Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 67.5% → 84.7%

Time: 14.9s

Alternatives: 14

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 67.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 84.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.55e+43)
     t_1
     (if (<= z 4.8e+65)
       (/ (+ (* z (- t a)) (* y x)) (+ y (* z (- b y))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.55e+43) {
		tmp = t_1;
	} else if (z <= 4.8e+65) {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.55d+43)) then
        tmp = t_1
    else if (z <= 4.8d+65) then
        tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - 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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.55e+43) {
		tmp = t_1;
	} else if (z <= 4.8e+65) {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.55e+43:
		tmp = t_1
	elif z <= 4.8e+65:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.55e+43)
		tmp = t_1;
	elseif (z <= 4.8e+65)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.55e+43)
		tmp = t_1;
	elseif (z <= 4.8e+65)
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+43], t$95$1, If[LessEqual[z, 4.8e+65], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5500000000000001e43 or 4.8000000000000003e65 < z

   1. Initial program 34.9%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 84.2%

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

   5. Simplified 84.2%

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

   if -1.5500000000000001e43 < z < 4.8000000000000003e65

   1. Initial program 87.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+43}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := y + z \cdot b\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-117}:\\ \;\;\;\;\frac{z \cdot a}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \frac{x}{t\_2}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-28}:\\ \;\;\;\;\frac{y \cdot x}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (+ y (* z b))))
   (if (<= z -4.8e-14)
     t_1
     (if (<= z -7.6e-117)
       (/ (* z a) (* y (+ z -1.0)))
       (if (<= z 1.8e-271)
         (* y (/ x t_2))
         (if (<= z 1.35e-28) (/ (* y x) t_2) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = y + (z * b);
	double tmp;
	if (z <= -4.8e-14) {
		tmp = t_1;
	} else if (z <= -7.6e-117) {
		tmp = (z * a) / (y * (z + -1.0));
	} else if (z <= 1.8e-271) {
		tmp = y * (x / t_2);
	} else if (z <= 1.35e-28) {
		tmp = (y * x) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = y + (z * b)
    if (z <= (-4.8d-14)) then
        tmp = t_1
    else if (z <= (-7.6d-117)) then
        tmp = (z * a) / (y * (z + (-1.0d0)))
    else if (z <= 1.8d-271) then
        tmp = y * (x / t_2)
    else if (z <= 1.35d-28) then
        tmp = (y * x) / t_2
    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 b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = y + (z * b);
	double tmp;
	if (z <= -4.8e-14) {
		tmp = t_1;
	} else if (z <= -7.6e-117) {
		tmp = (z * a) / (y * (z + -1.0));
	} else if (z <= 1.8e-271) {
		tmp = y * (x / t_2);
	} else if (z <= 1.35e-28) {
		tmp = (y * x) / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = y + (z * b)
	tmp = 0
	if z <= -4.8e-14:
		tmp = t_1
	elif z <= -7.6e-117:
		tmp = (z * a) / (y * (z + -1.0))
	elif z <= 1.8e-271:
		tmp = y * (x / t_2)
	elif z <= 1.35e-28:
		tmp = (y * x) / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(y + Float64(z * b))
	tmp = 0.0
	if (z <= -4.8e-14)
		tmp = t_1;
	elseif (z <= -7.6e-117)
		tmp = Float64(Float64(z * a) / Float64(y * Float64(z + -1.0)));
	elseif (z <= 1.8e-271)
		tmp = Float64(y * Float64(x / t_2));
	elseif (z <= 1.35e-28)
		tmp = Float64(Float64(y * x) / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = y + (z * b);
	tmp = 0.0;
	if (z <= -4.8e-14)
		tmp = t_1;
	elseif (z <= -7.6e-117)
		tmp = (z * a) / (y * (z + -1.0));
	elseif (z <= 1.8e-271)
		tmp = y * (x / t_2);
	elseif (z <= 1.35e-28)
		tmp = (y * x) / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-14], t$95$1, If[LessEqual[z, -7.6e-117], N[(N[(z * a), $MachinePrecision] / N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-271], N[(y * N[(x / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-28], N[(N[(y * x), $MachinePrecision] / t$95$2), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8e-14 or 1.3499999999999999e-28 < z

