Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A

Percentage Accurate: 85.3% → 98.0%

Time: 9.6s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

   1. +-commutative N/A

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

   2. associate-/l* N/A

      \[\leadsto y \cdot \frac{z - t}{z - a} + x \]

   3. *-commutative N/A

      \[\leadsto \frac{z - t}{z - a} \cdot y + x \]

   4. fma-define N/A

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

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

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

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

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

   7. --lowering--.f64 N/A

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

   8. --lowering--.f64 98.7%

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

4. Applied egg-rr 98.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{z - a}, y, x\right)} \]
5. Add Preprocessing

Alternative 2: 84.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{z - a}\\ t_2 := \frac{\left(z - t\right) \cdot y}{z - a}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+142}:\\ \;\;\;\;x + \frac{z \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y (- z a)))) (t_2 (/ (* (- z t) y) (- z a))))
   (if (<= t_2 -2e+113)
     t_1
     (if (<= t_2 5e+142) (+ x (/ (* z y) (- z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (z - a));
	double t_2 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_2 <= -2e+113) {
		tmp = t_1;
	} else if (t_2 <= 5e+142) {
		tmp = x + ((z * y) / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z - t) * (y / (z - a))
    t_2 = ((z - t) * y) / (z - a)
    if (t_2 <= (-2d+113)) then
        tmp = t_1
    else if (t_2 <= 5d+142) then
        tmp = x + ((z * y) / (z - a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / (z - a));
	double t_2 = ((z - t) * y) / (z - a);
	double tmp;
	if (t_2 <= -2e+113) {
		tmp = t_1;
	} else if (t_2 <= 5e+142) {
		tmp = x + ((z * y) / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / (z - a))
	t_2 = ((z - t) * y) / (z - a)
	tmp = 0
	if t_2 <= -2e+113:
		tmp = t_1
	elif t_2 <= 5e+142:
		tmp = x + ((z * y) / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / Float64(z - a)))
	t_2 = Float64(Float64(Float64(z - t) * y) / Float64(z - a))
	tmp = 0.0
	if (t_2 <= -2e+113)
		tmp = t_1;
	elseif (t_2 <= 5e+142)
		tmp = Float64(x + Float64(Float64(z * y) / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * (y / (z - a));
	t_2 = ((z - t) * y) / (z - a);
	tmp = 0.0;
	if (t_2 <= -2e+113)
		tmp = t_1;
	elseif (t_2 <= 5e+142)
		tmp = x + ((z * y) / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+113], t$95$1, If[LessEqual[t$95$2, 5e+142], N[(x + N[(N[(z * y), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -2e113 or 5.0000000000000001e142 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 59.1%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto y \cdot \frac{z - t}{z - a} + x \]

      3. *-commutative N/A

         \[\leadsto \frac{z - t}{z - a} \cdot y + x \]

      4. fma-define N/A

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

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

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

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

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

      7. --lowering--.f64 N/A

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

      8. --lowering--.f64 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

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

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 81.5%

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

   7. Simplified 81.5%

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

   if -2e113 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 5.0000000000000001e142

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{\left(y \cdot z\right)}, \mathsf{\_.f64}\left(z, a\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 88.5%

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

   5. Simplified 88.5%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq -2 \cdot 10^{+113}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{z - a} \leq 5 \cdot 10^{+142}:\\ \;\;\;\;x + \frac{z \cdot y}{z - a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+92}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-21}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e+92)
   (+ y x)
   (if (<= z -1.3e-21)
     (* (- z t) (/ y (- z a)))
     (if (<= z 4.9e-14) (+ x (/ t (/ a y))) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+92) {
		tmp = y + x;
	} else if (z <= -1.3e-21) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 4.9e-14) {
		tmp = x + (t / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.2d+92)) then
        tmp = y + x
    else if (z <= (-1.3d-21)) then
        tmp = (z - t) * (y / (z - a))
    else if (z <= 4.9d-14) then
        tmp = x + (t / (a / y))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+92) {
		tmp = y + x;
	} else if (z <= -1.3e-21) {
		tmp = (z - t) * (y / (z - a));
	} else if (z <= 4.9e-14) {
		tmp = x + (t / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e+92:
		tmp = y + x
	elif z <= -1.3e-21:
		tmp = (z - t) * (y / (z - a))
	elif z <= 4.9e-14:
		tmp = x + (t / (a / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e+92)
		tmp = Float64(y + x);
	elseif (z <= -1.3e-21)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(z - a)));
	elseif (z <= 4.9e-14)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e+92)
		tmp = y + x;
	elseif (z <= -1.3e-21)
		tmp = (z - t) * (y / (z - a));
	elseif (z <= 4.9e-14)
		tmp = x + (t / (a / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e+92], N[(y + x), $MachinePrecision], If[LessEqual[z, -1.3e-21], N[(N[(z - t), $MachinePrecision] * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e-14], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.20000000000000047e92 or 4.89999999999999995e-14 < z

