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

Percentage Accurate: 84.0% → 96.9%

Time: 10.0s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 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 82.9%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. remove-double-neg N/A

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

   4. lift--.f64 N/A

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

   5. remove-double-neg N/A

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

   6. lift-*.f64 N/A

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

   7. associate-/l* N/A

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

   8. clear-num N/A

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

   9. un-div-inv N/A

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

   10. lower-/.f64 N/A

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

   11. lower-/.f64 96.3

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

4. Applied egg-rr 96.3%

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

Alternative 2: 58.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-130}:\\ \;\;\;\;-\frac{x \cdot z}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e+71)
   x
   (if (<= z -1.65e-130)
     (- (/ (* x z) t))
     (if (<= z 3.5e-96) (/ (* x y) t) (fma x (/ t z) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+71) {
		tmp = x;
	} else if (z <= -1.65e-130) {
		tmp = -((x * z) / t);
	} else if (z <= 3.5e-96) {
		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 <= -4e+71)
		tmp = x;
	elseif (z <= -1.65e-130)
		tmp = Float64(-Float64(Float64(x * z) / t));
	elseif (z <= 3.5e-96)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = fma(x, Float64(t / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4e+71], x, If[LessEqual[z, -1.65e-130], (-N[(N[(x * z), $MachinePrecision] / t), $MachinePrecision]), If[LessEqual[z, 3.5e-96], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.0000000000000002e71

   1. Initial program 66.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. clear-num N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 61.9%

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

      1. /-rgt-identity 61.9

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

   9. Applied egg-rr 61.9%

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

   if -4.0000000000000002e71 < z < -1.6499999999999999e-130

   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

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. clear-num N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 97.1

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

   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. distribute-neg-frac2 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. remove-double-neg N/A

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

      9. sub-neg N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 60.5

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

   7. Simplified 60.5%

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

   8. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 48.7

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

   10. Simplified 48.7%

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

   if -1.6499999999999999e-130 < z < 3.4999999999999999e-96

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 79.8

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

   5. Simplified 79.8%

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

   if 3.4999999999999999e-96 < z

   1. Initial program 74.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. clear-num N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 98.6

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

   4. Applied egg-rr 98.6%

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

   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. distribute-neg-frac2 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. remove-double-neg N/A

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

      9. sub-neg N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 65.0

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

   7. Simplified 65.0%

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

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{t \cdot x}{z}} \]
   9. 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. lower-fma.f64 N/A

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

      5. lower-/.f64 52.8

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

   10. Simplified 52.8%

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

Alternative 3: 90.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+128}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z y) z))))
   (if (<= z -2.6e+170) t_1 (if (<= z 2e+128) (* (- y z) (/ x (- t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -2.6e+170) {
		tmp = t_1;
	} else if (z <= 2e+128) {
		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 - y) / z)
    if (z <= (-2.6d+170)) then
        tmp = t_1
    else if (z <= 2d+128) 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 - y) / z);
	double tmp;
	if (z <= -2.6e+170) {
		tmp = t_1;
	} else if (z <= 2e+128) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - y) / z)
	tmp = 0
	if z <= -2.6e+170:
		tmp = t_1
	elif z <= 2e+128:
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -2.6e+170)
		tmp = t_1;
	elseif (z <= 2e+128)
		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 - y) / z);
	tmp = 0.0;
	if (z <= -2.6e+170)
		tmp = t_1;
	elseif (z <= 2e+128)
		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[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+170], t$95$1, If[LessEqual[z, 2e+128], 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 < -2.5999999999999998e170 or 2.0000000000000002e128 < z

