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

Percentage Accurate: 98.5% → 98.5%

Time: 27.1s

Alternatives: 16

Speedup: 1.0×

• 47.6% 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: 98.5% 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: 98.5% 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]

Derivation

1. Initial program 98.6%

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

3. Final simplification 98.6%

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

Alternative 2: 88.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+102} \lor \neg \left(t + -1 \leq 4 \cdot 10^{+117}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow a t) a) y))))
   (if (<= (+ t -1.0) -5e+230)
     t_1
     (if (<= (+ t -1.0) 2e+31)
       (* x (/ (exp (- (- (* y (log z)) (log a)) b)) y))
       (if (or (<= (+ t -1.0) 2e+102) (not (<= (+ t -1.0) 4e+117)))
         t_1
         (* x (/ (/ (pow z y) a) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((pow(a, t) / a) / y);
	double tmp;
	if ((t + -1.0) <= -5e+230) {
		tmp = t_1;
	} else if ((t + -1.0) <= 2e+31) {
		tmp = x * (exp((((y * log(z)) - log(a)) - b)) / y);
	} else if (((t + -1.0) <= 2e+102) || !((t + -1.0) <= 4e+117)) {
		tmp = t_1;
	} else {
		tmp = x * ((pow(z, y) / a) / 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) :: t_1
    real(8) :: tmp
    t_1 = x * (((a ** t) / a) / y)
    if ((t + (-1.0d0)) <= (-5d+230)) then
        tmp = t_1
    else if ((t + (-1.0d0)) <= 2d+31) then
        tmp = x * (exp((((y * log(z)) - log(a)) - b)) / y)
    else if (((t + (-1.0d0)) <= 2d+102) .or. (.not. ((t + (-1.0d0)) <= 4d+117))) then
        tmp = t_1
    else
        tmp = x * (((z ** y) / a) / 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 t_1 = x * ((Math.pow(a, t) / a) / y);
	double tmp;
	if ((t + -1.0) <= -5e+230) {
		tmp = t_1;
	} else if ((t + -1.0) <= 2e+31) {
		tmp = x * (Math.exp((((y * Math.log(z)) - Math.log(a)) - b)) / y);
	} else if (((t + -1.0) <= 2e+102) || !((t + -1.0) <= 4e+117)) {
		tmp = t_1;
	} else {
		tmp = x * ((Math.pow(z, y) / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((math.pow(a, t) / a) / y)
	tmp = 0
	if (t + -1.0) <= -5e+230:
		tmp = t_1
	elif (t + -1.0) <= 2e+31:
		tmp = x * (math.exp((((y * math.log(z)) - math.log(a)) - b)) / y)
	elif ((t + -1.0) <= 2e+102) or not ((t + -1.0) <= 4e+117):
		tmp = t_1
	else:
		tmp = x * ((math.pow(z, y) / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((a ^ t) / a) / y))
	tmp = 0.0
	if (Float64(t + -1.0) <= -5e+230)
		tmp = t_1;
	elseif (Float64(t + -1.0) <= 2e+31)
		tmp = Float64(x * Float64(exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b)) / y));
	elseif ((Float64(t + -1.0) <= 2e+102) || !(Float64(t + -1.0) <= 4e+117))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (((a ^ t) / a) / y);
	tmp = 0.0;
	if ((t + -1.0) <= -5e+230)
		tmp = t_1;
	elseif ((t + -1.0) <= 2e+31)
		tmp = x * (exp((((y * log(z)) - log(a)) - b)) / y);
	elseif (((t + -1.0) <= 2e+102) || ~(((t + -1.0) <= 4e+117)))
		tmp = t_1;
	else
		tmp = x * (((z ^ y) / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+230], t$95$1, If[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+31], N[(x * N[(N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+102], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 4e+117]], $MachinePrecision]], t$95$1, N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t 1) < -5.0000000000000003e230 or 1.9999999999999999e31 < (-.f64 t 1) < 1.99999999999999995e102 or 4.0000000000000002e117 < (-.f64 t 1)

   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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. exp-diff 77.5%

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

      3. associate-/l/ 77.5%

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

      4. exp-sum 57.5%

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

      5. times-frac 57.5%

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

      6. *-commutative 57.5%

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

      7. exp-to-pow 57.5%

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

      8. *-commutative 57.5%

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

      9. exp-to-pow 57.5%

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

      10. sub-neg 57.5%

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

      11. metadata-eval 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in y around 0 76.3%

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

      1. associate-/l* 76.3%

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

      2. exp-to-pow 76.3%

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

      3. sub-neg 76.3%

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

      4. metadata-eval 76.3%

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

   7. Simplified 76.3%

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

      1. unpow-prod-up 76.3%

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

      2. unpow-1 76.3%

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

   9. Applied egg-rr 76.3%

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

       1. associate-*r/ 76.3%

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

       2. *-rgt-identity 76.3%

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

   11. Simplified 76.3%

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

   12. Taylor expanded in b around 0 92.6%

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

   if -5.0000000000000003e230 < (-.f64 t 1) < 1.9999999999999999e31

   1. Initial program 97.8%

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

      1. *-commutative 97.8%

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

      2. associate-/l* 88.1%

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

      3. associate--l+ 88.1%

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

      4. fma-define 88.1%

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

      5. sub-neg 88.1%

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

      6. metadata-eval 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in t around 0 91.9%

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

      1. associate-/l* 92.4%

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

      2. +-commutative 92.4%

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

      3. mul-1-neg 92.4%

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

      4. unsub-neg 92.4%

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

   7. Simplified 92.4%

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

   if 1.99999999999999995e102 < (-.f64 t 1) < 4.0000000000000002e117

   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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. associate--l+ 100.0%

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

      4. fma-define 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 100.0%

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

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

      4. unsub-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in b around 0 100.0%

