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

Percentage Accurate: 98.5% → 98.5%

Time: 17.6s

Alternatives: 20

Speedup: 1.0×

• Could not converge on a ground truth

  1. reg0 = (bf "1.922491550452554838596021478736955226639e-173")
  2. reg1 = (bf "1.216411025958871710933636351271827033093e-41")
  3. reg2 = (bf "3.351451002649018362421398155029284700735e-198")
  4. reg3 = (bf "2.739609385331147907887093884531208687555e156")
  5. reg4 = (bf "5.674997267363530060779204411578268297394e162")
  6. reg5 = (bf -104086210750898203477685634932408320)

• 47.1% 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 99.1%

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

3. Final simplification 99.1%

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

Alternative 2: 91.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -1.05:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{elif}\;t + -1 \leq 5 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -1.05)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (if (<= (+ t -1.0) 5e+79)
     (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
     (/ (* x (pow a t)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -1.05) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else if ((t + -1.0) <= 5e+79) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * pow(a, t)) / 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 + (-1.0d0)) <= (-1.05d0)) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else if ((t + (-1.0d0)) <= 5d+79) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * (a ** t)) / 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 + -1.0) <= -1.05) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else if ((t + -1.0) <= 5e+79) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.pow(a, t)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -1.05:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	elif (t + -1.0) <= 5e+79:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.pow(a, t)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -1.05)
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	elseif (Float64(t + -1.0) <= 5e+79)
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * (a ^ t)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -1.05)
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	elseif ((t + -1.0) <= 5e+79)
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * (a ^ t)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -1.05], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 5e+79], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -1.05000000000000004

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.2%

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

   if -1.05000000000000004 < (-.f64 t #s(literal 1 binary64)) < 5e79

   1. Initial program 98.5%

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

   3. Taylor expanded in t around 0 98.5%

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

      1. +-commutative 98.5%

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

      2. mul-1-neg 98.5%

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

      3. unsub-neg 98.5%

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

   5. Simplified 98.5%

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

   if 5e79 < (-.f64 t #s(literal 1 binary64))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.0%

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

   4. Taylor expanded in b around 0 94.0%

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

      1. exp-prod 94.0%

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

      2. remove-double-neg 94.0%

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

      3. log-rec 94.0%

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

      4. mul-1-neg 94.0%

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

      5. exp-prod 94.0%

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

      6. associate-*r* 94.0%

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

      7. associate-*r* 94.0%

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

      8. exp-prod 94.0%

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

      9. mul-1-neg 94.0%

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

      10. log-rec 94.0%

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

      11. remove-double-neg 94.0%

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

      12. rem-exp-log 94.0%

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

      13. sub-neg 94.0%

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

      14. metadata-eval 94.0%

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

      15. +-commutative 94.0%

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

   6. Simplified 94.0%

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

   7. Taylor expanded in t around inf 94.0%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1.05:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{elif}\;t + -1 \leq 5 \cdot 10^{+79}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+59} \lor \neg \left(y \leq 1.7 \cdot 10^{+162}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.6e+59) (not (<= y 1.7e+162)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.6e+59) || !(y <= 1.7e+162)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.6d+59)) .or. (.not. (y <= 1.7d+162))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.6e+59) || !(y <= 1.7e+162)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.6e+59) or not (y <= 1.7e+162):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.6e+59) || !(y <= 1.7e+162))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.6e+59) || ~((y <= 1.7e+162)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.6e+59], N[Not[LessEqual[y, 1.7e+162]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5999999999999996e59 or 1.70000000000000001e162 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 96.6%

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

      1. +-commutative 96.6%

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

      2. mul-1-neg 96.6%

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

      3. unsub-neg 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in b around 0 93.2%

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

      1. div-exp 93.2%

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

      2. *-commutative 93.2%

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

      3. exp-to-pow 93.2%

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

      4. rem-exp-log 93.2%

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

   8. Simplified 93.2%

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

   if -5.5999999999999996e59 < y < 1.70000000000000001e162

   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. Taylor expanded in y around 0 90.0%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+59} \lor \neg \left(y \leq 1.7 \cdot 10^{+162}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+32} \lor \neg \left(y \leq 485\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{y \cdot e^{b}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -9.5e+32) (not (<= y 485.0)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (/ (pow a t) (* y (exp b)))) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e+32) || !(y <= 485.0)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * (pow(a, t) / (y * exp(b)))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-9.5d+32)) .or. (.not. (y <= 485.0d0))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * ((a ** t) / (y * exp(b)))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -9.5e+32) || !(y <= 485.0)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * (Math.pow(a, t) / (y * Math.exp(b)))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -9.5e+32) or not (y <= 485.0):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * (math.pow(a, t) / (y * math.exp(b)))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -9.5e+32) || !(y <= 485.0))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ t) / Float64(y * exp(b)))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -9.5e+32) || ~((y <= 485.0)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * ((a ^ t) / (y * exp(b)))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -9.5e+32], N[Not[LessEqual[y, 485.0]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.50000000000000006e32 or 485 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 93.1%

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

      1. +-commutative 93.1%

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

      2. mul-1-neg 93.1%

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

      3. unsub-neg 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in b around 0 84.0%

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

      1. div-exp 84.0%

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

      2. *-commutative 84.0%

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

      3. exp-to-pow 84.0%

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

      4. rem-exp-log 84.0%

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

   8. Simplified 84.0%

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

   if -9.50000000000000006e32 < y < 485

   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. 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. associate--l+ 97.6%