   1. Initial program 57.1%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 51.6

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

   5. Simplified 51.6%

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

      1. lift--.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. frac-2neg N/A

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

      7. lift-neg.f64 N/A

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

      8. remove-double-neg N/A

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

      9. lower-/.f64 N/A

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

      10. neg-sub0 N/A

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. lift-neg.f64 N/A

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

      14. +-commutative N/A

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

      15. associate--r+ N/A

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

      16. neg-sub0 N/A

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

      17. lift-neg.f64 N/A

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

      18. remove-double-neg N/A

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

      19. lower--.f64 88.6

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

   7. Applied egg-rr 88.6%

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

   if -2.5999999999999998e170 < z < 2.0000000000000002e128

   1. Initial program 91.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 91.7

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

   4. Applied egg-rr 91.7%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+128}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - y}{z}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+23}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z y) z))))
   (if (<= z -9e+69) t_1 (if (<= z 1.3e+23) (/ (* x (- y z)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - y) / z);
	double tmp;
	if (z <= -9e+69) {
		tmp = t_1;
	} else if (z <= 1.3e+23) {
		tmp = (x * (y - 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 * ((z - y) / z)
    if (z <= (-9d+69)) then
        tmp = t_1
    else if (z <= 1.3d+23) then
        tmp = (x * (y - 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 * ((z - y) / z);
	double tmp;
	if (z <= -9e+69) {
		tmp = t_1;
	} else if (z <= 1.3e+23) {
		tmp = (x * (y - z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - y) / z)
	tmp = 0
	if z <= -9e+69:
		tmp = t_1
	elif z <= 1.3e+23:
		tmp = (x * (y - z)) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - y) / z))
	tmp = 0.0
	if (z <= -9e+69)
		tmp = t_1;
	elseif (z <= 1.3e+23)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - y) / z);
	tmp = 0.0;
	if (z <= -9e+69)
		tmp = t_1;
	elseif (z <= 1.3e+23)
		tmp = (x * (y - z)) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+69], t$95$1, If[LessEqual[z, 1.3e+23], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.9999999999999999e69 or 1.29999999999999996e23 < z

   1. Initial program 66.4%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 55.9

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

   5. Simplified 55.9%

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

      1. lift--.f64 N/A

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

      2. lift-neg.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. frac-2neg N/A

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

      7. lift-neg.f64 N/A

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

      8. remove-double-neg N/A

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

      9. lower-/.f64 N/A

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

      10. neg-sub0 N/A

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

      11. lift--.f64 N/A

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

      12. sub-neg N/A

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

      13. lift-neg.f64 N/A

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

      14. +-commutative N/A

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

      15. associate--r+ N/A

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

      16. neg-sub0 N/A

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

      17. lift-neg.f64 N/A

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

      18. remove-double-neg N/A

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

      19. lower--.f64 82.4

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

   7. Applied egg-rr 82.4%

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

   if -8.9999999999999999e69 < z < 1.29999999999999996e23

   1. Initial program 94.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 76.0

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

   5. Simplified 76.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+23}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{t - z}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t z)))))
   (if (<= y -3.5e-65) t_1 (if (<= y 9e-7) (* 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 <= -3.5e-65) {
		tmp = t_1;
	} else if (y <= 9e-7) {
		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 <= (-3.5d-65)) then
        tmp = t_1
    else if (y <= 9d-7) 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 <= -3.5e-65) {
		tmp = t_1;
	} else if (y <= 9e-7) {
		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 <= -3.5e-65:
		tmp = t_1
	elif y <= 9e-7:
		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 <= -3.5e-65)
		tmp = t_1;
	elseif (y <= 9e-7)
		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 <= -3.5e-65)
		tmp = t_1;
	elseif (y <= 9e-7)
		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, -3.5e-65], t$95$1, If[LessEqual[y, 9e-7], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.50000000000000005e-65 or 8.99999999999999959e-7 < y

   1. Initial program 83.1%

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

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 73.4

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

   5. Simplified 73.4%

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

   if -3.50000000000000005e-65 < y < 8.99999999999999959e-7

   1. Initial program 82.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. clear-num N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 95.7

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

   4. Applied egg-rr 95.7%

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

   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. distribute-neg-frac2 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. remove-double-neg N/A

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

      9. sub-neg N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 81.7

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

   7. Simplified 81.7%

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

Alternative 6: 69.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.2e+80) x (if (<= z 2.3e+137) (* x (/ y (- t z))) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.2e+80) {
		tmp = x;
	} else if (z <= 2.3e+137) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-8.2d+80)) then
        tmp = x
    else if (z <= 2.3d+137) then
        tmp = x * (y / (t - z))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.2e+80) {
		tmp = x;
	} else if (z <= 2.3e+137) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.2e+80:
		tmp = x
	elif z <= 2.3e+137:
		tmp = x * (y / (t - z))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.2e+80)
		tmp = x;
	elseif (z <= 2.3e+137)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.2e+80)
		tmp = x;
	elseif (z <= 2.3e+137)
		tmp = x * (y / (t - z));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.2e+80], x, If[LessEqual[z, 2.3e+137], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -8.20000000000000003e80 or 2.29999999999999999e137 < z

   1. Initial program 61.3%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. clear-num N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 66.0%

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

      1. /-rgt-identity 66.0

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

   9. Applied egg-rr 66.0%

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

   if -8.20000000000000003e80 < z < 2.29999999999999999e137

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 64.5

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

   5. Simplified 64.5%

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

Alternative 7: 59.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{t}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.1e-39) x (if (<= z 3.5e-96) (/ (* 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-39) {
		tmp = x;
	} else if (z <= 3.5e-96) {
		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-39)
		tmp = x;
	elseif (z <= 3.5e-96)
		tmp = Float64(Float64(x * 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-39], x, If[LessEqual[z, 3.5e-96], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.09999999999999993e-39

