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

Percentage Accurate: 98.5% → 98.5%

Time: 30.6s

Alternatives: 24

Speedup: 1.0×

• 46.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t + (-1.0d0)) * log(a))) - b))) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

3. Final simplification 98.8%

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

Alternative 2: 73.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-308}:\\ \;\;\;\;\frac{x}{a \cdot \frac{y}{{z}^{y}}}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{x \cdot e^{\left(-\log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow a t) a)) y)))
   (if (<= t -1.9e+86)
     t_1
     (if (<= t -8.2e-308)
       (/ x (* a (/ y (pow z y))))
       (if (<= t 8.2e-144)
         (/ (/ x (* y (exp b))) a)
         (if (<= t 2.7e-112)
           (* (/ x a) (/ (pow z y) y))
           (if (<= t 1.5e+42) (/ (* x (exp (- (- (log a)) b))) y) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(a, t) / a)) / y;
	double tmp;
	if (t <= -1.9e+86) {
		tmp = t_1;
	} else if (t <= -8.2e-308) {
		tmp = x / (a * (y / pow(z, y)));
	} else if (t <= 8.2e-144) {
		tmp = (x / (y * exp(b))) / a;
	} else if (t <= 2.7e-112) {
		tmp = (x / a) * (pow(z, y) / y);
	} else if (t <= 1.5e+42) {
		tmp = (x * exp((-log(a) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((a ** t) / a)) / y
    if (t <= (-1.9d+86)) then
        tmp = t_1
    else if (t <= (-8.2d-308)) then
        tmp = x / (a * (y / (z ** y)))
    else if (t <= 8.2d-144) then
        tmp = (x / (y * exp(b))) / a
    else if (t <= 2.7d-112) then
        tmp = (x / a) * ((z ** y) / y)
    else if (t <= 1.5d+42) then
        tmp = (x * exp((-log(a) - b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (Math.pow(a, t) / a)) / y;
	double tmp;
	if (t <= -1.9e+86) {
		tmp = t_1;
	} else if (t <= -8.2e-308) {
		tmp = x / (a * (y / Math.pow(z, y)));
	} else if (t <= 8.2e-144) {
		tmp = (x / (y * Math.exp(b))) / a;
	} else if (t <= 2.7e-112) {
		tmp = (x / a) * (Math.pow(z, y) / y);
	} else if (t <= 1.5e+42) {
		tmp = (x * Math.exp((-Math.log(a) - b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(a, t) / a)) / y
	tmp = 0
	if t <= -1.9e+86:
		tmp = t_1
	elif t <= -8.2e-308:
		tmp = x / (a * (y / math.pow(z, y)))
	elif t <= 8.2e-144:
		tmp = (x / (y * math.exp(b))) / a
	elif t <= 2.7e-112:
		tmp = (x / a) * (math.pow(z, y) / y)
	elif t <= 1.5e+42:
		tmp = (x * math.exp((-math.log(a) - b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((a ^ t) / a)) / y)
	tmp = 0.0
	if (t <= -1.9e+86)
		tmp = t_1;
	elseif (t <= -8.2e-308)
		tmp = Float64(x / Float64(a * Float64(y / (z ^ y))));
	elseif (t <= 8.2e-144)
		tmp = Float64(Float64(x / Float64(y * exp(b))) / a);
	elseif (t <= 2.7e-112)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	elseif (t <= 1.5e+42)
		tmp = Float64(Float64(x * exp(Float64(Float64(-log(a)) - b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((a ^ t) / a)) / y;
	tmp = 0.0;
	if (t <= -1.9e+86)
		tmp = t_1;
	elseif (t <= -8.2e-308)
		tmp = x / (a * (y / (z ^ y)));
	elseif (t <= 8.2e-144)
		tmp = (x / (y * exp(b))) / a;
	elseif (t <= 2.7e-112)
		tmp = (x / a) * ((z ^ y) / y);
	elseif (t <= 1.5e+42)
		tmp = (x * exp((-log(a) - b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -1.9e+86], t$95$1, If[LessEqual[t, -8.2e-308], N[(x / N[(a * N[(y / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e-144], N[(N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 2.7e-112], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+42], N[(N[(x * N[Exp[N[((-N[Log[a], $MachinePrecision]) - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.89999999999999989e86 or 1.50000000000000014e42 < 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 93.0%

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

   4. Taylor expanded in b around 0 89.1%

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

      1. *-commutative 89.1%

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

      2. exp-to-pow 89.1%

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

      3. sub-neg 89.1%

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

      4. metadata-eval 89.1%

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

      5. +-commutative 89.1%

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

   6. Simplified 89.1%

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

      1. +-commutative 89.1%

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

      2. unpow-prod-up 89.1%

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

      3. inv-pow 89.1%

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

   8. Applied egg-rr 89.1%

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

      1. associate-*r/ 89.1%

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

      2. *-rgt-identity 89.1%

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

   10. Simplified 89.1%

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

   if -1.89999999999999989e86 < t < -8.19999999999999965e-308

   1. Initial program 97.1%

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

      1. associate-*l/ 94.0%

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

      2. *-commutative 94.0%

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

      3. +-commutative 94.0%

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

      4. associate--l+ 94.0%

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

      5. exp-sum 84.5%

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

      6. *-commutative 84.5%

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

      7. exp-to-pow 85.0%

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

      8. sub-neg 85.0%

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

      9. metadata-eval 85.0%

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

      10. exp-diff 78.3%

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

      11. *-commutative 78.3%

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

      12. exp-to-pow 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in t around 0 80.3%

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

      1. times-frac 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in b around 0 61.1%