   1. Initial program 45.6%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 79.2%

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

   5. Simplified 79.2%

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

   if -4.8e-14 < z < -7.59999999999999945e-117

   1. Initial program 94.8%

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

      1. flip-- N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. clear-num N/A

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

      6. flip-- N/A

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

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

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

      8. --lowering--.f64 94.8%

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

   4. Applied egg-rr 94.8%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

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

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

      3. mul-1-neg N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(0 - a \cdot z\right), \left(\color{blue}{y} + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot z\right)\right), \left(\color{blue}{y} + z \cdot \left(b - y\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(z \cdot a\right)\right), \left(y + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \left(y + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(b - y\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(b - y\right)}\right)\right)\right) \]

      10. --lowering--.f64 54.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(b, \color{blue}{y}\right)\right)\right)\right) \]

   7. Simplified 54.5%

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

   8. Taylor expanded in y around -inf

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 54.4%

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

   10. Simplified 54.4%

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

   if -7.59999999999999945e-117 < z < 1.7999999999999999e-271

   1. Initial program 83.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 83.8%

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

   5. Simplified 83.8%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 55.5%

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

   8. Simplified 55.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-lowering-*.f64 66.4%

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

   10. Applied egg-rr 66.4%

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

   if 1.7999999999999999e-271 < z < 1.3499999999999999e-28

   1. Initial program 94.3%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 94.3%

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

   5. Simplified 94.3%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 63.4%

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

   8. Simplified 63.4%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{y + z \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-117}:\\ \;\;\;\;\frac{z \cdot a}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-271}:\\ \;\;\;\;y \cdot \frac{x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-28}:\\ \;\;\;\;\frac{y \cdot x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-141}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-24}:\\ \;\;\;\;\frac{y \cdot x - z \cdot a}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -7.5e-12)
     t_1
     (if (<= z -9.8e-141)
       (/ (+ (* z (- t a)) (* y x)) y)
       (if (<= z 3.9e-24) (/ (- (* y x) (* z a)) (+ y (* z b))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.5e-12) {
		tmp = t_1;
	} else if (z <= -9.8e-141) {
		tmp = ((z * (t - a)) + (y * x)) / y;
	} else if (z <= 3.9e-24) {
		tmp = ((y * x) - (z * a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-7.5d-12)) then
        tmp = t_1
    else if (z <= (-9.8d-141)) then
        tmp = ((z * (t - a)) + (y * x)) / y
    else if (z <= 3.9d-24) then
        tmp = ((y * x) - (z * a)) / (y + (z * b))
    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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.5e-12) {
		tmp = t_1;
	} else if (z <= -9.8e-141) {
		tmp = ((z * (t - a)) + (y * x)) / y;
	} else if (z <= 3.9e-24) {
		tmp = ((y * x) - (z * a)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -7.5e-12:
		tmp = t_1
	elif z <= -9.8e-141:
		tmp = ((z * (t - a)) + (y * x)) / y
	elif z <= 3.9e-24:
		tmp = ((y * x) - (z * a)) / (y + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -7.5e-12)
		tmp = t_1;
	elseif (z <= -9.8e-141)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / y);
	elseif (z <= 3.9e-24)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * a)) / Float64(y + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -7.5e-12)
		tmp = t_1;
	elseif (z <= -9.8e-141)
		tmp = ((z * (t - a)) + (y * x)) / y;
	elseif (z <= 3.9e-24)
		tmp = ((y * x) - (z * a)) / (y + (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e-12], t$95$1, If[LessEqual[z, -9.8e-141], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 3.9e-24], N[(N[(N[(y * x), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5e-12 or 3.9e-24 < z

   1. Initial program 45.2%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 79.8%

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

   5. Simplified 79.8%

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

   if -7.5e-12 < z < -9.80000000000000012e-141

   1. Initial program 95.8%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 94.3%

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

   5. Simplified 94.3%

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

   6. Taylor expanded in b around 0

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

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

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

      2. +-commutative N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 86.1%

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

   8. Simplified 86.1%

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

   if -9.80000000000000012e-141 < z < 3.9e-24

   1. Initial program 88.7%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 88.7%

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

   5. Simplified 88.7%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(-1 \cdot \left(a \cdot z\right) + x \cdot y\right)}, \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, b\right)\right)\right) \]
   7. Step-by-step derivation