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

      1. div-exp 100.0%

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

      2. *-commutative 100.0%

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

      3. exp-to-pow 100.0%

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

      4. rem-exp-log 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+102} \lor \neg \left(t + -1 \leq 4 \cdot 10^{+117}\right):\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{\left(t + -1\right) \cdot \log a - b} \cdot \frac{x}{y}\\ t_2 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-219}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y \cdot e^{b}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (exp (- (* (+ t -1.0) (log a)) b)) (/ x y)))
        (t_2 (* x (/ (/ (pow z y) a) y))))
   (if (<= y -3.2e+77)
     t_2
     (if (<= y -8.2e-219)
       t_1
       (if (<= y 2.7e-70)
         (* x (/ (/ (pow a t) a) (* y (exp b))))
         (if (<= y 5.5e+100) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = exp((((t + -1.0) * log(a)) - b)) * (x / y);
	double t_2 = x * ((pow(z, y) / a) / y);
	double tmp;
	if (y <= -3.2e+77) {
		tmp = t_2;
	} else if (y <= -8.2e-219) {
		tmp = t_1;
	} else if (y <= 2.7e-70) {
		tmp = x * ((pow(a, t) / a) / (y * exp(b)));
	} else if (y <= 5.5e+100) {
		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 = exp((((t + (-1.0d0)) * log(a)) - b)) * (x / y)
    t_2 = x * (((z ** y) / a) / y)
    if (y <= (-3.2d+77)) then
        tmp = t_2
    else if (y <= (-8.2d-219)) then
        tmp = t_1
    else if (y <= 2.7d-70) then
        tmp = x * (((a ** t) / a) / (y * exp(b)))
    else if (y <= 5.5d+100) 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 = Math.exp((((t + -1.0) * Math.log(a)) - b)) * (x / y);
	double t_2 = x * ((Math.pow(z, y) / a) / y);
	double tmp;
	if (y <= -3.2e+77) {
		tmp = t_2;
	} else if (y <= -8.2e-219) {
		tmp = t_1;
	} else if (y <= 2.7e-70) {
		tmp = x * ((Math.pow(a, t) / a) / (y * Math.exp(b)));
	} else if (y <= 5.5e+100) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.exp((((t + -1.0) * math.log(a)) - b)) * (x / y)
	t_2 = x * ((math.pow(z, y) / a) / y)
	tmp = 0
	if y <= -3.2e+77:
		tmp = t_2
	elif y <= -8.2e-219:
		tmp = t_1
	elif y <= 2.7e-70:
		tmp = x * ((math.pow(a, t) / a) / (y * math.exp(b)))
	elif y <= 5.5e+100:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b)) * Float64(x / y))
	t_2 = Float64(x * Float64(Float64((z ^ y) / a) / y))
	tmp = 0.0
	if (y <= -3.2e+77)
		tmp = t_2;
	elseif (y <= -8.2e-219)
		tmp = t_1;
	elseif (y <= 2.7e-70)
		tmp = Float64(x * Float64(Float64((a ^ t) / a) / Float64(y * exp(b))));
	elseif (y <= 5.5e+100)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = exp((((t + -1.0) * log(a)) - b)) * (x / y);
	t_2 = x * (((z ^ y) / a) / y);
	tmp = 0.0;
	if (y <= -3.2e+77)
		tmp = t_2;
	elseif (y <= -8.2e-219)
		tmp = t_1;
	elseif (y <= 2.7e-70)
		tmp = x * (((a ^ t) / a) / (y * exp(b)));
	elseif (y <= 5.5e+100)
		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[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+77], t$95$2, If[LessEqual[y, -8.2e-219], t$95$1, If[LessEqual[y, 2.7e-70], N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+100], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2000000000000002e77 or 5.5000000000000002e100 < 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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-/l* 90.3%

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

      3. associate--l+ 90.3%

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

      4. fma-define 90.3%

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

      5. sub-neg 90.3%

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

      6. metadata-eval 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in t around 0 92.6%

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

      1. associate-/l* 92.6%

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

      2. +-commutative 92.6%

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

      3. mul-1-neg 92.6%

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

      4. unsub-neg 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in b around 0 88.4%

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

      1. div-exp 88.4%

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

      2. *-commutative 88.4%

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

      3. exp-to-pow 88.4%

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

      4. rem-exp-log 88.4%

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

   10. Simplified 88.4%

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

   if -3.2000000000000002e77 < y < -8.2e-219 or 2.7000000000000001e-70 < y < 5.5000000000000002e100

   1. Initial program 98.8%

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

      1. *-commutative 98.8%

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

      2. associate-/l* 95.7%

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

      3. associate--l+ 95.7%

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

      4. fma-define 95.7%

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

      5. sub-neg 95.7%

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

      6. metadata-eval 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in y around 0 87.4%

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

   if -8.2e-219 < y < 2.7000000000000001e-70

   1. Initial program 95.8%

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

      1. associate-/l* 97.1%

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

      2. exp-diff 88.6%

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

      3. associate-/l/ 88.6%

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

      4. exp-sum 88.6%

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

      5. times-frac 88.6%

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

      6. *-commutative 88.6%

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

      7. exp-to-pow 88.6%

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

      8. *-commutative 88.6%

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

      9. exp-to-pow 89.6%

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

      10. sub-neg 89.6%

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

      11. metadata-eval 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in y around 0 85.7%

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

      1. associate-/l* 88.6%

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

      2. exp-to-pow 89.6%

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

      3. sub-neg 89.6%

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

      4. metadata-eval 89.6%

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

   7. Simplified 89.6%

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

      1. unpow-prod-up 89.8%

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

      2. unpow-1 89.8%

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

   9. Applied egg-rr 89.8%

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

       1. associate-*r/ 89.8%

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

       2. *-rgt-identity 89.8%

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

   11. Simplified 89.8%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-219}:\\ \;\;\;\;e^{\left(t + -1\right) \cdot \log a - b} \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y \cdot e^{b}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+100}:\\ \;\;\;\;e^{\left(t + -1\right) \cdot \log a - b} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+57} \lor \neg \left(y \leq 5.4 \cdot 10^{+103}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.2e+57) (not (<= y 5.4e+103)))
   (* x (/ (/ (pow z y) a) y))
   (* x (/ (/ (pow a t) a) (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.2e+57) || !(y <= 5.4e+103)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = x * ((pow(a, t) / a) / (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 ((y <= (-4.2d+57)) .or. (.not. (y <= 5.4d+103))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = x * (((a ** t) / a) / (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 ((y <= -4.2e+57) || !(y <= 5.4e+103)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = x * ((Math.pow(a, t) / a) / (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.2e+57) or not (y <= 5.4e+103):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = x * ((math.pow(a, t) / a) / (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.2e+57) || !(y <= 5.4e+103))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(x * Float64(Float64((a ^ t) / a) / Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4.2e+57) || ~((y <= 5.4e+103)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = x * (((a ^ t) / a) / (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.2e+57], N[Not[LessEqual[y, 5.4e+103]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.19999999999999982e57 or 5.39999999999999985e103 < 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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-/l* 90.9%

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

      3. associate--l+ 90.9%

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

      4. fma-define 90.9%

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

      5. sub-neg 90.9%

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

      6. metadata-eval 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around 0 92.0%

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

      1. associate-/l* 92.0%

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

      2. +-commutative 92.0%

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

      3. mul-1-neg 92.0%

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

      4. unsub-neg 92.0%

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

   7. Simplified 92.0%

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

   8. Taylor expanded in b around 0 88.1%

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

      1. div-exp 88.1%

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

      2. *-commutative 88.1%

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

      3. exp-to-pow 88.1%

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

      4. rem-exp-log 88.1%

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

   10. Simplified 88.1%

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

   if -4.19999999999999982e57 < y < 5.39999999999999985e103

   1. Initial program 97.6%

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

      1. associate-/l* 98.0%

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

      2. exp-diff 82.7%

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

      3. associate-/l/ 82.7%

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

      4. exp-sum 77.0%

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

      5. times-frac 77.0%

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

      6. *-commutative 77.0%

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

      7. exp-to-pow 77.0%

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

      8. *-commutative 77.0%

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

      9. exp-to-pow 77.7%

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

      10. sub-neg 77.7%

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

      11. metadata-eval 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around 0 78.1%

