Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A

Percentage Accurate: 98.3% → 98.3%

Time: 15.7s

Alternatives: 18

Speedup: 1.0×

• 47.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - 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 * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Initial Program: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - 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 * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Alternative 1: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \log a \cdot \left(t + -1\right)\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (log a) (+ t -1.0))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + (log(a) * (t + -1.0))) - 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 * exp((((y * log(z)) + (log(a) * (t + (-1.0d0)))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + (Math.log(a) * (t + -1.0))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + (math.log(a) * (t + -1.0))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(log(a) * Float64(t + -1.0))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + (log(a) * (t + -1.0))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Final simplification 98.0%

   \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \log a \cdot \left(t + -1\right)\right) - b}}{y} \]
4. Add Preprocessing

Alternative 2: 79.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot e^{y \cdot \log z - b}}{y}\\ \mathbf{if}\;b \leq -8.4 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot {z}^{\left(-y\right)}\right)}\\ \mathbf{elif}\;b \leq 42:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (exp (- (* y (log z)) b))) y)))
   (if (<= b -8.4e+18)
     t_1
     (if (<= b -3.9e-85)
       (* x (/ (pow a (+ t -1.0)) y))
       (if (<= b 5.4e-36)
         (/ x (* a (* y (pow z (- y)))))
         (if (<= b 42.0) (/ (* x (pow a t)) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * exp(((y * log(z)) - b))) / y;
	double tmp;
	if (b <= -8.4e+18) {
		tmp = t_1;
	} else if (b <= -3.9e-85) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else if (b <= 5.4e-36) {
		tmp = x / (a * (y * pow(z, -y)));
	} else if (b <= 42.0) {
		tmp = (x * pow(a, t)) / 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 = (x * exp(((y * log(z)) - b))) / y
    if (b <= (-8.4d+18)) then
        tmp = t_1
    else if (b <= (-3.9d-85)) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else if (b <= 5.4d-36) then
        tmp = x / (a * (y * (z ** -y)))
    else if (b <= 42.0d0) then
        tmp = (x * (a ** t)) / 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 = (x * Math.exp(((y * Math.log(z)) - b))) / y;
	double tmp;
	if (b <= -8.4e+18) {
		tmp = t_1;
	} else if (b <= -3.9e-85) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else if (b <= 5.4e-36) {
		tmp = x / (a * (y * Math.pow(z, -y)));
	} else if (b <= 42.0) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.exp(((y * math.log(z)) - b))) / y
	tmp = 0
	if b <= -8.4e+18:
		tmp = t_1
	elif b <= -3.9e-85:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	elif b <= 5.4e-36:
		tmp = x / (a * (y * math.pow(z, -y)))
	elif b <= 42.0:
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * exp(Float64(Float64(y * log(z)) - b))) / y)
	tmp = 0.0
	if (b <= -8.4e+18)
		tmp = t_1;
	elseif (b <= -3.9e-85)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	elseif (b <= 5.4e-36)
		tmp = Float64(x / Float64(a * Float64(y * (z ^ Float64(-y)))));
	elseif (b <= 42.0)
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * exp(((y * log(z)) - b))) / y;
	tmp = 0.0;
	if (b <= -8.4e+18)
		tmp = t_1;
	elseif (b <= -3.9e-85)
		tmp = x * ((a ^ (t + -1.0)) / y);
	elseif (b <= 5.4e-36)
		tmp = x / (a * (y * (z ^ -y)));
	elseif (b <= 42.0)
		tmp = (x * (a ^ t)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Exp[N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -8.4e+18], t$95$1, If[LessEqual[b, -3.9e-85], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.4e-36], N[(x / N[(a * N[(y * N[Power[z, (-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 42.0], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.4e18 or 42 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 93.2

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 93.2%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   if -8.4e18 < b < -3.89999999999999988e-85

   1. Initial program 95.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

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

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

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

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

      7. exp-prod N/A

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

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

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

          \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}} \cdot x}{y \cdot e^{b}} \]

      11. metadata-eval N/A

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

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

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

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

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

      14. exp-lowering-exp.f64 73.5

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

   5. Simplified 73.5%

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

   6. Taylor expanded in b around 0

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

      1. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

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

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

      4. exp-to-pow N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 85.4

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

   8. Simplified 85.4%

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

   if -3.89999999999999988e-85 < b < 5.40000000000000015e-36

   1. Initial program 95.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{e^{b}}}}{y} \]

      4. associate-/l/ N/A

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

      6. +-commutative N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + -1 \cdot \log a}}}{y \cdot e^{b}} \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \frac{e^{y \cdot \log z + \color{blue}{\left(\mathsf{neg}\left(\log a\right)\right)}}}{y \cdot e^{b}} \]

      8. unsub-neg N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z - \log a}}}{y \cdot e^{b}} \]

      9. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

      11. *-commutative N/A

          \[\leadsto x \cdot \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      12. exp-to-pow N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      13. pow-lowering-pow.f64 N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      14. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{\color{blue}{a}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{\color{blue}{y \cdot e^{b}}} \]

      16. exp-lowering-exp.f64 86.4

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot \color{blue}{e^{b}}} \]

   5. Simplified 86.4%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 82.2

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

   8. Simplified 82.2%

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

      1. clear-num N/A

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y \cdot a}{{z}^{y}}}} \]

      2. un-div-inv N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

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

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

      7. div-inv N/A

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

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

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

      9. pow-flip N/A

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

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

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

      11. neg-lowering-neg.f64 86.5

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

   10. Applied egg-rr 86.5%

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

   if 5.40000000000000015e-36 < b < 42

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      3. rem-exp-log N/A

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

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

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

      5. rem-exp-log 100.0

         \[\leadsto \frac{x \cdot e^{\log \color{blue}{a} \cdot t - b}}{y} \]

   5. Simplified 100.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. pow-lowering-pow.f64 100.0

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

   8. Simplified 100.0%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z - b}}{y}\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot {z}^{\left(-y\right)}\right)}\\ \mathbf{elif}\;b \leq 42:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z - b}}{y}\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot {z}^{\left(-y\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{t \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.5e+18)
   (/ (* x (exp (- (* y (log z)) b))) y)
   (if (<= b -9.6e-85)
     (* x (/ (pow a (+ t -1.0)) y))
     (if (<= b 3.5e-36)
       (/ x (* a (* y (pow z (- y)))))
       (/ (* x (exp (- (* t (log a)) b))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.5e+18) {
		tmp = (x * exp(((y * log(z)) - b))) / y;
	} else if (b <= -9.6e-85) {
		tmp = x * (pow(a, (t + -1.0)) / y);
	} else if (b <= 3.5e-36) {
		tmp = x / (a * (y * pow(z, -y)));
	} else {
		tmp = (x * exp(((t * log(a)) - b))) / y;
	}
	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 (b <= (-7.5d+18)) then
        tmp = (x * exp(((y * log(z)) - b))) / y
    else if (b <= (-9.6d-85)) then
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    else if (b <= 3.5d-36) then
        tmp = x / (a * (y * (z ** -y)))
    else
        tmp = (x * exp(((t * log(a)) - b))) / y
    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 (b <= -7.5e+18) {
		tmp = (x * Math.exp(((y * Math.log(z)) - b))) / y;
	} else if (b <= -9.6e-85) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else if (b <= 3.5e-36) {
		tmp = x / (a * (y * Math.pow(z, -y)));
	} else {
		tmp = (x * Math.exp(((t * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.5e+18:
		tmp = (x * math.exp(((y * math.log(z)) - b))) / y
	elif b <= -9.6e-85:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	elif b <= 3.5e-36:
		tmp = x / (a * (y * math.pow(z, -y)))
	else:
		tmp = (x * math.exp(((t * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.5e+18)
		tmp = Float64(Float64(x * exp(Float64(Float64(y * log(z)) - b))) / y);
	elseif (b <= -9.6e-85)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	elseif (b <= 3.5e-36)
		tmp = Float64(x / Float64(a * Float64(y * (z ^ Float64(-y)))));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(t * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.5e+18)
		tmp = (x * exp(((y * log(z)) - b))) / y;
	elseif (b <= -9.6e-85)
		tmp = x * ((a ^ (t + -1.0)) / y);
	elseif (b <= 3.5e-36)
		tmp = x / (a * (y * (z ^ -y)));
	else
		tmp = (x * exp(((t * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.5e+18], N[(N[(x * N[Exp[N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -9.6e-85], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e-36], N[(x / N[(a * N[(y * N[Power[z, (-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(t * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.5e18

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 95.7

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 95.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   if -7.5e18 < b < -9.6000000000000002e-85

   1. Initial program 95.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

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

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

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

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

      7. exp-prod N/A

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

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

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

          \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}} \cdot x}{y \cdot e^{b}} \]

      11. metadata-eval N/A

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

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

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

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

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

      14. exp-lowering-exp.f64 73.5

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

   5. Simplified 73.5%

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

   6. Taylor expanded in b around 0

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

      1. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

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

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

      4. exp-to-pow N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 85.4

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

   8. Simplified 85.4%

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

   if -9.6000000000000002e-85 < b < 3.5e-36

   1. Initial program 95.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{e^{b}}}}{y} \]

      4. associate-/l/ N/A

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

      6. +-commutative N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + -1 \cdot \log a}}}{y \cdot e^{b}} \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \frac{e^{y \cdot \log z + \color{blue}{\left(\mathsf{neg}\left(\log a\right)\right)}}}{y \cdot e^{b}} \]

      8. unsub-neg N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z - \log a}}}{y \cdot e^{b}} \]

      9. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

      11. *-commutative N/A

          \[\leadsto x \cdot \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      12. exp-to-pow N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      13. pow-lowering-pow.f64 N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      14. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{\color{blue}{a}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{\color{blue}{y \cdot e^{b}}} \]

      16. exp-lowering-exp.f64 86.4

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot \color{blue}{e^{b}}} \]

   5. Simplified 86.4%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 82.2

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

   8. Simplified 82.2%

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

      1. clear-num N/A

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y \cdot a}{{z}^{y}}}} \]