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

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

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

      5. *-commutative N/A

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 74.6%

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

   8. Simplified 74.6%

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

Alternative 4: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-158}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -7.2e-12)
     t_1
     (if (<= z -1.7e-158)
       (/ (+ (* z (- t a)) (* y x)) y)
       (if (<= z 4.9e-26) (* x (/ y (+ y (* z (- b y))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.2e-12) {
		tmp = t_1;
	} else if (z <= -1.7e-158) {
		tmp = ((z * (t - a)) + (y * x)) / y;
	} else if (z <= 4.9e-26) {
		tmp = x * (y / (y + (z * (b - y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-7.2d-12)) then
        tmp = t_1
    else if (z <= (-1.7d-158)) then
        tmp = ((z * (t - a)) + (y * x)) / y
    else if (z <= 4.9d-26) then
        tmp = x * (y / (y + (z * (b - 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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -7.2e-12) {
		tmp = t_1;
	} else if (z <= -1.7e-158) {
		tmp = ((z * (t - a)) + (y * x)) / y;
	} else if (z <= 4.9e-26) {
		tmp = x * (y / (y + (z * (b - y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -7.2e-12:
		tmp = t_1
	elif z <= -1.7e-158:
		tmp = ((z * (t - a)) + (y * x)) / y
	elif z <= 4.9e-26:
		tmp = x * (y / (y + (z * (b - y))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -7.2e-12)
		tmp = t_1;
	elseif (z <= -1.7e-158)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / y);
	elseif (z <= 4.9e-26)
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -7.2e-12)
		tmp = t_1;
	elseif (z <= -1.7e-158)
		tmp = ((z * (t - a)) + (y * x)) / y;
	elseif (z <= 4.9e-26)
		tmp = x * (y / (y + (z * (b - y))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e-12], t$95$1, If[LessEqual[z, -1.7e-158], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 4.9e-26], N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2e-12 or 4.8999999999999999e-26 < z

   1. Initial program 45.2%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 79.8%

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

   5. Simplified 79.8%

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

   if -7.2e-12 < z < -1.7e-158

   1. Initial program 96.5%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 95.3%

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

   5. Simplified 95.3%

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

   6. Taylor expanded in b around 0

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

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

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

      2. +-commutative N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 81.9%

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

   8. Simplified 81.9%

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

   if -1.7e-158 < z < 4.8999999999999999e-26

   1. Initial program 88.2%

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

   3. Taylor expanded in x around inf

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

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

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 59.8%

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

   5. Simplified 59.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-rgt-identity N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. associate-/r/ N/A

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

      9. /-rgt-identity N/A

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

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

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

      11. --lowering--.f64 71.4%

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

   7. Applied egg-rr 71.4%

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

Alternative 5: 65.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-117}:\\ \;\;\;\;\frac{z \cdot a}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -3.5e-14)
     t_1
     (if (<= z -7.6e-117)
       (/ (* z a) (* y (+ z -1.0)))
       (if (<= z 5.4e-28) (* x (/ y (+ y (* z (- b y))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.5e-14) {
		tmp = t_1;
	} else if (z <= -7.6e-117) {
		tmp = (z * a) / (y * (z + -1.0));
	} else if (z <= 5.4e-28) {
		tmp = x * (y / (y + (z * (b - y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-3.5d-14)) then
        tmp = t_1
    else if (z <= (-7.6d-117)) then
        tmp = (z * a) / (y * (z + (-1.0d0)))
    else if (z <= 5.4d-28) then
        tmp = x * (y / (y + (z * (b - 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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.5e-14) {
		tmp = t_1;
	} else if (z <= -7.6e-117) {
		tmp = (z * a) / (y * (z + -1.0));
	} else if (z <= 5.4e-28) {
		tmp = x * (y / (y + (z * (b - y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.5e-14:
		tmp = t_1
	elif z <= -7.6e-117:
		tmp = (z * a) / (y * (z + -1.0))
	elif z <= 5.4e-28:
		tmp = x * (y / (y + (z * (b - y))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.5e-14)
		tmp = t_1;
	elseif (z <= -7.6e-117)
		tmp = Float64(Float64(z * a) / Float64(y * Float64(z + -1.0)));
	elseif (z <= 5.4e-28)
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.5e-14)
		tmp = t_1;
	elseif (z <= -7.6e-117)
		tmp = (z * a) / (y * (z + -1.0));
	elseif (z <= 5.4e-28)
		tmp = x * (y / (y + (z * (b - y))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-14], t$95$1, If[LessEqual[z, -7.6e-117], N[(N[(z * a), $MachinePrecision] / N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-28], N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000002e-14 or 5.3999999999999998e-28 < z