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

      1. times-frac 63.6%

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

   10. Simplified 63.6%

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

       1. *-commutative 63.6%

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

       2. clear-num 63.6%

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

       3. frac-times 74.6%

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

       4. *-un-lft-identity 74.6%

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

   12. Applied egg-rr 74.6%

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

   if -8.19999999999999965e-308 < t < 8.2e-144

   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/ 88.4%

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

      2. *-commutative 88.4%

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

      3. +-commutative 88.4%

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

      4. associate--l+ 88.4%

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

      5. exp-sum 88.4%

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

      6. *-commutative 88.4%

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

      7. exp-to-pow 89.4%

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

      8. sub-neg 89.4%

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

      9. metadata-eval 89.4%

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

      10. exp-diff 81.5%

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

      11. *-commutative 81.5%

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

      12. exp-to-pow 81.5%

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

   3. Simplified 81.5%

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

   5. Taylor expanded in t around 0 87.4%

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

      1. times-frac 78.9%

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

   7. Simplified 78.9%

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

      1. associate-*l/ 92.0%

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

   9. Applied egg-rr 92.0%

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

   10. Taylor expanded in y around 0 80.3%

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

   if 8.2e-144 < t < 2.7000000000000001e-112

   1. Initial program 99.2%

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

      1. associate-*l/ 90.1%

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

      2. *-commutative 90.1%

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

      3. +-commutative 90.1%

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

      4. associate--l+ 90.1%

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

      5. exp-sum 90.1%

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

      6. *-commutative 90.1%

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

      7. exp-to-pow 90.8%

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

      8. sub-neg 90.8%

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

      9. metadata-eval 90.8%

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

      10. exp-diff 81.7%

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

      11. *-commutative 81.7%

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

      12. exp-to-pow 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in t around 0 90.9%

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

      1. times-frac 90.9%

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

   7. Simplified 90.9%

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

   8. Taylor expanded in b around 0 100.0%

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

      1. times-frac 100.0%

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

   10. Simplified 100.0%

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

   if 2.7000000000000001e-112 < t < 1.50000000000000014e42

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 84.3%

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

   4. Taylor expanded in t around 0 86.1%

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

      1. *-commutative 86.1%

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

      2. mul-1-neg 86.1%

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

   6. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{e^{\left(-\log a\right) - b} \cdot x}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+86}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-308}:\\ \;\;\;\;\frac{x}{a \cdot \frac{y}{{z}^{y}}}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-112}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+42}:\\ \;\;\;\;\frac{x \cdot e^{\left(-\log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{z}^{y}}{y \cdot e^{b}} \cdot \frac{x}{a}\\ t_2 := \frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{if}\;t \leq -4.75 \cdot 10^{+95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{a \cdot \frac{y}{{z}^{y}}}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow z y) (* y (exp b))) (/ x a)))
        (t_2 (/ (* x (/ (pow a t) a)) y)))
   (if (<= t -4.75e+95)
     t_2
     (if (<= t -6.2e-106)
       t_1
       (if (<= t -6e-289)
         (/ x (* a (/ y (pow z y))))
         (if (<= t 8.4e+52) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(z, y) / (y * exp(b))) * (x / a);
	double t_2 = (x * (pow(a, t) / a)) / y;
	double tmp;
	if (t <= -4.75e+95) {
		tmp = t_2;
	} else if (t <= -6.2e-106) {
		tmp = t_1;
	} else if (t <= -6e-289) {
		tmp = x / (a * (y / pow(z, y)));
	} else if (t <= 8.4e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((z ** y) / (y * exp(b))) * (x / a)
    t_2 = (x * ((a ** t) / a)) / y
    if (t <= (-4.75d+95)) then
        tmp = t_2
    else if (t <= (-6.2d-106)) then
        tmp = t_1
    else if (t <= (-6d-289)) then
        tmp = x / (a * (y / (z ** y)))
    else if (t <= 8.4d+52) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (Math.pow(z, y) / (y * Math.exp(b))) * (x / a);
	double t_2 = (x * (Math.pow(a, t) / a)) / y;
	double tmp;
	if (t <= -4.75e+95) {
		tmp = t_2;
	} else if (t <= -6.2e-106) {
		tmp = t_1;
	} else if (t <= -6e-289) {
		tmp = x / (a * (y / Math.pow(z, y)));
	} else if (t <= 8.4e+52) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(z, y) / (y * math.exp(b))) * (x / a)
	t_2 = (x * (math.pow(a, t) / a)) / y
	tmp = 0
	if t <= -4.75e+95:
		tmp = t_2
	elif t <= -6.2e-106:
		tmp = t_1
	elif t <= -6e-289:
		tmp = x / (a * (y / math.pow(z, y)))
	elif t <= 8.4e+52:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((z ^ y) / Float64(y * exp(b))) * Float64(x / a))
	t_2 = Float64(Float64(x * Float64((a ^ t) / a)) / y)
	tmp = 0.0
	if (t <= -4.75e+95)
		tmp = t_2;
	elseif (t <= -6.2e-106)
		tmp = t_1;
	elseif (t <= -6e-289)
		tmp = Float64(x / Float64(a * Float64(y / (z ^ y))));
	elseif (t <= 8.4e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z ^ y) / (y * exp(b))) * (x / a);
	t_2 = (x * ((a ^ t) / a)) / y;
	tmp = 0.0;
	if (t <= -4.75e+95)
		tmp = t_2;
	elseif (t <= -6.2e-106)
		tmp = t_1;
	elseif (t <= -6e-289)
		tmp = x / (a * (y / (z ^ y)));
	elseif (t <= 8.4e+52)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[Power[z, y], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -4.75e+95], t$95$2, If[LessEqual[t, -6.2e-106], t$95$1, If[LessEqual[t, -6e-289], N[(x / N[(a * N[(y / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.4e+52], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.7500000000000002e95 or 8.3999999999999999e52 < 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 92.9%

