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

Percentage Accurate: 83.5% → 97.2%

Time: 7.3s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 83.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.4%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
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. *-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 96.3

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

4. Applied rewrites 96.3%

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

Alternative 2: 69.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z - y}{z} \cdot x\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-189}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+152}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (- z y) z) x)))
   (if (<= z -4.7e+118)
     t_1
     (if (<= z 2.6e-189)
       (* (/ x (- t z)) y)
       (if (<= z 2.1e+152) (/ (* (- y z) x) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - y) / z) * x;
	double tmp;
	if (z <= -4.7e+118) {
		tmp = t_1;
	} else if (z <= 2.6e-189) {
		tmp = (x / (t - z)) * y;
	} else if (z <= 2.1e+152) {
		tmp = ((y - z) * x) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((z - y) / z) * x
    if (z <= (-4.7d+118)) then
        tmp = t_1
    else if (z <= 2.6d-189) then
        tmp = (x / (t - z)) * y
    else if (z <= 2.1d+152) then
        tmp = ((y - z) * x) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((z - y) / z) * x;
	double tmp;
	if (z <= -4.7e+118) {
		tmp = t_1;
	} else if (z <= 2.6e-189) {
		tmp = (x / (t - z)) * y;
	} else if (z <= 2.1e+152) {
		tmp = ((y - z) * x) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((z - y) / z) * x
	tmp = 0
	if z <= -4.7e+118:
		tmp = t_1
	elif z <= 2.6e-189:
		tmp = (x / (t - z)) * y
	elif z <= 2.1e+152:
		tmp = ((y - z) * x) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - y) / z) * x)
	tmp = 0.0
	if (z <= -4.7e+118)
		tmp = t_1;
	elseif (z <= 2.6e-189)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	elseif (z <= 2.1e+152)
		tmp = Float64(Float64(Float64(y - z) * x) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((z - y) / z) * x;
	tmp = 0.0;
	if (z <= -4.7e+118)
		tmp = t_1;
	elseif (z <= 2.6e-189)
		tmp = (x / (t - z)) * y;
	elseif (z <= 2.1e+152)
		tmp = ((y - z) * x) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[z, -4.7e+118], t$95$1, If[LessEqual[z, 2.6e-189], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 2.1e+152], N[(N[(N[(y - z), $MachinePrecision] * x), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6999999999999997e118 or 2.1000000000000002e152 < z

   1. Initial program 61.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 99.7

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

   4. Applied rewrites 99.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. frac-2neg N/A

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

      6. associate-/r/ N/A

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

      7. associate-*r* N/A

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

      8. div-inv N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. neg-sub0 N/A

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. lift-neg.f64 N/A

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

      15. +-commutative N/A

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

      16. associate--r+ N/A

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

      17. neg-sub0 N/A

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

      18. lift-neg.f64 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 N/A

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

      21. neg-sub0 N/A

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

      22. lift--.f64 N/A

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

      23. sub-neg N/A

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

      24. lift-neg.f64 N/A

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

      25. +-commutative N/A

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

   6. Applied rewrites 72.0%

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

   7. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. div-sub N/A

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

      4. *-inverses N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. *-inverses N/A