   1. Initial program 45.6%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 79.2%

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

   5. Simplified 79.2%

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

   if -3.5000000000000002e-14 < z < -7.59999999999999945e-117

   1. Initial program 94.8%

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

      1. flip-- N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. clear-num N/A

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

      6. flip-- N/A

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

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

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

      8. --lowering--.f64 94.8%

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

   4. Applied egg-rr 94.8%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

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

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

      3. mul-1-neg N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(0 - a \cdot z\right), \left(\color{blue}{y} + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot z\right)\right), \left(\color{blue}{y} + z \cdot \left(b - y\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(z \cdot a\right)\right), \left(y + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \left(y + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(b - y\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(b - y\right)}\right)\right)\right) \]

      10. --lowering--.f64 54.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(b, \color{blue}{y}\right)\right)\right)\right) \]

   7. Simplified 54.5%

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

   8. Taylor expanded in y around -inf

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 54.4%

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

   10. Simplified 54.4%

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

   if -7.59999999999999945e-117 < z < 5.3999999999999998e-28

   1. Initial program 89.1%

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

   3. Taylor expanded in x around inf

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

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

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. --lowering--.f64 59.5%

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

   5. Simplified 59.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-rgt-identity N/A

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

      5. associate-/r/ N/A

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

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

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

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

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

      8. associate-/r/ N/A

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

      9. /-rgt-identity N/A

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

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

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

      11. --lowering--.f64 69.3%

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

   7. Applied egg-rr 69.3%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-117}:\\ \;\;\;\;\frac{z \cdot a}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.85e+23)
     t_1
     (if (<= z 4.8e+65) (/ (+ (* z (- t a)) (* y x)) (+ y (* z b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.85e+23) {
		tmp = t_1;
	} else if (z <= 4.8e+65) {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.85d+23)) then
        tmp = t_1
    else if (z <= 4.8d+65) then
        tmp = ((z * (t - a)) + (y * x)) / (y + (z * b))
    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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.85e+23) {
		tmp = t_1;
	} else if (z <= 4.8e+65) {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.85e+23:
		tmp = t_1
	elif z <= 4.8e+65:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.85e+23)
		tmp = t_1;
	elseif (z <= 4.8e+65)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y + Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.85e+23)
		tmp = t_1;
	elseif (z <= 4.8e+65)
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+23], t$95$1, If[LessEqual[z, 4.8e+65], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85000000000000006e23 or 4.8000000000000003e65 < z

   1. Initial program 38.8%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 83.1%

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

   5. Simplified 83.1%

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

   if -1.85000000000000006e23 < z < 4.8000000000000003e65

   1. Initial program 88.7%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 86.6%

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

   5. Simplified 86.6%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+23}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-117}:\\ \;\;\;\;\frac{z \cdot a}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -6.6e-14)
     t_1
     (if (<= z -7e-117)
       (/ (* z a) (* y (+ z -1.0)))
       (if (<= z 4.9e-27) (* y (/ x (+ y (* z b)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -6.6e-14) {
		tmp = t_1;
	} else if (z <= -7e-117) {
		tmp = (z * a) / (y * (z + -1.0));
	} else if (z <= 4.9e-27) {
		tmp = y * (x / (y + (z * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-6.6d-14)) then
        tmp = t_1
    else if (z <= (-7d-117)) then
        tmp = (z * a) / (y * (z + (-1.0d0)))
    else if (z <= 4.9d-27) then
        tmp = y * (x / (y + (z * b)))
    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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -6.6e-14) {
		tmp = t_1;
	} else if (z <= -7e-117) {
		tmp = (z * a) / (y * (z + -1.0));
	} else if (z <= 4.9e-27) {
		tmp = y * (x / (y + (z * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -6.6e-14:
		tmp = t_1
	elif z <= -7e-117:
		tmp = (z * a) / (y * (z + -1.0))
	elif z <= 4.9e-27:
		tmp = y * (x / (y + (z * b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -6.6e-14)
		tmp = t_1;
	elseif (z <= -7e-117)
		tmp = Float64(Float64(z * a) / Float64(y * Float64(z + -1.0)));
	elseif (z <= 4.9e-27)
		tmp = Float64(y * Float64(x / Float64(y + Float64(z * b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -6.6e-14)
		tmp = t_1;
	elseif (z <= -7e-117)
		tmp = (z * a) / (y * (z + -1.0));
	elseif (z <= 4.9e-27)
		tmp = y * (x / (y + (z * b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e-14], t$95$1, If[LessEqual[z, -7e-117], N[(N[(z * a), $MachinePrecision] / N[(y * N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e-27], N[(y * N[(x / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5999999999999996e-14 or 4.89999999999999976e-27 < z