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

   4. Taylor expanded in b around 0 88.8%

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

      1. *-commutative 88.8%

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

      2. exp-to-pow 88.8%

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

      3. sub-neg 88.8%

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

      4. metadata-eval 88.8%

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

      5. +-commutative 88.8%

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

   6. Simplified 88.8%

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

      1. +-commutative 88.8%

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

      2. unpow-prod-up 88.8%

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

      3. inv-pow 88.8%

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

   8. Applied egg-rr 88.8%

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

      1. associate-*r/ 88.8%

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

      2. *-rgt-identity 88.8%

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

   10. Simplified 88.8%

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

   if -4.7500000000000002e95 < t < -6.19999999999999971e-106 or -5.9999999999999996e-289 < t < 8.3999999999999999e52

   1. Initial program 99.2%

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

      1. associate-*l/ 90.3%

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

      2. *-commutative 90.3%

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

      3. +-commutative 90.3%

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

      4. associate--l+ 90.3%

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

      5. exp-sum 79.6%

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

      6. *-commutative 79.6%

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

      7. exp-to-pow 80.2%

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

      8. sub-neg 80.2%

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

      9. metadata-eval 80.2%

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

      10. exp-diff 74.1%

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

      11. *-commutative 74.1%

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

      12. exp-to-pow 74.1%

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

   3. Simplified 74.1%

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

   5. Taylor expanded in t around 0 83.3%

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

      1. times-frac 82.3%

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

   7. Simplified 82.3%

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

   if -6.19999999999999971e-106 < t < -5.9999999999999996e-289

   1. Initial program 92.8%

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

      1. associate-*l/ 95.3%

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

      2. *-commutative 95.3%

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

      3. +-commutative 95.3%

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

      4. associate--l+ 95.3%

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

      5. exp-sum 95.4%

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

      6. *-commutative 95.4%

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

      7. exp-to-pow 96.3%

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

      8. sub-neg 96.3%

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

      9. metadata-eval 96.3%

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

      10. exp-diff 82.1%

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

      11. *-commutative 82.1%

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

      12. exp-to-pow 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in t around 0 82.1%

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

      1. times-frac 61.0%

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

   7. Simplified 61.0%

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

   8. Taylor expanded in b around 0 76.2%

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

      1. times-frac 71.9%

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

   10. Simplified 71.9%

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

       1. *-commutative 71.9%

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

       2. clear-num 71.9%

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

       3. frac-times 90.5%

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

       4. *-un-lft-identity 90.5%

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

   12. Applied egg-rr 90.5%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.75 \cdot 10^{+95}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{{z}^{y}}{y \cdot e^{b}} \cdot \frac{x}{a}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{a \cdot \frac{y}{{z}^{y}}}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+52}:\\ \;\;\;\;\frac{{z}^{y}}{y \cdot e^{b}} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+179} \lor \neg \left(y \leq 2.15 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x}{a \cdot \frac{y}{{z}^{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.45e+179) (not (<= y 2.15e+18)))
   (/ x (* a (/ y (pow z 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 <= -2.45e+179) || !(y <= 2.15e+18)) {
		tmp = x / (a * (y / pow(z, 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 <= (-2.45d+179)) .or. (.not. (y <= 2.15d+18))) then
        tmp = x / (a * (y / (z ** 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 <= -2.45e+179) || !(y <= 2.15e+18)) {
		tmp = x / (a * (y / Math.pow(z, 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 <= -2.45e+179) or not (y <= 2.15e+18):
		tmp = x / (a * (y / math.pow(z, 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 <= -2.45e+179) || !(y <= 2.15e+18))
		tmp = Float64(x / Float64(a * Float64(y / (z ^ 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 <= -2.45e+179) || ~((y <= 2.15e+18)))
		tmp = x / (a * (y / (z ^ 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, -2.45e+179], N[Not[LessEqual[y, 2.15e+18]], $MachinePrecision]], N[(x / N[(a * N[(y / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 < -2.4499999999999999e179 or 2.15e18 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 89.5%

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

      2. *-commutative 89.5%

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

      3. +-commutative 89.5%

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

      4. associate--l+ 89.5%

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

      5. exp-sum 69.5%

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

      6. *-commutative 69.5%

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

      7. exp-to-pow 69.5%

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

      8. sub-neg 69.5%

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

      9. metadata-eval 69.5%

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

      10. exp-diff 51.6%

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

      11. *-commutative 51.6%

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

      12. exp-to-pow 51.6%

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

   3. Simplified 51.6%

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

   5. Taylor expanded in t around 0 67.4%

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

      1. times-frac 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in b around 0 69.6%

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

      1. times-frac 79.1%

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

   10. Simplified 79.1%

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

       1. *-commutative 79.1%

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

       2. clear-num 79.1%

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

       3. frac-times 87.6%

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

       4. *-un-lft-identity 87.6%

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

   12. Applied egg-rr 87.6%

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

   if -2.4499999999999999e179 < y < 2.15e18

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 92.5%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+179} \lor \neg \left(y \leq 2.15 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x}{a \cdot \frac{y}{{z}^{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+94} \lor \neg \left(t \leq 1.05 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{a \cdot e^{b}} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1e+94) (not (<= t 1.05e+59)))
   (/ (* x (/ (pow a t) a)) y)
   (* (/ (pow z y) (* a (exp b))) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1e+94) || !(t <= 1.05e+59)) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else {
		tmp = (pow(z, y) / (a * exp(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 ((t <= (-1d+94)) .or. (.not. (t <= 1.05d+59))) then
        tmp = (x * ((a ** t) / a)) / y
    else
        tmp = ((z ** y) / (a * exp(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 ((t <= -1e+94) || !(t <= 1.05e+59)) {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	} else {
		tmp = (Math.pow(z, y) / (a * Math.exp(b))) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1e+94) or not (t <= 1.05e+59):
		tmp = (x * (math.pow(a, t) / a)) / y
	else:
		tmp = (math.pow(z, y) / (a * math.exp(b))) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1e+94) || !(t <= 1.05e+59))
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	else
		tmp = Float64(Float64((z ^ y) / Float64(a * exp(b))) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1e+94) || ~((t <= 1.05e+59)))
		tmp = (x * ((a ^ t) / a)) / y;
	else
		tmp = ((z ^ y) / (a * exp(b))) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1e+94], N[Not[LessEqual[t, 1.05e+59]], $MachinePrecision]], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Power[z, y], $MachinePrecision] / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1e94 or 1.04999999999999992e59 < 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 92.9%