   1. Initial program 72.8%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. clear-num N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 99.8

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 52.1%

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

      1. /-rgt-identity 52.1

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

   9. Applied egg-rr 52.1%

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

   if -2.09999999999999993e-39 < z < 3.4999999999999999e-96

   1. Initial program 95.4%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 72.7

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

   5. Simplified 72.7%

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

   if 3.4999999999999999e-96 < z

   1. Initial program 74.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. clear-num N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 98.6

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

   4. Applied egg-rr 98.6%

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

   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. distribute-neg-frac2 N/A

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

      3. sub-neg N/A

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

      4. mul-1-neg N/A

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

      5. +-commutative N/A

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

      6. distribute-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. remove-double-neg N/A

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

      9. sub-neg N/A

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

      10. associate-/l* N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 65.0

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

   7. Simplified 65.0%

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

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{t \cdot x}{z}} \]
   9. 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. lower-fma.f64 N/A

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

      5. lower-/.f64 52.8

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

   10. Simplified 52.8%

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

Alternative 8: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+21}:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.1e-39) x (if (<= z 1.95e+21) (/ (* x y) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e-39) {
		tmp = x;
	} else if (z <= 1.95e+21) {
		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 <= (-2.1d-39)) then
        tmp = x
    else if (z <= 1.95d+21) 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 <= -2.1e-39) {
		tmp = x;
	} else if (z <= 1.95e+21) {
		tmp = (x * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.1e-39:
		tmp = x
	elif z <= 1.95e+21:
		tmp = (x * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.1e-39)
		tmp = x;
	elseif (z <= 1.95e+21)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.1e-39)
		tmp = x;
	elseif (z <= 1.95e+21)
		tmp = (x * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.1e-39], x, If[LessEqual[z, 1.95e+21], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.09999999999999993e-39 or 1.95e21 < z

   1. Initial program 70.2%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. clear-num N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 55.2%

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

      1. /-rgt-identity 55.2

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

   9. Applied egg-rr 55.2%

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

   if -2.09999999999999993e-39 < z < 1.95e21

   1. Initial program 95.4%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 66.6

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

   5. Simplified 66.6%

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

Alternative 9: 61.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -24000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.55 \cdot 10^{+21}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -24000000000.0) x (if (<= z 3.55e+21) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -24000000000.0) {
		tmp = x;
	} else if (z <= 3.55e+21) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-24000000000.0d0)) then
        tmp = x
    else if (z <= 3.55d+21) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -24000000000.0) {
		tmp = x;
	} else if (z <= 3.55e+21) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -24000000000.0:
		tmp = x
	elif z <= 3.55e+21:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -24000000000.0)
		tmp = x;
	elseif (z <= 3.55e+21)
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -24000000000.0)
		tmp = x;
	elseif (z <= 3.55e+21)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -24000000000.0], x, If[LessEqual[z, 3.55e+21], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e10 or 3.55e21 < z

   1. Initial program 68.2%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. remove-double-neg N/A

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

      4. lift--.f64 N/A

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

      5. remove-double-neg N/A

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

      6. lift-*.f64 N/A

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

      7. associate-/l* N/A

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

      8. clear-num N/A

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

      9. un-div-inv N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 99.9

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

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

   7. Simplified 57.6%

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

      1. /-rgt-identity 57.6

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

   9. Applied egg-rr 57.6%

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

   if -2.4e10 < z < 3.55e21

   1. Initial program 95.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   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. lower-*.f64 63.1

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

   5. Simplified 63.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 61.2

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

   7. Applied egg-rr 61.2%

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

Alternative 10: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.9%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. remove-double-neg N/A

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

   4. lift--.f64 N/A

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

   5. remove-double-neg N/A

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

   6. lift-*.f64 N/A

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

   7. associate-/l* N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower-/.f64 96.1

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

4. Applied egg-rr 96.1%

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

5. Final simplification 96.1%

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

Alternative 11: 36.4% 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 82.9%

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

   1. lift--.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. remove-double-neg N/A

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

   4. lift--.f64 N/A

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

   5. remove-double-neg N/A

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

   6. lift-*.f64 N/A

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

   7. associate-/l* N/A

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

   8. clear-num N/A

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

   9. un-div-inv N/A

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

   10. lower-/.f64 N/A

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

   11. lower-/.f64 96.3

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

4. Applied egg-rr 96.3%

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

5. Taylor expanded in z around inf

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

7. Simplified 34.3%

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

   1. /-rgt-identity 34.3

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

9. Applied egg-rr 34.3%

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

Developer Target 1: 96.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024207 
(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)))