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

Percentage Accurate: 84.8% → 97.0%

Time: 8.6s

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: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 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]

Derivation

1. Initial program 86.1%

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

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 97.5

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

4. Applied rewrites 97.5%

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

Alternative 2: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{z - t} \cdot x\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ z (- z t)) x)))
   (if (<= z -1.5e+16)
     t_1
     (if (<= z 2e-303)
       (* (/ x (- t z)) y)
       (if (<= z 4.2e+52) (* (/ (- y z) t) x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z / (z - t)) * x;
	double tmp;
	if (z <= -1.5e+16) {
		tmp = t_1;
	} else if (z <= 2e-303) {
		tmp = (x / (t - z)) * y;
	} else if (z <= 4.2e+52) {
		tmp = ((y - z) / t) * x;
	} 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 <= (-1.5d+16)) then
        tmp = t_1
    else if (z <= 2d-303) then
        tmp = (x / (t - z)) * y
    else if (z <= 4.2d+52) then
        tmp = ((y - z) / t) * x
    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 <= -1.5e+16) {
		tmp = t_1;
	} else if (z <= 2e-303) {
		tmp = (x / (t - z)) * y;
	} else if (z <= 4.2e+52) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z / (z - t)) * x
	tmp = 0
	if z <= -1.5e+16:
		tmp = t_1
	elif z <= 2e-303:
		tmp = (x / (t - z)) * y
	elif z <= 4.2e+52:
		tmp = ((y - z) / t) * x
	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 <= -1.5e+16)
		tmp = t_1;
	elseif (z <= 2e-303)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	elseif (z <= 4.2e+52)
		tmp = Float64(Float64(Float64(y - z) / t) * x);
	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 <= -1.5e+16)
		tmp = t_1;
	elseif (z <= 2e-303)
		tmp = (x / (t - z)) * y;
	elseif (z <= 4.2e+52)
		tmp = ((y - z) / t) * x;
	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, -1.5e+16], t$95$1, If[LessEqual[z, 2e-303], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 4.2e+52], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e16 or 4.2e52 < z

   1. Initial program 76.7%

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

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 76.5

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

   9. Applied rewrites 76.5%

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

   if -1.5e16 < z < 1.99999999999999986e-303

   1. Initial program 91.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 82.5

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

   5. Applied rewrites 82.5%

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

   if 1.99999999999999986e-303 < z < 4.2e52

   1. Initial program 93.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 82.0

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

   5. Applied rewrites 82.0%

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

   7. Applied rewrites 84.4%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y \cdot x}{z}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+55}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (* y x) z))))
   (if (<= z -1.2e-7)
     t_1
     (if (<= z 2e-303)
       (* (/ x (- t z)) y)
       (if (<= z 1.25e+55) (* (/ (- y z) t) x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((y * x) / z);
	double tmp;
	if (z <= -1.2e-7) {
		tmp = t_1;
	} else if (z <= 2e-303) {
		tmp = (x / (t - z)) * y;
	} else if (z <= 1.25e+55) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y * x) / z)
    if (z <= (-1.2d-7)) then
        tmp = t_1
    else if (z <= 2d-303) then
        tmp = (x / (t - z)) * y
    else if (z <= 1.25d+55) then
        tmp = ((y - z) / t) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - ((y * x) / z);
	double tmp;
	if (z <= -1.2e-7) {
		tmp = t_1;
	} else if (z <= 2e-303) {
		tmp = (x / (t - z)) * y;
	} else if (z <= 1.25e+55) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y * x) / z)
	tmp = 0
	if z <= -1.2e-7:
		tmp = t_1
	elif z <= 2e-303:
		tmp = (x / (t - z)) * y
	elif z <= 1.25e+55:
		tmp = ((y - z) / t) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y * x) / z))
	tmp = 0.0
	if (z <= -1.2e-7)
		tmp = t_1;
	elseif (z <= 2e-303)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	elseif (z <= 1.25e+55)
		tmp = Float64(Float64(Float64(y - z) / t) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - ((y * x) / z);
	tmp = 0.0;
	if (z <= -1.2e-7)
		tmp = t_1;
	elseif (z <= 2e-303)
		tmp = (x / (t - z)) * y;
	elseif (z <= 1.25e+55)
		tmp = ((y - z) / t) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e-7], t$95$1, If[LessEqual[z, 2e-303], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 1.25e+55], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999989e-7 or 1.25000000000000011e55 < z