   1. Initial program 74.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 81.2%

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

   5. Simplified 81.2%

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

   if -8.20000000000000047e92 < z < -1.30000000000000009e-21

   1. Initial program 75.3%

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

         \[\leadsto y \cdot \frac{z - t}{z - a} + x \]

      3. *-commutative N/A

         \[\leadsto \frac{z - t}{z - a} \cdot y + x \]

      4. fma-define N/A

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

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

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

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

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

      7. --lowering--.f64 N/A

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

      8. --lowering--.f64 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. associate-/l* N/A

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

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

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

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

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 74.9%

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

   7. Simplified 74.9%

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

   if -1.30000000000000009e-21 < z < 4.89999999999999995e-14

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 76.4%

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

   5. Simplified 76.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t \cdot y}{a}\right)\right) \]

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 77.3%

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

   7. Applied egg-rr 77.3%

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

      1. +-commutative N/A

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

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

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

      3. clear-num N/A

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

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{t}{\frac{a}{y}}\right), x\right) \]

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

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

      6. /-lowering-/.f64 78.1%

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

   9. Applied egg-rr 78.1%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+92}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-21}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{z - a}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+25)
   (+ x (* y (/ z (- z a))))
   (if (<= z 2.15e-13) (+ x (/ t (/ a y))) (+ x (* y (- 1.0 (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+25) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 2.15e-13) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.8d+25)) then
        tmp = x + (y * (z / (z - a)))
    else if (z <= 2.15d-13) then
        tmp = x + (t / (a / y))
    else
        tmp = x + (y * (1.0d0 - (t / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+25) {
		tmp = x + (y * (z / (z - a)));
	} else if (z <= 2.15e-13) {
		tmp = x + (t / (a / y));
	} else {
		tmp = x + (y * (1.0 - (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+25:
		tmp = x + (y * (z / (z - a)))
	elif z <= 2.15e-13:
		tmp = x + (t / (a / y))
	else:
		tmp = x + (y * (1.0 - (t / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+25)
		tmp = Float64(x + Float64(y * Float64(z / Float64(z - a))));
	elseif (z <= 2.15e-13)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e+25)
		tmp = x + (y * (z / (z - a)));
	elseif (z <= 2.15e-13)
		tmp = x + (t / (a / y));
	else
		tmp = x + (y * (1.0 - (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+25], N[(x + N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e-13], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.79999999999999992e25

   1. Initial program 69.4%

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

   3. Taylor expanded in t around 0

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

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

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

      2. associate-/l* N/A

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

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

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

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

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

      5. --lowering--.f64 87.8%

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

   5. Simplified 87.8%

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

   if -4.79999999999999992e25 < z < 2.1499999999999999e-13

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 74.8%

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

   5. Simplified 74.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t \cdot y}{a}\right)\right) \]

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 77.1%

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

   7. Applied egg-rr 77.1%

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

      1. +-commutative N/A

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

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

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

      3. clear-num N/A

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

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{t}{\frac{a}{y}}\right), x\right) \]