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

   4. Taylor expanded in b around 0 88.8%

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

      1. *-commutative 88.8%

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

      2. exp-to-pow 88.8%

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

      3. sub-neg 88.8%

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

      4. metadata-eval 88.8%

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

      5. +-commutative 88.8%

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

   6. Simplified 88.8%

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

      1. +-commutative 88.8%

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

      2. unpow-prod-up 88.8%

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

      3. inv-pow 88.8%

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

   8. Applied egg-rr 88.8%

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

      1. associate-*r/ 88.8%

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

      2. *-rgt-identity 88.8%

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

   10. Simplified 88.8%

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

   if -1e94 < t < 1.04999999999999992e59

   1. Initial program 98.1%

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

      1. associate-*l/ 91.2%

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

      2. *-commutative 91.2%

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

      3. +-commutative 91.2%

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

      4. associate--l+ 91.2%

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

      5. exp-sum 82.4%

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

      6. *-commutative 82.4%

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

      7. exp-to-pow 83.0%

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

      8. sub-neg 83.0%

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

      9. metadata-eval 83.0%

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

      10. exp-diff 75.5%

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

      11. *-commutative 75.5%

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

      12. exp-to-pow 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in t around 0 81.2%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+94} \lor \neg \left(t \leq 1.05 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{a \cdot e^{b}} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+95} \lor \neg \left(t \leq 3.4 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y \cdot e^{b}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9.8e+95) (not (<= t 3.4e+47)))
   (/ (* x (/ (pow a t) a)) y)
   (/ x (/ a (/ (pow z y) (* y (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9.8e+95) || !(t <= 3.4e+47)) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else {
		tmp = x / (a / (pow(z, y) / (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 <= (-9.8d+95)) .or. (.not. (t <= 3.4d+47))) then
        tmp = (x * ((a ** t) / a)) / y
    else
        tmp = x / (a / ((z ** y) / (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 <= -9.8e+95) || !(t <= 3.4e+47)) {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	} else {
		tmp = x / (a / (Math.pow(z, y) / (y * Math.exp(b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9.8e+95) or not (t <= 3.4e+47):
		tmp = (x * (math.pow(a, t) / a)) / y
	else:
		tmp = x / (a / (math.pow(z, y) / (y * math.exp(b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9.8e+95) || !(t <= 3.4e+47))
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	else
		tmp = Float64(x / Float64(a / Float64((z ^ y) / Float64(y * exp(b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -9.8e+95) || ~((t <= 3.4e+47)))
		tmp = (x * ((a ^ t) / a)) / y;
	else
		tmp = x / (a / ((z ^ y) / (y * exp(b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9.8e+95], N[Not[LessEqual[t, 3.4e+47]], $MachinePrecision]], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.7999999999999998e95 or 3.3999999999999998e47 < 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 92.9%

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

   4. Taylor expanded in b around 0 88.8%

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

      1. *-commutative 88.8%

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

      2. exp-to-pow 88.8%

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

      3. sub-neg 88.8%

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

      4. metadata-eval 88.8%

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

      5. +-commutative 88.8%

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

   6. Simplified 88.8%

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

      1. +-commutative 88.8%

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

      2. unpow-prod-up 88.8%

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

      3. inv-pow 88.8%

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

   8. Applied egg-rr 88.8%

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

      1. associate-*r/ 88.8%

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

      2. *-rgt-identity 88.8%

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

   10. Simplified 88.8%

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

   if -9.7999999999999998e95 < t < 3.3999999999999998e47

   1. Initial program 98.1%

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

      1. associate-/l* 97.6%

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

      2. associate--l+ 97.6%

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

      3. exp-sum 83.7%

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

      4. associate-/r* 83.7%

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

      5. *-commutative 83.7%

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

      6. exp-to-pow 83.7%

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

      7. exp-diff 79.3%

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

      8. *-commutative 79.3%

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

      9. exp-to-pow 79.9%

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

      10. sub-neg 79.9%

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

      11. metadata-eval 79.9%

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

   3. Simplified 79.9%

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

   5. Taylor expanded in t around 0 83.1%

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

      1. associate-/l* 86.9%

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

   7. Simplified 86.9%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+95} \lor \neg \left(t \leq 3.4 \cdot 10^{+47}\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y \cdot e^{b}}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+98} \lor \neg \left(t \leq 9 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y \cdot e^{b}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.12e+98) (not (<= t 9e+43)))
   (/ (* x (/ (pow a t) a)) y)
   (/ (* x (/ (pow z y) (* y (exp b)))) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.12e+98) || !(t <= 9e+43)) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else {
		tmp = (x * (pow(z, y) / (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 <= (-1.12d+98)) .or. (.not. (t <= 9d+43))) then
        tmp = (x * ((a ** t) / a)) / y
    else
        tmp = (x * ((z ** y) / (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 <= -1.12e+98) || !(t <= 9e+43)) {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	} else {
		tmp = (x * (Math.pow(z, y) / (y * Math.exp(b)))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.12e+98) or not (t <= 9e+43):
		tmp = (x * (math.pow(a, t) / a)) / y
	else:
		tmp = (x * (math.pow(z, y) / (y * math.exp(b)))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.12e+98) || !(t <= 9e+43))
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	else
		tmp = Float64(Float64(x * Float64((z ^ y) / 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 <= -1.12e+98) || ~((t <= 9e+43)))
		tmp = (x * ((a ^ t) / a)) / y;
	else
		tmp = (x * ((z ^ y) / (y * exp(b)))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.12e+98], N[Not[LessEqual[t, 9e+43]], $MachinePrecision]], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.12e98 or 9e43 < 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 92.9%