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

      3. exp-sum 95.2%

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

      4. associate-/l* 95.2%

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

      5. *-commutative 95.2%

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

      6. exp-to-pow 95.2%

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

      7. exp-diff 85.0%

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

      8. *-commutative 85.0%

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

      9. exp-to-pow 85.8%

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

      10. sub-neg 85.8%

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

      11. metadata-eval 85.8%

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

   3. Simplified 85.8%

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

      1. associate-/l/ 85.8%

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

      2. unpow-prod-up 85.8%

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

      3. associate-/l* 84.3%

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

      4. unpow-1 84.3%

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

   6. Applied egg-rr 84.3%

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

      1. associate-/r* 84.3%

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

      2. associate-*r/ 84.3%

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

      3. *-rgt-identity 84.3%

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

      4. associate-*r* 78.8%

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

   8. Simplified 78.8%

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

   9. Taylor expanded in y around 0 85.7%

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

       1. *-un-lft-identity 85.7%

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

       2. times-frac 88.0%

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

   11. Applied egg-rr 88.0%

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

       1. associate-*l/ 88.0%

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

       2. *-lft-identity 88.0%

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

       3. associate-/l* 88.0%

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

   13. Simplified 88.0%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+32} \lor \neg \left(y \leq 485\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{y \cdot e^{b}}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {a}^{t}\\ \mathbf{if}\;t \leq -0.059:\\ \;\;\;\;\frac{t\_1}{y \cdot a}\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow a t))))
   (if (<= t -0.059)
     (/ t_1 (* y a))
     (if (<= t 1.18e-5) (* x (/ (pow z y) (* a (* y (exp b))))) (/ t_1 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(a, t);
	double tmp;
	if (t <= -0.059) {
		tmp = t_1 / (y * a);
	} else if (t <= 1.18e-5) {
		tmp = x * (pow(z, y) / (a * (y * exp(b))));
	} else {
		tmp = t_1 / 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)
    if (t <= (-0.059d0)) then
        tmp = t_1 / (y * a)
    else if (t <= 1.18d-5) then
        tmp = x * ((z ** y) / (a * (y * exp(b))))
    else
        tmp = t_1 / 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);
	double tmp;
	if (t <= -0.059) {
		tmp = t_1 / (y * a);
	} else if (t <= 1.18e-5) {
		tmp = x * (Math.pow(z, y) / (a * (y * Math.exp(b))));
	} else {
		tmp = t_1 / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(a, t)
	tmp = 0
	if t <= -0.059:
		tmp = t_1 / (y * a)
	elif t <= 1.18e-5:
		tmp = x * (math.pow(z, y) / (a * (y * math.exp(b))))
	else:
		tmp = t_1 / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (a ^ t))
	tmp = 0.0
	if (t <= -0.059)
		tmp = Float64(t_1 / Float64(y * a));
	elseif (t <= 1.18e-5)
		tmp = Float64(x * Float64((z ^ y) / Float64(a * Float64(y * exp(b)))));
	else
		tmp = Float64(t_1 / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (a ^ t);
	tmp = 0.0;
	if (t <= -0.059)
		tmp = t_1 / (y * a);
	elseif (t <= 1.18e-5)
		tmp = x * ((z ^ y) / (a * (y * exp(b))));
	else
		tmp = t_1 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.059], N[(t$95$1 / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.18e-5], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.058999999999999997

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. associate--l+ 99.8%

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

      3. exp-sum 68.3%

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

      4. associate-/l* 68.3%

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

      5. *-commutative 68.3%

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

      6. exp-to-pow 68.3%

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

      7. exp-diff 54.2%

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

      8. *-commutative 54.2%

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

      9. exp-to-pow 54.2%

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

      10. sub-neg 54.2%

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

      11. metadata-eval 54.2%

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

   3. Simplified 54.2%

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

      1. associate-/l/ 54.2%

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

      2. unpow-prod-up 54.3%

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

      3. associate-/l* 54.3%

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

      4. unpow-1 54.3%

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

   6. Applied egg-rr 54.3%

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

      1. associate-/r* 54.3%

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

      2. associate-*r/ 54.3%

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

      3. *-rgt-identity 54.3%

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

      4. associate-*r* 54.3%

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

   8. Simplified 54.3%

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

   9. Taylor expanded in y around 0 66.8%

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

   10. Taylor expanded in b around 0 74.1%

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

       1. *-commutative 74.1%

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

   12. Simplified 74.1%

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

   if -0.058999999999999997 < t < 1.18000000000000005e-5

   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* 97.8%

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

      2. associate--l+ 97.8%

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

      3. exp-sum 88.9%

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

      4. associate-/l* 84.4%

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

      5. *-commutative 84.4%

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

      6. exp-to-pow 84.4%

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

      7. exp-diff 84.4%

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

      8. *-commutative 84.4%

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

      9. exp-to-pow 85.2%

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

      10. sub-neg 85.2%

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

      11. metadata-eval 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in t around 0 85.3%

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

   if 1.18000000000000005e-5 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 89.2%

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

   4. Taylor expanded in b around 0 89.2%

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

      1. exp-prod 89.2%

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

      2. remove-double-neg 89.2%

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

      3. log-rec 89.2%

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

      4. mul-1-neg 89.2%

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

      5. exp-prod 89.2%

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

      6. associate-*r* 89.2%

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

      7. associate-*r* 89.2%

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

      8. exp-prod 89.2%

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

      9. mul-1-neg 89.2%

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

      10. log-rec 89.2%

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

      11. remove-double-neg 89.2%

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

      12. rem-exp-log 89.2%

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

      13. sub-neg 89.2%

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

      14. metadata-eval 89.2%

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

      15. +-commutative 89.2%

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

   6. Simplified 89.2%

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

   7. Taylor expanded in t around inf 89.2%

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

Alternative 6: 74.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -1.46 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{a \cdot t\_1}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-136}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;y \leq 13.2:\\ \;\;\;\;\frac{\frac{x}{t\_1}}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))) (t_2 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -1.46e+59)
     t_2
     (if (<= y -1.6e-71)
       (/ x (* a t_1))
       (if (<= y -1e-136)
         (/ (* x (pow a t)) (* y a))
         (if (<= y 13.2) (/ (/ x t_1) a) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * exp(b);
	double t_2 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -1.46e+59) {
		tmp = t_2;
	} else if (y <= -1.6e-71) {
		tmp = x / (a * t_1);
	} else if (y <= -1e-136) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if (y <= 13.2) {
		tmp = (x / t_1) / a;
	} 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 = y * exp(b)
    t_2 = (x * ((z ** y) / a)) / y
    if (y <= (-1.46d+59)) then
        tmp = t_2
    else if (y <= (-1.6d-71)) then
        tmp = x / (a * t_1)
    else if (y <= (-1d-136)) then
        tmp = (x * (a ** t)) / (y * a)
    else if (y <= 13.2d0) then
        tmp = (x / t_1) / a
    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 = y * Math.exp(b);
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -1.46e+59) {
		tmp = t_2;
	} else if (y <= -1.6e-71) {
		tmp = x / (a * t_1);
	} else if (y <= -1e-136) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if (y <= 13.2) {
		tmp = (x / t_1) / a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * math.exp(b)
	t_2 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -1.46e+59:
		tmp = t_2
	elif y <= -1.6e-71:
		tmp = x / (a * t_1)
	elif y <= -1e-136:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif y <= 13.2:
		tmp = (x / t_1) / a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * exp(b))
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -1.46e+59)
		tmp = t_2;
	elseif (y <= -1.6e-71)
		tmp = Float64(x / Float64(a * t_1));
	elseif (y <= -1e-136)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (y <= 13.2)
		tmp = Float64(Float64(x / t_1) / a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * exp(b);
	t_2 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -1.46e+59)
		tmp = t_2;
	elseif (y <= -1.6e-71)
		tmp = x / (a * t_1);
	elseif (y <= -1e-136)
		tmp = (x * (a ^ t)) / (y * a);
	elseif (y <= 13.2)
		tmp = (x / t_1) / a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.46e+59], t$95$2, If[LessEqual[y, -1.6e-71], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1e-136], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 13.2], N[(N[(x / t$95$1), $MachinePrecision] / a), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.45999999999999992e59 or 13.199999999999999 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 93.5%