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

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

      6. /-lowering-/.f64 77.9%

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

   9. Applied egg-rr 77.9%

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

   if 2.1499999999999999e-13 < z

   1. Initial program 79.1%

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

   3. Taylor expanded in a around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

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

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

      7. /-lowering-/.f64 93.3%

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

   5. Simplified 93.3%

      \[\leadsto \color{blue}{x + y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;x + y \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (- 1.0 (/ t z))))))
   (if (<= z -6.5e+37) t_1 (if (<= z 4.6e-9) (+ x (/ t (/ a y))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -6.5e+37) {
		tmp = t_1;
	} else if (z <= 4.6e-9) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (1.0d0 - (t / z)))
    if (z <= (-6.5d+37)) then
        tmp = t_1
    else if (z <= 4.6d-9) then
        tmp = x + (t / (a / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (1.0 - (t / z)));
	double tmp;
	if (z <= -6.5e+37) {
		tmp = t_1;
	} else if (z <= 4.6e-9) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (1.0 - (t / z)))
	tmp = 0
	if z <= -6.5e+37:
		tmp = t_1
	elif z <= 4.6e-9:
		tmp = x + (t / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(1.0 - Float64(t / z))))
	tmp = 0.0
	if (z <= -6.5e+37)
		tmp = t_1;
	elseif (z <= 4.6e-9)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (1.0 - (t / z)));
	tmp = 0.0;
	if (z <= -6.5e+37)
		tmp = t_1;
	elseif (z <= 4.6e-9)
		tmp = x + (t / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+37], t$95$1, If[LessEqual[z, 4.6e-9], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999998e37 or 4.5999999999999998e-9 < z

   1. Initial program 75.2%

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

   3. Taylor expanded in a around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

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

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

      7. /-lowering-/.f64 86.7%

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

   5. Simplified 86.7%

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

   if -6.4999999999999998e37 < z < 4.5999999999999998e-9

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 74.2%

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

   5. Simplified 74.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t \cdot y}{a}\right)\right) \]

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 76.5%

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

   7. Applied egg-rr 76.5%

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

      1. +-commutative N/A

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

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

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

      3. clear-num N/A

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

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{t}{\frac{a}{y}}\right), x\right) \]

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

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

      6. /-lowering-/.f64 77.3%

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

   9. Applied egg-rr 77.3%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-9}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+77}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+77) (+ y x) (if (<= z 1.75e-13) (+ x (/ t (/ a y))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+77) {
		tmp = y + x;
	} else if (z <= 1.75e-13) {
		tmp = x + (t / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.2d+77)) then
        tmp = y + x
    else if (z <= 1.75d-13) then
        tmp = x + (t / (a / y))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+77) {
		tmp = y + x;
	} else if (z <= 1.75e-13) {
		tmp = x + (t / (a / y));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+77:
		tmp = y + x
	elif z <= 1.75e-13:
		tmp = x + (t / (a / y))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+77)
		tmp = Float64(y + x);
	elseif (z <= 1.75e-13)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.2e+77)
		tmp = y + x;
	elseif (z <= 1.75e-13)
		tmp = x + (t / (a / y));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+77], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.75e-13], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999979e77 or 1.7500000000000001e-13 < z

   1. Initial program 75.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 80.8%

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

   5. Simplified 80.8%

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

   if -9.19999999999999979e77 < z < 1.7500000000000001e-13

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 71.5%

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

   5. Simplified 71.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t \cdot y}{a}\right)\right) \]

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 73.6%

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

   7. Applied egg-rr 73.6%

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

      1. +-commutative N/A

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

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

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

      3. clear-num N/A

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

      4. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{t}{\frac{a}{y}}\right), x\right) \]

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

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

      6. /-lowering-/.f64 74.3%

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

   9. Applied egg-rr 74.3%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+77}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+77}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+54}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e+77) (+ y x) (if (<= z 2.6e+54) (+ x (* y (/ t a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+77) {
		tmp = y + x;
	} else if (z <= 2.6e+54) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8.2d+77)) then
        tmp = y + x
    else if (z <= 2.6d+54) then
        tmp = x + (y * (t / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+77) {
		tmp = y + x;
	} else if (z <= 2.6e+54) {
		tmp = x + (y * (t / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e+77:
		tmp = y + x
	elif z <= 2.6e+54:
		tmp = x + (y * (t / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e+77)
		tmp = Float64(y + x);
	elseif (z <= 2.6e+54)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e+77)
		tmp = y + x;
	elseif (z <= 2.6e+54)
		tmp = x + (y * (t / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e+77], N[(y + x), $MachinePrecision], If[LessEqual[z, 2.6e+54], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.2000000000000002e77 or 2.60000000000000007e54 < z