   1. Initial program 45.6%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 79.2%

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

   5. Simplified 79.2%

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

   if -6.5999999999999996e-14 < z < -6.9999999999999997e-117

   1. Initial program 94.8%

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

      1. flip-- N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. clear-num N/A

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

      6. flip-- N/A

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

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

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

      8. --lowering--.f64 94.8%

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

   4. Applied egg-rr 94.8%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

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

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

      3. mul-1-neg N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(0 - a \cdot z\right), \left(\color{blue}{y} + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot z\right)\right), \left(\color{blue}{y} + z \cdot \left(b - y\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(z \cdot a\right)\right), \left(y + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \left(y + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(b - y\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(b - y\right)}\right)\right)\right) \]

      10. --lowering--.f64 54.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(b, \color{blue}{y}\right)\right)\right)\right) \]

   7. Simplified 54.5%

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

   8. Taylor expanded in y around -inf

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

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

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

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

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

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

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

      4. sub-neg N/A

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

      5. metadata-eval N/A

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

      6. +-lowering-+.f64 54.4%

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

   10. Simplified 54.4%

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

   if -6.9999999999999997e-117 < z < 4.89999999999999976e-27

   1. Initial program 89.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 59.5%

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

   8. Simplified 59.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-lowering-*.f64 60.0%

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

   10. Applied egg-rr 60.0%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-14}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-117}:\\ \;\;\;\;\frac{z \cdot a}{y \cdot \left(z + -1\right)}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-117}:\\ \;\;\;\;0 - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -3.5e-14)
     t_1
     (if (<= z -7.6e-117)
       (- 0.0 (/ (* z a) y))
       (if (<= z 3.8e-27) (* y (/ x (+ y (* z b)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.5e-14) {
		tmp = t_1;
	} else if (z <= -7.6e-117) {
		tmp = 0.0 - ((z * a) / y);
	} else if (z <= 3.8e-27) {
		tmp = y * (x / (y + (z * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-3.5d-14)) then
        tmp = t_1
    else if (z <= (-7.6d-117)) then
        tmp = 0.0d0 - ((z * a) / y)
    else if (z <= 3.8d-27) then
        tmp = y * (x / (y + (z * b)))
    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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -3.5e-14) {
		tmp = t_1;
	} else if (z <= -7.6e-117) {
		tmp = 0.0 - ((z * a) / y);
	} else if (z <= 3.8e-27) {
		tmp = y * (x / (y + (z * b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -3.5e-14:
		tmp = t_1
	elif z <= -7.6e-117:
		tmp = 0.0 - ((z * a) / y)
	elif z <= 3.8e-27:
		tmp = y * (x / (y + (z * b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -3.5e-14)
		tmp = t_1;
	elseif (z <= -7.6e-117)
		tmp = Float64(0.0 - Float64(Float64(z * a) / y));
	elseif (z <= 3.8e-27)
		tmp = Float64(y * Float64(x / Float64(y + Float64(z * b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -3.5e-14)
		tmp = t_1;
	elseif (z <= -7.6e-117)
		tmp = 0.0 - ((z * a) / y);
	elseif (z <= 3.8e-27)
		tmp = y * (x / (y + (z * b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e-14], t$95$1, If[LessEqual[z, -7.6e-117], N[(0.0 - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-27], N[(y * N[(x / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000002e-14 or 3.8e-27 < z

   1. Initial program 45.6%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 79.2%

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

   5. Simplified 79.2%

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

   if -3.5000000000000002e-14 < z < -7.59999999999999945e-117

   1. Initial program 94.8%

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

      1. flip-- N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. clear-num N/A

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

      6. flip-- N/A

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

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

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

      8. --lowering--.f64 94.8%

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

   4. Applied egg-rr 94.8%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

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

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

      3. mul-1-neg N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(0 - a \cdot z\right), \left(\color{blue}{y} + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot z\right)\right), \left(\color{blue}{y} + z \cdot \left(b - y\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(z \cdot a\right)\right), \left(y + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \left(y + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(b - y\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(b - y\right)}\right)\right)\right) \]