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

      11. div-sub N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 83.8

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

   9. Applied rewrites 83.8%

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

   if -4.6999999999999997e118 < z < 2.5999999999999999e-189

   1. Initial program 89.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-*l/ N/A

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

      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 84.7

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

   5. Applied rewrites 84.7%

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

   if 2.5999999999999999e-189 < z < 2.1000000000000002e152

   1. Initial program 94.2%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 69.6

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

   5. Applied rewrites 69.6%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+118}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-189}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+152}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+167} \lor \neg \left(z \leq 8.5 \cdot 10^{+151}\right):\\ \;\;\;\;\frac{z}{t - z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e+167) (not (<= z 8.5e+151)))
   (* (/ z (- t z)) (- x))
   (* (/ x (- t z)) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+167) || !(z <= 8.5e+151)) {
		tmp = (z / (t - z)) * -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 <= (-1.8d+167)) .or. (.not. (z <= 8.5d+151))) then
        tmp = (z / (t - z)) * -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 <= -1.8e+167) || !(z <= 8.5e+151)) {
		tmp = (z / (t - z)) * -x;
	} else {
		tmp = (x / (t - z)) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e+167) or not (z <= 8.5e+151):
		tmp = (z / (t - z)) * -x
	else:
		tmp = (x / (t - z)) * (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e+167) || !(z <= 8.5e+151))
		tmp = Float64(Float64(z / Float64(t - z)) * Float64(-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 <= -1.8e+167) || ~((z <= 8.5e+151)))
		tmp = (z / (t - z)) * -x;
	else
		tmp = (x / (t - z)) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e+167], N[Not[LessEqual[z, 8.5e+151]], $MachinePrecision]], N[(N[(z / N[(t - z), $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 < -1.80000000000000012e167 or 8.50000000000000051e151 < z

   1. Initial program 62.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 93.4

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

   5. Applied rewrites 93.4%

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

   if -1.80000000000000012e167 < z < 8.50000000000000051e151

   1. Initial program 89.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. *-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 91.6

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

   4. Applied rewrites 91.6%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+167} \lor \neg \left(z \leq 8.5 \cdot 10^{+151}\right):\\ \;\;\;\;\frac{z}{t - z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+165}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-25}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.8e+165)
   (* 1.0 x)
   (if (<= z -3.8e-25)
     (* (- y) (/ x z))
     (if (<= z 2.5e+152) (* (/ y t) x) (* 1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e+165) {
		tmp = 1.0 * x;
	} else if (z <= -3.8e-25) {
		tmp = -y * (x / z);
	} else if (z <= 2.5e+152) {
		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 <= (-5.8d+165)) then
        tmp = 1.0d0 * x
    else if (z <= (-3.8d-25)) then
        tmp = -y * (x / z)
    else if (z <= 2.5d+152) 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 <= -5.8e+165) {
		tmp = 1.0 * x;
	} else if (z <= -3.8e-25) {
		tmp = -y * (x / z);
	} else if (z <= 2.5e+152) {
		tmp = (y / t) * x;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.8e+165:
		tmp = 1.0 * x
	elif z <= -3.8e-25:
		tmp = -y * (x / z)
	elif z <= 2.5e+152:
		tmp = (y / t) * x
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.8e+165)
		tmp = Float64(1.0 * x);
	elseif (z <= -3.8e-25)
		tmp = Float64(Float64(-y) * Float64(x / z));
	elseif (z <= 2.5e+152)
		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 <= -5.8e+165)
		tmp = 1.0 * x;
	elseif (z <= -3.8e-25)
		tmp = -y * (x / z);
	elseif (z <= 2.5e+152)
		tmp = (y / t) * x;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.8e+165], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, -3.8e-25], N[((-y) * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+152], N[(N[(y / t), $MachinePrecision] * x), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.80000000000000011e165 or 2.5e152 < z

   1. Initial program 61.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. *-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 79.8%

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

   if -5.80000000000000011e165 < z < -3.7999999999999998e-25

   1. Initial program 72.5%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

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

      3. associate-/l* N/A

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

      4. div-sub N/A

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

      5. sub-neg N/A

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

      6. *-inverses N/A

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

      7. metadata-eval N/A

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

      8. distribute-rgt-in N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. mul-1-neg N/A

