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

Percentage Accurate: 84.6% → 96.9%

Time: 7.3s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.6% 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: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.3%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 98.0

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

4. Applied rewrites 98.0%

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

5. Final simplification 98.0%

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

Alternative 2: 58.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y - z\right)\\ t_2 := \frac{t\_1}{t}\\ t_3 := \frac{t\_1}{t - z}\\ t_4 := x - \frac{y}{z} \cdot x\\ \mathbf{if}\;t\_3 \leq -2:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{-301}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5000000000:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+110}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+255}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y z)))
        (t_2 (/ t_1 t))
        (t_3 (/ t_1 (- t z)))
        (t_4 (- x (* (/ y z) x))))
   (if (<= t_3 -2.0)
     (* (/ x (- t z)) y)
     (if (<= t_3 5e-301)
       t_2
       (if (<= t_3 5000000000.0)
         (* (/ z (- z t)) x)
         (if (<= t_3 2e+110) t_4 (if (<= t_3 5e+255) t_2 t_4)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y - z);
	double t_2 = t_1 / t;
	double t_3 = t_1 / (t - z);
	double t_4 = x - ((y / z) * x);
	double tmp;
	if (t_3 <= -2.0) {
		tmp = (x / (t - z)) * y;
	} else if (t_3 <= 5e-301) {
		tmp = t_2;
	} else if (t_3 <= 5000000000.0) {
		tmp = (z / (z - t)) * x;
	} else if (t_3 <= 2e+110) {
		tmp = t_4;
	} else if (t_3 <= 5e+255) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * (y - z)
    t_2 = t_1 / t
    t_3 = t_1 / (t - z)
    t_4 = x - ((y / z) * x)
    if (t_3 <= (-2.0d0)) then
        tmp = (x / (t - z)) * y
    else if (t_3 <= 5d-301) then
        tmp = t_2
    else if (t_3 <= 5000000000.0d0) then
        tmp = (z / (z - t)) * x
    else if (t_3 <= 2d+110) then
        tmp = t_4
    else if (t_3 <= 5d+255) then
        tmp = t_2
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y - z);
	double t_2 = t_1 / t;
	double t_3 = t_1 / (t - z);
	double t_4 = x - ((y / z) * x);
	double tmp;
	if (t_3 <= -2.0) {
		tmp = (x / (t - z)) * y;
	} else if (t_3 <= 5e-301) {
		tmp = t_2;
	} else if (t_3 <= 5000000000.0) {
		tmp = (z / (z - t)) * x;
	} else if (t_3 <= 2e+110) {
		tmp = t_4;
	} else if (t_3 <= 5e+255) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y - z)
	t_2 = t_1 / t
	t_3 = t_1 / (t - z)
	t_4 = x - ((y / z) * x)
	tmp = 0
	if t_3 <= -2.0:
		tmp = (x / (t - z)) * y
	elif t_3 <= 5e-301:
		tmp = t_2
	elif t_3 <= 5000000000.0:
		tmp = (z / (z - t)) * x
	elif t_3 <= 2e+110:
		tmp = t_4
	elif t_3 <= 5e+255:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y - z))
	t_2 = Float64(t_1 / t)
	t_3 = Float64(t_1 / Float64(t - z))
	t_4 = Float64(x - Float64(Float64(y / z) * x))
	tmp = 0.0
	if (t_3 <= -2.0)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	elseif (t_3 <= 5e-301)
		tmp = t_2;
	elseif (t_3 <= 5000000000.0)
		tmp = Float64(Float64(z / Float64(z - t)) * x);
	elseif (t_3 <= 2e+110)
		tmp = t_4;
	elseif (t_3 <= 5e+255)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y - z);
	t_2 = t_1 / t;
	t_3 = t_1 / (t - z);
	t_4 = x - ((y / z) * x);
	tmp = 0.0;
	if (t_3 <= -2.0)
		tmp = (x / (t - z)) * y;
	elseif (t_3 <= 5e-301)
		tmp = t_2;
	elseif (t_3 <= 5000000000.0)
		tmp = (z / (z - t)) * x;
	elseif (t_3 <= 2e+110)
		tmp = t_4;
	elseif (t_3 <= 5e+255)
		tmp = t_2;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / t), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x - N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2.0], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$3, 5e-301], t$95$2, If[LessEqual[t$95$3, 5000000000.0], N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$3, 2e+110], t$95$4, If[LessEqual[t$95$3, 5e+255], t$95$2, t$95$4]]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 69.9%

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

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 57.9

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

   5. Applied rewrites 57.9%

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

   if -2 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5.00000000000000013e-301 or 2e110 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5.0000000000000002e255