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

      1. +-commutative 93.5%

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

      2. mul-1-neg 93.5%

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

      3. unsub-neg 93.5%

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

   5. Simplified 93.5%

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

   6. Taylor expanded in b around 0 85.4%

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

      1. div-exp 85.4%

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

      2. *-commutative 85.4%

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

      3. exp-to-pow 85.4%

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

      4. rem-exp-log 85.4%

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

   8. Simplified 85.4%

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

   if -1.45999999999999992e59 < y < -1.5999999999999999e-71

   1. Initial program 98.9%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 78.2%

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

      4. associate-/l* 78.2%

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

      5. *-commutative 78.2%

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

      6. exp-to-pow 78.2%

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

      7. exp-diff 67.8%

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

      8. *-commutative 67.8%

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

      9. exp-to-pow 68.8%

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

      10. sub-neg 68.8%

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

      11. metadata-eval 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in t around 0 76.0%

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

   6. Taylor expanded in y around 0 76.4%

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

   if -1.5999999999999999e-71 < y < -1e-136

   1. Initial program 99.4%

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

      1. associate-/l* 99.4%

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

      2. associate--l+ 99.4%

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

      3. exp-sum 99.4%

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

      4. associate-/l* 99.4%

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

      5. *-commutative 99.4%

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

      6. exp-to-pow 99.4%

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

      7. exp-diff 53.9%

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

      8. *-commutative 53.9%

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

      9. exp-to-pow 54.5%

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

      10. sub-neg 54.5%

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

      11. metadata-eval 54.5%

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

   3. Simplified 54.5%

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

      1. associate-/l/ 54.5%

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

      2. unpow-prod-up 54.5%

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

      3. associate-/l* 54.5%

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

      4. unpow-1 54.5%

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

   6. Applied egg-rr 54.5%

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

      1. associate-/r* 54.5%

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

      2. associate-*r/ 54.5%

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

      3. *-rgt-identity 54.5%

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

      4. associate-*r* 54.5%

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

   8. Simplified 54.5%

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

   9. Taylor expanded in y around 0 54.5%

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

   10. Taylor expanded in b around 0 100.0%

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

       1. *-commutative 100.0%

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

   12. Simplified 100.0%

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

   if -1e-136 < y < 13.199999999999999

   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* 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. associate--l+ 97.2%

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

      3. exp-sum 97.2%

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

      4. associate-/l* 97.2%

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

      5. *-commutative 97.2%

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

      6. exp-to-pow 97.2%

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

      7. exp-diff 91.9%

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

      8. *-commutative 91.9%

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

      9. exp-to-pow 92.6%

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

      10. sub-neg 92.6%

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

      11. metadata-eval 92.6%

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

   3. Simplified 92.6%

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

      1. associate-/l/ 92.6%

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

      2. unpow-prod-up 92.7%

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

      3. associate-/l* 90.6%

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

      4. unpow-1 90.6%

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

   6. Applied egg-rr 90.6%

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

      1. associate-/r* 90.6%

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

      2. associate-*r/ 90.6%

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

      3. *-rgt-identity 90.6%

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

      4. associate-*r* 83.3%

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

   8. Simplified 83.3%

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

   9. Taylor expanded in y around 0 90.4%

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

       1. *-un-lft-identity 90.4%

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

       2. times-frac 93.4%

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

   11. Applied egg-rr 93.4%

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

       1. associate-*l/ 93.4%

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

       2. *-lft-identity 93.4%

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

       3. associate-/l* 93.4%

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

   13. Simplified 93.4%

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

   14. Taylor expanded in t around 0 81.2%

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

Alternative 7: 73.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -1.62 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{a \cdot t\_1}\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-136}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{elif}\;y \leq 3.2:\\ \;\;\;\;\frac{\frac{x}{t\_1}}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))) (t_2 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -1.62e+59)
     t_2
     (if (<= y -9.2e-74)
       (/ x (* a t_1))
       (if (<= y -4.7e-136)
         (/ (* x (pow a t)) y)
         (if (<= y 3.2) (/ (/ x t_1) a) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * exp(b);
	double t_2 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -1.62e+59) {
		tmp = t_2;
	} else if (y <= -9.2e-74) {
		tmp = x / (a * t_1);
	} else if (y <= -4.7e-136) {
		tmp = (x * pow(a, t)) / y;
	} else if (y <= 3.2) {
		tmp = (x / t_1) / a;
	} 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 = y * exp(b)
    t_2 = (x * ((z ** y) / a)) / y
    if (y <= (-1.62d+59)) then
        tmp = t_2
    else if (y <= (-9.2d-74)) then
        tmp = x / (a * t_1)
    else if (y <= (-4.7d-136)) then
        tmp = (x * (a ** t)) / y
    else if (y <= 3.2d0) then
        tmp = (x / t_1) / a
    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 = y * Math.exp(b);
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -1.62e+59) {
		tmp = t_2;
	} else if (y <= -9.2e-74) {
		tmp = x / (a * t_1);
	} else if (y <= -4.7e-136) {
		tmp = (x * Math.pow(a, t)) / y;
	} else if (y <= 3.2) {
		tmp = (x / t_1) / a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * math.exp(b)
	t_2 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -1.62e+59:
		tmp = t_2
	elif y <= -9.2e-74:
		tmp = x / (a * t_1)
	elif y <= -4.7e-136:
		tmp = (x * math.pow(a, t)) / y
	elif y <= 3.2:
		tmp = (x / t_1) / a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * exp(b))
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -1.62e+59)
		tmp = t_2;
	elseif (y <= -9.2e-74)
		tmp = Float64(x / Float64(a * t_1));
	elseif (y <= -4.7e-136)
		tmp = Float64(Float64(x * (a ^ t)) / y);
	elseif (y <= 3.2)
		tmp = Float64(Float64(x / t_1) / a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * exp(b);
	t_2 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -1.62e+59)
		tmp = t_2;
	elseif (y <= -9.2e-74)
		tmp = x / (a * t_1);
	elseif (y <= -4.7e-136)
		tmp = (x * (a ^ t)) / y;
	elseif (y <= 3.2)
		tmp = (x / t_1) / a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.62e+59], t$95$2, If[LessEqual[y, -9.2e-74], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.7e-136], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 3.2], N[(N[(x / t$95$1), $MachinePrecision] / a), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6200000000000001e59 or 3.2000000000000002 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 93.5%

