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

Percentage Accurate: 84.4% → 97.1%

Time: 10.4s

Alternatives: 14

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: 84.4% 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, 1.0× 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 87.1%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

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

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{y - z}\right)}\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{\left(y - z\right)}\right)\right) \]

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

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\color{blue}{y} - z\right)\right)\right) \]

   7. --lowering--.f64 96.5%

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

4. Applied egg-rr 96.5%

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

Alternative 2: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+203}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4e+114)
   (/ x (/ t (- y z)))
   (if (<= t 1.4e+203) (* (- y z) (/ x (- t z))) (* x (/ (- y z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e+114) {
		tmp = x / (t / (y - z));
	} else if (t <= 1.4e+203) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4d+114)) then
        tmp = x / (t / (y - z))
    else if (t <= 1.4d+203) then
        tmp = (y - z) * (x / (t - z))
    else
        tmp = x * ((y - z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e+114) {
		tmp = x / (t / (y - z));
	} else if (t <= 1.4e+203) {
		tmp = (y - z) * (x / (t - z));
	} else {
		tmp = x * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4e+114:
		tmp = x / (t / (y - z))
	elif t <= 1.4e+203:
		tmp = (y - z) * (x / (t - z))
	else:
		tmp = x * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4e+114)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	elseif (t <= 1.4e+203)
		tmp = Float64(Float64(y - z) * Float64(x / Float64(t - z)));
	else
		tmp = Float64(x * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4e+114)
		tmp = x / (t / (y - z));
	elseif (t <= 1.4e+203)
		tmp = (y - z) * (x / (t - z));
	else
		tmp = x * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4e+114], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+203], N[(N[(y - z), $MachinePrecision] * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4e114

   1. Initial program 95.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{y - z}\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{\left(y - z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      7. --lowering--.f64 97.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 97.7%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t}{y - z}\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(y - z\right)}\right)\right) \]

      2. --lowering--.f64 95.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 95.5%

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

   if -4e114 < t < 1.39999999999999995e203

   1. Initial program 87.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t - z}\right), \color{blue}{\left(y - z\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(t - z\right)\right), \left(\color{blue}{y} - z\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), \left(y - z\right)\right) \]

      7. --lowering--.f64 86.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   4. Applied egg-rr 86.5%

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

   if 1.39999999999999995e203 < t

   1. Initial program 72.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{t - z}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(t - z\right)\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(t - z\right)\right), x\right) \]

      6. --lowering--.f64 99.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{*.f64}\left(\color{blue}{\left(\frac{y - z}{t}\right)}, x\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), t\right), x\right) \]

      2. --lowering--.f64 95.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), t\right), x\right) \]

   7. Simplified 95.9%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+203}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.5e-48)
   (* x (- 1.0 (/ y z)))
   (if (<= z 5.2e-24) (/ (* x y) (- t z)) (* x (/ z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e-48) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 5.2e-24) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.5d-48)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= 5.2d-24) then
        tmp = (x * y) / (t - z)
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.5e-48) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 5.2e-24) {
		tmp = (x * y) / (t - z);
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.5e-48:
		tmp = x * (1.0 - (y / z))
	elif z <= 5.2e-24:
		tmp = (x * y) / (t - z)
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.5e-48)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= 5.2e-24)
		tmp = Float64(Float64(x * y) / Float64(t - z));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.5e-48)
		tmp = x * (1.0 - (y / z));
	elseif (z <= 5.2e-24)
		tmp = (x * y) / (t - z);
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.5e-48], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-24], N[(N[(x * y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.49999999999999991e-48

   1. Initial program 81.5%

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

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 66.8%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 66.8%

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

   if -3.49999999999999991e-48 < z < 5.2e-24

   1. Initial program 97.2%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t - z\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} - z\right)\right) \]

      3. --lowering--.f64 87.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   5. Simplified 87.1%

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

   if 5.2e-24 < z

   1. Initial program 73.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{t - z}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(t - z\right)\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(t - z\right)\right), x\right) \]