   1. Initial program 77.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 67.2

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

   5. Applied rewrites 67.2%

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

   if -1.19999999999999989e-7 < z < 1.99999999999999986e-303

   1. Initial program 91.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 83.1

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

   5. Applied rewrites 83.1%

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

   if 1.99999999999999986e-303 < z < 1.25000000000000011e55

   1. Initial program 93.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 82.3

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

   5. Applied rewrites 82.3%

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

   7. Applied rewrites 84.6%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-7}:\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+55}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+123}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.2e+123)
   (* 1.0 x)
   (if (<= z 2e-303)
     (* (/ x (- t z)) y)
     (if (<= z 2.2e+55) (* (/ (- y z) t) x) (* 1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.2e+123) {
		tmp = 1.0 * x;
	} else if (z <= 2e-303) {
		tmp = (x / (t - z)) * y;
	} else if (z <= 2.2e+55) {
		tmp = ((y - z) / 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 <= (-8.2d+123)) then
        tmp = 1.0d0 * x
    else if (z <= 2d-303) then
        tmp = (x / (t - z)) * y
    else if (z <= 2.2d+55) then
        tmp = ((y - z) / 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 <= -8.2e+123) {
		tmp = 1.0 * x;
	} else if (z <= 2e-303) {
		tmp = (x / (t - z)) * y;
	} else if (z <= 2.2e+55) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.2e+123:
		tmp = 1.0 * x
	elif z <= 2e-303:
		tmp = (x / (t - z)) * y
	elif z <= 2.2e+55:
		tmp = ((y - z) / t) * x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.2e+123)
		tmp = Float64(1.0 * x);
	elseif (z <= 2e-303)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	elseif (z <= 2.2e+55)
		tmp = Float64(Float64(Float64(y - z) / 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 <= -8.2e+123)
		tmp = 1.0 * x;
	elseif (z <= 2e-303)
		tmp = (x / (t - z)) * y;
	elseif (z <= 2.2e+55)
		tmp = ((y - z) / t) * x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.2e+123], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 2e-303], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 2.2e+55], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.19999999999999979e123 or 2.2000000000000001e55 < z

   1. Initial program 73.7%

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

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 62.0%

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

   if -8.19999999999999979e123 < z < 1.99999999999999986e-303

   1. Initial program 90.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 72.0

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

   5. Applied rewrites 72.0%

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

   if 1.99999999999999986e-303 < z < 2.2000000000000001e55

   1. Initial program 93.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 82.3

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

   5. Applied rewrites 82.3%

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

   7. Applied rewrites 84.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+123}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{y \cdot x}{-z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+54}:\\ \;\;\;\;\frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.45e+16)
   (* 1.0 x)
   (if (<= z -1.4e-82)
     (/ (* y x) (- z))
     (if (<= z 4.4e+54) (/ (* y x) t) (* 1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.45e+16) {
		tmp = 1.0 * x;
	} else if (z <= -1.4e-82) {
		tmp = (y * x) / -z;
	} else if (z <= 4.4e+54) {
		tmp = (y * x) / 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 <= (-1.45d+16)) then
        tmp = 1.0d0 * x
    else if (z <= (-1.4d-82)) then
        tmp = (y * x) / -z
    else if (z <= 4.4d+54) then
        tmp = (y * x) / 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 <= -1.45e+16) {
		tmp = 1.0 * x;
	} else if (z <= -1.4e-82) {
		tmp = (y * x) / -z;
	} else if (z <= 4.4e+54) {
		tmp = (y * x) / t;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.45e+16:
		tmp = 1.0 * x
	elif z <= -1.4e-82:
		tmp = (y * x) / -z
	elif z <= 4.4e+54:
		tmp = (y * x) / t
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.45e+16)
		tmp = Float64(1.0 * x);
	elseif (z <= -1.4e-82)
		tmp = Float64(Float64(y * x) / Float64(-z));
	elseif (z <= 4.4e+54)
		tmp = Float64(Float64(y * x) / 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 <= -1.45e+16)
		tmp = 1.0 * x;
	elseif (z <= -1.4e-82)
		tmp = (y * x) / -z;
	elseif (z <= 4.4e+54)
		tmp = (y * x) / t;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.45e+16], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, -1.4e-82], N[(N[(y * x), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 4.4e+54], N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45e16 or 4.3999999999999998e54 < z