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

      1. +-commutative 93.5%

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

      2. mul-1-neg 93.5%

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

      3. unsub-neg 93.5%

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

   5. Simplified 93.5%

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

   6. Taylor expanded in b around 0 85.4%

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

      1. div-exp 85.4%

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

      2. *-commutative 85.4%

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

      3. exp-to-pow 85.4%

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

      4. rem-exp-log 85.4%

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

   8. Simplified 85.4%

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

   if -1.6200000000000001e59 < y < -9.19999999999999922e-74

   1. Initial program 98.9%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 78.2%

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

      4. associate-/l* 78.2%

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

      5. *-commutative 78.2%

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

      6. exp-to-pow 78.2%

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

      7. exp-diff 67.8%

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

      8. *-commutative 67.8%

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

      9. exp-to-pow 68.8%

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

      10. sub-neg 68.8%

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

      11. metadata-eval 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in t around 0 76.0%

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

   6. Taylor expanded in y around 0 76.4%

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

   if -9.19999999999999922e-74 < y < -4.70000000000000022e-136

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 99.4%

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

   4. Taylor expanded in b around 0 99.4%

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

      1. exp-prod 99.4%

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

      2. remove-double-neg 99.4%

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

      3. log-rec 99.4%

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

      4. mul-1-neg 99.4%

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

      5. exp-prod 99.4%

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

      6. associate-*r* 99.4%

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

      7. associate-*r* 99.4%

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

      8. exp-prod 99.4%

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

      9. mul-1-neg 99.4%

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

      10. log-rec 99.4%

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

      11. remove-double-neg 99.4%

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

      12. rem-exp-log 99.9%

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

      13. sub-neg 99.9%

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

      14. metadata-eval 99.9%

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

      15. +-commutative 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in t around inf 91.5%

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

   if -4.70000000000000022e-136 < y < 3.2000000000000002

   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* 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. associate--l+ 97.2%

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

      3. exp-sum 97.2%

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

      4. associate-/l* 97.2%

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

      5. *-commutative 97.2%

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

      6. exp-to-pow 97.2%

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

      7. exp-diff 91.9%

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

      8. *-commutative 91.9%

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

      9. exp-to-pow 92.6%

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

      10. sub-neg 92.6%

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

      11. metadata-eval 92.6%

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

   3. Simplified 92.6%

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

      1. associate-/l/ 92.6%

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

      2. unpow-prod-up 92.7%

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

      3. associate-/l* 90.6%

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

      4. unpow-1 90.6%

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

   6. Applied egg-rr 90.6%

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

      1. associate-/r* 90.6%

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

      2. associate-*r/ 90.6%

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

      3. *-rgt-identity 90.6%

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

      4. associate-*r* 83.3%

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

   8. Simplified 83.3%

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

   9. Taylor expanded in y around 0 90.4%

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

       1. *-un-lft-identity 90.4%

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

       2. times-frac 93.4%

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

   11. Applied egg-rr 93.4%

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

       1. associate-*l/ 93.4%

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

       2. *-lft-identity 93.4%

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

       3. associate-/l* 93.4%

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

   13. Simplified 93.4%

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

   14. Taylor expanded in t around 0 81.2%

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

Alternative 8: 72.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -34000:\\ \;\;\;\;\frac{x \cdot e^{-b}}{y}\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -34000.0)
   (/ (* x (exp (- b))) y)
   (if (<= b 2.7e-11) (* (/ x a) (/ (pow z y) y)) (/ (/ x (* y (exp b))) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -34000.0) {
		tmp = (x * exp(-b)) / y;
	} else if (b <= 2.7e-11) {
		tmp = (x / a) * (pow(z, y) / y);
	} else {
		tmp = (x / (y * exp(b))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-34000.0d0)) then
        tmp = (x * exp(-b)) / y
    else if (b <= 2.7d-11) then
        tmp = (x / a) * ((z ** y) / y)
    else
        tmp = (x / (y * exp(b))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -34000.0) {
		tmp = (x * Math.exp(-b)) / y;
	} else if (b <= 2.7e-11) {
		tmp = (x / a) * (Math.pow(z, y) / y);
	} else {
		tmp = (x / (y * Math.exp(b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -34000.0:
		tmp = (x * math.exp(-b)) / y
	elif b <= 2.7e-11:
		tmp = (x / a) * (math.pow(z, y) / y)
	else:
		tmp = (x / (y * math.exp(b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -34000.0)
		tmp = Float64(Float64(x * exp(Float64(-b))) / y);
	elseif (b <= 2.7e-11)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	else
		tmp = Float64(Float64(x / Float64(y * exp(b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -34000.0)
		tmp = (x * exp(-b)) / y;
	elseif (b <= 2.7e-11)
		tmp = (x / a) * ((z ^ y) / y);
	else
		tmp = (x / (y * exp(b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -34000.0], N[(N[(x * N[Exp[(-b)], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.7e-11], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -34000

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 88.3%

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

      1. +-commutative 88.3%

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

      2. mul-1-neg 88.3%

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

      3. unsub-neg 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in b around inf 78.3%

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

      1. neg-mul-1 78.3%

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

   8. Simplified 78.3%

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

   if -34000 < b < 2.70000000000000005e-11

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0 78.3%

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

      1. +-commutative 78.3%

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

      2. mul-1-neg 78.3%

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

      3. unsub-neg 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in b around 0 78.2%