      6. --lowering--.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 99.9%

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

   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

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

      2. distribute-neg-frac2 N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(\left(t - z\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \left(\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{neg.f64}\left(\left(t - z\right)\right)\right) \]

      6. --lowering--.f64 57.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   7. Simplified 57.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z}{\mathsf{neg}\left(\left(t - z\right)\right)}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right), x\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(0 - \left(t - z\right)\right)\right), x\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(0 - \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), x\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(0 - \left(\left(\mathsf{neg}\left(z\right)\right) + t\right)\right)\right), x\right) \]

      8. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - t\right)\right), x\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - t\right)\right), x\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(z - t\right)\right), x\right) \]

      11. --lowering--.f64 81.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(z, t\right)\right), x\right) \]

   9. Applied egg-rr 81.4%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{x \cdot y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.6:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.2e+59)
   (* x (- 1.0 (/ y z)))
   (if (<= z 3.6) (/ x (/ t (- y z))) (* x (/ z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.2e+59) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 3.6) {
		tmp = x / (t / (y - z));
	} else {
		tmp = x * (z / (z - t));
	}
	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 <= (-9.2d+59)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= 3.6d0) then
        tmp = x / (t / (y - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.2e+59) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 3.6) {
		tmp = x / (t / (y - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.2e+59:
		tmp = x * (1.0 - (y / z))
	elif z <= 3.6:
		tmp = x / (t / (y - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.2e+59)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= 3.6)
		tmp = Float64(x / Float64(t / Float64(y - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.2e+59)
		tmp = x * (1.0 - (y / z));
	elseif (z <= 3.6)
		tmp = x / (t / (y - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.2e+59], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6], N[(x / N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.20000000000000032e59

   1. Initial program 75.7%

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

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 77.4%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 77.4%

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

   if -9.20000000000000032e59 < z < 3.60000000000000009

   1. Initial program 96.4%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{y - z}\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{\left(y - z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      7. --lowering--.f64 94.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 94.3%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t}{y - z}\right)}\right) \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{\left(y - z\right)}\right)\right) \]

      2. --lowering--.f64 76.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(t, \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   7. Simplified 76.6%

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

   if 3.60000000000000009 < z

   1. Initial program 71.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{t - z}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(t - z\right)\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(t - z\right)\right), x\right) \]

      6. --lowering--.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 99.9%

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

   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

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

      2. distribute-neg-frac2 N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(\left(t - z\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \left(\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{neg.f64}\left(\left(t - z\right)\right)\right) \]

      6. --lowering--.f64 57.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   7. Simplified 57.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z}{\mathsf{neg}\left(\left(t - z\right)\right)}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right), x\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(0 - \left(t - z\right)\right)\right), x\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(0 - \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), x\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(0 - \left(\left(\mathsf{neg}\left(z\right)\right) + t\right)\right)\right), x\right) \]

      8. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - t\right)\right), x\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - t\right)\right), x\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(z - t\right)\right), x\right) \]

      11. --lowering--.f64 82.7%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(z, t\right)\right), x\right) \]

   9. Applied egg-rr 82.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.6:\\ \;\;\;\;\frac{x}{\frac{t}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.35e+66)
   (* x (- 1.0 (/ y z)))
   (if (<= z 1.1e-23) (* x (/ y (- t z))) (* x (/ z (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.35e+66) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 1.1e-23) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	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 <= (-1.35d+66)) then
        tmp = x * (1.0d0 - (y / z))
    else if (z <= 1.1d-23) then
        tmp = x * (y / (t - z))
    else
        tmp = x * (z / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.35e+66) {
		tmp = x * (1.0 - (y / z));
	} else if (z <= 1.1e-23) {
		tmp = x * (y / (t - z));
	} else {
		tmp = x * (z / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.35e+66:
		tmp = x * (1.0 - (y / z))
	elif z <= 1.1e-23:
		tmp = x * (y / (t - z))
	else:
		tmp = x * (z / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.35e+66)
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.1e-23)
		tmp = Float64(x * Float64(y / Float64(t - z)));
	else
		tmp = Float64(x * Float64(z / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.35e+66)
		tmp = x * (1.0 - (y / z));
	elseif (z <= 1.1e-23)
		tmp = x * (y / (t - z));
	else
		tmp = x * (z / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.35e+66], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e-23], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e66