      10. --lowering--.f64 54.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(b, \color{blue}{y}\right)\right)\right)\right) \]

   7. Simplified 54.5%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \color{blue}{y}\right) \]
   9. Step-by-step derivation

   10. Simplified 53.8%

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

   if -7.59999999999999945e-117 < z < 3.8e-27

   1. Initial program 89.1%

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

   3. Taylor expanded in b around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 59.5%

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

   8. Simplified 59.5%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-lowering-*.f64 60.0%

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

   10. Applied egg-rr 60.0%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-117}:\\ \;\;\;\;0 - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-126}:\\ \;\;\;\;0 - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.3e-13)
     t_1
     (if (<= z -5.8e-126)
       (- 0.0 (/ (* z a) y))
       (if (<= z 1.2e-67) (+ x (* z x)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.3e-13) {
		tmp = t_1;
	} else if (z <= -5.8e-126) {
		tmp = 0.0 - ((z * a) / y);
	} else if (z <= 1.2e-67) {
		tmp = x + (z * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.3d-13)) then
        tmp = t_1
    else if (z <= (-5.8d-126)) then
        tmp = 0.0d0 - ((z * a) / y)
    else if (z <= 1.2d-67) then
        tmp = x + (z * x)
    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 b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.3e-13) {
		tmp = t_1;
	} else if (z <= -5.8e-126) {
		tmp = 0.0 - ((z * a) / y);
	} else if (z <= 1.2e-67) {
		tmp = x + (z * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.3e-13:
		tmp = t_1
	elif z <= -5.8e-126:
		tmp = 0.0 - ((z * a) / y)
	elif z <= 1.2e-67:
		tmp = x + (z * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.3e-13)
		tmp = t_1;
	elseif (z <= -5.8e-126)
		tmp = Float64(0.0 - Float64(Float64(z * a) / y));
	elseif (z <= 1.2e-67)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.3e-13)
		tmp = t_1;
	elseif (z <= -5.8e-126)
		tmp = 0.0 - ((z * a) / y);
	elseif (z <= 1.2e-67)
		tmp = x + (z * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e-13], t$95$1, If[LessEqual[z, -5.8e-126], N[(0.0 - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e-67], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e-13 or 1.2e-67 < z

   1. Initial program 49.8%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. --lowering--.f64 75.4%

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

   5. Simplified 75.4%

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

   if -1.3e-13 < z < -5.79999999999999975e-126

   1. Initial program 95.1%

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

      1. flip-- N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. clear-num N/A

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

      6. flip-- N/A

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

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

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

      8. --lowering--.f64 95.0%

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

   4. Applied egg-rr 95.0%

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

   5. Taylor expanded in a around inf

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

      1. associate-*r/ N/A

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

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

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

      3. mul-1-neg N/A

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

      4. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(0 - a \cdot z\right), \left(\color{blue}{y} + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(a \cdot z\right)\right), \left(\color{blue}{y} + z \cdot \left(b - y\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \left(z \cdot a\right)\right), \left(y + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \left(y + z \cdot \left(b - y\right)\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \color{blue}{\left(z \cdot \left(b - y\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \color{blue}{\left(b - y\right)}\right)\right)\right) \]

      10. --lowering--.f64 51.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(b, \color{blue}{y}\right)\right)\right)\right) \]

   7. Simplified 51.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, \mathsf{*.f64}\left(z, a\right)\right), \color{blue}{y}\right) \]
   9. Step-by-step derivation

   10. Simplified 51.3%

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

   if -5.79999999999999975e-126 < z < 1.2e-67

   1. Initial program 87.8%

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

   3. Taylor expanded in y around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 62.0%

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

   8. Simplified 62.0%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-126}:\\ \;\;\;\;0 - \frac{z \cdot a}{y}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-67}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -9e+40) t_1 (if (<= y 7.5e-28) (/ (- t a) b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -9e+40) {
		tmp = t_1;
	} else if (y <= 7.5e-28) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-9d+40)) then
        tmp = t_1
    else if (y <= 7.5d-28) then
        tmp = (t - a) / b
    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 b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -9e+40) {
		tmp = t_1;
	} else if (y <= 7.5e-28) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -9e+40:
		tmp = t_1
	elif y <= 7.5e-28:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -9e+40)
		tmp = t_1;
	elseif (y <= 7.5e-28)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -9e+40)
		tmp = t_1;
	elseif (y <= 7.5e-28)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+40], t$95$1, If[LessEqual[y, 7.5e-28], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.00000000000000064e40 or 7.5000000000000003e-28 < y