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

      1. associate-/l* 80.4%

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

      2. exp-to-pow 81.0%

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

      3. sub-neg 81.0%

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

      4. metadata-eval 81.0%

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

   7. Simplified 81.0%

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

      1. unpow-prod-up 81.1%

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

      2. unpow-1 81.1%

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

   9. Applied egg-rr 81.1%

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

       1. associate-*r/ 81.1%

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

       2. *-rgt-identity 81.1%

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

   11. Simplified 81.1%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+57} \lor \neg \left(y \leq 5.4 \cdot 10^{+103}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ t_2 := x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{if}\;t \leq -5.7 \cdot 10^{+134}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-292}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-160}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+36} \lor \neg \left(t \leq 4.4 \cdot 10^{+103}\right) \land t \leq 3.9 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow z y) a) y))) (t_2 (* x (/ (/ (pow a t) a) y))))
   (if (<= t -5.7e+134)
     t_2
     (if (<= t -5.9e-292)
       t_1
       (if (<= t 6e-160)
         (/ x (* y (* a (exp b))))
         (if (or (<= t 3.9e+36) (and (not (<= t 4.4e+103)) (<= t 3.9e+117)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * ((pow(z, y) / a) / y);
	double t_2 = x * ((pow(a, t) / a) / y);
	double tmp;
	if (t <= -5.7e+134) {
		tmp = t_2;
	} else if (t <= -5.9e-292) {
		tmp = t_1;
	} else if (t <= 6e-160) {
		tmp = x / (y * (a * exp(b)));
	} else if ((t <= 3.9e+36) || (!(t <= 4.4e+103) && (t <= 3.9e+117))) {
		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 * (((z ** y) / a) / y)
    t_2 = x * (((a ** t) / a) / y)
    if (t <= (-5.7d+134)) then
        tmp = t_2
    else if (t <= (-5.9d-292)) then
        tmp = t_1
    else if (t <= 6d-160) then
        tmp = x / (y * (a * exp(b)))
    else if ((t <= 3.9d+36) .or. (.not. (t <= 4.4d+103)) .and. (t <= 3.9d+117)) 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(z, y) / a) / y);
	double t_2 = x * ((Math.pow(a, t) / a) / y);
	double tmp;
	if (t <= -5.7e+134) {
		tmp = t_2;
	} else if (t <= -5.9e-292) {
		tmp = t_1;
	} else if (t <= 6e-160) {
		tmp = x / (y * (a * Math.exp(b)));
	} else if ((t <= 3.9e+36) || (!(t <= 4.4e+103) && (t <= 3.9e+117))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * ((math.pow(z, y) / a) / y)
	t_2 = x * ((math.pow(a, t) / a) / y)
	tmp = 0
	if t <= -5.7e+134:
		tmp = t_2
	elif t <= -5.9e-292:
		tmp = t_1
	elif t <= 6e-160:
		tmp = x / (y * (a * math.exp(b)))
	elif (t <= 3.9e+36) or (not (t <= 4.4e+103) and (t <= 3.9e+117)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((z ^ y) / a) / y))
	t_2 = Float64(x * Float64(Float64((a ^ t) / a) / y))
	tmp = 0.0
	if (t <= -5.7e+134)
		tmp = t_2;
	elseif (t <= -5.9e-292)
		tmp = t_1;
	elseif (t <= 6e-160)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	elseif ((t <= 3.9e+36) || (!(t <= 4.4e+103) && (t <= 3.9e+117)))
		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 * (((z ^ y) / a) / y);
	t_2 = x * (((a ^ t) / a) / y);
	tmp = 0.0;
	if (t <= -5.7e+134)
		tmp = t_2;
	elseif (t <= -5.9e-292)
		tmp = t_1;
	elseif (t <= 6e-160)
		tmp = x / (y * (a * exp(b)));
	elseif ((t <= 3.9e+36) || (~((t <= 4.4e+103)) && (t <= 3.9e+117)))
		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[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.7e+134], t$95$2, If[LessEqual[t, -5.9e-292], t$95$1, If[LessEqual[t, 6e-160], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 3.9e+36], And[N[Not[LessEqual[t, 4.4e+103]], $MachinePrecision], LessEqual[t, 3.9e+117]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.70000000000000038e134 or 3.90000000000000021e36 < t < 4.39999999999999985e103 or 3.8999999999999999e117 < t

   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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. exp-diff 79.0%

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

      3. associate-/l/ 79.0%

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

      4. exp-sum 61.0%

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

      5. times-frac 61.0%

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

      6. *-commutative 61.0%

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

      7. exp-to-pow 61.0%

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

      8. *-commutative 61.0%

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

      9. exp-to-pow 61.0%

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

      10. sub-neg 61.0%

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

      11. metadata-eval 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in y around 0 76.1%

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

      1. associate-/l* 76.1%

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

      2. exp-to-pow 76.1%

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

      3. sub-neg 76.1%

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

      4. metadata-eval 76.1%

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

   7. Simplified 76.1%

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

      1. unpow-prod-up 76.1%

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

      2. unpow-1 76.1%

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

   9. Applied egg-rr 76.1%

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

       1. associate-*r/ 76.1%

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

       2. *-rgt-identity 76.1%

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

   11. Simplified 76.1%

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

   12. Taylor expanded in b around 0 90.2%

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

   if -5.70000000000000038e134 < t < -5.9000000000000001e-292 or 5.99999999999999993e-160 < t < 3.90000000000000021e36 or 4.39999999999999985e103 < t < 3.8999999999999999e117

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 90.7%

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

      3. associate--l+ 90.7%

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

      4. fma-define 90.7%

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

      5. sub-neg 90.7%

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

      6. metadata-eval 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in t around 0 93.1%

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

      1. associate-/l* 92.4%

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

      2. +-commutative 92.4%

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

      3. mul-1-neg 92.4%

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

      4. unsub-neg 92.4%

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

   7. Simplified 92.4%

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

   8. Taylor expanded in b around 0 79.6%

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

      1. div-exp 79.6%

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

      2. *-commutative 79.6%

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

      3. exp-to-pow 79.6%

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

      4. rem-exp-log 80.3%

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

   10. Simplified 80.3%

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

   if -5.9000000000000001e-292 < t < 5.99999999999999993e-160

   1. Initial program 97.8%

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

      1. associate-/l* 97.2%

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

      2. exp-diff 73.5%

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

      3. associate-/l/ 73.5%

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

      4. exp-sum 73.5%

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

      5. times-frac 73.5%

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

      6. *-commutative 73.5%

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

      7. exp-to-pow 73.5%

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

      8. *-commutative 73.5%

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

      9. exp-to-pow 73.8%

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

      10. sub-neg 73.8%

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

      11. metadata-eval 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in y around 0 82.5%