   1. Initial program 74.5%

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

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 76.3%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 76.3%

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

   if -1.35e66 < z < 1.1e-23

   1. Initial program 96.4%

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t - z\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} - z\right)\right) \]

      3. --lowering--.f64 80.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   5. Simplified 80.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{t - z}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(t - z\right)\right), x\right) \]

      5. --lowering--.f64 77.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), x\right) \]

   7. Applied egg-rr 77.2%

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

   if 1.1e-23 < z

   1. Initial program 73.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{t - z}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(t - z\right)\right), x\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(t - z\right)\right), x\right) \]

      6. --lowering--.f64 99.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(t, z\right)\right), x\right) \]

   4. Applied egg-rr 99.9%

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

   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

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

      2. distribute-neg-frac2 N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{\left(\mathsf{neg}\left(\left(t - z\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \left(\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{neg.f64}\left(\left(t - z\right)\right)\right) \]

      6. --lowering--.f64 57.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(t, z\right)\right)\right) \]

   7. Simplified 57.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{z}{\mathsf{neg}\left(\left(t - z\right)\right)}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right), x\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(0 - \left(t - z\right)\right)\right), x\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(0 - \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), x\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(0 - \left(\left(\mathsf{neg}\left(z\right)\right) + t\right)\right)\right), x\right) \]

      8. associate--r+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - t\right)\right), x\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - t\right)\right), x\right) \]

      10. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \left(z - t\right)\right), x\right) \]

      11. --lowering--.f64 81.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, \mathsf{\_.f64}\left(z, t\right)\right), x\right) \]

   9. Applied egg-rr 81.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+66}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -5.8e+65) t_1 (if (<= z 3.6) (* x (/ y (- t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -5.8e+65) {
		tmp = t_1;
	} else if (z <= 3.6) {
		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 * (1.0d0 - (y / z))
    if (z <= (-5.8d+65)) then
        tmp = t_1
    else if (z <= 3.6d0) 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 * (1.0 - (y / z));
	double tmp;
	if (z <= -5.8e+65) {
		tmp = t_1;
	} else if (z <= 3.6) {
		tmp = x * (y / (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -5.8e+65:
		tmp = t_1
	elif z <= 3.6:
		tmp = x * (y / (t - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -5.8e+65)
		tmp = t_1;
	elseif (z <= 3.6)
		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 * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -5.8e+65)
		tmp = t_1;
	elseif (z <= 3.6)
		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[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+65], t$95$1, If[LessEqual[z, 3.6], N[(x * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000001e65 or 3.60000000000000009 < z

   1. Initial program 72.5%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 74.7%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 74.7%

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

   if -5.8000000000000001e65 < z < 3.60000000000000009

   1. Initial program 96.5%

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

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t - z\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} - z\right)\right) \]

      3. --lowering--.f64 79.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   5. Simplified 79.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{t - z}\right), \color{blue}{x}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \left(t - z\right)\right), x\right) \]

      5. --lowering--.f64 75.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), x\right) \]

   7. Applied egg-rr 75.9%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 3.6:\\ \;\;\;\;x \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -2.35e+59) t_1 (if (<= z 3.1) (* (- y z) (/ x t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.35e+59) {
		tmp = t_1;
	} else if (z <= 3.1) {
		tmp = (y - z) * (x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-2.35d+59)) then
        tmp = t_1
    else if (z <= 3.1d0) then
        tmp = (y - z) * (x / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.35e+59) {
		tmp = t_1;
	} else if (z <= 3.1) {
		tmp = (y - z) * (x / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -2.35e+59:
		tmp = t_1
	elif z <= 3.1:
		tmp = (y - z) * (x / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -2.35e+59)
		tmp = t_1;
	elseif (z <= 3.1)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -2.35e+59)
		tmp = t_1;
	elseif (z <= 3.1)
		tmp = (y - z) * (x / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e+59], t$95$1, If[LessEqual[z, 3.1], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.35e59 or 3.10000000000000009 < z