   1. Initial program 72.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 81.8%

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

   5. Simplified 81.8%

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

   if -8.2000000000000002e77 < z < 2.60000000000000007e54

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 71.1%

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

   5. Simplified 71.1%

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

      1. +-commutative N/A

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

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

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

      3. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{t}{a}\right), x\right) \]

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

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

      5. /-lowering-/.f64 73.6%

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

   7. Applied egg-rr 73.6%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+77}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+54}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.82 \cdot 10^{+84}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-14}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.82e+84) (+ y x) (if (<= z 4.3e-14) (+ x (* t (/ y a))) (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.82e+84) {
		tmp = y + x;
	} else if (z <= 4.3e-14) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.82d+84)) then
        tmp = y + x
    else if (z <= 4.3d-14) then
        tmp = x + (t * (y / a))
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.82e+84) {
		tmp = y + x;
	} else if (z <= 4.3e-14) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.82e+84:
		tmp = y + x
	elif z <= 4.3e-14:
		tmp = x + (t * (y / a))
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.82e+84)
		tmp = Float64(y + x);
	elseif (z <= 4.3e-14)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.82e+84)
		tmp = y + x;
	elseif (z <= 4.3e-14)
		tmp = x + (t * (y / a));
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.82e+84], N[(y + x), $MachinePrecision], If[LessEqual[z, 4.3e-14], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8200000000000001e84 or 4.29999999999999998e-14 < z

   1. Initial program 75.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 80.8%

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

   5. Simplified 80.8%

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

   if -1.8200000000000001e84 < z < 4.29999999999999998e-14

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 71.5%

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

   5. Simplified 71.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{t \cdot y}{a}\right)\right) \]

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 73.6%

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

   7. Applied egg-rr 73.6%

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

Alternative 9: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+207}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e+106)
   (* y (/ (- t z) a))
   (if (<= t 1.95e+207) (+ y x) (* y (- 1.0 (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+106) {
		tmp = y * ((t - z) / a);
	} else if (t <= 1.95e+207) {
		tmp = y + x;
	} else {
		tmp = y * (1.0 - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.5d+106)) then
        tmp = y * ((t - z) / a)
    else if (t <= 1.95d+207) then
        tmp = y + x
    else
        tmp = y * (1.0d0 - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+106) {
		tmp = y * ((t - z) / a);
	} else if (t <= 1.95e+207) {
		tmp = y + x;
	} else {
		tmp = y * (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.5e+106:
		tmp = y * ((t - z) / a)
	elif t <= 1.95e+207:
		tmp = y + x
	else:
		tmp = y * (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.5e+106)
		tmp = Float64(y * Float64(Float64(t - z) / a));
	elseif (t <= 1.95e+207)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.5e+106)
		tmp = y * ((t - z) / a);
	elseif (t <= 1.95e+207)
		tmp = y + x;
	else
		tmp = y * (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.5e+106], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+207], N[(y + x), $MachinePrecision], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4999999999999999e106

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

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

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

      7. --lowering--.f64 67.0%

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

   5. Simplified 67.0%

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

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

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. --lowering--.f64 67.1%

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

   7. Applied egg-rr 67.1%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. div-sub N/A

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

      4. distribute-lft-out-- N/A

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

      5. associate-/l* N/A

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

      6. associate-*r/ N/A

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

      7. *-commutative N/A

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

      8. unsub-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{y \cdot z}{a} + \left(\mathsf{neg}\left(\frac{t \cdot y}{a}\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{y \cdot z}{a} + -1 \cdot \frac{t \cdot y}{a}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(-1 \cdot \frac{t \cdot y}{a} + \frac{y \cdot z}{a}\right)\right) \]

      11. distribute-neg-out N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. *-commutative N/A

          \[\leadsto \frac{t \cdot y}{a} - \frac{z \cdot y}{a} \]

      16. associate-*r/ N/A

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

      17. associate-/l* N/A

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

      18. distribute-rgt-out-- N/A

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

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

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

      20. /-lowering-/.f64 N/A

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

      21. --lowering--.f64 48.6%

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

   10. Simplified 48.6%

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

       1. *-commutative N/A

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

       2. clear-num N/A

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

       3. associate-*r/ N/A

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

       4. div-inv N/A

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

       5. times-frac N/A

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

       6. clear-num N/A

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

       7. /-rgt-identity N/A

          \[\leadsto \frac{t - z}{a} \cdot y \]