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

      1. associate-/l* 79.1%

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

      2. div-exp 79.1%

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

      3. *-commutative 79.1%

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

      4. exp-to-pow 79.1%

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

      5. rem-exp-log 79.9%

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

      6. associate-/r* 73.0%

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

      7. associate-/l* 73.0%

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

      8. times-frac 77.4%

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

   8. Simplified 77.4%

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

   if 2.70000000000000005e-11 < b

   1. Initial program 99.8%

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

      1. associate-/l* 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. associate--l+ 98.6%

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

      3. exp-sum 77.4%

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

      4. associate-/l* 77.4%

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

      5. *-commutative 77.4%

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

      6. exp-to-pow 77.4%

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

      7. exp-diff 65.3%

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

      8. *-commutative 65.3%

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

      9. exp-to-pow 65.3%

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

      10. sub-neg 65.3%

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

      11. metadata-eval 65.3%

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

   3. Simplified 65.3%

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

      1. associate-/l/ 65.3%

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

      2. unpow-prod-up 65.3%

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

      3. associate-/l* 65.3%

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

      4. unpow-1 65.3%

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

   6. Applied egg-rr 65.3%

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

      1. associate-/r* 65.3%

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

      2. associate-*r/ 65.3%

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

      3. *-rgt-identity 65.3%

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

      4. associate-*r* 54.7%

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

   8. Simplified 54.7%

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

   9. Taylor expanded in y around 0 73.0%

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

       1. *-un-lft-identity 73.0%

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

       2. times-frac 74.4%

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

   11. Applied egg-rr 74.4%

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

       1. associate-*l/ 74.4%

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

       2. *-lft-identity 74.4%

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

       3. associate-/l* 74.4%

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

   13. Simplified 74.4%

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

   14. Taylor expanded in t around 0 80.6%

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

Alternative 9: 74.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -60000000000 \lor \neg \left(t \leq 3.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -60000000000.0) (not (<= t 3.4e-11)))
   (/ (* x (pow a t)) y)
   (/ (/ x (* y (exp b))) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -60000000000.0) || !(t <= 3.4e-11)) {
		tmp = (x * pow(a, t)) / y;
	} else {
		tmp = (x / (y * exp(b))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-60000000000.0d0)) .or. (.not. (t <= 3.4d-11))) then
        tmp = (x * (a ** t)) / y
    else
        tmp = (x / (y * exp(b))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -60000000000.0) || !(t <= 3.4e-11)) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = (x / (y * Math.exp(b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -60000000000.0) or not (t <= 3.4e-11):
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = (x / (y * math.exp(b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -60000000000.0) || !(t <= 3.4e-11))
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = Float64(Float64(x / Float64(y * exp(b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -60000000000.0) || ~((t <= 3.4e-11)))
		tmp = (x * (a ^ t)) / y;
	else
		tmp = (x / (y * exp(b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -60000000000.0], N[Not[LessEqual[t, 3.4e-11]], $MachinePrecision]], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6e10 or 3.3999999999999999e-11 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 88.5%

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

   4. Taylor expanded in b around 0 81.1%

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

      1. exp-prod 81.1%

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

      2. remove-double-neg 81.1%

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

      3. log-rec 81.1%

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

      4. mul-1-neg 81.1%

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

      5. exp-prod 81.1%

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

      6. associate-*r* 81.1%

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

      7. associate-*r* 81.1%

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

      8. exp-prod 81.1%

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

      9. mul-1-neg 81.1%

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

      10. log-rec 81.1%

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

      11. remove-double-neg 81.1%

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

      12. rem-exp-log 81.1%

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

      13. sub-neg 81.1%

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

      14. metadata-eval 81.1%

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

      15. +-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in t around inf 81.1%

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

   if -6e10 < t < 3.3999999999999999e-11

   1. Initial program 98.3%

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

      1. associate-/l* 97.7%

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

      2. associate--l+ 97.7%

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

      3. exp-sum 88.2%

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

      4. associate-/l* 84.5%

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

      5. *-commutative 84.5%

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

      6. exp-to-pow 84.5%

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

      7. exp-diff 84.5%

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

      8. *-commutative 84.5%

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

      9. exp-to-pow 85.3%

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

      10. sub-neg 85.3%

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

      11. metadata-eval 85.3%

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

   3. Simplified 85.3%

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

      1. associate-/l/ 85.3%

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

      2. unpow-prod-up 85.3%

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

      3. associate-/l* 85.3%

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

      4. unpow-1 85.3%

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

   6. Applied egg-rr 85.3%

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

      1. associate-/r* 85.3%

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

      2. associate-*r/ 85.3%

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

      3. *-rgt-identity 85.3%

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

      4. associate-*r* 80.9%

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

   8. Simplified 80.9%

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

   9. Taylor expanded in y around 0 69.8%

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

       1. *-un-lft-identity 69.8%

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

       2. times-frac 69.1%

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

   11. Applied egg-rr 69.1%

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

       1. associate-*l/ 69.2%

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

       2. *-lft-identity 69.2%

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

       3. associate-/l* 69.2%

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

   13. Simplified 69.2%

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

   14. Taylor expanded in t around 0 69.9%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -60000000000 \lor \neg \left(t \leq 3.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -20000000 \lor \neg \left(t \leq 3.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -20000000.0) (not (<= t 3.4e-11)))
   (/ (* x (pow a t)) y)
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -20000000.0) || !(t <= 3.4e-11)) {
		tmp = (x * pow(a, t)) / y;
	} else {
		tmp = x / (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 ((t <= (-20000000.0d0)) .or. (.not. (t <= 3.4d-11))) then
        tmp = (x * (a ** t)) / y
    else
        tmp = x / (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 ((t <= -20000000.0) || !(t <= 3.4e-11)) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -20000000.0) or not (t <= 3.4e-11):
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -20000000.0) || !(t <= 3.4e-11))
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -20000000.0) || ~((t <= 3.4e-11)))
		tmp = (x * (a ^ t)) / y;
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -20000000.0], N[Not[LessEqual[t, 3.4e-11]], $MachinePrecision]], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2e7 or 3.3999999999999999e-11 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 88.5%