   1. Initial program 53.3%

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

   3. Taylor expanded in y around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 58.5%

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

   5. Simplified 58.5%

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

   if -9.00000000000000064e40 < y < 7.5000000000000003e-28

   1. Initial program 81.1%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]
   4. Step-by-step derivation

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

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

      2. --lowering--.f64 57.9%

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

   5. Simplified 57.9%

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

Alternative 11: 42.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -8 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -8e-77) t_1 (if (<= y 3.5e-29) (/ t b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -8e-77) {
		tmp = t_1;
	} else if (y <= 3.5e-29) {
		tmp = t / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-8d-77)) then
        tmp = t_1
    else if (y <= 3.5d-29) then
        tmp = t / b
    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 b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -8e-77) {
		tmp = t_1;
	} else if (y <= 3.5e-29) {
		tmp = t / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -8e-77:
		tmp = t_1
	elif y <= 3.5e-29:
		tmp = t / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -8e-77)
		tmp = t_1;
	elseif (y <= 3.5e-29)
		tmp = Float64(t / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -8e-77)
		tmp = t_1;
	elseif (y <= 3.5e-29)
		tmp = t / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e-77], t$95$1, If[LessEqual[y, 3.5e-29], N[(t / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.9999999999999994e-77 or 3.4999999999999997e-29 < y

   1. Initial program 57.6%

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

   3. Taylor expanded in y around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 52.6%

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

   5. Simplified 52.6%

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

   if -7.9999999999999994e-77 < y < 3.4999999999999997e-29

   1. Initial program 82.4%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right) + \frac{t}{b}\right) - \frac{a}{b}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right) + \color{blue}{\left(\frac{t}{b} - \frac{a}{b}\right)} \]

      2. div-sub N/A

         \[\leadsto y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right) + \frac{t - a}{\color{blue}{b}} \]

      3. +-commutative N/A

         \[\leadsto \frac{t - a}{b} + \color{blue}{y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{t - a}{b}\right), \color{blue}{\left(y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(t - a\right), b\right), \left(\color{blue}{y} \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \left(y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot z}\right), \color{blue}{\left(\frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \left(b \cdot z\right)\right), \left(\frac{\color{blue}{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}}{{b}^{2} \cdot z}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \left(z \cdot b\right)\right), \left(\frac{\left(1 + -1 \cdot z\right) \cdot \color{blue}{\left(t - a\right)}}{{b}^{2} \cdot z}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, b\right)\right), \left(\frac{\left(1 + -1 \cdot z\right) \cdot \color{blue}{\left(t - a\right)}}{{b}^{2} \cdot z}\right)\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, b\right)\right), \mathsf{/.f64}\left(\left(\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)\right), \color{blue}{\left({b}^{2} \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 45.9%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 74.1%

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

   8. Simplified 74.1%

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

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{t}{b}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 40.5%

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

   11. Simplified 40.5%

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

Alternative 12: 36.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-64}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.8e-7) (/ t b) (if (<= z 5e-64) (+ x (* z x)) (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.8e-7) {
		tmp = t / b;
	} else if (z <= 5e-64) {
		tmp = x + (z * x);
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-8.8d-7)) then
        tmp = t / b
    else if (z <= 5d-64) then
        tmp = x + (z * x)
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.8e-7) {
		tmp = t / b;
	} else if (z <= 5e-64) {
		tmp = x + (z * x);
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.8e-7:
		tmp = t / b
	elif z <= 5e-64:
		tmp = x + (z * x)
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.8e-7)
		tmp = Float64(t / b);
	elseif (z <= 5e-64)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.8e-7)
		tmp = t / b;
	elseif (z <= 5e-64)
		tmp = x + (z * x);
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.8e-7], N[(t / b), $MachinePrecision], If[LessEqual[z, 5e-64], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000004e-7 or 5.00000000000000033e-64 < z

   1. Initial program 49.5%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right) + \frac{t}{b}\right) - \frac{a}{b}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right) + \color{blue}{\left(\frac{t}{b} - \frac{a}{b}\right)} \]

      2. div-sub N/A

         \[\leadsto y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right) + \frac{t - a}{\color{blue}{b}} \]