   1. Initial program 73.1%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 75.2%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 75.2%

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

   if -2.35e59 < z < 3.10000000000000009

   1. Initial program 96.4%

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

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

      2. associate-/l* N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(y - z\right), \color{blue}{\left(\frac{x}{t}\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(\frac{\color{blue}{x}}{t}\right)\right) \]

      5. /-lowering-/.f64 73.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{/.f64}\left(x, \color{blue}{t}\right)\right) \]

   5. Simplified 73.2%

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

Alternative 8: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.15:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -1.05e-49) t_1 (if (<= z 3.15) (/ (* x y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -1.05e-49) {
		tmp = t_1;
	} else if (z <= 3.15) {
		tmp = (x * y) / 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 * (1.0d0 - (y / z))
    if (z <= (-1.05d-49)) then
        tmp = t_1
    else if (z <= 3.15d0) then
        tmp = (x * y) / 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 * (1.0 - (y / z));
	double tmp;
	if (z <= -1.05e-49) {
		tmp = t_1;
	} else if (z <= 3.15) {
		tmp = (x * y) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -1.05e-49:
		tmp = t_1
	elif z <= 3.15:
		tmp = (x * y) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -1.05e-49)
		tmp = t_1;
	elseif (z <= 3.15)
		tmp = Float64(Float64(x * y) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -1.05e-49)
		tmp = t_1;
	elseif (z <= 3.15)
		tmp = (x * y) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e-49], t$95$1, If[LessEqual[z, 3.15], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0499999999999999e-49 or 3.14999999999999991 < z

   1. Initial program 76.7%

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

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

      2. associate-/l* N/A

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

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

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

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

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\frac{y - z}{z}\right)\right)}\right) \]

      5. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\frac{y - z}{z}}\right)\right) \]

      6. div-sub N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - \color{blue}{\frac{z}{z}}\right)\right)\right) \]

      7. *-inverses N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(0 - \left(\frac{y}{z} - 1\right)\right)\right) \]

      8. associate-+l- N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(0 - \frac{y}{z}\right) + \color{blue}{1}\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z}\right)\right) + 1\right)\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(-1 \cdot \frac{y}{z} + 1\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \color{blue}{-1 \cdot \frac{y}{z}}\right)\right) \]

      12. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 + \left(\mathsf{neg}\left(\frac{y}{z}\right)\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(1 - \color{blue}{\frac{y}{z}}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      15. /-lowering-/.f64 70.0%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 70.0%

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

   if -1.0499999999999999e-49 < z < 3.14999999999999991

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 73.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), t\right) \]

   5. Simplified 73.5%

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

Alternative 9: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.2:\\ \;\;\;\;\frac{x \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7e-48) x (if (<= z 3.2) (/ (* x y) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7e-48) {
		tmp = x;
	} else if (z <= 3.2) {
		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 <= (-7d-48)) then
        tmp = x
    else if (z <= 3.2d0) 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 <= -7e-48) {
		tmp = x;
	} else if (z <= 3.2) {
		tmp = (x * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7e-48:
		tmp = x
	elif z <= 3.2:
		tmp = (x * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7e-48)
		tmp = x;
	elseif (z <= 3.2)
		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 <= -7e-48)
		tmp = x;
	elseif (z <= 3.2)
		tmp = (x * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7e-48], x, If[LessEqual[z, 3.2], N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.99999999999999982e-48 or 3.2000000000000002 < z

   1. Initial program 76.7%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 55.1%

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

   if -6.99999999999999982e-48 < z < 3.2000000000000002

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot y\right), \color{blue}{t}\right) \]

      2. *-lowering-*.f64 73.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, y\right), t\right) \]