      2. un-div-inv N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

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

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

      7. div-inv N/A

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

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

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

      9. pow-flip N/A

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

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

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

      11. neg-lowering-neg.f64 86.5

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

   10. Applied egg-rr 86.5%

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

   if 3.5e-36 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      3. rem-exp-log N/A

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

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

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

      5. rem-exp-log 97.1

         \[\leadsto \frac{x \cdot e^{\log \color{blue}{a} \cdot t - b}}{y} \]

   5. Simplified 97.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot e^{y \cdot \log z - b}}{y}\\ \mathbf{elif}\;b \leq -9.6 \cdot 10^{-85}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot {z}^{\left(-y\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{t \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.8% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {z}^{y}}{y}\\ t_2 := {a}^{\left(t + -1\right)}\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+108}:\\ \;\;\;\;-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \frac{t\_2}{y}\\ \mathbf{elif}\;b \leq 1.82 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 330:\\ \;\;\;\;t\_2 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow z y)) y)) (t_2 (pow a (+ t -1.0))))
   (if (<= b -7.2e+108)
     (* -0.16666666666666666 (/ (* x (* b (* b b))) y))
     (if (<= b -1.12e+28)
       t_1
       (if (<= b 5.2e-207)
         (* x (/ t_2 y))
         (if (<= b 1.82e-75)
           t_1
           (if (<= b 330.0) (* t_2 (/ x y)) (/ x (* y (exp b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(z, y)) / y;
	double t_2 = pow(a, (t + -1.0));
	double tmp;
	if (b <= -7.2e+108) {
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	} else if (b <= -1.12e+28) {
		tmp = t_1;
	} else if (b <= 5.2e-207) {
		tmp = x * (t_2 / y);
	} else if (b <= 1.82e-75) {
		tmp = t_1;
	} else if (b <= 330.0) {
		tmp = t_2 * (x / y);
	} else {
		tmp = x / (y * exp(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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (z ** y)) / y
    t_2 = a ** (t + (-1.0d0))
    if (b <= (-7.2d+108)) then
        tmp = (-0.16666666666666666d0) * ((x * (b * (b * b))) / y)
    else if (b <= (-1.12d+28)) then
        tmp = t_1
    else if (b <= 5.2d-207) then
        tmp = x * (t_2 / y)
    else if (b <= 1.82d-75) then
        tmp = t_1
    else if (b <= 330.0d0) then
        tmp = t_2 * (x / y)
    else
        tmp = x / (y * exp(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 t_1 = (x * Math.pow(z, y)) / y;
	double t_2 = Math.pow(a, (t + -1.0));
	double tmp;
	if (b <= -7.2e+108) {
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	} else if (b <= -1.12e+28) {
		tmp = t_1;
	} else if (b <= 5.2e-207) {
		tmp = x * (t_2 / y);
	} else if (b <= 1.82e-75) {
		tmp = t_1;
	} else if (b <= 330.0) {
		tmp = t_2 * (x / y);
	} else {
		tmp = x / (y * Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(z, y)) / y
	t_2 = math.pow(a, (t + -1.0))
	tmp = 0
	if b <= -7.2e+108:
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y)
	elif b <= -1.12e+28:
		tmp = t_1
	elif b <= 5.2e-207:
		tmp = x * (t_2 / y)
	elif b <= 1.82e-75:
		tmp = t_1
	elif b <= 330.0:
		tmp = t_2 * (x / y)
	else:
		tmp = x / (y * math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (z ^ y)) / y)
	t_2 = a ^ Float64(t + -1.0)
	tmp = 0.0
	if (b <= -7.2e+108)
		tmp = Float64(-0.16666666666666666 * Float64(Float64(x * Float64(b * Float64(b * b))) / y));
	elseif (b <= -1.12e+28)
		tmp = t_1;
	elseif (b <= 5.2e-207)
		tmp = Float64(x * Float64(t_2 / y));
	elseif (b <= 1.82e-75)
		tmp = t_1;
	elseif (b <= 330.0)
		tmp = Float64(t_2 * Float64(x / y));
	else
		tmp = Float64(x / Float64(y * exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (z ^ y)) / y;
	t_2 = a ^ (t + -1.0);
	tmp = 0.0;
	if (b <= -7.2e+108)
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	elseif (b <= -1.12e+28)
		tmp = t_1;
	elseif (b <= 5.2e-207)
		tmp = x * (t_2 / y);
	elseif (b <= 1.82e-75)
		tmp = t_1;
	elseif (b <= 330.0)
		tmp = t_2 * (x / y);
	else
		tmp = x / (y * exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[b, -7.2e+108], N[(-0.16666666666666666 * N[(N[(x * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.12e+28], t$95$1, If[LessEqual[b, 5.2e-207], N[(x * N[(t$95$2 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.82e-75], t$95$1, If[LessEqual[b, 330.0], N[(t$95$2 * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.2e108

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 97.9

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 97.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 95.7

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 95.7%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-b}}}{y} \]

   9. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}}{y} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right) + 1\right)}}{y} \]

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

          \[\leadsto \frac{x \cdot \color{blue}{\mathsf{fma}\left(b, b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1, 1\right)}}{y} \]

       3. sub-neg N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \color{blue}{b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)}, 1\right)}{y} \]

       4. metadata-eval N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \color{blue}{-1}, 1\right)}{y} \]

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

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(b, \frac{1}{2} + \frac{-1}{6} \cdot b, -1\right)}, 1\right)}{y} \]

       6. +-commutative N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{\frac{-1}{6} \cdot b + \frac{1}{2}}, -1\right), 1\right)}{y} \]

       7. *-commutative N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{b \cdot \frac{-1}{6}} + \frac{1}{2}, -1\right), 1\right)}{y} \]

       8. accelerator-lowering-fma.f64 95.7

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(b, -0.16666666666666666, 0.5\right)}, -1\right), 1\right)}{y} \]

   11. Simplified 95.7%

       \[\leadsto \frac{x \cdot \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(b, \mathsf{fma}\left(b, -0.16666666666666666, 0.5\right), -1\right), 1\right)}}{y} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   13. Step-by-step derivation

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

          \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]

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

          \[\leadsto \frac{-1}{6} \cdot \color{blue}{\frac{{b}^{3} \cdot x}{y}} \]

       3. *-commutative N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{x \cdot {b}^{3}}}{y} \]

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

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{x \cdot {b}^{3}}}{y} \]

       5. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot b\right)\right)}}{y} \]

       6. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \left(b \cdot \color{blue}{{b}^{2}}\right)}{y} \]

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

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \color{blue}{\left(b \cdot {b}^{2}\right)}}{y} \]

       8. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \left(b \cdot \color{blue}{\left(b \cdot b\right)}\right)}{y} \]

       9. *-lowering-*.f64 95.7

          \[\leadsto -0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \color{blue}{\left(b \cdot b\right)}\right)}{y} \]

   14. Simplified 95.7%

       \[\leadsto \color{blue}{-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}} \]

   if -7.2e108 < b < -1.12e28 or 5.1999999999999998e-207 < b < 1.81999999999999991e-75

   1. Initial program 99.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 78.7

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 78.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. pow-lowering-pow.f64 75.6

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

   8. Simplified 75.6%

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

   if -1.12e28 < b < 5.1999999999999998e-207

   1. Initial program 93.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

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

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

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

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

      7. exp-prod N/A

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

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

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

          \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}} \cdot x}{y \cdot e^{b}} \]

      11. metadata-eval N/A

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

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

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

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

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

      14. exp-lowering-exp.f64 65.5

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

   5. Simplified 65.5%

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

   6. Taylor expanded in b around 0

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

      1. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

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

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

      4. exp-to-pow N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 71.0

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

   8. Simplified 71.0%

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

   if 1.81999999999999991e-75 < b < 330

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

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

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

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

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

      7. exp-prod N/A

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

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

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

          \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}} \cdot x}{y \cdot e^{b}} \]

      11. metadata-eval N/A

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

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

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

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

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

      14. exp-lowering-exp.f64 82.7

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

   5. Simplified 82.7%

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

   6. Taylor expanded in b around 0

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

   8. Simplified 82.7%

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

      1. associate-/l* N/A

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

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

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

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

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

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

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

      5. /-lowering-/.f64 82.9

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

   10. Applied egg-rr 82.9%

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

   if 330 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 90.3

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 90.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 87.1

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 87.1%

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

      1. exp-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b}}}}{y} \]

      2. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]

      3. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \frac{x}{\color{blue}{y \cdot e^{b}}} \]

      6. exp-lowering-exp.f64 87.1

         \[\leadsto \frac{x}{y \cdot \color{blue}{e^{b}}} \]