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

   4. Taylor expanded in b around 0 81.1%

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

      1. exp-prod 81.1%

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

      2. remove-double-neg 81.1%

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

      3. log-rec 81.1%

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

      4. mul-1-neg 81.1%

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

      5. exp-prod 81.1%

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

      6. associate-*r* 81.1%

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

      7. associate-*r* 81.1%

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

      8. exp-prod 81.1%

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

      9. mul-1-neg 81.1%

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

      10. log-rec 81.1%

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

      11. remove-double-neg 81.1%

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

      12. rem-exp-log 81.1%

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

      13. sub-neg 81.1%

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

      14. metadata-eval 81.1%

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

      15. +-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in t around inf 81.1%

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

   if -2e7 < t < 3.3999999999999999e-11

   1. Initial program 98.3%

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

      1. associate-/l* 97.7%

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

      2. associate--l+ 97.7%

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

      3. exp-sum 88.2%

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

      4. associate-/l* 84.5%

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

      5. *-commutative 84.5%

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

      6. exp-to-pow 84.5%

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

      7. exp-diff 84.5%

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

      8. *-commutative 84.5%

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

      9. exp-to-pow 85.3%

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

      10. sub-neg 85.3%

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

      11. metadata-eval 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in t around 0 84.7%

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

   6. Taylor expanded in y around 0 69.9%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -20000000 \lor \neg \left(t \leq 3.4 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -65000000000 \lor \neg \left(t \leq 5.8 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{-b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -65000000000.0) (not (<= t 5.8e+53)))
   (/ (* x (pow a t)) y)
   (/ (* x (exp (- b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -65000000000.0) || !(t <= 5.8e+53)) {
		tmp = (x * pow(a, t)) / 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 <= (-65000000000.0d0)) .or. (.not. (t <= 5.8d+53))) then
        tmp = (x * (a ** t)) / 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 <= -65000000000.0) || !(t <= 5.8e+53)) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = (x * Math.exp(-b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -65000000000.0) or not (t <= 5.8e+53):
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = (x * math.exp(-b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -65000000000.0) || !(t <= 5.8e+53))
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(-b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -65000000000.0) || ~((t <= 5.8e+53)))
		tmp = (x * (a ^ t)) / y;
	else
		tmp = (x * exp(-b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -65000000000.0], N[Not[LessEqual[t, 5.8e+53]], $MachinePrecision]], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[(-b)], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.5e10 or 5.8000000000000004e53 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 90.3%

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

   4. Taylor expanded in b around 0 83.3%

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

      1. exp-prod 83.3%

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

      2. remove-double-neg 83.3%

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

      3. log-rec 83.3%

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

      4. mul-1-neg 83.3%

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

      5. exp-prod 83.3%

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

      6. associate-*r* 83.3%

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

      7. associate-*r* 83.3%

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

      8. exp-prod 83.3%

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

      9. mul-1-neg 83.3%

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

      10. log-rec 83.3%

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

      11. remove-double-neg 83.3%

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

      12. rem-exp-log 83.3%

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

      13. sub-neg 83.3%

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

      14. metadata-eval 83.3%

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

      15. +-commutative 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in t around inf 83.3%

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

   if -6.5e10 < t < 5.8000000000000004e53

   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. Add Preprocessing

   3. Taylor expanded in t around 0 97.8%

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

      1. +-commutative 97.8%

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

      2. mul-1-neg 97.8%

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

      3. unsub-neg 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in b around inf 50.3%

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

      1. neg-mul-1 50.3%

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

   8. Simplified 50.3%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -65000000000 \lor \neg \left(t \leq 5.8 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{-b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-5} \lor \neg \left(b \leq 330\right):\\ \;\;\;\;\frac{x \cdot e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.4e-5) (not (<= b 330.0)))
   (/ (* x (exp (- b))) y)
   (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.4e-5) || !(b <= 330.0)) {
		tmp = (x * exp(-b)) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.4d-5)) .or. (.not. (b <= 330.0d0))) then
        tmp = (x * exp(-b)) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.4e-5) || !(b <= 330.0)) {
		tmp = (x * Math.exp(-b)) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.4e-5) or not (b <= 330.0):
		tmp = (x * math.exp(-b)) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.4e-5) || !(b <= 330.0))
		tmp = Float64(Float64(x * exp(Float64(-b))) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.4e-5) || ~((b <= 330.0)))
		tmp = (x * exp(-b)) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.4e-5], N[Not[LessEqual[b, 330.0]], $MachinePrecision]], N[(N[(x * N[Exp[(-b)], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.4000000000000001e-5 or 330 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 89.8%

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

      1. +-commutative 89.8%

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

      2. mul-1-neg 89.8%

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

      3. unsub-neg 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in b around inf 78.7%

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

      1. neg-mul-1 78.7%

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

   8. Simplified 78.7%

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

   if -2.4000000000000001e-5 < b < 330

   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. Add Preprocessing

   3. Taylor expanded in t around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. mul-1-neg 77.5%

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

      3. unsub-neg 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in b around 0 76.8%

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

      1. associate-/l* 77.6%

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

      2. div-exp 77.6%

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

      3. *-commutative 77.6%

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

      4. exp-to-pow 77.6%

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

      5. rem-exp-log 78.4%

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

      6. associate-/r* 73.1%

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

      7. associate-/l* 73.1%

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

      8. times-frac 76.0%

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

   8. Simplified 76.0%

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

   9. Taylor expanded in y around 0 38.4%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-5} \lor \neg \left(b \leq 330\right):\\ \;\;\;\;\frac{x \cdot e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.7% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e+16)
   (/ (* x (+ 1.0 (* b (+ (* b (+ 0.5 (* b -0.16666666666666666))) -1.0)))) y)
   (* (/ x a) (/ 1.0 y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e+16) {
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	} else {
		tmp = (x / a) * (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.5d+16)) then
        tmp = (x * (1.0d0 + (b * ((b * (0.5d0 + (b * (-0.16666666666666666d0)))) + (-1.0d0))))) / y
    else
        tmp = (x / a) * (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e+16) {
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	} else {
		tmp = (x / a) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.5e+16:
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y
	else:
		tmp = (x / a) * (1.0 / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.5e+16)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))) + -1.0)))) / y);
	else
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.5e+16)
		tmp = (x * (1.0 + (b * ((b * (0.5 + (b * -0.16666666666666666))) + -1.0)))) / y;
	else
		tmp = (x / a) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.5e+16], N[(N[(x * N[(1.0 + N[(b * N[(N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.5e16

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 89.8%

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

      1. +-commutative 89.8%

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

      2. mul-1-neg 89.8%

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

      3. unsub-neg 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in b around inf 77.9%