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

      12. unsub-neg N/A

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

      13. associate-+l- N/A

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

      14. neg-sub0 N/A

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

      15. associate-/l* N/A

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

      16. *-commutative N/A

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

      17. distribute-lft-neg-in N/A

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

      18. mul-1-neg N/A

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

      19. lower-fma.f64 N/A

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

   5. Applied rewrites 65.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 48.7%

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

   if -3.7999999999999998e-25 < z < 2.5e152

   1. Initial program 94.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 94.1

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

   4. Applied rewrites 94.1%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 64.2

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

   7. Applied rewrites 64.2%

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

Alternative 5: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+14} \lor \neg \left(t \leq 1.6 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.9e+14) (not (<= t 1.6e-77)))
   (* (/ (- y z) t) x)
   (- x (* (/ y z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.9e+14) || !(t <= 1.6e-77)) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = x - ((y / z) * 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 ((t <= (-3.9d+14)) .or. (.not. (t <= 1.6d-77))) then
        tmp = ((y - z) / t) * x
    else
        tmp = x - ((y / z) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.9e+14) || !(t <= 1.6e-77)) {
		tmp = ((y - z) / t) * x;
	} else {
		tmp = x - ((y / z) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.9e+14) or not (t <= 1.6e-77):
		tmp = ((y - z) / t) * x
	else:
		tmp = x - ((y / z) * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.9e+14) || !(t <= 1.6e-77))
		tmp = Float64(Float64(Float64(y - z) / t) * x);
	else
		tmp = Float64(x - Float64(Float64(y / z) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.9e+14) || ~((t <= 1.6e-77)))
		tmp = ((y - z) / t) * x;
	else
		tmp = x - ((y / z) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.9e+14], N[Not[LessEqual[t, 1.6e-77]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * x), $MachinePrecision], N[(x - N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9e14 or 1.6e-77 < t

   1. Initial program 84.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. *-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 96.1

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

   4. Applied rewrites 96.1%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 80.9

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

   7. Applied rewrites 80.9%

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

   if -3.9e14 < t < 1.6e-77

   1. Initial program 82.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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-rgt-in N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. mul-1-neg N/A

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

      12. unsub-neg N/A

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

      13. associate-+l- N/A

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

      14. neg-sub0 N/A

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

      15. associate-/l* N/A

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

      16. *-commutative N/A

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

      17. distribute-lft-neg-in N/A

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

      18. mul-1-neg N/A

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

      19. lower-fma.f64 N/A

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

   5. Applied rewrites 82.8%

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

   7. Applied rewrites 82.8%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+14} \lor \neg \left(t \leq 1.6 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{y - z}{t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+118} \lor \neg \left(z \leq 6600000\right):\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.7e+118) (not (<= z 6600000.0)))
   (* (/ (- z y) z) x)
   (* (/ x (- t z)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.7e+118) || !(z <= 6600000.0)) {
		tmp = ((z - y) / z) * x;
	} else {
		tmp = (x / (t - z)) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.7d+118)) .or. (.not. (z <= 6600000.0d0))) then
        tmp = ((z - y) / z) * x
    else
        tmp = (x / (t - z)) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.7e+118) || !(z <= 6600000.0)) {
		tmp = ((z - y) / z) * x;
	} else {
		tmp = (x / (t - z)) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.7e+118) or not (z <= 6600000.0):
		tmp = ((z - y) / z) * x
	else:
		tmp = (x / (t - z)) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.7e+118) || !(z <= 6600000.0))
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	else
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.7e+118) || ~((z <= 6600000.0)))
		tmp = ((z - y) / z) * x;
	else
		tmp = (x / (t - z)) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.7e+118], N[Not[LessEqual[z, 6600000.0]], $MachinePrecision]], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6999999999999997e118 or 6.6e6 < z

   1. Initial program 70.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. *-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 99.7

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

   4. Applied rewrites 99.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. frac-2neg N/A

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

      6. associate-/r/ N/A

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

      7. associate-*r* N/A

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

      8. div-inv N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. neg-sub0 N/A

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. lift-neg.f64 N/A

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

      15. +-commutative N/A

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

      16. associate--r+ N/A

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

      17. neg-sub0 N/A

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

      18. lift-neg.f64 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 N/A

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

      21. neg-sub0 N/A

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

      22. lift--.f64 N/A

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

      23. sub-neg N/A

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

      24. lift-neg.f64 N/A

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

      25. +-commutative N/A

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

   6. Applied rewrites 73.8%

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

   7. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. div-sub N/A

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

      4. *-inverses N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. *-inverses N/A