   10. Applied egg-rr 87.1%

       \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+108}:\\ \;\;\;\;-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 1.82 \cdot 10^{-75}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;b \leq 330:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {z}^{y}}{y}\\ t_2 := x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;b \leq -7.8 \cdot 10^{+100}:\\ \;\;\;\;-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 10^{-211}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.82 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 720:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow z y)) y)) (t_2 (* x (/ (pow a (+ t -1.0)) y))))
   (if (<= b -7.8e+100)
     (* -0.16666666666666666 (/ (* x (* b (* b b))) y))
     (if (<= b -6.5e+27)
       t_1
       (if (<= b 1e-211)
         t_2
         (if (<= b 1.82e-75)
           t_1
           (if (<= b 720.0) t_2 (/ x (* y (exp b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(z, y)) / y;
	double t_2 = x * (pow(a, (t + -1.0)) / y);
	double tmp;
	if (b <= -7.8e+100) {
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	} else if (b <= -6.5e+27) {
		tmp = t_1;
	} else if (b <= 1e-211) {
		tmp = t_2;
	} else if (b <= 1.82e-75) {
		tmp = t_1;
	} else if (b <= 720.0) {
		tmp = t_2;
	} else {
		tmp = x / (y * exp(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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (z ** y)) / y
    t_2 = x * ((a ** (t + (-1.0d0))) / y)
    if (b <= (-7.8d+100)) then
        tmp = (-0.16666666666666666d0) * ((x * (b * (b * b))) / y)
    else if (b <= (-6.5d+27)) then
        tmp = t_1
    else if (b <= 1d-211) then
        tmp = t_2
    else if (b <= 1.82d-75) then
        tmp = t_1
    else if (b <= 720.0d0) then
        tmp = t_2
    else
        tmp = x / (y * exp(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 t_1 = (x * Math.pow(z, y)) / y;
	double t_2 = x * (Math.pow(a, (t + -1.0)) / y);
	double tmp;
	if (b <= -7.8e+100) {
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	} else if (b <= -6.5e+27) {
		tmp = t_1;
	} else if (b <= 1e-211) {
		tmp = t_2;
	} else if (b <= 1.82e-75) {
		tmp = t_1;
	} else if (b <= 720.0) {
		tmp = t_2;
	} else {
		tmp = x / (y * Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(z, y)) / y
	t_2 = x * (math.pow(a, (t + -1.0)) / y)
	tmp = 0
	if b <= -7.8e+100:
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y)
	elif b <= -6.5e+27:
		tmp = t_1
	elif b <= 1e-211:
		tmp = t_2
	elif b <= 1.82e-75:
		tmp = t_1
	elif b <= 720.0:
		tmp = t_2
	else:
		tmp = x / (y * math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (z ^ y)) / y)
	t_2 = Float64(x * Float64((a ^ Float64(t + -1.0)) / y))
	tmp = 0.0
	if (b <= -7.8e+100)
		tmp = Float64(-0.16666666666666666 * Float64(Float64(x * Float64(b * Float64(b * b))) / y));
	elseif (b <= -6.5e+27)
		tmp = t_1;
	elseif (b <= 1e-211)
		tmp = t_2;
	elseif (b <= 1.82e-75)
		tmp = t_1;
	elseif (b <= 720.0)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(y * exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (z ^ y)) / y;
	t_2 = x * ((a ^ (t + -1.0)) / y);
	tmp = 0.0;
	if (b <= -7.8e+100)
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	elseif (b <= -6.5e+27)
		tmp = t_1;
	elseif (b <= 1e-211)
		tmp = t_2;
	elseif (b <= 1.82e-75)
		tmp = t_1;
	elseif (b <= 720.0)
		tmp = t_2;
	else
		tmp = x / (y * exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.8e+100], N[(-0.16666666666666666 * N[(N[(x * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.5e+27], t$95$1, If[LessEqual[b, 1e-211], t$95$2, If[LessEqual[b, 1.82e-75], t$95$1, If[LessEqual[b, 720.0], t$95$2, N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.8e100

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 97.9

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 97.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 95.7

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 95.7%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-b}}}{y} \]

   9. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}}{y} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right) + 1\right)}}{y} \]

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

          \[\leadsto \frac{x \cdot \color{blue}{\mathsf{fma}\left(b, b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1, 1\right)}}{y} \]

       3. sub-neg N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \color{blue}{b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)}, 1\right)}{y} \]

       4. metadata-eval N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \color{blue}{-1}, 1\right)}{y} \]

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

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(b, \frac{1}{2} + \frac{-1}{6} \cdot b, -1\right)}, 1\right)}{y} \]

       6. +-commutative N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{\frac{-1}{6} \cdot b + \frac{1}{2}}, -1\right), 1\right)}{y} \]

       7. *-commutative N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{b \cdot \frac{-1}{6}} + \frac{1}{2}, -1\right), 1\right)}{y} \]

       8. accelerator-lowering-fma.f64 95.7

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(b, -0.16666666666666666, 0.5\right)}, -1\right), 1\right)}{y} \]

   11. Simplified 95.7%

       \[\leadsto \frac{x \cdot \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(b, \mathsf{fma}\left(b, -0.16666666666666666, 0.5\right), -1\right), 1\right)}}{y} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   13. Step-by-step derivation

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

          \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]

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

          \[\leadsto \frac{-1}{6} \cdot \color{blue}{\frac{{b}^{3} \cdot x}{y}} \]

       3. *-commutative N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{x \cdot {b}^{3}}}{y} \]

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

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{x \cdot {b}^{3}}}{y} \]

       5. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot b\right)\right)}}{y} \]

       6. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \left(b \cdot \color{blue}{{b}^{2}}\right)}{y} \]

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

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \color{blue}{\left(b \cdot {b}^{2}\right)}}{y} \]

       8. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \left(b \cdot \color{blue}{\left(b \cdot b\right)}\right)}{y} \]

       9. *-lowering-*.f64 95.7

          \[\leadsto -0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \color{blue}{\left(b \cdot b\right)}\right)}{y} \]

   14. Simplified 95.7%

       \[\leadsto \color{blue}{-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}} \]

   if -7.8e100 < b < -6.5000000000000005e27 or 1.00000000000000009e-211 < b < 1.81999999999999991e-75

   1. Initial program 99.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 78.7

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 78.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. pow-lowering-pow.f64 75.6

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

   8. Simplified 75.6%

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

   if -6.5000000000000005e27 < b < 1.00000000000000009e-211 or 1.81999999999999991e-75 < b < 720

   1. Initial program 94.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

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

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

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

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

      7. exp-prod N/A

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

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

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

          \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}} \cdot x}{y \cdot e^{b}} \]

      11. metadata-eval N/A

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

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

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

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

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

      14. exp-lowering-exp.f64 68.7

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

   5. Simplified 68.7%

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

   6. Taylor expanded in b around 0

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

      1. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

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

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

      4. exp-to-pow N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 73.2

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

   8. Simplified 73.2%

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

   if 720 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 90.3

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 90.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 87.1

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 87.1%

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

      1. exp-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b}}}}{y} \]

      2. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]

      3. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \frac{x}{\color{blue}{y \cdot e^{b}}} \]

      6. exp-lowering-exp.f64 87.1

         \[\leadsto \frac{x}{y \cdot \color{blue}{e^{b}}} \]

   10. Applied egg-rr 87.1%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+100}:\\ \;\;\;\;-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+27}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;b \leq 10^{-211}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 1.82 \cdot 10^{-75}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;b \leq 720:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{t}}{y}\\ t_2 := \frac{x}{y \cdot e^{b}}\\ \mathbf{if}\;b \leq -1 \cdot 10^{+41}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-225}:\\ \;\;\;\;x \cdot \frac{\frac{1}{y}}{a}\\ \mathbf{elif}\;b \leq 700:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a t)) y)) (t_2 (/ x (* y (exp b)))))
   (if (<= b -1e+41)
     t_2
     (if (<= b -6e-81)
       t_1
       (if (<= b 1.6e-225) (* x (/ (/ 1.0 y) a)) (if (<= b 700.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, t)) / y;
	double t_2 = x / (y * exp(b));
	double tmp;
	if (b <= -1e+41) {
		tmp = t_2;
	} else if (b <= -6e-81) {
		tmp = t_1;
	} else if (b <= 1.6e-225) {
		tmp = x * ((1.0 / y) / a);
	} else if (b <= 700.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = (x * (a ** t)) / y
    t_2 = x / (y * exp(b))
    if (b <= (-1d+41)) then
        tmp = t_2
    else if (b <= (-6d-81)) then
        tmp = t_1
    else if (b <= 1.6d-225) then
        tmp = x * ((1.0d0 / y) / a)
    else if (b <= 700.0d0) then
        tmp = t_1
    else
        tmp = t_2
    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 * Math.pow(a, t)) / y;
	double t_2 = x / (y * Math.exp(b));
	double tmp;
	if (b <= -1e+41) {
		tmp = t_2;
	} else if (b <= -6e-81) {
		tmp = t_1;
	} else if (b <= 1.6e-225) {
		tmp = x * ((1.0 / y) / a);
	} else if (b <= 700.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, t)) / y
	t_2 = x / (y * math.exp(b))
	tmp = 0
	if b <= -1e+41:
		tmp = t_2
	elif b <= -6e-81:
		tmp = t_1
	elif b <= 1.6e-225:
		tmp = x * ((1.0 / y) / a)
	elif b <= 700.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ t)) / y)
	t_2 = Float64(x / Float64(y * exp(b)))
	tmp = 0.0
	if (b <= -1e+41)
		tmp = t_2;
	elseif (b <= -6e-81)
		tmp = t_1;
	elseif (b <= 1.6e-225)
		tmp = Float64(x * Float64(Float64(1.0 / y) / a));
	elseif (b <= 700.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ t)) / y;
	t_2 = x / (y * exp(b));
	tmp = 0.0;
	if (b <= -1e+41)
		tmp = t_2;
	elseif (b <= -6e-81)
		tmp = t_1;
	elseif (b <= 1.6e-225)
		tmp = x * ((1.0 / y) / a);
	elseif (b <= 700.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+41], t$95$2, If[LessEqual[b, -6e-81], t$95$1, If[LessEqual[b, 1.6e-225], N[(x * N[(N[(1.0 / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 700.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.00000000000000001e41 or 700 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 92.7

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 92.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 87.9

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 87.9%

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

      1. exp-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b}}}}{y} \]

      2. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]

      3. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \frac{x}{\color{blue}{y \cdot e^{b}}} \]

      6. exp-lowering-exp.f64 87.9

         \[\leadsto \frac{x}{y \cdot \color{blue}{e^{b}}} \]

   10. Applied egg-rr 87.9%

       \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

   if -1.00000000000000001e41 < b < -5.9999999999999998e-81 or 1.59999999999999987e-225 < b < 700

   1. Initial program 98.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      3. rem-exp-log N/A

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

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

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

      5. rem-exp-log 59.2

         \[\leadsto \frac{x \cdot e^{\log \color{blue}{a} \cdot t - b}}{y} \]

   5. Simplified 59.2%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. pow-lowering-pow.f64 57.1

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

   8. Simplified 57.1%

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

   if -5.9999999999999998e-81 < b < 1.59999999999999987e-225

   1. Initial program 92.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{e^{b}}}}{y} \]

      4. associate-/l/ N/A

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

      6. +-commutative N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + -1 \cdot \log a}}}{y \cdot e^{b}} \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \frac{e^{y \cdot \log z + \color{blue}{\left(\mathsf{neg}\left(\log a\right)\right)}}}{y \cdot e^{b}} \]

      8. unsub-neg N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z - \log a}}}{y \cdot e^{b}} \]