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

      1. neg-mul-1 77.9%

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

   8. Simplified 77.9%

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

   9. Taylor expanded in b around 0 66.4%

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

   if -2.5e16 < b

   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. Add Preprocessing

   3. Taylor expanded in t around 0 81.6%

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

      1. +-commutative 81.6%

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

      2. mul-1-neg 81.6%

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

      3. unsub-neg 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in b around 0 64.4%

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

      1. associate-/l* 64.0%

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

      2. div-exp 64.0%

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

      3. *-commutative 64.0%

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

      4. exp-to-pow 64.0%

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

      5. rem-exp-log 64.5%

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

      6. associate-/r* 58.4%

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

      7. associate-/l* 58.4%

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

      8. times-frac 62.3%

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

   8. Simplified 62.3%

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

   9. Taylor expanded in y around 0 31.6%

      \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{1}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot \left(0.5 + b \cdot -0.16666666666666666\right) + -1\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 40.0% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot 0.5 + -1\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.6e+15)
   (/ (* x (+ 1.0 (* b (+ (* b 0.5) -1.0)))) y)
   (* (/ x a) (/ 1.0 y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e+15) {
		tmp = (x * (1.0 + (b * ((b * 0.5) + -1.0)))) / y;
	} else {
		tmp = (x / a) * (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.6d+15)) then
        tmp = (x * (1.0d0 + (b * ((b * 0.5d0) + (-1.0d0))))) / y
    else
        tmp = (x / a) * (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e+15) {
		tmp = (x * (1.0 + (b * ((b * 0.5) + -1.0)))) / y;
	} else {
		tmp = (x / a) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.6e+15:
		tmp = (x * (1.0 + (b * ((b * 0.5) + -1.0)))) / y
	else:
		tmp = (x / a) * (1.0 / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.6e+15)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(Float64(b * 0.5) + -1.0)))) / y);
	else
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.6e+15)
		tmp = (x * (1.0 + (b * ((b * 0.5) + -1.0)))) / y;
	else
		tmp = (x / a) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.6e+15], N[(N[(x * N[(1.0 + N[(b * N[(N[(b * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.6e15

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 89.8%

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

      1. +-commutative 89.8%

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

      2. mul-1-neg 89.8%

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

      3. unsub-neg 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in b around inf 77.9%

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

      1. neg-mul-1 77.9%

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

   8. Simplified 77.9%

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

   9. Taylor expanded in b around 0 53.5%

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

   if -3.6e15 < b

   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. Add Preprocessing

   3. Taylor expanded in t around 0 81.6%

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

      1. +-commutative 81.6%

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

      2. mul-1-neg 81.6%

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

      3. unsub-neg 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in b around 0 64.4%

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

      1. associate-/l* 64.0%

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

      2. div-exp 64.0%

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

      3. *-commutative 64.0%

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

      4. exp-to-pow 64.0%

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

      5. rem-exp-log 64.5%

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

      6. associate-/r* 58.4%

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

      7. associate-/l* 58.4%

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

      8. times-frac 62.3%

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

   8. Simplified 62.3%

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

   9. Taylor expanded in y around 0 31.6%

      \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{1}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(b \cdot 0.5 + -1\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.8% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.8 \cdot 10^{+141}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{b} - x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 4.8e+141) (* (/ x a) (/ 1.0 y)) (/ (* b (- (/ x b) x)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.8e+141) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = (b * ((x / b) - x)) / 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 (x <= 4.8d+141) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = (b * ((x / b) - x)) / 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 (x <= 4.8e+141) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = (b * ((x / b) - x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 4.8e+141:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = (b * ((x / b) - x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 4.8e+141)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(Float64(b * Float64(Float64(x / b) - x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 4.8e+141)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = (b * ((x / b) - x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 4.8e+141], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(x / b), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.79999999999999995e141

   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. Add Preprocessing

   3. Taylor expanded in t around 0 83.0%

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

      1. +-commutative 83.0%

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

      2. mul-1-neg 83.0%

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

      3. unsub-neg 83.0%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in b around 0 62.3%

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

      1. associate-/l* 61.9%

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

      2. div-exp 61.9%

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

      3. *-commutative 61.9%

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

      4. exp-to-pow 61.9%

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

      5. rem-exp-log 62.3%

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

      6. associate-/r* 56.4%

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

      7. associate-/l* 56.4%

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

      8. times-frac 60.4%

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

   8. Simplified 60.4%

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

   9. Taylor expanded in y around 0 30.6%

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

   if 4.79999999999999995e141 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 86.7%

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

      1. +-commutative 86.7%

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

      2. mul-1-neg 86.7%

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

      3. unsub-neg 86.7%

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

   5. Simplified 86.7%

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

   6. Taylor expanded in b around inf 49.2%

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

      1. neg-mul-1 49.2%

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

   8. Simplified 49.2%

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

   9. Taylor expanded in b around 0 21.9%

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

       1. *-lft-identity 21.9%

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

       2. associate-*r* 21.9%

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

       3. distribute-rgt-out 21.9%

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

       4. mul-1-neg 21.9%

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

       5. unsub-neg 21.9%

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

   11. Simplified 21.9%

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

   12. Taylor expanded in b around inf 32.2%

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

       1. neg-mul-1 32.2%

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

       2. +-commutative 32.2%

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

       3. unsub-neg 32.2%

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

   14. Simplified 32.2%

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

Alternative 16: 34.6% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{b}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.4e+81) (* x (/ b (- y))) (* (/ x a) (/ 1.0 y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.4e+81) {
		tmp = x * (b / -y);
	} else {
		tmp = (x / a) * (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.4d+81)) then
        tmp = x * (b / -y)
    else
        tmp = (x / a) * (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.4e+81) {
		tmp = x * (b / -y);
	} else {
		tmp = (x / a) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.4e+81:
		tmp = x * (b / -y)
	else:
		tmp = (x / a) * (1.0 / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.4e+81)
		tmp = Float64(x * Float64(b / Float64(-y)));
	else
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.4e+81)
		tmp = x * (b / -y);
	else
		tmp = (x / a) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.4e+81], N[(x * N[(b / (-y)), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.4e81

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 91.3%

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

      1. +-commutative 91.3%

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

      2. mul-1-neg 91.3%

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

      3. unsub-neg 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in b around inf 80.3%