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

      11. div-sub N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 74.7

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

   9. Applied rewrites 74.7%

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

   if -4.6999999999999997e118 < z < 6.6e6

   1. Initial program 91.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 79.7

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

   5. Applied rewrites 79.7%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+118} \lor \neg \left(z \leq 6600000\right):\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-31} \lor \neg \left(z \leq 9.4 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.8e-31) (not (<= z 9.4e-38)))
   (* (/ (- z y) z) x)
   (* (/ y t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e-31) || !(z <= 9.4e-38)) {
		tmp = ((z - y) / z) * x;
	} else {
		tmp = (y / t) * 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 <= (-3.8d-31)) .or. (.not. (z <= 9.4d-38))) then
        tmp = ((z - y) / z) * x
    else
        tmp = (y / t) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.8e-31) || !(z <= 9.4e-38)) {
		tmp = ((z - y) / z) * x;
	} else {
		tmp = (y / t) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.8e-31) or not (z <= 9.4e-38):
		tmp = ((z - y) / z) * x
	else:
		tmp = (y / t) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.8e-31) || !(z <= 9.4e-38))
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	else
		tmp = Float64(Float64(y / t) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.8e-31) || ~((z <= 9.4e-38)))
		tmp = ((z - y) / z) * x;
	else
		tmp = (y / t) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.8e-31], N[Not[LessEqual[z, 9.4e-38]], $MachinePrecision]], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8e-31 or 9.39999999999999996e-38 < z

   1. Initial program 74.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. 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 99.7

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

   4. Applied rewrites 99.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. frac-2neg N/A

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

      6. associate-/r/ N/A

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

      7. associate-*r* N/A

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

      8. div-inv N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. neg-sub0 N/A

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. lift-neg.f64 N/A

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

      15. +-commutative N/A

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

      16. associate--r+ N/A

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

      17. neg-sub0 N/A

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

      18. lift-neg.f64 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 N/A

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

      21. neg-sub0 N/A

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

      22. lift--.f64 N/A

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

      23. sub-neg N/A

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

      24. lift-neg.f64 N/A

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

      25. +-commutative N/A

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

   6. Applied rewrites 80.7%

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

   7. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. div-sub N/A

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

      4. *-inverses N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. *-inverses N/A

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

      11. div-sub N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 70.0

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

   9. Applied rewrites 70.0%

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

   if -3.8e-31 < z < 9.39999999999999996e-38

   1. Initial program 94.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. 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 91.8

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

   4. Applied rewrites 91.8%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 74.0

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

   7. Applied rewrites 74.0%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-31} \lor \neg \left(z \leq 9.4 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+118}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{elif}\;z \leq 6600000:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.7e+118)
   (* (/ (- z y) z) x)
   (if (<= z 6600000.0) (* (/ x (- t z)) y) (- x (* (/ y z) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.7e+118) {
		tmp = ((z - y) / z) * x;
	} else if (z <= 6600000.0) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = x - ((y / z) * 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 <= (-4.7d+118)) then
        tmp = ((z - y) / z) * x
    else if (z <= 6600000.0d0) then
        tmp = (x / (t - z)) * y
    else
        tmp = x - ((y / z) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.7e+118) {
		tmp = ((z - y) / z) * x;
	} else if (z <= 6600000.0) {
		tmp = (x / (t - z)) * y;
	} else {
		tmp = x - ((y / z) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.7e+118:
		tmp = ((z - y) / z) * x
	elif z <= 6600000.0:
		tmp = (x / (t - z)) * y
	else:
		tmp = x - ((y / z) * x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.7e+118)
		tmp = Float64(Float64(Float64(z - y) / z) * x);
	elseif (z <= 6600000.0)
		tmp = Float64(Float64(x / Float64(t - z)) * y);
	else
		tmp = Float64(x - Float64(Float64(y / z) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.7e+118)
		tmp = ((z - y) / z) * x;
	elseif (z <= 6600000.0)
		tmp = (x / (t - z)) * y;
	else
		tmp = x - ((y / z) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.7e+118], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 6600000.0], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(x - N[(N[(y / z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6999999999999997e118

   1. Initial program 67.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 99.7

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

   4. Applied rewrites 99.7%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. clear-num N/A

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

      5. frac-2neg N/A

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

      6. associate-/r/ N/A

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

      7. associate-*r* N/A

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

      8. div-inv N/A

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

      9. lower-*.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. neg-sub0 N/A

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

      12. lift--.f64 N/A

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

      13. sub-neg N/A

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

      14. lift-neg.f64 N/A

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

      15. +-commutative N/A

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

      16. associate--r+ N/A

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

      17. neg-sub0 N/A

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

      18. lift-neg.f64 N/A

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

      19. remove-double-neg N/A

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

      20. lower--.f64 N/A

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

      21. neg-sub0 N/A

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

      22. lift--.f64 N/A

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

      23. sub-neg N/A

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

      24. lift-neg.f64 N/A

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

      25. +-commutative N/A

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

   6. Applied rewrites 71.2%

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

   7. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. div-sub N/A

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

      4. *-inverses N/A

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

      5. unsub-neg N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. mul-1-neg N/A