      9. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

      11. *-commutative N/A

          \[\leadsto x \cdot \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      12. exp-to-pow N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      13. pow-lowering-pow.f64 N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      14. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{\color{blue}{a}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{\color{blue}{y \cdot e^{b}}} \]

      16. exp-lowering-exp.f64 86.6

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot \color{blue}{e^{b}}} \]

   5. Simplified 86.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 86.6

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

   8. Simplified 86.6%

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

   9. Taylor expanded in y around 0

      \[\leadsto x \cdot \frac{\color{blue}{1}}{y \cdot a} \]
   10. Step-by-step derivation

   11. Simplified 54.0%

       \[\leadsto x \cdot \frac{\color{blue}{1}}{y \cdot a} \]
   12. Step-by-step derivation

       1. associate-/r* N/A

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

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

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

       3. /-lowering-/.f64 54.1

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

   13. Applied egg-rr 54.1%

       \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{y}}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 73.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {z}^{y}}{y}\\ \mathbf{if}\;y \leq -28000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-160}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 10^{+122}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow z y)) y)))
   (if (<= y -28000.0)
     t_1
     (if (<= y 5e-160)
       (/ x (* a (* y (exp b))))
       (if (<= y 1e+122) (* x (/ (pow a (+ t -1.0)) y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(z, y)) / y;
	double tmp;
	if (y <= -28000.0) {
		tmp = t_1;
	} else if (y <= 5e-160) {
		tmp = x / (a * (y * exp(b)));
	} else if (y <= 1e+122) {
		tmp = x * (pow(a, (t + -1.0)) / 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 = (x * (z ** y)) / y
    if (y <= (-28000.0d0)) then
        tmp = t_1
    else if (y <= 5d-160) then
        tmp = x / (a * (y * exp(b)))
    else if (y <= 1d+122) then
        tmp = x * ((a ** (t + (-1.0d0))) / 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 = (x * Math.pow(z, y)) / y;
	double tmp;
	if (y <= -28000.0) {
		tmp = t_1;
	} else if (y <= 5e-160) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (y <= 1e+122) {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(z, y)) / y
	tmp = 0
	if y <= -28000.0:
		tmp = t_1
	elif y <= 5e-160:
		tmp = x / (a * (y * math.exp(b)))
	elif y <= 1e+122:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (z ^ y)) / y)
	tmp = 0.0
	if (y <= -28000.0)
		tmp = t_1;
	elseif (y <= 5e-160)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (y <= 1e+122)
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (z ^ y)) / y;
	tmp = 0.0;
	if (y <= -28000.0)
		tmp = t_1;
	elseif (y <= 5e-160)
		tmp = x / (a * (y * exp(b)));
	elseif (y <= 1e+122)
		tmp = x * ((a ^ (t + -1.0)) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -28000.0], t$95$1, If[LessEqual[y, 5e-160], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+122], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -28000 or 1.00000000000000001e122 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 94.8

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 94.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. pow-lowering-pow.f64 84.3

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

   8. Simplified 84.3%

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

   if -28000 < y < 4.99999999999999994e-160

   1. Initial program 94.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

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

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

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

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

      7. exp-prod N/A

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

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

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

          \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}} \cdot x}{y \cdot e^{b}} \]

      11. metadata-eval N/A

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

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

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

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

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

      14. exp-lowering-exp.f64 81.0

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

   5. Simplified 81.0%

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

   6. Taylor expanded in t around 0

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

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

         \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

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

         \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}} \]

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

         \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot e^{b}\right)}} \]

      4. exp-lowering-exp.f64 85.5

         \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{e^{b}}\right)} \]

   8. Simplified 85.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   if 4.99999999999999994e-160 < y < 1.00000000000000001e122

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

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

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

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

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

      7. exp-prod N/A

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

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

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

          \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}} \cdot x}{y \cdot e^{b}} \]

      11. metadata-eval N/A

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

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

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

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

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

      14. exp-lowering-exp.f64 69.2

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

   5. Simplified 69.2%

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

   6. Taylor expanded in b around 0

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

      1. associate-/l* N/A

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

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

         \[\leadsto \color{blue}{x \cdot \frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}} \]

      4. exp-to-pow N/A

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

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

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

      6. sub-neg N/A

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

      7. metadata-eval N/A

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

      8. +-commutative N/A

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

      9. +-lowering-+.f64 69.8

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

   8. Simplified 69.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -28000:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-160}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 10^{+122}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+109}:\\ \;\;\;\;-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot {z}^{\left(-y\right)}\right)}\\ \mathbf{elif}\;b \leq 1300:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4e+109)
   (* -0.16666666666666666 (/ (* x (* b (* b b))) y))
   (if (<= b 2.1e-36)
     (/ x (* a (* y (pow z (- y)))))
     (if (<= b 1300.0) (/ (* x (pow a t)) y) (/ x (* y (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4e+109) {
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	} else if (b <= 2.1e-36) {
		tmp = x / (a * (y * pow(z, -y)));
	} else if (b <= 1300.0) {
		tmp = (x * pow(a, t)) / y;
	} else {
		tmp = x / (y * exp(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 (b <= (-4d+109)) then
        tmp = (-0.16666666666666666d0) * ((x * (b * (b * b))) / y)
    else if (b <= 2.1d-36) then
        tmp = x / (a * (y * (z ** -y)))
    else if (b <= 1300.0d0) then
        tmp = (x * (a ** t)) / y
    else
        tmp = x / (y * exp(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 (b <= -4e+109) {
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	} else if (b <= 2.1e-36) {
		tmp = x / (a * (y * Math.pow(z, -y)));
	} else if (b <= 1300.0) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = x / (y * Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4e+109:
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y)
	elif b <= 2.1e-36:
		tmp = x / (a * (y * math.pow(z, -y)))
	elif b <= 1300.0:
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = x / (y * math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4e+109)
		tmp = Float64(-0.16666666666666666 * Float64(Float64(x * Float64(b * Float64(b * b))) / y));
	elseif (b <= 2.1e-36)
		tmp = Float64(x / Float64(a * Float64(y * (z ^ Float64(-y)))));
	elseif (b <= 1300.0)
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = Float64(x / Float64(y * exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4e+109)
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	elseif (b <= 2.1e-36)
		tmp = x / (a * (y * (z ^ -y)));
	elseif (b <= 1300.0)
		tmp = (x * (a ^ t)) / y;
	else
		tmp = x / (y * exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4e+109], N[(-0.16666666666666666 * N[(N[(x * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-36], N[(x / N[(a * N[(y * N[Power[z, (-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1300.0], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.99999999999999993e109

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 97.9

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 97.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 95.7

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 95.7%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-b}}}{y} \]

   9. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}}{y} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right) + 1\right)}}{y} \]

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

          \[\leadsto \frac{x \cdot \color{blue}{\mathsf{fma}\left(b, b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1, 1\right)}}{y} \]

       3. sub-neg N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \color{blue}{b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)}, 1\right)}{y} \]

       4. metadata-eval N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \color{blue}{-1}, 1\right)}{y} \]

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

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(b, \frac{1}{2} + \frac{-1}{6} \cdot b, -1\right)}, 1\right)}{y} \]

       6. +-commutative N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{\frac{-1}{6} \cdot b + \frac{1}{2}}, -1\right), 1\right)}{y} \]

       7. *-commutative N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{b \cdot \frac{-1}{6}} + \frac{1}{2}, -1\right), 1\right)}{y} \]

       8. accelerator-lowering-fma.f64 95.7

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(b, -0.16666666666666666, 0.5\right)}, -1\right), 1\right)}{y} \]

   11. Simplified 95.7%

       \[\leadsto \frac{x \cdot \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(b, \mathsf{fma}\left(b, -0.16666666666666666, 0.5\right), -1\right), 1\right)}}{y} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   13. Step-by-step derivation

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

          \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]

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

          \[\leadsto \frac{-1}{6} \cdot \color{blue}{\frac{{b}^{3} \cdot x}{y}} \]

       3. *-commutative N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{x \cdot {b}^{3}}}{y} \]

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

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{x \cdot {b}^{3}}}{y} \]

       5. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot b\right)\right)}}{y} \]

       6. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \left(b \cdot \color{blue}{{b}^{2}}\right)}{y} \]

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

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \color{blue}{\left(b \cdot {b}^{2}\right)}}{y} \]

       8. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \left(b \cdot \color{blue}{\left(b \cdot b\right)}\right)}{y} \]

       9. *-lowering-*.f64 95.7

          \[\leadsto -0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \color{blue}{\left(b \cdot b\right)}\right)}{y} \]

   14. Simplified 95.7%

       \[\leadsto \color{blue}{-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}} \]

   if -3.99999999999999993e109 < b < 2.09999999999999991e-36

   1. Initial program 96.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{e^{b}}}}{y} \]

      4. associate-/l/ N/A

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

      6. +-commutative N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + -1 \cdot \log a}}}{y \cdot e^{b}} \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \frac{e^{y \cdot \log z + \color{blue}{\left(\mathsf{neg}\left(\log a\right)\right)}}}{y \cdot e^{b}} \]

      8. unsub-neg N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z - \log a}}}{y \cdot e^{b}} \]

      9. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

      11. *-commutative N/A

          \[\leadsto x \cdot \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      12. exp-to-pow N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      13. pow-lowering-pow.f64 N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      14. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{\color{blue}{a}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{\color{blue}{y \cdot e^{b}}} \]

      16. exp-lowering-exp.f64 75.8

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot \color{blue}{e^{b}}} \]

   5. Simplified 75.8%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 78.1

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

   8. Simplified 78.1%

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

      1. clear-num N/A

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y \cdot a}{{z}^{y}}}} \]

      2. un-div-inv N/A

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

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

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

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

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

      7. div-inv N/A

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

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

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

      9. pow-flip N/A

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

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

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

      11. neg-lowering-neg.f64 81.6

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

   10. Applied egg-rr 81.6%

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

   if 2.09999999999999991e-36 < b < 1300

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      3. rem-exp-log N/A

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

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

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

      5. rem-exp-log 100.0

         \[\leadsto \frac{x \cdot e^{\log \color{blue}{a} \cdot t - b}}{y} \]

   5. Simplified 100.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. pow-lowering-pow.f64 100.0

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

   8. Simplified 100.0%

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

   if 1300 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 90.3

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 90.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 87.1