   1. Initial program 99.3%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 65.0

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

   5. Applied rewrites 65.0%

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

   if 5.00000000000000013e-301 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5e9

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 59.3

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

   5. Applied rewrites 59.3%

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

   7. Applied rewrites 59.3%

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

   if 5e9 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 2e110 or 5.0000000000000002e255 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 71.0%

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

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

      2. neg-sub0 N/A

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

      3. associate-/l* N/A

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

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. *-inverses N/A

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

      7. metadata-eval N/A

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

      8. distribute-lft-out N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. mul-1-neg N/A

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

      12. unsub-neg N/A

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

      13. associate-+l- N/A

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

      14. neg-sub0 N/A

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

      15. mul-1-neg N/A

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

      16. +-commutative N/A

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

      17. mul-1-neg N/A

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

      18. unsub-neg N/A

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

      19. lower--.f64 N/A

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

      20. lower-/.f64 N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 62.7

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

   5. Applied rewrites 62.7%

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

   7. Applied rewrites 68.3%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -2:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 5 \cdot 10^{-301}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 5000000000:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 2 \cdot 10^{+110}:\\ \;\;\;\;x - \frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 5 \cdot 10^{+255}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y - z\right)\\ t_2 := \frac{t\_1}{t - z}\\ t_3 := \frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-143}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-301}:\\ \;\;\;\;\frac{t\_1}{t}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- y z)))
        (t_2 (/ t_1 (- t z)))
        (t_3 (* (/ x (- t z)) (- y z))))
   (if (<= t_2 -1e-143)
     t_3
     (if (<= t_2 5e-301)
       (/ t_1 t)
       (if (<= t_2 5e-157) (* (/ z (- z t)) x) t_3)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y - z);
	double t_2 = t_1 / (t - z);
	double t_3 = (x / (t - z)) * (y - z);
	double tmp;
	if (t_2 <= -1e-143) {
		tmp = t_3;
	} else if (t_2 <= 5e-301) {
		tmp = t_1 / t;
	} else if (t_2 <= 5e-157) {
		tmp = (z / (z - t)) * x;
	} else {
		tmp = t_3;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (y - z)
    t_2 = t_1 / (t - z)
    t_3 = (x / (t - z)) * (y - z)
    if (t_2 <= (-1d-143)) then
        tmp = t_3
    else if (t_2 <= 5d-301) then
        tmp = t_1 / t
    else if (t_2 <= 5d-157) then
        tmp = (z / (z - t)) * x
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y - z);
	double t_2 = t_1 / (t - z);
	double t_3 = (x / (t - z)) * (y - z);
	double tmp;
	if (t_2 <= -1e-143) {
		tmp = t_3;
	} else if (t_2 <= 5e-301) {
		tmp = t_1 / t;
	} else if (t_2 <= 5e-157) {
		tmp = (z / (z - t)) * x;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y - z)
	t_2 = t_1 / (t - z)
	t_3 = (x / (t - z)) * (y - z)
	tmp = 0
	if t_2 <= -1e-143:
		tmp = t_3
	elif t_2 <= 5e-301:
		tmp = t_1 / t
	elif t_2 <= 5e-157:
		tmp = (z / (z - t)) * x
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y - z))
	t_2 = Float64(t_1 / Float64(t - z))
	t_3 = Float64(Float64(x / Float64(t - z)) * Float64(y - z))
	tmp = 0.0
	if (t_2 <= -1e-143)
		tmp = t_3;
	elseif (t_2 <= 5e-301)
		tmp = Float64(t_1 / t);
	elseif (t_2 <= 5e-157)
		tmp = Float64(Float64(z / Float64(z - t)) * x);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y - z);
	t_2 = t_1 / (t - z);
	t_3 = (x / (t - z)) * (y - z);
	tmp = 0.0;
	if (t_2 <= -1e-143)
		tmp = t_3;
	elseif (t_2 <= 5e-301)
		tmp = t_1 / t;
	elseif (t_2 <= 5e-157)
		tmp = (z / (z - t)) * x;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-143], t$95$3, If[LessEqual[t$95$2, 5e-301], N[(t$95$1 / t), $MachinePrecision], If[LessEqual[t$95$2, 5e-157], N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < -9.9999999999999995e-144 or 5.0000000000000002e-157 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

   1. Initial program 79.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 91.1

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

   4. Applied rewrites 91.1%

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

   if -9.9999999999999995e-144 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5.00000000000000013e-301

   1. Initial program 99.1%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 67.1

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

   5. Applied rewrites 67.1%

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

   if 5.00000000000000013e-301 < (/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z)) < 5.0000000000000002e-157