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

      9. unsub-neg N/A

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

      10. *-inverses N/A

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

      11. div-sub N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 83.4

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

   9. Applied rewrites 83.4%

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

   if -4.6999999999999997e118 < z < 6.6e6

   1. Initial program 91.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 79.7

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

   5. Applied rewrites 79.7%

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

   if 6.6e6 < z

   1. Initial program 73.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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-rgt-in N/A

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

      9. *-commutative N/A

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

      10. associate-/l* N/A

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

      11. mul-1-neg N/A

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

      12. unsub-neg N/A

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

      13. associate-+l- N/A

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

      14. neg-sub0 N/A

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

      15. associate-/l* N/A

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

      16. *-commutative N/A

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

      17. distribute-lft-neg-in N/A

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

      18. mul-1-neg N/A

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

      19. lower-fma.f64 N/A

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

   5. Applied rewrites 68.3%

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

   7. Applied rewrites 68.3%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+118}:\\ \;\;\;\;\frac{z - y}{z} \cdot x\\ \mathbf{elif}\;z \leq 6600000:\\ \;\;\;\;\frac{x}{t - z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+119} \lor \neg \left(z \leq 2.5 \cdot 10^{+152}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.15e+119) (not (<= z 2.5e+152))) (* 1.0 x) (* (/ y t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+119) || !(z <= 2.5e+152)) {
		tmp = 1.0 * x;
	} else {
		tmp = (y / t) * 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 <= (-1.15d+119)) .or. (.not. (z <= 2.5d+152))) then
        tmp = 1.0d0 * x
    else
        tmp = (y / t) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+119) || !(z <= 2.5e+152)) {
		tmp = 1.0 * x;
	} else {
		tmp = (y / t) * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.15e+119) or not (z <= 2.5e+152):
		tmp = 1.0 * x
	else:
		tmp = (y / t) * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.15e+119) || !(z <= 2.5e+152))
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(y / t) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.15e+119) || ~((z <= 2.5e+152)))
		tmp = 1.0 * x;
	else
		tmp = (y / t) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.15e+119], N[Not[LessEqual[z, 2.5e+152]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e119 or 2.5e152 < z

   1. Initial program 61.6%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 70.3%

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

   if -1.15e119 < z < 2.5e152

   1. Initial program 91.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. *-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 95.1

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

   4. Applied rewrites 95.1%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 59.1

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

   7. Applied rewrites 59.1%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+119} \lor \neg \left(z \leq 2.5 \cdot 10^{+152}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+119} \lor \neg \left(z \leq 8500000000\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.15e+119) (not (<= z 8500000000.0))) (* 1.0 x) (* (/ x t) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+119) || !(z <= 8500000000.0)) {
		tmp = 1.0 * x;
	} else {
		tmp = (x / t) * y;
	}
	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 <= (-1.15d+119)) .or. (.not. (z <= 8500000000.0d0))) then
        tmp = 1.0d0 * x
    else
        tmp = (x / t) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+119) || !(z <= 8500000000.0)) {
		tmp = 1.0 * x;
	} else {
		tmp = (x / t) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.15e+119) or not (z <= 8500000000.0):
		tmp = 1.0 * x
	else:
		tmp = (x / t) * y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.15e+119) || !(z <= 8500000000.0))
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(x / t) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.15e+119) || ~((z <= 8500000000.0)))
		tmp = 1.0 * x;
	else
		tmp = (x / t) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.15e+119], N[Not[LessEqual[z, 8500000000.0]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], N[(N[(x / t), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e119 or 8.5e9 < z

   1. Initial program 70.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. *-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 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 59.1%

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

   if -1.15e119 < z < 8.5e9

   1. Initial program 91.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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 59.6

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

   5. Applied rewrites 59.6%

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

   7. Applied rewrites 60.7%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+119} \lor \neg \left(z \leq 8500000000\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} \cdot y\\ \end{array} \]
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 83.4%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
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. *-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 96.3

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

4. Applied rewrites 96.3%

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

5. Taylor expanded in z around inf

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

7. Applied rewrites 27.1%

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

Developer Target 1: 97.2% 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 2024313 
(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)))