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 87.1%

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

      1. exp-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b}}}}{y} \]

      2. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]

      3. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \frac{x}{\color{blue}{y \cdot e^{b}}} \]

      6. exp-lowering-exp.f64 87.1

         \[\leadsto \frac{x}{y \cdot \color{blue}{e^{b}}} \]

   10. Applied egg-rr 87.1%

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

Alternative 9: 71.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot e^{b}}\\ \mathbf{if}\;b \leq -1 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \mathbf{elif}\;b \leq 950:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y (exp b)))))
   (if (<= b -1e+76)
     t_1
     (if (<= b 5.8e-36)
       (* x (/ (pow z y) (* y a)))
       (if (<= b 950.0) (/ (* x (pow a t)) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * exp(b));
	double tmp;
	if (b <= -1e+76) {
		tmp = t_1;
	} else if (b <= 5.8e-36) {
		tmp = x * (pow(z, y) / (y * a));
	} else if (b <= 950.0) {
		tmp = (x * pow(a, t)) / 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 = x / (y * exp(b))
    if (b <= (-1d+76)) then
        tmp = t_1
    else if (b <= 5.8d-36) then
        tmp = x * ((z ** y) / (y * a))
    else if (b <= 950.0d0) then
        tmp = (x * (a ** t)) / 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 = x / (y * Math.exp(b));
	double tmp;
	if (b <= -1e+76) {
		tmp = t_1;
	} else if (b <= 5.8e-36) {
		tmp = x * (Math.pow(z, y) / (y * a));
	} else if (b <= 950.0) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * math.exp(b))
	tmp = 0
	if b <= -1e+76:
		tmp = t_1
	elif b <= 5.8e-36:
		tmp = x * (math.pow(z, y) / (y * a))
	elif b <= 950.0:
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * exp(b)))
	tmp = 0.0
	if (b <= -1e+76)
		tmp = t_1;
	elseif (b <= 5.8e-36)
		tmp = Float64(x * Float64((z ^ y) / Float64(y * a)));
	elseif (b <= 950.0)
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * exp(b));
	tmp = 0.0;
	if (b <= -1e+76)
		tmp = t_1;
	elseif (b <= 5.8e-36)
		tmp = x * ((z ^ y) / (y * a));
	elseif (b <= 950.0)
		tmp = (x * (a ^ t)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+76], t$95$1, If[LessEqual[b, 5.8e-36], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 950.0], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1e76 or 950 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 93.2

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 93.2%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 88.9

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 88.9%

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

      1. exp-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b}}}}{y} \]

      2. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]

      3. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \frac{x}{\color{blue}{y \cdot e^{b}}} \]

      6. exp-lowering-exp.f64 88.9

         \[\leadsto \frac{x}{y \cdot \color{blue}{e^{b}}} \]

   10. Applied egg-rr 88.9%

       \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

   if -1e76 < b < 5.80000000000000026e-36

   1. Initial program 96.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{e^{b}}}}{y} \]

      4. associate-/l/ N/A

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

      6. +-commutative N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + -1 \cdot \log a}}}{y \cdot e^{b}} \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \frac{e^{y \cdot \log z + \color{blue}{\left(\mathsf{neg}\left(\log a\right)\right)}}}{y \cdot e^{b}} \]

      8. unsub-neg N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z - \log a}}}{y \cdot e^{b}} \]

      9. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

      11. *-commutative N/A

          \[\leadsto x \cdot \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      12. exp-to-pow N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      13. pow-lowering-pow.f64 N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      14. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{\color{blue}{a}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{\color{blue}{y \cdot e^{b}}} \]

      16. exp-lowering-exp.f64 77.3

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot \color{blue}{e^{b}}} \]

   5. Simplified 77.3%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 79.7

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

   8. Simplified 79.7%

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

   if 5.80000000000000026e-36 < b < 950

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      3. rem-exp-log N/A

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

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

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

      5. rem-exp-log 100.0

         \[\leadsto \frac{x \cdot e^{\log \color{blue}{a} \cdot t - b}}{y} \]

   5. Simplified 100.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. pow-lowering-pow.f64 100.0

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

   8. Simplified 100.0%

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

Alternative 10: 65.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-39}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{y}\\ \mathbf{elif}\;b \leq 105000:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.6e+102)
   (* -0.16666666666666666 (/ (* x (* b (* b b))) y))
   (if (<= b 5.1e-39)
     (/ (* x (pow z y)) y)
     (if (<= b 105000.0) (/ (* x (pow a t)) y) (/ x (* y (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.6e+102) {
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	} else if (b <= 5.1e-39) {
		tmp = (x * pow(z, y)) / y;
	} else if (b <= 105000.0) {
		tmp = (x * pow(a, t)) / y;
	} else {
		tmp = x / (y * exp(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 (b <= (-5.6d+102)) then
        tmp = (-0.16666666666666666d0) * ((x * (b * (b * b))) / y)
    else if (b <= 5.1d-39) then
        tmp = (x * (z ** y)) / y
    else if (b <= 105000.0d0) then
        tmp = (x * (a ** t)) / y
    else
        tmp = x / (y * exp(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 (b <= -5.6e+102) {
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	} else if (b <= 5.1e-39) {
		tmp = (x * Math.pow(z, y)) / y;
	} else if (b <= 105000.0) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = x / (y * Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.6e+102:
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y)
	elif b <= 5.1e-39:
		tmp = (x * math.pow(z, y)) / y
	elif b <= 105000.0:
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = x / (y * math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.6e+102)
		tmp = Float64(-0.16666666666666666 * Float64(Float64(x * Float64(b * Float64(b * b))) / y));
	elseif (b <= 5.1e-39)
		tmp = Float64(Float64(x * (z ^ y)) / y);
	elseif (b <= 105000.0)
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = Float64(x / Float64(y * exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.6e+102)
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	elseif (b <= 5.1e-39)
		tmp = (x * (z ^ y)) / y;
	elseif (b <= 105000.0)
		tmp = (x * (a ^ t)) / y;
	else
		tmp = x / (y * exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.6e+102], N[(-0.16666666666666666 * N[(N[(x * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.1e-39], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 105000.0], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.60000000000000037e102

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 97.9

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 97.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 95.7

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 95.7%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-b}}}{y} \]

   9. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}}{y} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right) + 1\right)}}{y} \]

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

          \[\leadsto \frac{x \cdot \color{blue}{\mathsf{fma}\left(b, b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1, 1\right)}}{y} \]

       3. sub-neg N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \color{blue}{b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)}, 1\right)}{y} \]

       4. metadata-eval N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \color{blue}{-1}, 1\right)}{y} \]

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

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(b, \frac{1}{2} + \frac{-1}{6} \cdot b, -1\right)}, 1\right)}{y} \]

       6. +-commutative N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{\frac{-1}{6} \cdot b + \frac{1}{2}}, -1\right), 1\right)}{y} \]

       7. *-commutative N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{b \cdot \frac{-1}{6}} + \frac{1}{2}, -1\right), 1\right)}{y} \]

       8. accelerator-lowering-fma.f64 95.7

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(b, -0.16666666666666666, 0.5\right)}, -1\right), 1\right)}{y} \]

   11. Simplified 95.7%

       \[\leadsto \frac{x \cdot \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(b, \mathsf{fma}\left(b, -0.16666666666666666, 0.5\right), -1\right), 1\right)}}{y} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   13. Step-by-step derivation

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

          \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]

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

          \[\leadsto \frac{-1}{6} \cdot \color{blue}{\frac{{b}^{3} \cdot x}{y}} \]

       3. *-commutative N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{x \cdot {b}^{3}}}{y} \]

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

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{x \cdot {b}^{3}}}{y} \]

       5. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot b\right)\right)}}{y} \]

       6. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \left(b \cdot \color{blue}{{b}^{2}}\right)}{y} \]

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

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \color{blue}{\left(b \cdot {b}^{2}\right)}}{y} \]

       8. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \left(b \cdot \color{blue}{\left(b \cdot b\right)}\right)}{y} \]

       9. *-lowering-*.f64 95.7

          \[\leadsto -0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \color{blue}{\left(b \cdot b\right)}\right)}{y} \]

   14. Simplified 95.7%

       \[\leadsto \color{blue}{-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}} \]

   if -5.60000000000000037e102 < b < 5.09999999999999988e-39

   1. Initial program 96.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 65.1

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 65.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. pow-lowering-pow.f64 62.4

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

   8. Simplified 62.4%

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

   if 5.09999999999999988e-39 < b < 105000

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

      3. rem-exp-log N/A

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

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

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

      5. rem-exp-log 100.0

         \[\leadsto \frac{x \cdot e^{\log \color{blue}{a} \cdot t - b}}{y} \]

   5. Simplified 100.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. pow-lowering-pow.f64 100.0

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

   8. Simplified 100.0%

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

   if 105000 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 90.3

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 90.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 87.1

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 87.1%

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

      1. exp-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b}}}}{y} \]

      2. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]

      3. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \frac{x}{\color{blue}{y \cdot e^{b}}} \]

      6. exp-lowering-exp.f64 87.1

         \[\leadsto \frac{x}{y \cdot \color{blue}{e^{b}}} \]