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 61.2

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

   5. Applied rewrites 61.2%

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

   7. Applied rewrites 61.2%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq -1 \cdot 10^{-143}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 5 \cdot 10^{-301}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{t - z} \leq 5 \cdot 10^{-157}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{z - t} \cdot x\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{+23}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z (- z t)) x)))
   (if (<= z -4.1e-44) t_1 (if (<= z 1e+23) (* (/ x (- t z)) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / (z - t)) * x;
	double tmp;
	if (z <= -4.1e-44) {
		tmp = t_1;
	} else if (z <= 1e+23) {
		tmp = (x / (t - z)) * y;
	} 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 = (z / (z - t)) * x
    if (z <= (-4.1d-44)) then
        tmp = t_1
    else if (z <= 1d+23) then
        tmp = (x / (t - z)) * y
    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 = (z / (z - t)) * x;
	double tmp;
	if (z <= -4.1e-44) {
		tmp = t_1;
	} else if (z <= 1e+23) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / (z - t)) * x
	tmp = 0
	if z <= -4.1e-44:
		tmp = t_1
	elif z <= 1e+23:
		tmp = (x / (t - z)) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z / Float64(z - t)) * x)
	tmp = 0.0
	if (z <= -4.1e-44)
		tmp = t_1;
	elseif (z <= 1e+23)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z / (z - t)) * x;
	tmp = 0.0;
	if (z <= -4.1e-44)
		tmp = t_1;
	elseif (z <= 1e+23)
		tmp = (x / (t - z)) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -4.1e-44], t$95$1, If[LessEqual[z, 1e+23], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.09999999999999992e-44 or 9.9999999999999992e22 < z

   1. Initial program 74.5%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 75.0

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

   5. Applied rewrites 75.0%

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

   7. Applied rewrites 75.0%

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

   if -4.09999999999999992e-44 < z < 9.9999999999999992e22

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 76.3

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

   5. Applied rewrites 76.3%

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

Alternative 5: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z} \cdot y\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{-104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z - t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x (- t z)) y)))
   (if (<= y -2.25e-104) t_1 (if (<= y 1.4e-11) (* (/ x (- z t)) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / (t - z)) * y;
	double tmp;
	if (y <= -2.25e-104) {
		tmp = t_1;
	} else if (y <= 1.4e-11) {
		tmp = (x / (z - 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 / (t - z)) * y
    if (y <= (-2.25d-104)) then
        tmp = t_1
    else if (y <= 1.4d-11) then
        tmp = (x / (z - 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 / (t - z)) * y;
	double tmp;
	if (y <= -2.25e-104) {
		tmp = t_1;
	} else if (y <= 1.4e-11) {
		tmp = (x / (z - t)) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / (t - z)) * y
	tmp = 0
	if y <= -2.25e-104:
		tmp = t_1
	elif y <= 1.4e-11:
		tmp = (x / (z - t)) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(t - z)) * y)
	tmp = 0.0
	if (y <= -2.25e-104)
		tmp = t_1;
	elseif (y <= 1.4e-11)
		tmp = Float64(Float64(x / Float64(z - t)) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / (t - z)) * y;
	tmp = 0.0;
	if (y <= -2.25e-104)
		tmp = t_1;
	elseif (y <= 1.4e-11)
		tmp = (x / (z - t)) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.25e-104], t$95$1, If[LessEqual[y, 1.4e-11], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2499999999999999e-104 or 1.4e-11 < y

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 67.2

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

   5. Applied rewrites 67.2%

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

   if -2.2499999999999999e-104 < y < 1.4e-11

   1. Initial program 83.9%

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

   3. Taylor expanded in y around 0

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

      1. associate-/l* N/A

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

      2. associate-*r* N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 84.4

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

   5. Applied rewrites 84.4%

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

   7. Applied rewrites 72.7%

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

Alternative 6: 68.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+77}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.9e+77)
   (* 1.0 x)
   (if (<= z 3.2e+48) (* (/ x (- t z)) y) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.9e+77) {
		tmp = 1.0 * x;
	} else if (z <= 3.2e+48) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = 1.0 * 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 <= (-3.9d+77)) then
        tmp = 1.0d0 * x
    else if (z <= 3.2d+48) then
        tmp = (x / (t - z)) * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.9e+77) {
		tmp = 1.0 * x;
	} else if (z <= 3.2e+48) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.9e+77:
		tmp = 1.0 * x
	elif z <= 3.2e+48:
		tmp = (x / (t - z)) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.9e+77)
		tmp = Float64(1.0 * x);
	elseif (z <= 3.2e+48)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.9e+77)
		tmp = 1.0 * x;
	elseif (z <= 3.2e+48)
		tmp = (x / (t - z)) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.9e+77], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 3.2e+48], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8999999999999998e77 or 3.2000000000000001e48 < z