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

      1. neg-mul-1 80.3%

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

   8. Simplified 80.3%

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

   9. Taylor expanded in b around 0 35.6%

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

       1. *-lft-identity 35.6%

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

       2. associate-*r* 35.6%

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

       3. distribute-rgt-out 35.6%

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

       4. mul-1-neg 35.6%

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

       5. unsub-neg 35.6%

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

   11. Simplified 35.6%

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

   12. Taylor expanded in b around inf 35.6%

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

       1. *-commutative 35.6%

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

       2. associate-*r/ 35.6%

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

       3. neg-mul-1 35.6%

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

       4. distribute-lft-neg-in 35.6%

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

       5. associate-/l* 39.8%

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

   14. Simplified 39.8%

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

   if -6.4e81 < b

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 81.8%

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

      1. +-commutative 81.8%

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

      2. mul-1-neg 81.8%

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

      3. unsub-neg 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in b around 0 64.3%

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

      1. associate-/l* 63.4%

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

      2. div-exp 63.4%

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

      3. *-commutative 63.4%

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

      4. exp-to-pow 63.4%

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

      5. rem-exp-log 63.9%

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

      6. associate-/r* 57.8%

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

      7. associate-/l* 57.8%

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

      8. times-frac 62.4%

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

   8. Simplified 62.4%

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

   9. Taylor expanded in y around 0 31.7%

      \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{1}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+81}:\\ \;\;\;\;x \cdot \frac{b}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 34.6% accurate, 28.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \frac{b}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.9e+88) (* x (/ b (- y))) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e+88) {
		tmp = x * (b / -y);
	} else {
		tmp = (x / 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) :: tmp
    if (b <= (-2.9d+88)) then
        tmp = x * (b / -y)
    else
        tmp = (x / 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 tmp;
	if (b <= -2.9e+88) {
		tmp = x * (b / -y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.9e+88:
		tmp = x * (b / -y)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.9e+88)
		tmp = Float64(x * Float64(b / Float64(-y)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.9e+88)
		tmp = x * (b / -y);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.9e+88], N[(x * N[(b / (-y)), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.9e88

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 91.3%

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

      1. +-commutative 91.3%

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

      2. mul-1-neg 91.3%

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

      3. unsub-neg 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in b around inf 80.3%

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

      1. neg-mul-1 80.3%

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

   8. Simplified 80.3%

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

   9. Taylor expanded in b around 0 35.6%

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

       1. *-lft-identity 35.6%

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

       2. associate-*r* 35.6%

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

       3. distribute-rgt-out 35.6%

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

       4. mul-1-neg 35.6%

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

       5. unsub-neg 35.6%

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

   11. Simplified 35.6%

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

   12. Taylor expanded in b around inf 35.6%

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

       1. *-commutative 35.6%

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

       2. associate-*r/ 35.6%

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

       3. neg-mul-1 35.6%

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

       4. distribute-lft-neg-in 35.6%

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

       5. associate-/l* 39.8%

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

   14. Simplified 39.8%

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

   if -2.9e88 < b

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 75.8%

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

   4. Taylor expanded in b around 0 60.1%

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

      1. exp-prod 60.1%

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

      2. remove-double-neg 60.1%

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

      3. log-rec 60.1%

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

      4. mul-1-neg 60.1%

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

      5. exp-prod 60.1%

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

      6. associate-*r* 60.1%

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

      7. associate-*r* 60.1%

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

      8. exp-prod 60.1%

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

      9. mul-1-neg 60.1%

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

      10. log-rec 60.1%

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

      11. remove-double-neg 60.1%

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

      12. rem-exp-log 60.5%

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

      13. sub-neg 60.5%

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

      14. metadata-eval 60.5%

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

      15. +-commutative 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in t around 0 31.7%

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

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \frac{b}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.1% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{+189}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 5.5e+189) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 5.5e+189) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 5.5d+189) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 5.5e+189) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 5.5e+189:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 5.5e+189)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 5.5e+189)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 5.5e+189], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 5.5e189

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 79.9%

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

   4. Taylor expanded in b around 0 58.5%

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

      1. exp-prod 58.5%

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

      2. remove-double-neg 58.5%

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

      3. log-rec 58.5%

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

      4. mul-1-neg 58.5%

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

      5. exp-prod 58.5%

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

      6. associate-*r* 58.5%

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

      7. associate-*r* 58.5%

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

      8. exp-prod 58.5%

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

      9. mul-1-neg 58.5%

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

      10. log-rec 58.5%

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

      11. remove-double-neg 58.5%

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

      12. rem-exp-log 58.8%

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

      13. sub-neg 58.8%

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

      14. metadata-eval 58.8%

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

      15. +-commutative 58.8%

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

   6. Simplified 58.8%

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

   7. Taylor expanded in t around 0 32.0%

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

   if 5.5e189 < a

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in b around 0 44.0%

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

      1. associate-/l* 46.1%

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

      2. div-exp 46.1%

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

      3. *-commutative 46.1%

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

      4. exp-to-pow 46.1%

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

      5. rem-exp-log 46.4%

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

      6. associate-/r* 31.4%

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

      7. associate-/l* 31.4%

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

      8. times-frac 41.5%

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

   8. Simplified 41.5%

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

   9. Taylor expanded in y around 0 31.8%

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

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5.5 \cdot 10^{+189}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.2% 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 99.1%

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

3. Taylor expanded in t around 0 83.5%

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

   1. +-commutative 83.5%

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

   2. mul-1-neg 83.5%

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

   3. unsub-neg 83.5%

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

5. Simplified 83.5%

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

6. Taylor expanded in b around 0 61.5%

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

   1. associate-/l* 61.1%

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

   2. div-exp 61.1%

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

   3. *-commutative 61.1%

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

   4. exp-to-pow 61.1%

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

   5. rem-exp-log 61.6%

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

   6. associate-/r* 54.9%

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

   7. associate-/l* 54.9%

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

   8. times-frac 59.5%

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

8. Simplified 59.5%

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

9. Taylor expanded in y around 0 29.8%

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

10. Final simplification 29.8%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Alternative 20: 16.2% 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 99.1%

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

3. Taylor expanded in t around 0 83.5%

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

   1. +-commutative 83.5%

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

   2. mul-1-neg 83.5%

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

   3. unsub-neg 83.5%

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

5. Simplified 83.5%

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

6. Taylor expanded in b around inf 46.5%

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

   1. neg-mul-1 46.5%

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

8. Simplified 46.5%

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

9. Taylor expanded in b around 0 15.8%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
10. Add Preprocessing

Developer Target 1: 72.4% 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 2024141 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8845848504127471/10000000000000000) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 8520312288374073/10000000000) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))