   1. Initial program 76.4%

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

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 55.4%

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

   if -1.45e16 < z < -1.40000000000000012e-82

   1. Initial program 94.8%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 70.5

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

   5. Applied rewrites 70.5%

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

   6. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 57.3

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

   8. Applied rewrites 57.3%

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

   if -1.40000000000000012e-82 < z < 4.3999999999999998e54

   1. Initial program 92.4%

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

   3. Taylor expanded in z around 0

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

      1. 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 69.4

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

   5. Applied rewrites 69.4%

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

Alternative 6: 67.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+128}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.55e+128)
   (* 1.0 x)
   (if (<= z 2.2e+55) (* (/ (- y z) t) x) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.55e+128) {
		tmp = 1.0 * x;
	} else if (z <= 2.2e+55) {
		tmp = ((y - z) / 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 <= (-2.55d+128)) then
        tmp = 1.0d0 * x
    else if (z <= 2.2d+55) then
        tmp = ((y - z) / 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 <= -2.55e+128) {
		tmp = 1.0 * x;
	} else if (z <= 2.2e+55) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.55e+128:
		tmp = 1.0 * x
	elif z <= 2.2e+55:
		tmp = ((y - z) / t) * x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.55e+128)
		tmp = Float64(1.0 * x);
	elseif (z <= 2.2e+55)
		tmp = Float64(Float64(Float64(y - z) / 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 <= -2.55e+128)
		tmp = 1.0 * x;
	elseif (z <= 2.2e+55)
		tmp = ((y - z) / t) * x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.55e+128], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 2.2e+55], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5499999999999999e128 or 2.2000000000000001e55 < z

   1. Initial program 73.7%

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

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 62.0%

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

   if -2.5499999999999999e128 < z < 2.2000000000000001e55

   1. Initial program 92.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 69.9

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

   5. Applied rewrites 69.9%

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

   7. Applied rewrites 71.8%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+128}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -700000:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -700000.0) (* 1.0 x) (if (<= z 3.8e+54) (* (/ x t) y) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -700000.0) {
		tmp = 1.0 * x;
	} else if (z <= 3.8e+54) {
		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 <= (-700000.0d0)) then
        tmp = 1.0d0 * x
    else if (z <= 3.8d+54) 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 <= -700000.0) {
		tmp = 1.0 * x;
	} else if (z <= 3.8e+54) {
		tmp = (x / t) * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -700000.0:
		tmp = 1.0 * x
	elif z <= 3.8e+54:
		tmp = (x / t) * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -700000.0)
		tmp = Float64(1.0 * x);
	elseif (z <= 3.8e+54)
		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 <= -700000.0)
		tmp = 1.0 * x;
	elseif (z <= 3.8e+54)
		tmp = (x / t) * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -700000.0], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 3.8e+54], N[(N[(x / t), $MachinePrecision] * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7e5 or 3.8000000000000002e54 < z

