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

Percentage Accurate: 83.7% → 97.1%

Time: 10.6s

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: 83.7% 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: 97.1% 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 86.3%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

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

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

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

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

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

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

   7. --lowering--.f64 97.6

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

4. Applied egg-rr 97.6%

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

Alternative 2: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-104}:\\ \;\;\;\;\frac{x \cdot z}{z - t}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* y (/ x z)))))
   (if (<= z -3.5e+35)
     t_1
     (if (<= z -1.9e-104)
       (/ (* x z) (- z t))
       (if (<= z 9.6e+76) (* x (/ y (- t z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y * (x / z));
	double tmp;
	if (z <= -3.5e+35) {
		tmp = t_1;
	} else if (z <= -1.9e-104) {
		tmp = (x * z) / (z - t);
	} else if (z <= 9.6e+76) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (x / z))
    if (z <= (-3.5d+35)) then
        tmp = t_1
    else if (z <= (-1.9d-104)) then
        tmp = (x * z) / (z - t)
    else if (z <= 9.6d+76) then
        tmp = x * (y / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y * (x / z));
	double tmp;
	if (z <= -3.5e+35) {
		tmp = t_1;
	} else if (z <= -1.9e-104) {
		tmp = (x * z) / (z - t);
	} else if (z <= 9.6e+76) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y * (x / z))
	tmp = 0
	if z <= -3.5e+35:
		tmp = t_1
	elif z <= -1.9e-104:
		tmp = (x * z) / (z - t)
	elif z <= 9.6e+76:
		tmp = x * (y / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y * Float64(x / z)))
	tmp = 0.0
	if (z <= -3.5e+35)
		tmp = t_1;
	elseif (z <= -1.9e-104)
		tmp = Float64(Float64(x * z) / Float64(z - t));
	elseif (z <= 9.6e+76)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y * (x / z));
	tmp = 0.0;
	if (z <= -3.5e+35)
		tmp = t_1;
	elseif (z <= -1.9e-104)
		tmp = (x * z) / (z - t);
	elseif (z <= 9.6e+76)
		tmp = x * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+35], t$95$1, If[LessEqual[z, -1.9e-104], N[(N[(x * z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+76], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000001e35 or 9.5999999999999999e76 < z

   1. Initial program 73.9%

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

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

      20. *-commutative N/A

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

      21. associate-/l* N/A

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

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

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

      23. /-lowering-/.f64 82.2

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

   5. Simplified 82.2%

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

   if -3.5000000000000001e35 < z < -1.9e-104

   1. Initial program 93.4%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 96.2

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-frac2 N/A

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

      9. mul-1-neg N/A

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

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

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 62.4

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

   7. Simplified 62.4%

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

      1. associate-*r/ N/A

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

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

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

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

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

      4. --lowering--.f64 69.0

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

   9. Applied egg-rr 69.0%

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

   if -1.9e-104 < z < 9.5999999999999999e76

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 76.8

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

   5. Simplified 76.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+35}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-104}:\\ \;\;\;\;\frac{x \cdot z}{z - t}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{z - t}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+139}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z (- z t)))))
   (if (<= z -9.5e+187)
     t_1
     (if (<= z 1.85e+139) (* (- y z) (/ x (- t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -9.5e+187) {
		tmp = t_1;
	} else if (z <= 1.85e+139) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / (z - t))
    if (z <= (-9.5d+187)) then
        tmp = t_1
    else if (z <= 1.85d+139) then
        tmp = (y - z) * (x / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / (z - t));
	double tmp;
	if (z <= -9.5e+187) {
		tmp = t_1;
	} else if (z <= 1.85e+139) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / (z - t))
	tmp = 0
	if z <= -9.5e+187:
		tmp = t_1
	elif z <= 1.85e+139:
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / Float64(z - t)))
	tmp = 0.0
	if (z <= -9.5e+187)
		tmp = t_1;
	elseif (z <= 1.85e+139)
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / (z - t));
	tmp = 0.0;
	if (z <= -9.5e+187)
		tmp = t_1;
	elseif (z <= 1.85e+139)
		tmp = (y - z) * (x / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+187], t$95$1, If[LessEqual[z, 1.85e+139], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999996e187 or 1.84999999999999996e139 < z