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

   4. Taylor expanded in b around 0 88.8%

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

      1. *-commutative 88.8%

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

      2. exp-to-pow 88.8%

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

      3. sub-neg 88.8%

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

      4. metadata-eval 88.8%

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

      5. +-commutative 88.8%

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

   6. Simplified 88.8%

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

      1. +-commutative 88.8%

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

      2. unpow-prod-up 88.8%

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

      3. inv-pow 88.8%

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

   8. Applied egg-rr 88.8%

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

      1. associate-*r/ 88.8%

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

      2. *-rgt-identity 88.8%

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

   10. Simplified 88.8%

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

   if -1.12e98 < t < 9e43

   1. Initial program 98.1%

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

      1. associate-*l/ 91.2%

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

      2. *-commutative 91.2%

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

      3. +-commutative 91.2%

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

      4. associate--l+ 91.2%

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

      5. exp-sum 82.4%

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

      6. *-commutative 82.4%

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

      7. exp-to-pow 83.0%

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

      8. sub-neg 83.0%

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

      9. metadata-eval 83.0%

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

      10. exp-diff 75.5%

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

      11. *-commutative 75.5%

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

      12. exp-to-pow 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in t around 0 83.1%

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

      1. times-frac 78.6%

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

   7. Simplified 78.6%

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

      1. associate-*l/ 87.5%

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

   9. Applied egg-rr 87.5%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{+98} \lor \neg \left(t \leq 9 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{y \cdot e^{b}}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+68} \lor \neg \left(y \leq 195000000\right):\\ \;\;\;\;\frac{x}{a \cdot \frac{y}{{z}^{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.6e+68) (not (<= y 195000000.0)))
   (/ x (* a (/ y (pow z y))))
   (/ (/ x (* y (exp b))) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4.6e+68) || !(y <= 195000000.0)) {
		tmp = x / (a * (y / pow(z, 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 ((y <= (-4.6d+68)) .or. (.not. (y <= 195000000.0d0))) then
        tmp = x / (a * (y / (z ** 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 ((y <= -4.6e+68) || !(y <= 195000000.0)) {
		tmp = x / (a * (y / Math.pow(z, y)));
	} else {
		tmp = (x / (y * Math.exp(b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4.6e+68) or not (y <= 195000000.0):
		tmp = x / (a * (y / math.pow(z, y)))
	else:
		tmp = (x / (y * math.exp(b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4.6e+68) || !(y <= 195000000.0))
		tmp = Float64(x / Float64(a * Float64(y / (z ^ 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 ((y <= -4.6e+68) || ~((y <= 195000000.0)))
		tmp = x / (a * (y / (z ^ y)));
	else
		tmp = (x / (y * exp(b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4.6e+68], N[Not[LessEqual[y, 195000000.0]], $MachinePrecision]], N[(x / N[(a * N[(y / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6e68 or 1.95e8 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 88.0%

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

      2. *-commutative 88.0%

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

      3. +-commutative 88.0%

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

      4. associate--l+ 88.0%

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

      5. exp-sum 65.8%

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

      6. *-commutative 65.8%

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

      7. exp-to-pow 65.8%

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

      8. sub-neg 65.8%

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

      9. metadata-eval 65.8%

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

      10. exp-diff 49.6%

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

      11. *-commutative 49.6%

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

      12. exp-to-pow 49.6%

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

   3. Simplified 49.6%

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

   5. Taylor expanded in t around 0 64.2%

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

      1. times-frac 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in b around 0 66.9%

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

      1. times-frac 74.6%

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

   10. Simplified 74.6%

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

       1. *-commutative 74.6%

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

       2. clear-num 74.6%

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

       3. frac-times 82.3%

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

       4. *-un-lft-identity 82.3%

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

   12. Applied egg-rr 82.3%

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

   if -4.6e68 < y < 1.95e8

   1. Initial program 97.8%

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

      1. associate-*l/ 92.1%

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

      2. *-commutative 92.1%

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

      3. +-commutative 92.1%

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

      4. associate--l+ 92.1%

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

      5. exp-sum 81.3%

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

      6. *-commutative 81.3%

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

      7. exp-to-pow 82.0%

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

      8. sub-neg 82.0%

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

      9. metadata-eval 82.0%

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

      10. exp-diff 81.3%

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

      11. *-commutative 81.3%

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

      12. exp-to-pow 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in t around 0 71.3%