   5. Simplified 73.5%

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

Alternative 10: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.8e+59) x (if (<= z 3.5) (/ x (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.8e+59) {
		tmp = x;
	} else if (z <= 3.5) {
		tmp = x / (t / y);
	} 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 <= (-3.8d+59)) then
        tmp = x
    else if (z <= 3.5d0) then
        tmp = x / (t / y)
    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 <= -3.8e+59) {
		tmp = x;
	} else if (z <= 3.5) {
		tmp = x / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.8e+59:
		tmp = x
	elif z <= 3.5:
		tmp = x / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.8e+59)
		tmp = x;
	elseif (z <= 3.5)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.8e+59)
		tmp = x;
	elseif (z <= 3.5)
		tmp = x / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.8e+59], x, If[LessEqual[z, 3.5], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000001e59 or 3.5 < z

   1. Initial program 73.1%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 62.1%

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

   if -3.8000000000000001e59 < z < 3.5

   1. Initial program 96.4%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{y - z}\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{\left(y - z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      7. --lowering--.f64 94.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 94.3%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 65.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right) \]

   7. Simplified 65.1%

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

Alternative 11: 61.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2e+59) x (if (<= z 3.3) (* x (/ y t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+59) {
		tmp = x;
	} else if (z <= 3.3) {
		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 <= (-2.2d+59)) then
        tmp = x
    else if (z <= 3.3d0) 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 <= -2.2e+59) {
		tmp = x;
	} else if (z <= 3.3) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.2e+59:
		tmp = x
	elif z <= 3.3:
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2e+59)
		tmp = x;
	elseif (z <= 3.3)
		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 <= -2.2e+59)
		tmp = x;
	elseif (z <= 3.3)
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.2e+59], x, If[LessEqual[z, 3.3], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e59 or 3.2999999999999998 < z

   1. Initial program 73.1%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 62.1%

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

   if -2.2e59 < z < 3.2999999999999998

   1. Initial program 96.4%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{y - z}\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{\left(y - z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      7. --lowering--.f64 94.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 94.3%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 65.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right) \]

   7. Simplified 65.1%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. clear-num N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{t}\right), \color{blue}{x}\right) \]

      5. /-lowering-/.f64 64.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), x\right) \]

   9. Applied egg-rr 64.8%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.3:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.8e+59) x (if (<= z 3.5) (* y (/ x t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.8e+59) {
		tmp = x;
	} else if (z <= 3.5) {
		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 <= (-1.8d+59)) then
        tmp = x
    else if (z <= 3.5d0) 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 <= -1.8e+59) {
		tmp = x;
	} else if (z <= 3.5) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.8e+59:
		tmp = x
	elif z <= 3.5:
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.8e+59)
		tmp = x;
	elseif (z <= 3.5)
		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 <= -1.8e+59)
		tmp = x;
	elseif (z <= 3.5)
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.8e+59], x, If[LessEqual[z, 3.5], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7999999999999999e59 or 3.5 < z

   1. Initial program 73.1%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 62.1%

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

   if -1.7999999999999999e59 < z < 3.5

   1. Initial program 96.4%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t - z}{y - z}\right)}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{\left(y - z\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \left(\color{blue}{y} - z\right)\right)\right) \]

      7. --lowering--.f64 94.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   4. Applied egg-rr 94.3%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{t}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 65.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right) \]

   7. Simplified 65.1%

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

      1. associate-/r/ N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{t}\right), \color{blue}{y}\right) \]

      3. /-lowering-/.f64 62.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, t\right), y\right) \]

   9. Applied egg-rr 62.7%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+59}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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 87.1%

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

   1. associate-/l* N/A

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

   2. *-commutative N/A

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

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

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{y - z}{t - z}\right), \color{blue}{x}\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - z\right), \left(t - z\right)\right), x\right) \]

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

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \left(t - z\right)\right), x\right) \]

   6. --lowering--.f64 96.2%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, z\right), \mathsf{\_.f64}\left(t, z\right)\right), x\right) \]

4. Applied egg-rr 96.2%

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

5. Final simplification 96.2%

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

Alternative 14: 34.9% accurate, 9.0× 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 87.1%

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

3. Taylor expanded in z around inf

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

5. Simplified 31.4%

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

Developer Target 1: 97.1% accurate, 1.0× 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 2024138 
(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)))