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

      1. associate-/l* 84.3%

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

      2. exp-to-pow 84.6%

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

      3. sub-neg 84.6%

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

      4. metadata-eval 84.6%

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

   7. Simplified 84.6%

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

   8. Taylor expanded in t around 0 84.6%

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

      1. *-commutative 84.6%

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

      2. associate-*l* 84.6%

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

      3. *-commutative 84.6%

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

   10. Simplified 84.6%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-292}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-160}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+36} \lor \neg \left(t \leq 4.4 \cdot 10^{+103}\right) \land t \leq 3.9 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot e^{b}}\\ \mathbf{if}\;b \leq -8 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -100:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \frac{\frac{1}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y (exp b)))))
   (if (<= b -8e+43)
     t_1
     (if (<= b -100.0)
       (* x (/ (exp b) y))
       (if (<= b 6.6e-40) (* x (/ (/ 1.0 y) a)) 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 <= -8e+43) {
		tmp = t_1;
	} else if (b <= -100.0) {
		tmp = x * (exp(b) / y);
	} else if (b <= 6.6e-40) {
		tmp = x * ((1.0 / y) / a);
	} 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 <= (-8d+43)) then
        tmp = t_1
    else if (b <= (-100.0d0)) then
        tmp = x * (exp(b) / y)
    else if (b <= 6.6d-40) then
        tmp = x * ((1.0d0 / y) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * Math.exp(b));
	double tmp;
	if (b <= -8e+43) {
		tmp = t_1;
	} else if (b <= -100.0) {
		tmp = x * (Math.exp(b) / y);
	} else if (b <= 6.6e-40) {
		tmp = x * ((1.0 / y) / a);
	} 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 <= -8e+43:
		tmp = t_1
	elif b <= -100.0:
		tmp = x * (math.exp(b) / y)
	elif b <= 6.6e-40:
		tmp = x * ((1.0 / y) / a)
	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 <= -8e+43)
		tmp = t_1;
	elseif (b <= -100.0)
		tmp = Float64(x * Float64(exp(b) / y));
	elseif (b <= 6.6e-40)
		tmp = Float64(x * Float64(Float64(1.0 / y) / a));
	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 <= -8e+43)
		tmp = t_1;
	elseif (b <= -100.0)
		tmp = x * (exp(b) / y);
	elseif (b <= 6.6e-40)
		tmp = x * ((1.0 / y) / a);
	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, -8e+43], t$95$1, If[LessEqual[b, -100.0], N[(x * N[(N[Exp[b], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.6e-40], N[(x * N[(N[(1.0 / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.00000000000000011e43 or 6.59999999999999986e-40 < 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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-/l* 89.3%

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

      3. associate--l+ 89.3%

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

      4. fma-define 89.3%

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

      5. sub-neg 89.3%

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

      6. metadata-eval 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in b around inf 66.8%

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

      1. neg-mul-1 66.8%

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

   7. Simplified 66.8%

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

      1. exp-neg 66.8%

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

      2. frac-times 74.3%

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

      3. *-un-lft-identity 74.3%

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

      4. *-commutative 74.3%

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

   9. Applied egg-rr 74.3%

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

   if -8.00000000000000011e43 < b < -100

   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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-/l* 83.3%

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

      3. associate--l+ 83.3%

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

      4. fma-define 83.3%

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

      5. sub-neg 83.3%

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

      6. metadata-eval 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in b around inf 1.6%

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

      1. neg-mul-1 1.6%

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

   7. Simplified 1.6%

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

      1. exp-neg 1.6%

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

      2. frac-times 1.6%

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

      3. *-un-lft-identity 1.6%

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

      4. *-commutative 1.6%

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

   9. Applied egg-rr 1.6%

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

       1. div-inv 1.6%

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

       2. *-commutative 1.6%

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

       3. associate-/l/ 1.6%

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

       4. exp-neg 1.6%

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

       5. add-sqr-sqrt 1.6%

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

       6. sqrt-unprod 1.6%

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

       7. sqr-neg 1.6%

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

       8. sqrt-unprod 0.0%

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

       9. add-sqr-sqrt 100.0%

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

   11. Applied egg-rr 100.0%

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

   if -100 < b < 6.59999999999999986e-40

   1. Initial program 97.1%

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

      1. associate-/l* 97.6%

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

      2. exp-diff 97.6%

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

      3. associate-/l/ 97.6%

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

      4. exp-sum 81.9%

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

      5. times-frac 82.0%

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

      6. *-commutative 82.0%

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

      7. exp-to-pow 82.0%

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

      8. *-commutative 82.0%

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

      9. exp-to-pow 82.8%

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

      10. sub-neg 82.8%

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

      11. metadata-eval 82.8%

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

   3. Simplified 82.8%

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

   5. Taylor expanded in y around 0 72.1%

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

      1. associate-/l* 73.3%

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

      2. exp-to-pow 74.1%

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

      3. sub-neg 74.1%

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

      4. metadata-eval 74.1%

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

   7. Simplified 74.1%

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

      1. unpow-prod-up 74.2%

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

      2. unpow-1 74.2%

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

   9. Applied egg-rr 74.2%

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

       1. associate-*r/ 74.2%

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

       2. *-rgt-identity 74.2%

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

   11. Simplified 74.2%

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

   12. Taylor expanded in b around 0 73.6%

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

   13. Taylor expanded in t around 0 38.7%

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

       1. *-commutative 38.7%

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

       2. associate-/r* 38.7%

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

   15. Simplified 38.7%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq -100:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \frac{\frac{1}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+19} \lor \neg \left(t \leq 550000000\right):\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.5e+19) (not (<= t 550000000.0)))
   (* x (/ (/ (pow a t) a) y))
   (/ x (* y (* a (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.5e+19) || !(t <= 550000000.0)) {
		tmp = x * ((pow(a, t) / a) / y);
	} else {
		tmp = x / (y * (a * 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 ((t <= (-7.5d+19)) .or. (.not. (t <= 550000000.0d0))) then
        tmp = x * (((a ** t) / a) / y)
    else
        tmp = x / (y * (a * 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 ((t <= -7.5e+19) || !(t <= 550000000.0)) {
		tmp = x * ((Math.pow(a, t) / a) / y);
	} else {
		tmp = x / (y * (a * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.5e+19) or not (t <= 550000000.0):
		tmp = x * ((math.pow(a, t) / a) / y)
	else:
		tmp = x / (y * (a * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.5e+19) || !(t <= 550000000.0))
		tmp = Float64(x * Float64(Float64((a ^ t) / a) / y));
	else
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.5e+19) || ~((t <= 550000000.0)))
		tmp = x * (((a ^ t) / a) / y);
	else
		tmp = x / (y * (a * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.5e+19], N[Not[LessEqual[t, 550000000.0]], $MachinePrecision]], N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.5e19 or 5.5e8 < t

   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. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. exp-diff 78.0%

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

      3. associate-/l/ 78.0%

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

      4. exp-sum 57.5%

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

      5. times-frac 57.5%

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

      6. *-commutative 57.5%

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

      7. exp-to-pow 57.5%

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

      8. *-commutative 57.5%

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

      9. exp-to-pow 57.5%

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

      10. sub-neg 57.5%

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

      11. metadata-eval 57.5%

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

   3. Simplified 57.5%

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

   5. Taylor expanded in y around 0 69.4%

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

      1. associate-/l* 69.4%

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

      2. exp-to-pow 69.4%

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

      3. sub-neg 69.4%

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

      4. metadata-eval 69.4%

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

   7. Simplified 69.4%

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

      1. unpow-prod-up 69.4%

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

      2. unpow-1 69.4%

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

   9. Applied egg-rr 69.4%

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

       1. associate-*r/ 69.4%

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

       2. *-rgt-identity 69.4%

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

   11. Simplified 69.4%

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

   12. Taylor expanded in b around 0 83.7%

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

   if -7.5e19 < t < 5.5e8

   1. Initial program 97.1%

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

      1. associate-/l* 97.6%

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

      2. exp-diff 81.3%

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

      3. associate-/l/ 81.3%

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

      4. exp-sum 79.8%

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

      5. times-frac 79.8%

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

      6. *-commutative 79.8%

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

      7. exp-to-pow 79.8%

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

      8. *-commutative 79.8%

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

      9. exp-to-pow 80.6%

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

      10. sub-neg 80.6%

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

      11. metadata-eval 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in y around 0 64.6%

