
	elseif (z <= 2.9e+63)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e-62], x, If[LessEqual[z, 2.9e+63], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6999999999999998e-62 or 2.8999999999999999e63 < z

   1. Initial program 75.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 61.1%

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

   if -3.6999999999999998e-62 < z < 2.8999999999999999e63

   1. Initial program 91.9%

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

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

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

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

      3. --lowering--.f64 74.6

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

   5. Simplified 74.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 77.7

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

   7. Applied egg-rr 77.7%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. associate-*r* N/A

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

      5. div-inv N/A

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

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

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

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

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

      8. --lowering--.f64 77.1

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

   9. Applied egg-rr 77.1%

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

   10. Taylor expanded in y around inf

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

   12. Simplified 66.8%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.3% 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 83.7%

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

3. Taylor expanded in z around inf

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

5. Simplified 35.5%

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

Developer Target 1: 97.3% 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 2024195 
(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)))