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

      1. times-frac 68.2%

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

   7. Simplified 68.2%

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

      1. associate-*l/ 74.0%

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

   9. Applied egg-rr 74.0%

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

   10. Taylor expanded in y around 0 74.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+68} \lor \neg \left(y \leq 195000000\right):\\ \;\;\;\;\frac{x}{a \cdot \frac{y}{{z}^{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+25} \lor \neg \left(b \leq 1.65 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.35e+25) (not (<= b 1.65e-19)))
   (/ (/ x (exp b)) y)
   (/ (* x (/ (pow a t) a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.35e+25) || !(b <= 1.65e-19)) {
		tmp = (x / exp(b)) / y;
	} else {
		tmp = (x * (pow(a, t) / 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 <= (-1.35d+25)) .or. (.not. (b <= 1.65d-19))) then
        tmp = (x / exp(b)) / y
    else
        tmp = (x * ((a ** t) / 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 <= -1.35e+25) || !(b <= 1.65e-19)) {
		tmp = (x / Math.exp(b)) / y;
	} else {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.35e+25) or not (b <= 1.65e-19):
		tmp = (x / math.exp(b)) / y
	else:
		tmp = (x * (math.pow(a, t) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.35e+25) || !(b <= 1.65e-19))
		tmp = Float64(Float64(x / exp(b)) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.35e+25) || ~((b <= 1.65e-19)))
		tmp = (x / exp(b)) / y;
	else
		tmp = (x * ((a ^ t) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.35e+25], N[Not[LessEqual[b, 1.65e-19]], $MachinePrecision]], N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.35e25 or 1.6499999999999999e-19 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 90.5%

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

   4. Taylor expanded in b around inf 85.7%

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

      1. neg-mul-1 85.7%

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

   6. Simplified 85.7%

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

      1. exp-neg 85.7%

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

      2. un-div-inv 85.7%

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

   8. Applied egg-rr 85.7%

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

   if -1.35e25 < b < 1.6499999999999999e-19

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 72.4%

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

   4. Taylor expanded in b around 0 71.6%

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

      1. *-commutative 71.6%

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

      2. exp-to-pow 72.3%

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

      3. sub-neg 72.3%

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

      4. metadata-eval 72.3%

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

      5. +-commutative 72.3%

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

   6. Simplified 72.3%

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

      1. +-commutative 72.3%

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

      2. unpow-prod-up 72.3%

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

      3. inv-pow 72.3%

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

   8. Applied egg-rr 72.3%

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

      1. associate-*r/ 72.3%

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

      2. *-rgt-identity 72.3%

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

   10. Simplified 72.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+25} \lor \neg \left(b \leq 1.65 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.0053:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \mathbf{elif}\;b \leq 9.8:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{a}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.0053)
   (/ (/ x (* y (exp b))) a)
   (if (<= b 9.8) (* (/ x a) (/ (pow z y) y)) (* x (/ (/ a (exp b)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.0053) {
		tmp = (x / (y * exp(b))) / a;
	} else if (b <= 9.8) {
		tmp = (x / a) * (pow(z, y) / y);
	} else {
		tmp = x * ((a / 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 (b <= (-0.0053d0)) then
        tmp = (x / (y * exp(b))) / a
    else if (b <= 9.8d0) then
        tmp = (x / a) * ((z ** y) / y)
    else
        tmp = x * ((a / 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 (b <= -0.0053) {
		tmp = (x / (y * Math.exp(b))) / a;
	} else if (b <= 9.8) {
		tmp = (x / a) * (Math.pow(z, y) / y);
	} else {
		tmp = x * ((a / Math.exp(b)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.0053:
		tmp = (x / (y * math.exp(b))) / a
	elif b <= 9.8:
		tmp = (x / a) * (math.pow(z, y) / y)
	else:
		tmp = x * ((a / math.exp(b)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.0053)
		tmp = Float64(Float64(x / Float64(y * exp(b))) / a);
	elseif (b <= 9.8)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / y));
	else
		tmp = Float64(x * Float64(Float64(a / exp(b)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.0053)
		tmp = (x / (y * exp(b))) / a;
	elseif (b <= 9.8)
		tmp = (x / a) * ((z ^ y) / y);
	else
		tmp = x * ((a / exp(b)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.0053], N[(N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 9.8], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(a / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.00530000000000000002

   1. Initial program 98.7%

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

      1. associate-*l/ 85.9%

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

      2. *-commutative 85.9%

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

      3. +-commutative 85.9%

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

      4. associate--l+ 85.9%

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

      5. exp-sum 69.3%

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

      6. *-commutative 69.3%

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

      7. exp-to-pow 69.4%

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

      8. sub-neg 69.4%

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

      9. metadata-eval 69.4%

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

      10. exp-diff 55.6%

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

      11. *-commutative 55.6%

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

      12. exp-to-pow 55.6%

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

   3. Simplified 55.6%

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

   5. Taylor expanded in t around 0 75.1%

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

      1. times-frac 65.5%

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

   7. Simplified 65.5%

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

      1. associate-*l/ 75.1%

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

   9. Applied egg-rr 75.1%

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

   10. Taylor expanded in y around 0 83.6%

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

   if -0.00530000000000000002 < b < 9.8000000000000007

   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/ 92.2%

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

      2. *-commutative 92.2%

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

      3. +-commutative 92.2%

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

      4. associate--l+ 92.2%

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

      5. exp-sum 74.7%

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

      6. *-commutative 74.7%

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

      7. exp-to-pow 75.4%

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

      8. sub-neg 75.4%

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

      9. metadata-eval 75.4%

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

      10. exp-diff 75.4%

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

      11. *-commutative 75.4%

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

      12. exp-to-pow 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in t around 0 61.2%

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

      1. times-frac 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in b around 0 61.2%