   1. Initial program 62.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 57.2

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

   5. Simplified 57.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. distribute-frac-neg N/A

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

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

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

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

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

      7. --lowering--.f64 92.2

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

   7. Applied egg-rr 92.2%

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

   if -9.4999999999999996e187 < z < 1.84999999999999996e139

   1. Initial program 94.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 91.3

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

   4. Applied egg-rr 91.3%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+139}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= y -1.95e+123) t_1 (if (<= y 7.6e+22) (* x (/ z (- z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -1.95e+123) {
		tmp = t_1;
	} else if (y <= 7.6e+22) {
		tmp = x * (z / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (y <= (-1.95d+123)) then
        tmp = t_1
    else if (y <= 7.6d+22) then
        tmp = x * (z / (z - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -1.95e+123) {
		tmp = t_1;
	} else if (y <= 7.6e+22) {
		tmp = x * (z / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if y <= -1.95e+123:
		tmp = t_1
	elif y <= 7.6e+22:
		tmp = x * (z / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -1.95e+123)
		tmp = t_1;
	elseif (y <= 7.6e+22)
		tmp = Float64(x * Float64(z / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (y <= -1.95e+123)
		tmp = t_1;
	elseif (y <= 7.6e+22)
		tmp = x * (z / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.95e+123], t$95$1, If[LessEqual[y, 7.6e+22], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.94999999999999996e123 or 7.6000000000000008e22 < y

   1. Initial program 84.9%

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

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

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

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

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

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

      4. --lowering--.f64 84.3

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

   5. Simplified 84.3%

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

   if -1.94999999999999996e123 < y < 7.6000000000000008e22

   1. Initial program 87.0%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 69.8

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

   5. Simplified 69.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. distribute-frac-neg N/A

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

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

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

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

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

      7. --lowering--.f64 80.9

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

   7. Applied egg-rr 80.9%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{x}{z}\\ \mathbf{if}\;z \leq -0.032:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+76}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* y (/ x z)))))
   (if (<= z -0.032) t_1 (if (<= z 2.8e+76) (* x (/ y (- t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y * (x / z));
	double tmp;
	if (z <= -0.032) {
		tmp = t_1;
	} else if (z <= 2.8e+76) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y * (x / z))
    if (z <= (-0.032d0)) then
        tmp = t_1
    else if (z <= 2.8d+76) then
        tmp = x * (y / (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y * (x / z));
	double tmp;
	if (z <= -0.032) {
		tmp = t_1;
	} else if (z <= 2.8e+76) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y * (x / z))
	tmp = 0
	if z <= -0.032:
		tmp = t_1
	elif z <= 2.8e+76:
		tmp = x * (y / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y * Float64(x / z)))
	tmp = 0.0
	if (z <= -0.032)
		tmp = t_1;
	elseif (z <= 2.8e+76)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y * (x / z));
	tmp = 0.0;
	if (z <= -0.032)
		tmp = t_1;
	elseif (z <= 2.8e+76)
		tmp = x * (y / (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.032], t$95$1, If[LessEqual[z, 2.8e+76], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.032000000000000001 or 2.7999999999999999e76 < z

   1. Initial program 75.5%

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

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

      20. *-commutative N/A

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

      21. associate-/l* N/A

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

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

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

      23. /-lowering-/.f64 81.6

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

   5. Simplified 81.6%

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

   if -0.032000000000000001 < z < 2.7999999999999999e76

   1. Initial program 94.6%

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

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

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

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

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

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

      4. --lowering--.f64 72.1

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

   5. Simplified 72.1%

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

Alternative 6: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= y -3.8e-23) t_1 (if (<= y 4.2e+20) (* z (/ x (- z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -3.8e-23) {
		tmp = t_1;
	} else if (y <= 4.2e+20) {
		tmp = z * (x / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / (t - z))
    if (y <= (-3.8d-23)) then
        tmp = t_1
    else if (y <= 4.2d+20) then
        tmp = z * (x / (z - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (y / (t - z));
	double tmp;
	if (y <= -3.8e-23) {
		tmp = t_1;
	} else if (y <= 4.2e+20) {
		tmp = z * (x / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / (t - z))
	tmp = 0
	if y <= -3.8e-23:
		tmp = t_1
	elif y <= 4.2e+20:
		tmp = z * (x / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(t - z)))
	tmp = 0.0
	if (y <= -3.8e-23)
		tmp = t_1;
	elseif (y <= 4.2e+20)
		tmp = Float64(z * Float64(x / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / (t - z));
	tmp = 0.0;
	if (y <= -3.8e-23)
		tmp = t_1;
	elseif (y <= 4.2e+20)
		tmp = z * (x / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e-23], t$95$1, If[LessEqual[y, 4.2e+20], N[(z * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000011e-23 or 4.2e20 < y