   1. Initial program 69.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 63.2%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -3.8999999999999998e77 < z < 3.2000000000000001e48

   1. Initial program 96.5%

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

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 70.3

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

   5. Applied rewrites 70.3%

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

Alternative 7: 61.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+69}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.9e+69) (* 1.0 x) (if (<= z 3.2e+48) (* (/ y t) x) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.9e+69) {
		tmp = 1.0 * x;
	} else if (z <= 3.2e+48) {
		tmp = (y / t) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.9d+69)) then
        tmp = 1.0d0 * x
    else if (z <= 3.2d+48) then
        tmp = (y / t) * x
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.9e+69) {
		tmp = 1.0 * x;
	} else if (z <= 3.2e+48) {
		tmp = (y / t) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.9e+69:
		tmp = 1.0 * x
	elif z <= 3.2e+48:
		tmp = (y / t) * x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.9e+69)
		tmp = Float64(1.0 * x);
	elseif (z <= 3.2e+48)
		tmp = Float64(Float64(y / t) * x);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.9e+69)
		tmp = 1.0 * x;
	elseif (z <= 3.2e+48)
		tmp = (y / t) * x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.9e+69], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 3.2e+48], N[(N[(y / t), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.90000000000000004e69 or 3.2000000000000001e48 < z

   1. Initial program 69.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 63.2%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -5.90000000000000004e69 < z < 3.2000000000000001e48

   1. Initial program 96.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 96.7

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

   4. Applied rewrites 96.7%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 60.6

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

   7. Applied rewrites 60.6%

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

Alternative 8: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+69}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.9e+69) (* 1.0 x) (if (<= z 2.4e+48) (/ (* x y) t) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.9e+69) {
		tmp = 1.0 * x;
	} else if (z <= 2.4e+48) {
		tmp = (x * y) / t;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.9d+69)) then
        tmp = 1.0d0 * x
    else if (z <= 2.4d+48) then
        tmp = (x * y) / t
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.9e+69) {
		tmp = 1.0 * x;
	} else if (z <= 2.4e+48) {
		tmp = (x * y) / t;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.9e+69:
		tmp = 1.0 * x
	elif z <= 2.4e+48:
		tmp = (x * y) / t
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.9e+69)
		tmp = Float64(1.0 * x);
	elseif (z <= 2.4e+48)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.9e+69)
		tmp = 1.0 * x;
	elseif (z <= 2.4e+48)
		tmp = (x * y) / t;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.9e+69], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 2.4e+48], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.90000000000000004e69 or 2.4000000000000001e48 < z

   1. Initial program 69.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 63.2%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -5.90000000000000004e69 < z < 2.4000000000000001e48

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 59.4

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

   5. Applied rewrites 59.4%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+69}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+69}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.9e+69) (* 1.0 x) (if (<= z 2.4e+48) (* (/ x t) y) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.9e+69) {
		tmp = 1.0 * x;
	} else if (z <= 2.4e+48) {
		tmp = (x / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.9d+69)) then
        tmp = 1.0d0 * x
    else if (z <= 2.4d+48) then
        tmp = (x / t) * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.9e+69) {
		tmp = 1.0 * x;
	} else if (z <= 2.4e+48) {
		tmp = (x / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.9e+69:
		tmp = 1.0 * x
	elif z <= 2.4e+48:
		tmp = (x / t) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.9e+69)
		tmp = Float64(1.0 * x);
	elseif (z <= 2.4e+48)
		tmp = Float64(Float64(x / t) * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.9e+69)
		tmp = 1.0 * x;
	elseif (z <= 2.4e+48)
		tmp = (x / t) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.9e+69], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 2.4e+48], N[(N[(x / t), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.90000000000000004e69 or 2.4000000000000001e48 < z

   1. Initial program 69.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 63.2%

      \[\leadsto \color{blue}{1} \cdot x \]

   if -5.90000000000000004e69 < z < 2.4000000000000001e48

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 59.4

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

   5. Applied rewrites 59.4%

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

   7. Applied rewrites 54.6%

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

Alternative 10: 35.2% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ 1 \cdot x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 1.0 x))

C

double code(double x, double y, double z, double t) {
	return 1.0 * 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 = 1.0d0 * x
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 * x;
}

Python

def code(x, y, z, t):
	return 1.0 * x

Julia

function code(x, y, z, t)
	return Float64(1.0 * x)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 * x;
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 * x), $MachinePrecision]

Derivation

1. Initial program 85.3%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 98.0

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

4. Applied rewrites 98.0%

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

5. Taylor expanded in z around inf

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

7. Applied rewrites 32.9%

   \[\leadsto \color{blue}{1} \cdot x \]
8. Add Preprocessing

Developer Target 1: 96.9% 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 2024249 
(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)))