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

      1. associate-/l* 68.1%

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

      2. exp-to-pow 68.9%

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

      3. sub-neg 68.9%

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

      4. metadata-eval 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in t around 0 70.4%

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

      1. *-commutative 70.4%

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

      2. associate-*l* 70.4%

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

      3. *-commutative 70.4%

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

   10. Simplified 70.4%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+19} \lor \neg \left(t \leq 550000000\right):\\ \;\;\;\;x \cdot \frac{\frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 32.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.6 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \frac{\frac{1}{y}}{a}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+150}:\\ \;\;\;\;\frac{x \cdot y - y \cdot \left(x \cdot b\right)}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 4.6e-61)
   (* x (/ (/ 1.0 y) a))
   (if (<= t 8e+150)
     (/ (- (* x y) (* y (* x b))) (* y y))
     (* x (/ (exp b) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 4.6e-61) {
		tmp = x * ((1.0 / y) / a);
	} else if (t <= 8e+150) {
		tmp = ((x * y) - (y * (x * b))) / (y * y);
	} else {
		tmp = x * (exp(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 (t <= 4.6d-61) then
        tmp = x * ((1.0d0 / y) / a)
    else if (t <= 8d+150) then
        tmp = ((x * y) - (y * (x * b))) / (y * y)
    else
        tmp = x * (exp(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 (t <= 4.6e-61) {
		tmp = x * ((1.0 / y) / a);
	} else if (t <= 8e+150) {
		tmp = ((x * y) - (y * (x * b))) / (y * y);
	} else {
		tmp = x * (Math.exp(b) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 4.6e-61:
		tmp = x * ((1.0 / y) / a)
	elif t <= 8e+150:
		tmp = ((x * y) - (y * (x * b))) / (y * y)
	else:
		tmp = x * (math.exp(b) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 4.6e-61)
		tmp = Float64(x * Float64(Float64(1.0 / y) / a));
	elseif (t <= 8e+150)
		tmp = Float64(Float64(Float64(x * y) - Float64(y * Float64(x * b))) / Float64(y * y));
	else
		tmp = Float64(x * Float64(exp(b) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 4.6e-61)
		tmp = x * ((1.0 / y) / a);
	elseif (t <= 8e+150)
		tmp = ((x * y) - (y * (x * b))) / (y * y);
	else
		tmp = x * (exp(b) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 4.6e-61], N[(x * N[(N[(1.0 / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+150], N[(N[(N[(x * y), $MachinePrecision] - N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Exp[b], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 4.59999999999999984e-61

   1. Initial program 98.4%

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

      1. associate-/l* 98.3%

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

      2. exp-diff 79.4%

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

      3. associate-/l/ 79.4%

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

      4. exp-sum 74.4%

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

      5. times-frac 74.4%

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

      6. *-commutative 74.4%

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

      7. exp-to-pow 74.4%

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

      8. *-commutative 74.4%

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

      9. exp-to-pow 75.0%

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

      10. sub-neg 75.0%

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

      11. metadata-eval 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in y around 0 67.3%

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

      1. associate-/l* 69.4%

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

      2. exp-to-pow 70.0%

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

      3. sub-neg 70.0%

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

      4. metadata-eval 70.0%

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

   7. Simplified 70.0%

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

      1. unpow-prod-up 70.0%

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

      2. unpow-1 70.0%

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

   9. Applied egg-rr 70.0%

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

       1. associate-*r/ 70.0%

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

       2. *-rgt-identity 70.0%

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

   11. Simplified 70.0%

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

   12. Taylor expanded in b around 0 58.0%

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

   13. Taylor expanded in t around 0 41.7%

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

       1. *-commutative 41.7%

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

       2. associate-/r* 41.8%

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

   15. Simplified 41.8%

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

   if 4.59999999999999984e-61 < t < 7.99999999999999985e150

   1. Initial program 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-/l* 95.3%

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

      3. associate--l+ 95.3%

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

      4. fma-define 95.3%

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

      5. sub-neg 95.3%

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

      6. metadata-eval 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in b around inf 42.8%

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

      1. neg-mul-1 42.8%

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

   7. Simplified 42.8%

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

      1. exp-neg 42.8%

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

      2. frac-times 42.8%

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

      3. *-un-lft-identity 42.8%

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

      4. *-commutative 42.8%

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

   9. Applied egg-rr 42.8%

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

   10. Taylor expanded in b around 0 16.5%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]
   11. Step-by-step derivation

       1. +-commutative 16.5%

          \[\leadsto \color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}} \]

       2. mul-1-neg 16.5%

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

       3. unsub-neg 16.5%

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

       4. *-commutative 16.5%

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

       5. associate-/l* 22.9%

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

   12. Simplified 22.9%

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

       1. frac-2neg 22.9%

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

       2. associate-*r/ 16.5%

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

       3. frac-sub 33.0%

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

   14. Applied egg-rr 33.0%

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

   if 7.99999999999999985e150 < t

   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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-/l* 93.8%

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

      3. associate--l+ 93.8%

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

      4. fma-define 93.8%

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

      5. sub-neg 93.8%

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

      6. metadata-eval 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in b around inf 26.2%

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

      1. neg-mul-1 26.2%

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

   7. Simplified 26.2%

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

      1. exp-neg 26.2%

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

      2. frac-times 26.2%

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

      3. *-un-lft-identity 26.2%

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

      4. *-commutative 26.2%

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

   9. Applied egg-rr 26.2%

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

       1. div-inv 26.2%

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

       2. *-commutative 26.2%

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

       3. associate-/l/ 26.2%

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

       4. exp-neg 26.2%

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

       5. add-sqr-sqrt 16.8%

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

       6. sqrt-unprod 35.4%

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

       7. sqr-neg 35.4%

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

       8. sqrt-unprod 18.6%

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

       9. add-sqr-sqrt 38.5%

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

   11. Applied egg-rr 38.5%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.6 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \frac{\frac{1}{y}}{a}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+150}:\\ \;\;\;\;\frac{x \cdot y - y \cdot \left(x \cdot b\right)}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+172}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 5.2e+172) (/ x (* y (* a (exp b)))) (* x (/ (exp b) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 5.2e+172) {
		tmp = x / (y * (a * exp(b)));
	} else {
		tmp = x * (exp(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 (t <= 5.2d+172) then
        tmp = x / (y * (a * exp(b)))
    else
        tmp = x * (exp(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 (t <= 5.2e+172) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = x * (Math.exp(b) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 5.2e+172:
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = x * (math.exp(b) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 5.2e+172)
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	else
		tmp = Float64(x * Float64(exp(b) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 5.2e+172)
		tmp = x / (y * (a * exp(b)));
	else
		tmp = x * (exp(b) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 5.2e+172], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Exp[b], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.2e172

   1. Initial program 98.4%

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

      1. associate-/l* 98.6%

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

      2. exp-diff 80.0%

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

      3. associate-/l/ 80.0%

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

      4. exp-sum 72.1%

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

      5. times-frac 72.1%

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

      6. *-commutative 72.1%

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

      7. exp-to-pow 72.1%

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

      8. *-commutative 72.1%

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

      9. exp-to-pow 72.6%

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

      10. sub-neg 72.6%

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

      11. metadata-eval 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in y around 0 65.9%