   10. Applied egg-rr 87.1%

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

Alternative 11: 57.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot e^{b}}\\ \mathbf{if}\;b \leq -230:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-205}:\\ \;\;\;\;-\frac{-1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-73}:\\ \;\;\;\;-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y (exp b)))))
   (if (<= b -230.0)
     t_1
     (if (<= b 1.55e-205)
       (- (/ -1.0 (* a (/ y x))))
       (if (<= b 1.36e-73)
         (* -0.16666666666666666 (/ (* x (* b (* b b))) y))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * exp(b));
	double tmp;
	if (b <= -230.0) {
		tmp = t_1;
	} else if (b <= 1.55e-205) {
		tmp = -(-1.0 / (a * (y / x)));
	} else if (b <= 1.36e-73) {
		tmp = -0.16666666666666666 * ((x * (b * (b * 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 = x / (y * exp(b))
    if (b <= (-230.0d0)) then
        tmp = t_1
    else if (b <= 1.55d-205) then
        tmp = -((-1.0d0) / (a * (y / x)))
    else if (b <= 1.36d-73) then
        tmp = (-0.16666666666666666d0) * ((x * (b * (b * 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 = x / (y * Math.exp(b));
	double tmp;
	if (b <= -230.0) {
		tmp = t_1;
	} else if (b <= 1.55e-205) {
		tmp = -(-1.0 / (a * (y / x)));
	} else if (b <= 1.36e-73) {
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * math.exp(b))
	tmp = 0
	if b <= -230.0:
		tmp = t_1
	elif b <= 1.55e-205:
		tmp = -(-1.0 / (a * (y / x)))
	elif b <= 1.36e-73:
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * exp(b)))
	tmp = 0.0
	if (b <= -230.0)
		tmp = t_1;
	elseif (b <= 1.55e-205)
		tmp = Float64(-Float64(-1.0 / Float64(a * Float64(y / x))));
	elseif (b <= 1.36e-73)
		tmp = Float64(-0.16666666666666666 * Float64(Float64(x * Float64(b * Float64(b * b))) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * exp(b));
	tmp = 0.0;
	if (b <= -230.0)
		tmp = t_1;
	elseif (b <= 1.55e-205)
		tmp = -(-1.0 / (a * (y / x)));
	elseif (b <= 1.36e-73)
		tmp = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -230.0], t$95$1, If[LessEqual[b, 1.55e-205], (-N[(-1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[b, 1.36e-73], N[(-0.16666666666666666 * N[(N[(x * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -230 or 1.36e-73 < b

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 87.2

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 87.2%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 77.0

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 77.0%

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

      1. exp-neg N/A

         \[\leadsto \frac{x \cdot \color{blue}{\frac{1}{e^{b}}}}{y} \]

      2. un-div-inv N/A

         \[\leadsto \frac{\color{blue}{\frac{x}{e^{b}}}}{y} \]

      3. associate-/l/ N/A

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

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

         \[\leadsto \frac{x}{\color{blue}{y \cdot e^{b}}} \]

      6. exp-lowering-exp.f64 77.0

         \[\leadsto \frac{x}{y \cdot \color{blue}{e^{b}}} \]

   10. Applied egg-rr 77.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

   if -230 < b < 1.54999999999999991e-205

   1. Initial program 93.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{e^{b}}}}{y} \]

      4. associate-/l/ N/A

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

      6. +-commutative N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + -1 \cdot \log a}}}{y \cdot e^{b}} \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \frac{e^{y \cdot \log z + \color{blue}{\left(\mathsf{neg}\left(\log a\right)\right)}}}{y \cdot e^{b}} \]

      8. unsub-neg N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z - \log a}}}{y \cdot e^{b}} \]

      9. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

      11. *-commutative N/A

          \[\leadsto x \cdot \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      12. exp-to-pow N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      13. pow-lowering-pow.f64 N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      14. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{\color{blue}{a}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{\color{blue}{y \cdot e^{b}}} \]

      16. exp-lowering-exp.f64 82.2

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot \color{blue}{e^{b}}} \]

   5. Simplified 82.2%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 79.3

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

   8. Simplified 79.3%

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

   9. Taylor expanded in y around 0

      \[\leadsto x \cdot \frac{\color{blue}{1}}{y \cdot a} \]
   10. Step-by-step derivation

   11. Simplified 49.1%

       \[\leadsto x \cdot \frac{\color{blue}{1}}{y \cdot a} \]
   12. Step-by-step derivation

       1. associate-*r/ N/A

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

       2. times-frac N/A

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

       3. clear-num N/A

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

       4. frac-2neg N/A

          \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\frac{y}{x}\right)}} \cdot \frac{1}{a} \]

       5. metadata-eval N/A

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

       6. frac-times N/A

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

       7. metadata-eval N/A

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

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

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

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

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

       10. distribute-neg-frac2 N/A

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

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

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

       12. neg-lowering-neg.f64 50.4

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

   13. Applied egg-rr 50.4%

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

   if 1.54999999999999991e-205 < b < 1.36e-73

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 71.4

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 71.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 11.1

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 11.1%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-b}}}{y} \]

   9. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}}{y} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right) + 1\right)}}{y} \]

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

          \[\leadsto \frac{x \cdot \color{blue}{\mathsf{fma}\left(b, b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1, 1\right)}}{y} \]

       3. sub-neg N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \color{blue}{b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)}, 1\right)}{y} \]

       4. metadata-eval N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \color{blue}{-1}, 1\right)}{y} \]

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

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(b, \frac{1}{2} + \frac{-1}{6} \cdot b, -1\right)}, 1\right)}{y} \]

       6. +-commutative N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{\frac{-1}{6} \cdot b + \frac{1}{2}}, -1\right), 1\right)}{y} \]

       7. *-commutative N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{b \cdot \frac{-1}{6}} + \frac{1}{2}, -1\right), 1\right)}{y} \]

       8. accelerator-lowering-fma.f64 11.1

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(b, -0.16666666666666666, 0.5\right)}, -1\right), 1\right)}{y} \]

   11. Simplified 11.1%

       \[\leadsto \frac{x \cdot \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(b, \mathsf{fma}\left(b, -0.16666666666666666, 0.5\right), -1\right), 1\right)}}{y} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   13. Step-by-step derivation

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

          \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]

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

          \[\leadsto \frac{-1}{6} \cdot \color{blue}{\frac{{b}^{3} \cdot x}{y}} \]

       3. *-commutative N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{x \cdot {b}^{3}}}{y} \]

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

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{x \cdot {b}^{3}}}{y} \]

       5. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot b\right)\right)}}{y} \]

       6. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \left(b \cdot \color{blue}{{b}^{2}}\right)}{y} \]

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

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \color{blue}{\left(b \cdot {b}^{2}\right)}}{y} \]

       8. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \left(b \cdot \color{blue}{\left(b \cdot b\right)}\right)}{y} \]

       9. *-lowering-*.f64 39.4

          \[\leadsto -0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \color{blue}{\left(b \cdot b\right)}\right)}{y} \]

   14. Simplified 39.4%

       \[\leadsto \color{blue}{-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -230:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{-205}:\\ \;\;\;\;-\frac{-1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-73}:\\ \;\;\;\;-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.4% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{a}{-x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* -0.16666666666666666 (/ (* x (* b (* b b))) y))))
   (if (<= b -7.2e+18)
     t_1
     (if (<= b 7.5e-206)
       (/ x (* y a))
       (if (<= b 3.4e-75) t_1 (/ -1.0 (* y (/ a (- x)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	double tmp;
	if (b <= -7.2e+18) {
		tmp = t_1;
	} else if (b <= 7.5e-206) {
		tmp = x / (y * a);
	} else if (b <= 3.4e-75) {
		tmp = t_1;
	} else {
		tmp = -1.0 / (y * (a / -x));
	}
	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 = (-0.16666666666666666d0) * ((x * (b * (b * b))) / y)
    if (b <= (-7.2d+18)) then
        tmp = t_1
    else if (b <= 7.5d-206) then
        tmp = x / (y * a)
    else if (b <= 3.4d-75) then
        tmp = t_1
    else
        tmp = (-1.0d0) / (y * (a / -x))
    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 = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	double tmp;
	if (b <= -7.2e+18) {
		tmp = t_1;
	} else if (b <= 7.5e-206) {
		tmp = x / (y * a);
	} else if (b <= 3.4e-75) {
		tmp = t_1;
	} else {
		tmp = -1.0 / (y * (a / -x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -0.16666666666666666 * ((x * (b * (b * b))) / y)
	tmp = 0
	if b <= -7.2e+18:
		tmp = t_1
	elif b <= 7.5e-206:
		tmp = x / (y * a)
	elif b <= 3.4e-75:
		tmp = t_1
	else:
		tmp = -1.0 / (y * (a / -x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(-0.16666666666666666 * Float64(Float64(x * Float64(b * Float64(b * b))) / y))
	tmp = 0.0
	if (b <= -7.2e+18)
		tmp = t_1;
	elseif (b <= 7.5e-206)
		tmp = Float64(x / Float64(y * a));
	elseif (b <= 3.4e-75)
		tmp = t_1;
	else
		tmp = Float64(-1.0 / Float64(y * Float64(a / Float64(-x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -0.16666666666666666 * ((x * (b * (b * b))) / y);
	tmp = 0.0;
	if (b <= -7.2e+18)
		tmp = t_1;
	elseif (b <= 7.5e-206)
		tmp = x / (y * a);
	elseif (b <= 3.4e-75)
		tmp = t_1;
	else
		tmp = -1.0 / (y * (a / -x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(-0.16666666666666666 * N[(N[(x * N[(b * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+18], t$95$1, If[LessEqual[b, 7.5e-206], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e-75], t$95$1, N[(-1.0 / N[(y * N[(a / (-x)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.2e18 or 7.5e-206 < b < 3.40000000000000015e-75

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 87.5

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 87.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 57.7

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 57.7%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-b}}}{y} \]

   9. Taylor expanded in b around 0

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right)\right)}}{y} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1\right) + 1\right)}}{y} \]

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

          \[\leadsto \frac{x \cdot \color{blue}{\mathsf{fma}\left(b, b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) - 1, 1\right)}}{y} \]

       3. sub-neg N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \color{blue}{b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \left(\mathsf{neg}\left(1\right)\right)}, 1\right)}{y} \]

       4. metadata-eval N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, b \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot b\right) + \color{blue}{-1}, 1\right)}{y} \]

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

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(b, \frac{1}{2} + \frac{-1}{6} \cdot b, -1\right)}, 1\right)}{y} \]

       6. +-commutative N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{\frac{-1}{6} \cdot b + \frac{1}{2}}, -1\right), 1\right)}{y} \]

       7. *-commutative N/A

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{b \cdot \frac{-1}{6}} + \frac{1}{2}, -1\right), 1\right)}{y} \]

       8. accelerator-lowering-fma.f64 56.1

          \[\leadsto \frac{x \cdot \mathsf{fma}\left(b, \mathsf{fma}\left(b, \color{blue}{\mathsf{fma}\left(b, -0.16666666666666666, 0.5\right)}, -1\right), 1\right)}{y} \]