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

      1. times-frac 67.2%

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

   10. Simplified 67.2%

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

   if 9.8000000000000007 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.8%

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

   4. Taylor expanded in t around 0 84.7%

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

      1. *-commutative 84.7%

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

      2. mul-1-neg 84.7%

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

   6. Simplified 84.7%

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

      1. associate-/l* 77.8%

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

      2. associate-/r/ 84.7%

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

      3. exp-diff 84.7%

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

      4. add-sqr-sqrt 36.3%

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

      5. sqrt-unprod 84.7%

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

      6. sqr-neg 84.7%

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

      7. sqrt-unprod 48.4%

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

      8. add-sqr-sqrt 84.8%

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

      9. add-exp-log 84.8%

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

   8. Applied egg-rr 84.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0053:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \mathbf{elif}\;b \leq 9.8:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{a}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 56.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{a}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.7e-18)
   (/ (/ x (exp b)) y)
   (if (<= b 3.8e-72) (* (/ x a) (/ 1.0 y)) (* x (/ (/ a (exp b)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.7e-18) {
		tmp = (x / exp(b)) / y;
	} else if (b <= 3.8e-72) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x * ((a / 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 (b <= (-1.7d-18)) then
        tmp = (x / exp(b)) / y
    else if (b <= 3.8d-72) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = x * ((a / 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 (b <= -1.7e-18) {
		tmp = (x / Math.exp(b)) / y;
	} else if (b <= 3.8e-72) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x * ((a / Math.exp(b)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.7e-18:
		tmp = (x / math.exp(b)) / y
	elif b <= 3.8e-72:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = x * ((a / math.exp(b)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.7e-18)
		tmp = Float64(Float64(x / exp(b)) / y);
	elseif (b <= 3.8e-72)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(x * Float64(Float64(a / exp(b)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.7e-18)
		tmp = (x / exp(b)) / y;
	elseif (b <= 3.8e-72)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = x * ((a / exp(b)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.7e-18], N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.8e-72], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(a / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.70000000000000001e-18

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 89.7%

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

   4. Taylor expanded in b around inf 79.3%

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

      1. neg-mul-1 79.3%

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

   6. Simplified 79.3%

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

      1. exp-neg 79.3%

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

      2. un-div-inv 79.3%

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

   8. Applied egg-rr 79.3%

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

   if -1.70000000000000001e-18 < b < 3.80000000000000002e-72

   1. Initial program 98.1%

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

      1. associate-*l/ 92.9%

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

      2. *-commutative 92.9%

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

      3. +-commutative 92.9%

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

      4. associate--l+ 92.9%

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

      5. exp-sum 75.8%

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

      6. *-commutative 75.8%

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

      7. exp-to-pow 76.6%

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

      8. sub-neg 76.6%

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

      9. metadata-eval 76.6%

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

      10. exp-diff 76.6%

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

      11. *-commutative 76.6%

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

      12. exp-to-pow 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in t around 0 62.9%

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

      1. times-frac 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in b around 0 62.9%

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

      1. times-frac 69.0%

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

   10. Simplified 69.0%

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

   11. Taylor expanded in y around 0 45.1%

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

   if 3.80000000000000002e-72 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.6%

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

   4. Taylor expanded in t around 0 77.3%

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

      1. *-commutative 77.3%

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

      2. mul-1-neg 77.3%

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

   6. Simplified 77.3%

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

      1. associate-/l* 70.3%

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

      2. associate-/r/ 76.1%

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

      3. exp-diff 76.1%

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

      4. add-sqr-sqrt 30.6%

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

      5. sqrt-unprod 76.6%

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

      6. sqr-neg 76.6%

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

      7. sqrt-unprod 46.0%

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

      8. add-sqr-sqrt 77.8%

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

      9. add-exp-log 77.8%

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

   8. Applied egg-rr 77.8%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{a}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-18} \lor \neg \left(b \leq 1.65 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.7e-18) (not (<= b 1.65e-19)))
   (/ (/ x (exp 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 <= -1.7e-18) || !(b <= 1.65e-19)) {
		tmp = (x / exp(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 <= (-1.7d-18)) .or. (.not. (b <= 1.65d-19))) then
        tmp = (x / exp(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 <= -1.7e-18) || !(b <= 1.65e-19)) {
		tmp = (x / Math.exp(b)) / y;
	} else {
		tmp = (x / a) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.7e-18) or not (b <= 1.65e-19):
		tmp = (x / math.exp(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 <= -1.7e-18) || !(b <= 1.65e-19))
		tmp = Float64(Float64(x / exp(b)) / 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 <= -1.7e-18) || ~((b <= 1.65e-19)))
		tmp = (x / exp(b)) / y;
	else
		tmp = (x / a) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.7e-18], N[Not[LessEqual[b, 1.65e-19]], $MachinePrecision]], N[(N[(x / N[Exp[b], $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 < -1.70000000000000001e-18 or 1.6499999999999999e-19 < b

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 89.1%

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

   4. Taylor expanded in b around inf 81.8%

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

      1. neg-mul-1 81.8%

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

   6. Simplified 81.8%

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

      1. exp-neg 81.8%

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

      2. un-div-inv 81.8%

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

   8. Applied egg-rr 81.8%

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

   if -1.70000000000000001e-18 < b < 1.6499999999999999e-19

   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/ 92.7%

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

      2. *-commutative 92.7%

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

      3. +-commutative 92.7%

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

      4. associate--l+ 92.7%

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

      5. exp-sum 75.3%

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

      6. *-commutative 75.3%

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

      7. exp-to-pow 76.0%

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

      8. sub-neg 76.0%

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

      9. metadata-eval 76.0%

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

      10. exp-diff 76.0%

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

      11. *-commutative 76.0%

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

      12. exp-to-pow 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in t around 0 61.3%

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

      1. times-frac 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in b around 0 61.3%