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

      1. associate-/l* 67.8%

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

      2. exp-to-pow 68.3%

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

      3. sub-neg 68.3%

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

      4. metadata-eval 68.3%

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

   7. Simplified 68.3%

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

   8. Taylor expanded in t around 0 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-*l* 59.7%

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

      3. *-commutative 59.7%

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

   10. Simplified 59.7%

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

   if 5.2e172 < t

   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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-/l* 92.3%

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

      3. associate--l+ 92.3%

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

      4. fma-define 92.3%

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

      5. sub-neg 92.3%

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

      6. metadata-eval 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in b around inf 20.4%

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

      1. neg-mul-1 20.4%

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

   7. Simplified 20.4%

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

      1. exp-neg 20.4%

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

      2. frac-times 20.4%

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

      3. *-un-lft-identity 20.4%

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

      4. *-commutative 20.4%

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

   9. Applied egg-rr 20.4%

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

       1. div-inv 20.4%

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

       2. *-commutative 20.4%

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

       3. associate-/l/ 20.4%

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

       4. exp-neg 20.4%

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

       5. add-sqr-sqrt 8.9%

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

       6. sqrt-unprod 27.9%

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

       7. sqr-neg 27.9%

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

       8. sqrt-unprod 19.0%

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

       9. add-sqr-sqrt 39.3%

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

   11. Applied egg-rr 39.3%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.2 \cdot 10^{+172}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.8% accurate, 15.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.4 \cdot 10^{-283} \lor \neg \left(b \leq 2.3 \cdot 10^{-147}\right) \land b \leq 7.5 \cdot 10^{+159}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b 3.4e-283) (and (not (<= b 2.3e-147)) (<= b 7.5e+159)))
   (/ x (* y a))
   (/ x (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= 3.4e-283) || (!(b <= 2.3e-147) && (b <= 7.5e+159))) {
		tmp = x / (y * a);
	} else {
		tmp = x / (y * 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 <= 3.4d-283) .or. (.not. (b <= 2.3d-147)) .and. (b <= 7.5d+159)) then
        tmp = x / (y * a)
    else
        tmp = x / (y * 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 <= 3.4e-283) || (!(b <= 2.3e-147) && (b <= 7.5e+159))) {
		tmp = x / (y * a);
	} else {
		tmp = x / (y * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= 3.4e-283) or (not (b <= 2.3e-147) and (b <= 7.5e+159)):
		tmp = x / (y * a)
	else:
		tmp = x / (y * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= 3.4e-283) || (!(b <= 2.3e-147) && (b <= 7.5e+159)))
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x / Float64(y * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= 3.4e-283) || (~((b <= 2.3e-147)) && (b <= 7.5e+159)))
		tmp = x / (y * a);
	else
		tmp = x / (y * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, 3.4e-283], And[N[Not[LessEqual[b, 2.3e-147]], $MachinePrecision], LessEqual[b, 7.5e+159]]], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.3999999999999998e-283 or 2.2999999999999999e-147 < b < 7.4999999999999997e159

   1. Initial program 98.2%

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

      1. *-commutative 98.2%

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

      2. associate-/l* 88.8%

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

      3. associate--l+ 88.8%

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

      4. fma-define 88.8%

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

      5. sub-neg 88.8%

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

      6. metadata-eval 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in t around 0 74.1%

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

      1. associate-/l* 75.5%

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

      2. +-commutative 75.5%

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

      3. mul-1-neg 75.5%

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

      4. unsub-neg 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in b around 0 64.3%

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

      1. div-exp 64.3%

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

      2. *-commutative 64.3%

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

      3. exp-to-pow 64.3%

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

      4. rem-exp-log 64.8%

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

   10. Simplified 64.8%

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

   11. Taylor expanded in y around 0 37.5%

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

   if 3.3999999999999998e-283 < b < 2.2999999999999999e-147 or 7.4999999999999997e159 < 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. Step-by-step derivation

      1. *-commutative 99.7%

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

      2. associate-/l* 92.3%

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

      3. associate--l+ 92.3%

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

      4. fma-define 92.3%

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

      5. sub-neg 92.3%

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

      6. metadata-eval 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in b around inf 46.9%

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

      1. neg-mul-1 46.9%

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

   7. Simplified 46.9%

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

      1. exp-neg 46.9%

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

      2. frac-times 51.3%

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

      3. *-un-lft-identity 51.3%

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

      4. *-commutative 51.3%

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

   9. Applied egg-rr 51.3%

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

   10. Taylor expanded in b around 0 33.4%

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

       1. distribute-rgt1-in 33.4%

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

   12. Simplified 33.4%

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

   13. Taylor expanded in b around inf 43.7%

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

       1. *-commutative 43.7%

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

   15. Simplified 43.7%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.4 \cdot 10^{-283} \lor \neg \left(b \leq 2.3 \cdot 10^{-147}\right) \land b \leq 7.5 \cdot 10^{+159}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 32.0% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.25 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{\frac{1}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - y \cdot \left(x \cdot b\right)}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 2.25e-58)
   (* x (/ (/ 1.0 y) a))
   (/ (- (* x y) (* y (* x b))) (* y y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 2.25e-58) {
		tmp = x * ((1.0 / y) / a);
	} else {
		tmp = ((x * y) - (y * (x * b))) / (y * 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 (t <= 2.25d-58) then
        tmp = x * ((1.0d0 / y) / a)
    else
        tmp = ((x * y) - (y * (x * b))) / (y * 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 (t <= 2.25e-58) {
		tmp = x * ((1.0 / y) / a);
	} else {
		tmp = ((x * y) - (y * (x * b))) / (y * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 2.25e-58:
		tmp = x * ((1.0 / y) / a)
	else:
		tmp = ((x * y) - (y * (x * b))) / (y * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 2.25e-58)
		tmp = Float64(x * Float64(Float64(1.0 / y) / a));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(y * Float64(x * b))) / Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 2.25e-58)
		tmp = x * ((1.0 / y) / a);
	else
		tmp = ((x * y) - (y * (x * b))) / (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 2.25e-58], N[(x * N[(N[(1.0 / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.2500000000000001e-58

   1. Initial program 98.4%

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

      1. associate-/l* 98.3%

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

      2. exp-diff 79.4%

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

      3. associate-/l/ 79.4%

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

      4. exp-sum 74.4%

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

      5. times-frac 74.4%

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

      6. *-commutative 74.4%

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

      7. exp-to-pow 74.4%

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

      8. *-commutative 74.4%

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

      9. exp-to-pow 75.0%

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

      10. sub-neg 75.0%

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

      11. metadata-eval 75.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in y around 0 67.3%

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

      1. associate-/l* 69.4%

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

      2. exp-to-pow 70.0%

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

      3. sub-neg 70.0%

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

      4. metadata-eval 70.0%

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

   7. Simplified 70.0%

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

      1. unpow-prod-up 70.0%

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

      2. unpow-1 70.0%

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

   9. Applied egg-rr 70.0%

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

       1. associate-*r/ 70.0%

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

       2. *-rgt-identity 70.0%

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

   11. Simplified 70.0%

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

   12. Taylor expanded in b around 0 58.0%

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

   13. Taylor expanded in t around 0 41.7%

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

       1. *-commutative 41.7%

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

       2. associate-/r* 41.8%

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

   15. Simplified 41.8%

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

   if 2.2500000000000001e-58 < t

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

      2. associate-/l* 94.6%

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

      3. associate--l+ 94.6%

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

      4. fma-define 94.6%

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

      5. sub-neg 94.6%

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

      6. metadata-eval 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in b around inf 35.8%