   11. Simplified 56.1%

       \[\leadsto \frac{x \cdot \color{blue}{\mathsf{fma}\left(b, \mathsf{fma}\left(b, \mathsf{fma}\left(b, -0.16666666666666666, 0.5\right), -1\right), 1\right)}}{y} \]

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]
   13. Step-by-step derivation

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

          \[\leadsto \color{blue}{\frac{-1}{6} \cdot \frac{{b}^{3} \cdot x}{y}} \]

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

          \[\leadsto \frac{-1}{6} \cdot \color{blue}{\frac{{b}^{3} \cdot x}{y}} \]

       3. *-commutative N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{x \cdot {b}^{3}}}{y} \]

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

          \[\leadsto \frac{-1}{6} \cdot \frac{\color{blue}{x \cdot {b}^{3}}}{y} \]

       5. cube-mult N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \color{blue}{\left(b \cdot \left(b \cdot b\right)\right)}}{y} \]

       6. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \left(b \cdot \color{blue}{{b}^{2}}\right)}{y} \]

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

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \color{blue}{\left(b \cdot {b}^{2}\right)}}{y} \]

       8. unpow2 N/A

          \[\leadsto \frac{-1}{6} \cdot \frac{x \cdot \left(b \cdot \color{blue}{\left(b \cdot b\right)}\right)}{y} \]

       9. *-lowering-*.f64 65.7

          \[\leadsto -0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \color{blue}{\left(b \cdot b\right)}\right)}{y} \]

   14. Simplified 65.7%

       \[\leadsto \color{blue}{-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}} \]

   if -7.2e18 < b < 7.5e-206

   1. Initial program 93.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

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

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

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

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

      7. exp-prod N/A

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

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

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

          \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}} \cdot x}{y \cdot e^{b}} \]

      11. metadata-eval N/A

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

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

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

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

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

      14. exp-lowering-exp.f64 64.6

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

   5. Simplified 64.6%

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

   6. Taylor expanded in b around 0

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

   8. Simplified 66.3%

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

   9. Taylor expanded in t around 0

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

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

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

       2. *-lowering-*.f64 48.6

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

   11. Simplified 48.6%

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

   if 3.40000000000000015e-75 < b

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{e^{b}}}}{y} \]

      4. associate-/l/ N/A

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

      6. +-commutative N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + -1 \cdot \log a}}}{y \cdot e^{b}} \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \frac{e^{y \cdot \log z + \color{blue}{\left(\mathsf{neg}\left(\log a\right)\right)}}}{y \cdot e^{b}} \]

      8. unsub-neg N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z - \log a}}}{y \cdot e^{b}} \]

      9. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

      11. *-commutative N/A

          \[\leadsto x \cdot \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      12. exp-to-pow N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      13. pow-lowering-pow.f64 N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      14. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{\color{blue}{a}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{\color{blue}{y \cdot e^{b}}} \]

      16. exp-lowering-exp.f64 66.6

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot \color{blue}{e^{b}}} \]

   5. Simplified 66.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 35.2

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

   8. Simplified 35.2%

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

   9. Taylor expanded in y around 0

      \[\leadsto x \cdot \frac{\color{blue}{1}}{y \cdot a} \]
   10. Step-by-step derivation

   11. Simplified 22.1%

       \[\leadsto x \cdot \frac{\color{blue}{1}}{y \cdot a} \]
   12. Step-by-step derivation

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. times-frac N/A

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

       4. clear-num N/A

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

       5. frac-2neg N/A

          \[\leadsto \frac{1}{\frac{a}{x}} \cdot \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(y\right)}} \]

       6. metadata-eval N/A

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

       7. frac-times N/A

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

       8. metadata-eval N/A

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

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

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

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

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

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

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

       12. neg-lowering-neg.f64 26.9

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

   13. Applied egg-rr 26.9%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-75}:\\ \;\;\;\;-0.16666666666666666 \cdot \frac{x \cdot \left(b \cdot \left(b \cdot b\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{y \cdot \frac{a}{-x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.7% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, b \cdot \mathsf{fma}\left(b, 0.5, -1\right), x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.2e+18)
   (/ (fma x (* b (fma b 0.5 -1.0)) x) y)
   (/ 1.0 (/ (* y a) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e+18) {
		tmp = fma(x, (b * fma(b, 0.5, -1.0)), x) / y;
	} else {
		tmp = 1.0 / ((y * a) / x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.2e+18)
		tmp = Float64(fma(x, Float64(b * fma(b, 0.5, -1.0)), x) / y);
	else
		tmp = Float64(1.0 / Float64(Float64(y * a) / x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.2e+18], N[(N[(x * N[(b * N[(b * 0.5 + -1.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] / y), $MachinePrecision], N[(1.0 / N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2e18

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 95.8

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 95.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 83.1

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 83.1%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-b}}}{y} \]

   9. Taylor expanded in b around 0

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

       1. +-commutative N/A

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

       2. +-commutative N/A

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

       3. distribute-lft-in N/A

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

       4. associate-*r* N/A

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

       5. associate-*r* N/A

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

       6. associate-*r* N/A

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

       7. *-commutative N/A

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

       8. distribute-rgt-out N/A

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

       9. *-commutative N/A

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

       10. distribute-lft-in N/A

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

       11. metadata-eval N/A

           \[\leadsto \frac{x \cdot \left(b \cdot \left(\frac{1}{2} \cdot b + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right) + x}{y} \]

       12. sub-neg N/A

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

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

           \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, b \cdot \left(\frac{1}{2} \cdot b - 1\right), x\right)}}{y} \]

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

           \[\leadsto \frac{\mathsf{fma}\left(x, \color{blue}{b \cdot \left(\frac{1}{2} \cdot b - 1\right)}, x\right)}{y} \]

       15. sub-neg N/A

           \[\leadsto \frac{\mathsf{fma}\left(x, b \cdot \color{blue}{\left(\frac{1}{2} \cdot b + \left(\mathsf{neg}\left(1\right)\right)\right)}, x\right)}{y} \]

       16. *-commutative N/A

           \[\leadsto \frac{\mathsf{fma}\left(x, b \cdot \left(\color{blue}{b \cdot \frac{1}{2}} + \left(\mathsf{neg}\left(1\right)\right)\right), x\right)}{y} \]

       17. metadata-eval N/A

           \[\leadsto \frac{\mathsf{fma}\left(x, b \cdot \left(b \cdot \frac{1}{2} + \color{blue}{-1}\right), x\right)}{y} \]

       18. accelerator-lowering-fma.f64 72.5

           \[\leadsto \frac{\mathsf{fma}\left(x, b \cdot \color{blue}{\mathsf{fma}\left(b, 0.5, -1\right)}, x\right)}{y} \]

   11. Simplified 72.5%

       \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, b \cdot \mathsf{fma}\left(b, 0.5, -1\right), x\right)}}{y} \]

   if -7.2e18 < b

   1. Initial program 97.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{e^{b}}}}{y} \]

      4. associate-/l/ N/A

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

      6. +-commutative N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + -1 \cdot \log a}}}{y \cdot e^{b}} \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \frac{e^{y \cdot \log z + \color{blue}{\left(\mathsf{neg}\left(\log a\right)\right)}}}{y \cdot e^{b}} \]

      8. unsub-neg N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z - \log a}}}{y \cdot e^{b}} \]

      9. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

      11. *-commutative N/A

          \[\leadsto x \cdot \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      12. exp-to-pow N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      13. pow-lowering-pow.f64 N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      14. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{\color{blue}{a}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{\color{blue}{y \cdot e^{b}}} \]

      16. exp-lowering-exp.f64 75.1

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot \color{blue}{e^{b}}} \]

   5. Simplified 75.1%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 60.5

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

   8. Simplified 60.5%

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

   9. Taylor expanded in y around 0

      \[\leadsto x \cdot \frac{\color{blue}{1}}{y \cdot a} \]
   10. Step-by-step derivation

   11. Simplified 32.7%

       \[\leadsto x \cdot \frac{\color{blue}{1}}{y \cdot a} \]
   12. Step-by-step derivation

       1. un-div-inv N/A

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

       2. clear-num N/A

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

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

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

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

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 33.1

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

   13. Applied egg-rr 33.1%

       \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, b \cdot \mathsf{fma}\left(b, 0.5, -1\right), x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 33.9% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+18}:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7e+18) (/ (- x (* x b)) y) (/ 1.0 (/ (* y a) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e+18) {
		tmp = (x - (x * b)) / y;
	} else {
		tmp = 1.0 / ((y * a) / x);
	}
	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 (b <= (-7d+18)) then
        tmp = (x - (x * b)) / y
    else
        tmp = 1.0d0 / ((y * a) / x)
    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 (b <= -7e+18) {
		tmp = (x - (x * b)) / y;
	} else {
		tmp = 1.0 / ((y * a) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7e+18:
		tmp = (x - (x * b)) / y
	else:
		tmp = 1.0 / ((y * a) / x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7e+18)
		tmp = Float64(Float64(x - Float64(x * b)) / y);
	else
		tmp = Float64(1.0 / Float64(Float64(y * a) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7e+18)
		tmp = (x - (x * b)) / y;
	else
		tmp = 1.0 / ((y * a) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7e+18], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(1.0 / N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7e18

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 95.8

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 95.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 83.1

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 83.1%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-b}}}{y} \]

   9. Taylor expanded in b around 0

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

       1. mul-1-neg N/A

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

       2. unsub-neg N/A

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

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

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

       4. *-commutative N/A

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

       5. *-lowering-*.f64 39.9

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

   11. Simplified 39.9%

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

   if -7e18 < b

   1. Initial program 97.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. associate-/l* N/A

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

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

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

      3. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{e^{b}}}}{y} \]

      4. associate-/l/ N/A

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

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

         \[\leadsto x \cdot \color{blue}{\frac{e^{-1 \cdot \log a + y \cdot \log z}}{y \cdot e^{b}}} \]

      6. +-commutative N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + -1 \cdot \log a}}}{y \cdot e^{b}} \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot \frac{e^{y \cdot \log z + \color{blue}{\left(\mathsf{neg}\left(\log a\right)\right)}}}{y \cdot e^{b}} \]