   1. Initial program 76.7%

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

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 54.9%

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

   if -7e5 < z < 3.8000000000000002e54

   1. Initial program 92.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 64.1

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

   5. Applied rewrites 64.1%

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

   7. Applied rewrites 64.6%

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

Alternative 8: 62.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+38}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+54}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e+38) (* 1.0 x) (if (<= z 4.4e+54) (* (/ y t) x) (* 1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+38) {
		tmp = 1.0 * x;
	} else if (z <= 4.4e+54) {
		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 <= (-2.7d+38)) then
        tmp = 1.0d0 * x
    else if (z <= 4.4d+54) 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 <= -2.7e+38) {
		tmp = 1.0 * x;
	} else if (z <= 4.4e+54) {
		tmp = (y / t) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e+38:
		tmp = 1.0 * x
	elif z <= 4.4e+54:
		tmp = (y / t) * x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e+38)
		tmp = Float64(1.0 * x);
	elseif (z <= 4.4e+54)
		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 <= -2.7e+38)
		tmp = 1.0 * x;
	elseif (z <= 4.4e+54)
		tmp = (y / t) * x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e+38], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 4.4e+54], N[(N[(y / t), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.69999999999999996e38 or 4.3999999999999998e54 < z

   1. Initial program 75.5%

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

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 56.6%

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

   if -2.69999999999999996e38 < z < 4.3999999999999998e54

   1. Initial program 93.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 62.8

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

   5. Applied rewrites 62.8%

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

   7. Applied rewrites 62.4%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+38}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+54}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+147}:\\ \;\;\;\;\frac{z}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e+147) (* (/ z (- z t)) x) (* (/ x (- t z)) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+147) {
		tmp = (z / (z - t)) * x;
	} else {
		tmp = (x / (t - z)) * (y - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.2d+147)) then
        tmp = (z / (z - t)) * x
    else
        tmp = (x / (t - z)) * (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+147) {
		tmp = (z / (z - t)) * x;
	} else {
		tmp = (x / (t - z)) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e+147:
		tmp = (z / (z - t)) * x
	else:
		tmp = (x / (t - z)) * (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e+147)
		tmp = Float64(Float64(z / Float64(z - t)) * x);
	else
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e+147)
		tmp = (z / (z - t)) * x;
	else
		tmp = (x / (t - z)) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e+147], N[(N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000001e147

   1. Initial program 71.3%

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

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. lower-/.f64 N/A

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

      9. neg-sub0 N/A

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

      10. lift--.f64 N/A

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

      11. sub-neg N/A

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

      12. +-commutative N/A

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

      13. associate--r+ N/A

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

      14. neg-sub0 N/A

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

      15. remove-double-neg N/A

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

      16. lower--.f64 N/A

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

      17. neg-sub0 N/A

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

      18. lift--.f64 N/A

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

      19. sub-neg N/A

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

      20. +-commutative N/A

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

      21. associate--r+ N/A

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

      22. neg-sub0 N/A

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

      23. remove-double-neg N/A

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

      24. lower--.f64 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 91.4

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

   9. Applied rewrites 91.4%

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

   if -1.20000000000000001e147 < z

   1. Initial program 88.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. *-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 90.5

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

   4. Applied rewrites 90.5%

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

Alternative 10: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.1%

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

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

4. Applied rewrites 97.5%

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

Alternative 11: 35.3% 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 86.1%

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

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

   5. un-div-inv N/A

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

   6. lower-/.f64 N/A

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

   7. lower-/.f64 97.5

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

4. Applied rewrites 97.5%

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

   1. lift-/.f64 N/A

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

   2. clear-num N/A

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

   3. associate-/r/ N/A

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

   4. lift-/.f64 N/A

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

   5. clear-num N/A

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

   6. lower-*.f64 N/A

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

   7. frac-2neg N/A

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

   8. lower-/.f64 N/A

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

   9. neg-sub0 N/A

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

   10. lift--.f64 N/A

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

   11. sub-neg N/A

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

   12. +-commutative N/A

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

   13. associate--r+ N/A

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

   14. neg-sub0 N/A

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

   15. remove-double-neg N/A

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

   16. lower--.f64 N/A

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

   17. neg-sub0 N/A

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

   18. lift--.f64 N/A

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

   19. sub-neg N/A

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

   20. +-commutative N/A

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

   21. associate--r+ N/A

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

   22. neg-sub0 N/A

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

   23. remove-double-neg N/A

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

   24. lower--.f64 97.5

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

6. Applied rewrites 97.5%

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

7. Taylor expanded in z around inf

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

9. Applied rewrites 29.2%

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

Developer Target 1: 97.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024277 
(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)))