   1. Initial program 86.4%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

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

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

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

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

      4. --lowering--.f64 75.2

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

   5. Simplified 75.2%

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

   if -3.80000000000000011e-23 < y < 4.2e20

   1. Initial program 86.1%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 97.1

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

   4. Applied egg-rr 97.1%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. mul-1-neg N/A

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

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

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

      7. mul-1-neg N/A

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

      8. distribute-neg-frac2 N/A

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

      9. mul-1-neg N/A

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

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

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. distribute-neg-in N/A

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

      15. unsub-neg N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 72.8

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

   7. Simplified 72.8%

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

Alternative 7: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.49:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.49)
   x
   (if (<= z 1.9e+139) (* x (/ y (- t z))) (fma x (/ t z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.49) {
		tmp = x;
	} else if (z <= 1.9e+139) {
		tmp = x * (y / (t - z));
	} else {
		tmp = fma(x, (t / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.49)
		tmp = x;
	elseif (z <= 1.9e+139)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = fma(x, Float64(t / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.49], x, If[LessEqual[z, 1.9e+139], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.48999999999999999

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 71.1%

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

   if -0.48999999999999999 < z < 1.9e139

   1. Initial program 94.6%

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

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

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

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

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

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

      4. --lowering--.f64 70.4

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

   5. Simplified 70.4%

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

   if 1.9e139 < z

   1. Initial program 70.2%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 62.0

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

   5. Simplified 62.0%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. /-lowering-/.f64 85.4

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

   8. Simplified 85.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{t}{z}, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 60.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.1e-60) x (if (<= z 3.4e+87) (* x (/ y t)) (fma x (/ t z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e-60) {
		tmp = x;
	} else if (z <= 3.4e+87) {
		tmp = x * (y / t);
	} else {
		tmp = fma(x, (t / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.1e-60)
		tmp = x;
	elseif (z <= 3.4e+87)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = fma(x, Float64(t / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.1e-60], x, If[LessEqual[z, 3.4e+87], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.09999999999999991e-60

   1. Initial program 75.2%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 66.6%

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

   if -2.09999999999999991e-60 < z < 3.4000000000000002e87

   1. Initial program 95.7%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 95.6

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

   4. Applied egg-rr 95.6%

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

   5. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 74.2

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

   7. Simplified 74.2%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. clear-num N/A

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

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

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

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

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

      6. --lowering--.f64 74.2

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

   9. Applied egg-rr 74.2%

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

   10. Taylor expanded in t around inf

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

       1. /-lowering-/.f64 63.3

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

   12. Simplified 63.3%

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

   if 3.4000000000000002e87 < z

   1. Initial program 75.7%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 59.1

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

      5. /-lowering-/.f64 74.5

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

   8. Simplified 74.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{t}{z}, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.3e-60) x (if (<= z 4.5e+88) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e-60) {
		tmp = x;
	} else if (z <= 4.5e+88) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.3d-60)) then
        tmp = x
    else if (z <= 4.5d+88) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.3e-60) {
		tmp = x;
	} else if (z <= 4.5e+88) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.3e-60:
		tmp = x
	elif z <= 4.5e+88:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.3e-60)
		tmp = x;
	elseif (z <= 4.5e+88)
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.3e-60)
		tmp = x;
	elseif (z <= 4.5e+88)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.3e-60], x, If[LessEqual[z, 4.5e+88], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2999999999999999e-60 or 4.5e88 < z

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 69.5%

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

   if -1.2999999999999999e-60 < z < 4.5e88

   1. Initial program 95.7%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 95.6

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

   4. Applied egg-rr 95.6%

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

   5. Taylor expanded in y around inf

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

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

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

      2. --lowering--.f64 74.2

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

   7. Simplified 74.2%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. clear-num N/A

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

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

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

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

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

      6. --lowering--.f64 74.2

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

   9. Applied egg-rr 74.2%

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

   10. Taylor expanded in t around inf

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

       1. /-lowering-/.f64 63.3

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

   12. Simplified 63.3%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.3%

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

   1. associate-/l* N/A

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

   2. *-commutative N/A

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

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

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

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

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

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

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

   6. --lowering--.f64 97.6

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

4. Applied egg-rr 97.6%

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

5. Final simplification 97.6%

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

Alternative 11: 34.8% accurate, 23.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 86.3%

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

3. Taylor expanded in z around inf

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

5. Simplified 40.8%

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

Developer Target 1: 97.1% 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 2024199 
(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)))