      8. unsub-neg N/A

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z - \log a}}}{y \cdot e^{b}} \]

      9. exp-diff N/A

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y \cdot e^{b}} \]

      11. *-commutative N/A

          \[\leadsto x \cdot \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      12. exp-to-pow N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      13. pow-lowering-pow.f64 N/A

          \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y \cdot e^{b}} \]

      14. rem-exp-log N/A

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{\color{blue}{a}}}{y \cdot e^{b}} \]

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

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{\color{blue}{y \cdot e^{b}}} \]

      16. exp-lowering-exp.f64 75.1

          \[\leadsto x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot \color{blue}{e^{b}}} \]

   5. Simplified 75.1%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}} \]

   6. Taylor expanded in b around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 60.5

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

   8. Simplified 60.5%

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

   9. Taylor expanded in y around 0

      \[\leadsto x \cdot \frac{\color{blue}{1}}{y \cdot a} \]
   10. Step-by-step derivation

   11. Simplified 32.7%

       \[\leadsto x \cdot \frac{\color{blue}{1}}{y \cdot a} \]
   12. Step-by-step derivation

       1. un-div-inv N/A

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

       2. clear-num N/A

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

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

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

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

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 33.1

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

   13. Applied egg-rr 33.1%

       \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+18}:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 33.8% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.2e+18) (/ (- x (* x b)) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2e+18) {
		tmp = (x - (x * b)) / y;
	} else {
		tmp = x / (y * a);
	}
	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 (b <= (-7.2d+18)) then
        tmp = (x - (x * b)) / y
    else
        tmp = x / (y * a)
    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 (b <= -7.2e+18) {
		tmp = (x - (x * b)) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.2e+18:
		tmp = (x - (x * b)) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.2e+18)
		tmp = Float64(Float64(x - Float64(x * b)) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.2e+18)
		tmp = (x - (x * b)) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.2e+18], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.2e18

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 95.8

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 95.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 83.1

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 83.1%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-b}}}{y} \]

   9. Taylor expanded in b around 0

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

       1. mul-1-neg N/A

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

       2. unsub-neg N/A

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

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

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

       4. *-commutative N/A

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

       5. *-lowering-*.f64 39.9

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

   11. Simplified 39.9%

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

   if -7.2e18 < b

   1. Initial program 97.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

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

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

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

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

      7. exp-prod N/A

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

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

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

          \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}} \cdot x}{y \cdot e^{b}} \]

      11. metadata-eval N/A

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

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

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

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

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

      14. exp-lowering-exp.f64 66.6

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

   5. Simplified 66.6%

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

   6. Taylor expanded in b around 0

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

   8. Simplified 62.3%

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

   9. Taylor expanded in t around 0

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

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

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

       2. *-lowering-*.f64 32.7

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

   11. Simplified 32.7%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.9% accurate, 12.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{y} \cdot \left(1 - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.1e+34) (* (/ x y) (- 1.0 b)) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e+34) {
		tmp = (x / y) * (1.0 - b);
	} else {
		tmp = x / (y * a);
	}
	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 (b <= (-1.1d+34)) then
        tmp = (x / y) * (1.0d0 - b)
    else
        tmp = x / (y * a)
    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 (b <= -1.1e+34) {
		tmp = (x / y) * (1.0 - b);
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.1e+34:
		tmp = (x / y) * (1.0 - b)
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.1e+34)
		tmp = Float64(Float64(x / y) * Float64(1.0 - b));
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.1e+34)
		tmp = (x / y) * (1.0 - b);
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.1e+34], N[(N[(x / y), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1000000000000001e34

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

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

         \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

      2. log-lowering-log.f64 95.5

         \[\leadsto \frac{x \cdot e^{y \cdot \color{blue}{\log z} - b}}{y} \]

   5. Simplified 95.5%

      \[\leadsto \frac{x \cdot e^{\color{blue}{y \cdot \log z} - b}}{y} \]

   6. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]
   7. Step-by-step derivation

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

         \[\leadsto \frac{\color{blue}{x \cdot e^{\mathsf{neg}\left(b\right)}}}{y} \]

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

         \[\leadsto \frac{x \cdot \color{blue}{e^{\mathsf{neg}\left(b\right)}}}{y} \]

      3. neg-lowering-neg.f64 84.9

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 84.9%

      \[\leadsto \frac{\color{blue}{x \cdot e^{-b}}}{y} \]

   9. Taylor expanded in b around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]
   10. Step-by-step derivation

       1. associate-/l* N/A

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

       2. associate-*r* N/A

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

       3. distribute-lft1-in N/A

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

       4. +-commutative N/A

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

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

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

       6. neg-mul-1 N/A

          \[\leadsto \left(1 + \color{blue}{\left(\mathsf{neg}\left(b\right)\right)}\right) \cdot \frac{x}{y} \]

       7. unsub-neg N/A

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

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

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

       9. /-lowering-/.f64 38.0

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

   11. Simplified 38.0%

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

   if -1.1000000000000001e34 < b

   1. Initial program 97.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. exp-diff N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l/ N/A

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

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

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

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

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

      7. exp-prod N/A

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

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

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

      9. rem-exp-log N/A

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

      10. sub-neg N/A

          \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}} \cdot x}{y \cdot e^{b}} \]

      11. metadata-eval N/A

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

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

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

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

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

      14. exp-lowering-exp.f64 65.9

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

   5. Simplified 65.9%

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

   6. Taylor expanded in b around 0

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

   8. Simplified 61.7%

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

   9. Taylor expanded in t around 0

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

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

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

       2. *-lowering-*.f64 32.4

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

   11. Simplified 32.4%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{y} \cdot \left(1 - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.8% accurate, 19.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

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

C

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

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 * a)
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right) - b} \cdot x}}{y} \]

   2. exp-diff N/A

      \[\leadsto \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}} \cdot x}{y} \]

   3. associate-*l/ N/A

      \[\leadsto \frac{\color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{e^{b}}}}{y} \]

   4. associate-/l/ N/A

      \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{y \cdot e^{b}}} \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)} \cdot x}{y \cdot e^{b}}} \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y \cdot e^{b}} \]

   7. exp-prod N/A

      \[\leadsto \frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}} \cdot x}{y \cdot e^{b}} \]

   8. pow-lowering-pow.f64 N/A

      \[\leadsto \frac{\color{blue}{{\left(e^{\log a}\right)}^{\left(t - 1\right)}} \cdot x}{y \cdot e^{b}} \]

   9. rem-exp-log N/A

      \[\leadsto \frac{{\color{blue}{a}}^{\left(t - 1\right)} \cdot x}{y \cdot e^{b}} \]

   10. sub-neg N/A

       \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(\mathsf{neg}\left(1\right)\right)\right)}} \cdot x}{y \cdot e^{b}} \]

   11. metadata-eval N/A

       \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)} \cdot x}{y \cdot e^{b}} \]

   12. +-lowering-+.f64 N/A

       \[\leadsto \frac{{a}^{\color{blue}{\left(t + -1\right)}} \cdot x}{y \cdot e^{b}} \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \frac{{a}^{\left(t + -1\right)} \cdot x}{\color{blue}{y \cdot e^{b}}} \]

   14. exp-lowering-exp.f64 65.6

       \[\leadsto \frac{{a}^{\left(t + -1\right)} \cdot x}{y \cdot \color{blue}{e^{b}}} \]

5. Simplified 65.6%

   \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)} \cdot x}{y \cdot e^{b}}} \]

6. Taylor expanded in b around 0

   \[\leadsto \frac{{a}^{\left(t + -1\right)} \cdot x}{\color{blue}{y}} \]
7. Step-by-step derivation

8. Simplified 56.3%

   \[\leadsto \frac{{a}^{\left(t + -1\right)} \cdot x}{\color{blue}{y}} \]

9. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
10. Step-by-step derivation

    1. /-lowering-/.f64 N/A

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

    2. *-lowering-*.f64 31.4

       \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]

11. Simplified 31.4%

    \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

12. Final simplification 31.4%

    \[\leadsto \frac{x}{y \cdot a} \]
13. Add Preprocessing

Alternative 18: 16.2% accurate, 28.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / 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
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Python

def code(x, y, z, t, a, b):
	return x / y

Julia

function code(x, y, z, t, a, b)
	return Float64(x / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in t around inf

   \[\leadsto \frac{x \cdot e^{\color{blue}{t \cdot \log a} - b}}{y} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

   3. rem-exp-log N/A

      \[\leadsto \frac{x \cdot e^{\log \color{blue}{\left(e^{\log a}\right)} \cdot t - b}}{y} \]

   4. log-lowering-log.f64 N/A

      \[\leadsto \frac{x \cdot e^{\color{blue}{\log \left(e^{\log a}\right)} \cdot t - b}}{y} \]

   5. rem-exp-log 71.0

      \[\leadsto \frac{x \cdot e^{\log \color{blue}{a} \cdot t - b}}{y} \]

5. Simplified 71.0%

   \[\leadsto \frac{x \cdot e^{\color{blue}{\log a \cdot t} - b}}{y} \]

6. Taylor expanded in b around 0

   \[\leadsto \color{blue}{\frac{x \cdot {a}^{t}}{y}} \]
7. Step-by-step derivation

   1. /-lowering-/.f64 N/A

      \[\leadsto \color{blue}{\frac{x \cdot {a}^{t}}{y}} \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \frac{\color{blue}{x \cdot {a}^{t}}}{y} \]

   3. pow-lowering-pow.f64 48.1

      \[\leadsto \frac{x \cdot \color{blue}{{a}^{t}}}{y} \]

8. Simplified 48.1%

   \[\leadsto \color{blue}{\frac{x \cdot {a}^{t}}{y}} \]

9. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\frac{x}{y}} \]
10. Step-by-step derivation

    1. /-lowering-/.f64 16.1

       \[\leadsto \color{blue}{\frac{x}{y}} \]

11. Simplified 16.1%

    \[\leadsto \color{blue}{\frac{x}{y}} \]
12. Add Preprocessing

Developer Target 1: 72.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	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 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    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 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024198 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8845848504127471/10000000000000000) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 8520312288374073/10000000000) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))