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

      1. neg-mul-1 35.8%

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

   7. Simplified 35.8%

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

      1. exp-neg 35.8%

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

      2. frac-times 35.8%

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

      3. *-un-lft-identity 35.8%

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

      4. *-commutative 35.8%

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

   9. Applied egg-rr 35.8%

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

   10. Taylor expanded in b around 0 16.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]
   11. Step-by-step derivation

       1. +-commutative 16.7%

          \[\leadsto \color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}} \]

       2. mul-1-neg 16.7%

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

       3. unsub-neg 16.7%

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

       4. *-commutative 16.7%

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

       5. associate-/l* 20.4%

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

   12. Simplified 20.4%

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

       1. frac-2neg 20.4%

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

       2. associate-*r/ 16.7%

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

       3. frac-sub 29.8%

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

   14. Applied egg-rr 29.8%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.25 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{\frac{1}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - y \cdot \left(x \cdot b\right)}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{b}{-y}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.06e+95)
   (* x (/ b (- y)))
   (if (<= b 1.25e+161) (* x (/ 1.0 (* y a))) (/ x (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.06e+95) {
		tmp = x * (b / -y);
	} else if (b <= 1.25e+161) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * 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 <= (-1.06d+95)) then
        tmp = x * (b / -y)
    else if (b <= 1.25d+161) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = x / (y * 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 <= -1.06e+95) {
		tmp = x * (b / -y);
	} else if (b <= 1.25e+161) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.06e+95:
		tmp = x * (b / -y)
	elif b <= 1.25e+161:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (y * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.06e+95)
		tmp = Float64(x * Float64(b / Float64(-y)));
	elseif (b <= 1.25e+161)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(x / Float64(y * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.06e+95)
		tmp = x * (b / -y);
	elseif (b <= 1.25e+161)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (y * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.06e+95], N[(x * N[(b / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+161], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.06000000000000001e95

   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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-/l* 95.0%

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

      3. associate--l+ 95.0%

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

      4. fma-define 95.0%

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

      5. sub-neg 95.0%

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

      6. metadata-eval 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in b around inf 75.2%

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

      1. neg-mul-1 75.2%

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

   7. Simplified 75.2%

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

      1. exp-neg 75.2%

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

      2. frac-times 80.3%

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

      3. *-un-lft-identity 80.3%

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

      4. *-commutative 80.3%

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

   9. Applied egg-rr 80.3%

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

   10. Taylor expanded in b around 0 30.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]
   11. Step-by-step derivation

       1. +-commutative 30.8%

          \[\leadsto \color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}} \]

       2. mul-1-neg 30.8%

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

       3. unsub-neg 30.8%

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

       4. *-commutative 30.8%

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

       5. associate-/l* 42.7%

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

   12. Simplified 42.7%

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

   13. Taylor expanded in b around inf 30.8%

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

       1. mul-1-neg 30.8%

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

       2. *-commutative 30.8%

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

       3. distribute-frac-neg2 30.8%

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

       4. associate-*r/ 42.7%

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

   15. Simplified 42.7%

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

   if -1.06000000000000001e95 < b < 1.2499999999999999e161

   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. Step-by-step derivation

      1. *-commutative 98.0%

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

      2. associate-/l* 89.0%

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

      3. associate--l+ 89.0%

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

      4. fma-define 89.0%

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

      5. sub-neg 89.0%

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

      6. metadata-eval 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in t around 0 67.9%

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

      1. associate-/l* 68.9%

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

      2. +-commutative 68.9%

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

      3. mul-1-neg 68.9%

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

      4. unsub-neg 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in b around 0 64.4%

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

      1. div-exp 64.4%

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

      2. *-commutative 64.4%

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

      3. exp-to-pow 64.4%

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

      4. rem-exp-log 64.9%

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

   10. Simplified 64.9%

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

   11. Taylor expanded in y around 0 36.4%

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

   if 1.2499999999999999e161 < 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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-/l* 87.9%

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

      3. associate--l+ 87.9%

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

      4. fma-define 87.9%

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

      5. sub-neg 87.9%

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

      6. metadata-eval 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in b around inf 79.0%

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

      1. neg-mul-1 79.0%

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

   7. Simplified 79.0%

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

      1. exp-neg 79.0%

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

      2. frac-times 88.1%

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

      3. *-un-lft-identity 88.1%

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

      4. *-commutative 88.1%

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

   9. Applied egg-rr 88.1%

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

   10. Taylor expanded in b around 0 51.2%

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

       1. distribute-rgt1-in 51.2%

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

   12. Simplified 51.2%

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

   13. Taylor expanded in b around inf 51.2%

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

       1. *-commutative 51.2%

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

   15. Simplified 51.2%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.06 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{b}{-y}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.8% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \frac{b}{-y}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \frac{\frac{1}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.3e+89)
   (* x (/ b (- y)))
   (if (<= b 3.5e+159) (* x (/ (/ 1.0 y) a)) (/ x (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.3e+89) {
		tmp = x * (b / -y);
	} else if (b <= 3.5e+159) {
		tmp = x * ((1.0 / y) / a);
	} else {
		tmp = x / (y * 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 <= (-3.3d+89)) then
        tmp = x * (b / -y)
    else if (b <= 3.5d+159) then
        tmp = x * ((1.0d0 / y) / a)
    else
        tmp = x / (y * 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 <= -3.3e+89) {
		tmp = x * (b / -y);
	} else if (b <= 3.5e+159) {
		tmp = x * ((1.0 / y) / a);
	} else {
		tmp = x / (y * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.3e+89:
		tmp = x * (b / -y)
	elif b <= 3.5e+159:
		tmp = x * ((1.0 / y) / a)
	else:
		tmp = x / (y * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.3e+89)
		tmp = Float64(x * Float64(b / Float64(-y)));
	elseif (b <= 3.5e+159)
		tmp = Float64(x * Float64(Float64(1.0 / y) / a));
	else
		tmp = Float64(x / Float64(y * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.3e+89)
		tmp = x * (b / -y);
	elseif (b <= 3.5e+159)
		tmp = x * ((1.0 / y) / a);
	else
		tmp = x / (y * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.3e+89], N[(x * N[(b / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+159], N[(x * N[(N[(1.0 / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.29999999999999974e89

   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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-/l* 95.0%

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

      3. associate--l+ 95.0%

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

      4. fma-define 95.0%

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

      5. sub-neg 95.0%

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

      6. metadata-eval 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in b around inf 75.2%

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

      1. neg-mul-1 75.2%

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

   7. Simplified 75.2%

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

      1. exp-neg 75.2%

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

      2. frac-times 80.3%

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

      3. *-un-lft-identity 80.3%

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

      4. *-commutative 80.3%

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

   9. Applied egg-rr 80.3%

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

   10. Taylor expanded in b around 0 30.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]
   11. Step-by-step derivation

       1. +-commutative 30.8%

          \[\leadsto \color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}} \]