      3. +-commutative N/A

         \[\leadsto \frac{t - a}{b} + \color{blue}{y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{t - a}{b}\right), \color{blue}{\left(y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(t - a\right), b\right), \left(\color{blue}{y} \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \left(y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot z}\right), \color{blue}{\left(\frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \left(b \cdot z\right)\right), \left(\frac{\color{blue}{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}}{{b}^{2} \cdot z}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \left(z \cdot b\right)\right), \left(\frac{\left(1 + -1 \cdot z\right) \cdot \color{blue}{\left(t - a\right)}}{{b}^{2} \cdot z}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, b\right)\right), \left(\frac{\left(1 + -1 \cdot z\right) \cdot \color{blue}{\left(t - a\right)}}{{b}^{2} \cdot z}\right)\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, b\right)\right), \mathsf{/.f64}\left(\left(\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)\right), \color{blue}{\left({b}^{2} \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 33.5%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 51.2%

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

   8. Simplified 51.2%

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

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{t}{b}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 29.7%

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

   11. Simplified 29.7%

       \[\leadsto \color{blue}{\frac{t}{b}} \]

   if -8.8000000000000004e-7 < z < 5.00000000000000033e-64

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf

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

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

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. --lowering--.f64 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in z around 0

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

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

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

      2. *-lowering-*.f64 55.2%

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

   8. Simplified 55.2%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-64}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.3e-8) (/ t b) (if (<= z 1.08e-63) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e-8) {
		tmp = t / b;
	} else if (z <= 1.08e-63) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.3d-8)) then
        tmp = t / b
    else if (z <= 1.08d-63) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3e-8) {
		tmp = t / b;
	} else if (z <= 1.08e-63) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.3e-8:
		tmp = t / b
	elif z <= 1.08e-63:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.3e-8)
		tmp = Float64(t / b);
	elseif (z <= 1.08e-63)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.3e-8)
		tmp = t / b;
	elseif (z <= 1.08e-63)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.3e-8], N[(t / b), $MachinePrecision], If[LessEqual[z, 1.08e-63], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3000000000000001e-8 or 1.07999999999999994e-63 < z

   1. Initial program 49.5%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\left(y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right) + \frac{t}{b}\right) - \frac{a}{b}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right) + \color{blue}{\left(\frac{t}{b} - \frac{a}{b}\right)} \]

      2. div-sub N/A

         \[\leadsto y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right) + \frac{t - a}{\color{blue}{b}} \]

      3. +-commutative N/A

         \[\leadsto \frac{t - a}{b} + \color{blue}{y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{t - a}{b}\right), \color{blue}{\left(y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(t - a\right), b\right), \left(\color{blue}{y} \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \left(y \cdot \left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{x}{b \cdot z} - \frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)}\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\frac{x}{b \cdot z}\right), \color{blue}{\left(\frac{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}{{b}^{2} \cdot z}\right)}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \left(b \cdot z\right)\right), \left(\frac{\color{blue}{\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)}}{{b}^{2} \cdot z}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \left(z \cdot b\right)\right), \left(\frac{\left(1 + -1 \cdot z\right) \cdot \color{blue}{\left(t - a\right)}}{{b}^{2} \cdot z}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, b\right)\right), \left(\frac{\left(1 + -1 \cdot z\right) \cdot \color{blue}{\left(t - a\right)}}{{b}^{2} \cdot z}\right)\right)\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, a\right), b\right), \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, b\right)\right), \mathsf{/.f64}\left(\left(\left(1 + -1 \cdot z\right) \cdot \left(t - a\right)\right), \color{blue}{\left({b}^{2} \cdot z\right)}\right)\right)\right)\right) \]

   5. Simplified 33.5%

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

   6. Taylor expanded in b around inf

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

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

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

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

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 51.2%

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

   8. Simplified 51.2%

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

   9. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{t}{b}} \]
   10. Step-by-step derivation

       1. /-lowering-/.f64 29.7%

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

   11. Simplified 29.7%

       \[\leadsto \color{blue}{\frac{t}{b}} \]

   if -2.3000000000000001e-8 < z < 1.07999999999999994e-63

   1. Initial program 89.2%

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

   3. Taylor expanded in z around 0

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

   5. Simplified 55.2%

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

Alternative 14: 25.5% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.3%

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

3. Taylor expanded in z around 0

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

5. Simplified 27.2%

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

Developer Target 1: 74.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024161 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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