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

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

       9. /-lowering-/.f64 N/A

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

       10. --lowering--.f64 48.7%

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

   12. Applied egg-rr 48.7%

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

   if -2.4999999999999999e106 < t < 1.94999999999999986e207

   1. Initial program 86.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 69.1%

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

   5. Simplified 69.1%

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

   if 1.94999999999999986e207 < t

   1. Initial program 82.0%

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

   3. Taylor expanded in a around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

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

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

      7. /-lowering-/.f64 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. /-lowering-/.f64 60.1%

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

   8. Simplified 60.1%

      \[\leadsto \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+207}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{+208}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9e+106)
   (* (/ y a) (- t z))
   (if (<= t 1.82e+208) (+ y x) (* y (- 1.0 (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e+106) {
		tmp = (y / a) * (t - z);
	} else if (t <= 1.82e+208) {
		tmp = y + x;
	} else {
		tmp = y * (1.0 - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.9d+106)) then
        tmp = (y / a) * (t - z)
    else if (t <= 1.82d+208) then
        tmp = y + x
    else
        tmp = y * (1.0d0 - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e+106) {
		tmp = (y / a) * (t - z);
	} else if (t <= 1.82e+208) {
		tmp = y + x;
	} else {
		tmp = y * (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.9e+106:
		tmp = (y / a) * (t - z)
	elif t <= 1.82e+208:
		tmp = y + x
	else:
		tmp = y * (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9e+106)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (t <= 1.82e+208)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.9e+106)
		tmp = (y / a) * (t - z);
	elseif (t <= 1.82e+208)
		tmp = y + x;
	else
		tmp = y * (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9e+106], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.82e+208], N[(y + x), $MachinePrecision], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9000000000000002e106

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

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

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

      7. --lowering--.f64 67.0%

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

   5. Simplified 67.0%

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

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

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. --lowering--.f64 67.1%

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

   7. Applied egg-rr 67.1%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. div-sub N/A

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

      4. distribute-lft-out-- N/A

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

      5. associate-/l* N/A

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

      6. associate-*r/ N/A

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

      7. *-commutative N/A

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

      8. unsub-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{y \cdot z}{a} + \left(\mathsf{neg}\left(\frac{t \cdot y}{a}\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{y \cdot z}{a} + -1 \cdot \frac{t \cdot y}{a}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(-1 \cdot \frac{t \cdot y}{a} + \frac{y \cdot z}{a}\right)\right) \]

      11. distribute-neg-out N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. *-commutative N/A

          \[\leadsto \frac{t \cdot y}{a} - \frac{z \cdot y}{a} \]

      16. associate-*r/ N/A

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

      17. associate-/l* N/A

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

      18. distribute-rgt-out-- N/A

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

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

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

      20. /-lowering-/.f64 N/A

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

      21. --lowering--.f64 48.6%

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

   10. Simplified 48.6%

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

   if -2.9000000000000002e106 < t < 1.81999999999999999e208

   1. Initial program 86.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 69.1%

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

   5. Simplified 69.1%

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

   if 1.81999999999999999e208 < t

   1. Initial program 82.0%

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

   3. Taylor expanded in a around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

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

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

      7. /-lowering-/.f64 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. /-lowering-/.f64 60.1%

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

   8. Simplified 60.1%

      \[\leadsto \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 59.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+203}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.9e+106)
   (* t (/ y a))
   (if (<= t 2.55e+203) (+ y x) (* y (- 1.0 (/ t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e+106) {
		tmp = t * (y / a);
	} else if (t <= 2.55e+203) {
		tmp = y + x;
	} else {
		tmp = y * (1.0 - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.9d+106)) then
        tmp = t * (y / a)
    else if (t <= 2.55d+203) then
        tmp = y + x
    else
        tmp = y * (1.0d0 - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.9e+106) {
		tmp = t * (y / a);
	} else if (t <= 2.55e+203) {
		tmp = y + x;
	} else {
		tmp = y * (1.0 - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.9e+106:
		tmp = t * (y / a)
	elif t <= 2.55e+203:
		tmp = y + x
	else:
		tmp = y * (1.0 - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.9e+106)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 2.55e+203)
		tmp = Float64(y + x);
	else
		tmp = Float64(y * Float64(1.0 - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.9e+106)
		tmp = t * (y / a);
	elseif (t <= 2.55e+203)
		tmp = y + x;
	else
		tmp = y * (1.0 - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.9e+106], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e+203], N[(y + x), $MachinePrecision], N[(y * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9000000000000002e106