       2. mul-1-neg 30.8%

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

       3. unsub-neg 30.8%

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

       4. *-commutative 30.8%

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

       5. associate-/l* 42.7%

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

   12. Simplified 42.7%

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

   13. Taylor expanded in b around inf 30.8%

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

       1. mul-1-neg 30.8%

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

       2. *-commutative 30.8%

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

       3. distribute-frac-neg2 30.8%

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

       4. associate-*r/ 42.7%

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

   15. Simplified 42.7%

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

   if -3.29999999999999974e89 < b < 3.4999999999999999e159

   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. Step-by-step derivation

      1. associate-/l* 98.3%

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

      2. exp-diff 86.3%

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

      3. associate-/l/ 86.3%

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

      4. exp-sum 73.7%

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

      5. times-frac 73.7%

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

      6. *-commutative 73.7%

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

      7. exp-to-pow 73.7%

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

      8. *-commutative 73.7%

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

      9. exp-to-pow 74.3%

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

      10. sub-neg 74.3%

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

      11. metadata-eval 74.3%

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

   3. Simplified 74.3%

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

   5. Taylor expanded in y around 0 66.9%

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

      1. associate-/l* 67.7%

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

      2. exp-to-pow 68.3%

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

      3. sub-neg 68.3%

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

      4. metadata-eval 68.3%

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

   7. Simplified 68.3%

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

      1. unpow-prod-up 68.4%

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

      2. unpow-1 68.4%

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

   9. Applied egg-rr 68.4%

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

       1. associate-*r/ 68.4%

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

       2. *-rgt-identity 68.4%

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

   11. Simplified 68.4%

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

   12. Taylor expanded in b around 0 71.5%

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

   13. Taylor expanded in t around 0 36.4%

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

       1. *-commutative 36.4%

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

       2. associate-/r* 36.4%

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

   15. Simplified 36.4%

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

   if 3.4999999999999999e159 < 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. Step-by-step derivation

      1. *-commutative 100.0%

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

      2. associate-/l* 87.9%

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

      3. associate--l+ 87.9%

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

      4. fma-define 87.9%

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

      5. sub-neg 87.9%

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

      6. metadata-eval 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in b around inf 79.0%

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

      1. neg-mul-1 79.0%

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

   7. Simplified 79.0%

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

      1. exp-neg 79.0%

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

      2. frac-times 88.1%

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

      3. *-un-lft-identity 88.1%

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

      4. *-commutative 88.1%

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

   9. Applied egg-rr 88.1%

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

   10. Taylor expanded in b around 0 51.2%

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

       1. distribute-rgt1-in 51.2%

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

   12. Simplified 51.2%

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

   13. Taylor expanded in b around inf 51.2%

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

       1. *-commutative 51.2%

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

   15. Simplified 51.2%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \frac{b}{-y}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+159}:\\ \;\;\;\;x \cdot \frac{\frac{1}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.4% accurate, 28.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.25 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{b}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 2.25e-58) (/ x (* y a)) (* x (/ b (- y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 2.25e-58) {
		tmp = x / (y * a);
	} else {
		tmp = x * (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 (t <= 2.25d-58) then
        tmp = x / (y * a)
    else
        tmp = x * (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 (t <= 2.25e-58) {
		tmp = x / (y * a);
	} else {
		tmp = x * (b / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 2.25e-58:
		tmp = x / (y * a)
	else:
		tmp = x * (b / -y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 2.25e-58)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x * Float64(b / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 2.25e-58)
		tmp = x / (y * a);
	else
		tmp = x * (b / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 2.25e-58], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x * N[(b / (-y)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.2500000000000001e-58

   1. Initial program 98.4%

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

      1. *-commutative 98.4%

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

      2. associate-/l* 87.7%

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

      3. associate--l+ 87.7%

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

      4. fma-define 87.7%

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

      5. sub-neg 87.7%

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

      6. metadata-eval 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in t around 0 85.8%

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

      1. associate-/l* 86.8%

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

      2. +-commutative 86.8%

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

      3. mul-1-neg 86.8%

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

      4. unsub-neg 86.8%

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

   7. Simplified 86.8%

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

   8. Taylor expanded in b around 0 69.0%

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

      1. div-exp 69.0%

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

      2. *-commutative 69.0%

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

      3. exp-to-pow 69.0%

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

      4. rem-exp-log 69.6%

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

   10. Simplified 69.6%

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

   11. Taylor expanded in y around 0 41.2%

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

   if 2.2500000000000001e-58 < t

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

      2. associate-/l* 94.6%

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

      3. associate--l+ 94.6%

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

      4. fma-define 94.6%

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

      5. sub-neg 94.6%

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

      6. metadata-eval 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in b around inf 35.8%

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

      1. neg-mul-1 35.8%

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

   7. Simplified 35.8%

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

      1. exp-neg 35.8%

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

      2. frac-times 35.8%

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

      3. *-un-lft-identity 35.8%

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

      4. *-commutative 35.8%

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

   9. Applied egg-rr 35.8%

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

   10. Taylor expanded in b around 0 16.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]
   11. Step-by-step derivation

       1. +-commutative 16.7%

          \[\leadsto \color{blue}{\frac{x}{y} + -1 \cdot \frac{b \cdot x}{y}} \]

       2. mul-1-neg 16.7%

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

       3. unsub-neg 16.7%

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

       4. *-commutative 16.7%

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

       5. associate-/l* 20.4%

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

   12. Simplified 20.4%

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

   13. Taylor expanded in b around inf 20.7%

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

       1. mul-1-neg 20.7%

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

       2. *-commutative 20.7%

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

       3. distribute-frac-neg2 20.7%

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

       4. associate-*r/ 24.4%

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

   15. Simplified 24.4%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.25 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{b}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.2% accurate, 63.0× 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 98.6%

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

   1. *-commutative 98.6%

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

   2. associate-/l* 89.8%

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

   3. associate--l+ 89.8%

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

   4. fma-define 89.8%

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

   5. sub-neg 89.8%

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

   6. metadata-eval 89.8%

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

3. Simplified 89.8%

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

5. Taylor expanded in t around 0 76.3%

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

   1. associate-/l* 77.0%

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

   2. +-commutative 77.0%

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

   3. mul-1-neg 77.0%

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

   4. unsub-neg 77.0%

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

7. Simplified 77.0%

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

8. Taylor expanded in b around 0 60.8%

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

   1. div-exp 60.8%

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

   2. *-commutative 60.8%

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

   3. exp-to-pow 60.8%

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

   4. rem-exp-log 61.2%

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

10. Simplified 61.2%

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

11. Taylor expanded in y around 0 33.7%

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

12. Final simplification 33.7%

    \[\leadsto \frac{x}{y \cdot a} \]
13. Add Preprocessing

Alternative 16: 15.7% accurate, 105.0× 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 98.6%

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

   1. *-commutative 98.6%

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

   2. associate-/l* 89.8%

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

   3. associate--l+ 89.8%

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

   4. fma-define 89.8%

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

   5. sub-neg 89.8%

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

   6. metadata-eval 89.8%

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

3. Simplified 89.8%

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

5. Taylor expanded in b around inf 40.2%

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

   1. neg-mul-1 40.2%

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

7. Simplified 40.2%

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

8. Taylor expanded in b around 0 16.4%

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

9. Final simplification 16.4%

   \[\leadsto \frac{x}{y} \]
10. Add Preprocessing

Developer target: 71.8% 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 2024053 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))