   1. Initial program 76.3%

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

   3. Taylor expanded in a around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

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

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

      7. --lowering--.f64 67.0%

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

   5. Simplified 67.0%

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

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

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. --lowering--.f64 67.1%

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

   7. Applied egg-rr 67.1%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. associate-/l* N/A

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

      3. div-sub N/A

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

      4. distribute-lft-out-- N/A

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

      5. associate-/l* N/A

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

      6. associate-*r/ N/A

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

      7. *-commutative N/A

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

      8. unsub-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{y \cdot z}{a} + \left(\mathsf{neg}\left(\frac{t \cdot y}{a}\right)\right)\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\left(\frac{y \cdot z}{a} + -1 \cdot \frac{t \cdot y}{a}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{neg}\left(\left(-1 \cdot \frac{t \cdot y}{a} + \frac{y \cdot z}{a}\right)\right) \]

      11. distribute-neg-out N/A

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

      12. mul-1-neg N/A

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

      13. remove-double-neg N/A

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

      14. sub-neg N/A

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

      15. *-commutative N/A

          \[\leadsto \frac{t \cdot y}{a} - \frac{z \cdot y}{a} \]

      16. associate-*r/ N/A

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

      17. associate-/l* N/A

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

      18. distribute-rgt-out-- N/A

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

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

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

      20. /-lowering-/.f64 N/A

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

      21. --lowering--.f64 48.6%

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

   10. Simplified 48.6%

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

   11. Taylor expanded in t around inf

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

   13. Simplified 48.4%

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

   if -2.9000000000000002e106 < t < 2.5500000000000001e203

   1. Initial program 86.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 69.1%

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

   5. Simplified 69.1%

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

   if 2.5500000000000001e203 < t

   1. Initial program 82.0%

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

   3. Taylor expanded in a around 0

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

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

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

      2. associate-/l* N/A

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

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

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

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

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

      7. /-lowering-/.f64 66.2%

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

   5. Simplified 66.2%

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

   6. Taylor expanded in x around 0

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

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

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

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

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

      3. /-lowering-/.f64 60.1%

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

   8. Simplified 60.1%

      \[\leadsto \color{blue}{y \cdot \left(1 - \frac{t}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+203}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{t}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+18}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e+18) (+ y x) (if (<= z 1.95e-13) x (+ y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+18) {
		tmp = y + x;
	} else if (z <= 1.95e-13) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.5d+18)) then
        tmp = y + x
    else if (z <= 1.95d-13) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e+18) {
		tmp = y + x;
	} else if (z <= 1.95e-13) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e+18:
		tmp = y + x
	elif z <= 1.95e-13:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e+18)
		tmp = Float64(y + x);
	elseif (z <= 1.95e-13)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e+18)
		tmp = y + x;
	elseif (z <= 1.95e-13)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e+18], N[(y + x), $MachinePrecision], If[LessEqual[z, 1.95e-13], x, N[(y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5e18 or 1.95000000000000002e-13 < z

   1. Initial program 73.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 76.4%

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

   5. Simplified 76.4%

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

   if -9.5e18 < z < 1.95000000000000002e-13

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 52.6%

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

Alternative 13: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

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

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

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

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

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

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

   7. --lowering--.f64 98.3%

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

4. Applied egg-rr 98.3%

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

Alternative 14: 51.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+245}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= z -3.7e+245) y x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.7e+245) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.7d+245)) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.7e+245) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.7e+245:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.7e+245)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.7e+245)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.7e+245], y, x]

Derivation

1. Split input into 2 regimes

2. if z < -3.7000000000000001e245

   1. Initial program 43.5%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y} \]
   7. Step-by-step derivation

   8. Simplified 54.6%

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

   if -3.7000000000000001e245 < z

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 53.5%

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

Alternative 15: 51.2% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.4%

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

3. Taylor expanded in x around inf

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

5. Simplified 51.7%

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

Developer Target 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024138 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- z a) (- z t)))))

  (+ x (/ (* y (- z t)) (- z a))))