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

      1. times-frac 67.5%

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

   10. Simplified 67.5%

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

   11. Taylor expanded in y around 0 44.1%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{-18} \lor \neg \left(b \leq 1.65 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a}{\frac{e^{b}}{x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.25e-6) (/ (/ x (* y (exp b))) a) (/ (/ a (/ (exp b) x)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.25e-6) {
		tmp = (x / (y * exp(b))) / a;
	} else {
		tmp = (a / (exp(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 (t <= 1.25d-6) then
        tmp = (x / (y * exp(b))) / a
    else
        tmp = (a / (exp(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 (t <= 1.25e-6) {
		tmp = (x / (y * Math.exp(b))) / a;
	} else {
		tmp = (a / (Math.exp(b) / x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.25e-6:
		tmp = (x / (y * math.exp(b))) / a
	else:
		tmp = (a / (math.exp(b) / x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.25e-6)
		tmp = Float64(Float64(x / Float64(y * exp(b))) / a);
	else
		tmp = Float64(Float64(a / Float64(exp(b) / x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1.25e-6)
		tmp = (x / (y * exp(b))) / a;
	else
		tmp = (a / (exp(b) / x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.25e-6], N[(N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(a / N[(N[Exp[b], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.2500000000000001e-6

   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/ 90.9%

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

      2. *-commutative 90.9%

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

      3. +-commutative 90.9%

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

      4. associate--l+ 90.9%

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

      5. exp-sum 82.9%

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

      6. *-commutative 82.9%

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

      7. exp-to-pow 83.4%

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

      8. sub-neg 83.4%

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

      9. metadata-eval 83.4%

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

      10. exp-diff 76.5%

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

      11. *-commutative 76.5%

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

      12. exp-to-pow 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in t around 0 77.4%

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

      1. times-frac 75.0%

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

   7. Simplified 75.0%

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

      1. associate-*l/ 81.1%

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

   9. Applied egg-rr 81.1%

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

   10. Taylor expanded in y around 0 67.5%

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

   if 1.2500000000000001e-6 < 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 88.6%

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

   4. Taylor expanded in t around 0 48.0%

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

      1. *-commutative 48.0%

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

      2. mul-1-neg 48.0%

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

   6. Simplified 48.0%

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

      1. expm1-log1p-u 28.8%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{\left(-\log a\right) - b} \cdot x\right)\right)}}{y} \]

      2. expm1-udef 36.9%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(e^{\left(-\log a\right) - b} \cdot x\right)} - 1}}{y} \]

   8. Applied egg-rr 36.7%

      \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(\frac{a \cdot x}{e^{b}}\right)} - 1}}{y} \]
   9. Step-by-step derivation

      1. expm1-def 32.9%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{a \cdot x}{e^{b}}\right)\right)}}{y} \]

      2. expm1-log1p 56.6%

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

      3. associate-/l* 59.5%

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

   10. Simplified 59.5%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{x}{y \cdot e^{b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a}{\frac{e^{b}}{x}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.5% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+139}:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.65e+139)
   (/ (- x (* x b)) y)
   (if (<= b 2.2e+81) (* (/ x a) (/ 1.0 y)) (/ (/ x (+ y (* y b))) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.65e+139) {
		tmp = (x - (x * b)) / y;
	} else if (b <= 2.2e+81) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = (x / (y + (y * 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 <= (-1.65d+139)) then
        tmp = (x - (x * b)) / y
    else if (b <= 2.2d+81) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = (x / (y + (y * 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 <= -1.65e+139) {
		tmp = (x - (x * b)) / y;
	} else if (b <= 2.2e+81) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = (x / (y + (y * b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.65e+139:
		tmp = (x - (x * b)) / y
	elif b <= 2.2e+81:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = (x / (y + (y * b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.65e+139)
		tmp = Float64(Float64(x - Float64(x * b)) / y);
	elseif (b <= 2.2e+81)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(Float64(x / Float64(y + Float64(y * b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.65e+139)
		tmp = (x - (x * b)) / y;
	elseif (b <= 2.2e+81)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = (x / (y + (y * b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.65e+139], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.2e+81], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.6500000000000001e139

   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 0 100.0%

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

   4. Taylor expanded in b around inf 90.2%

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

      1. neg-mul-1 90.2%

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

   6. Simplified 90.2%

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

   7. Taylor expanded in b around 0 39.7%

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

      1. associate-*r* 39.7%

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

      2. mul-1-neg 39.7%

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

   9. Simplified 39.7%

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

   if -1.6500000000000001e139 < b < 2.19999999999999987e81

   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/ 93.6%

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

      2. *-commutative 93.6%

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

      3. +-commutative 93.6%

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

      4. associate--l+ 93.6%

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

      5. exp-sum 77.8%

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

      6. *-commutative 77.8%

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

      7. exp-to-pow 78.4%

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

      8. sub-neg 78.4%

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

      9. metadata-eval 78.4%

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

      10. exp-diff 73.1%

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

      11. *-commutative 73.1%

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

      12. exp-to-pow 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in t around 0 63.9%

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

      1. times-frac 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in b around 0 57.9%

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

      1. times-frac 64.5%

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

   10. Simplified 64.5%

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

   11. Taylor expanded in y around 0 40.5%

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

   if 2.19999999999999987e81 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 88.9%

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

      2. *-commutative 88.9%

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

      3. +-commutative 88.9%

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

      4. associate--l+ 88.9%

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

      5. exp-sum 77.8%

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

      6. *-commutative 77.8%

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

      7. exp-to-pow 77.8%

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

      8. sub-neg 77.8%

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

      9. metadata-eval 77.8%

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

      10. exp-diff 60.0%

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

      11. *-commutative 60.0%

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

      12. exp-to-pow 60.0%

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

   3. Simplified 60.0%

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

   5. Taylor expanded in t around 0 75.6%

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

      1. times-frac 66.7%

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

   7. Simplified 66.7%

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

      1. associate-*l/ 75.6%

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

   9. Applied egg-rr 75.6%

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

   10. Taylor expanded in y around 0 86.9%

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

   11. Taylor expanded in b around 0 53.2%

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

4. Final simplification 42.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+139}:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 38.9% accurate, 19.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.4e+53)
   (/ (* x (- (/ 1.0 a) (/ b a))) y)
   (/ (/ x (+ y (* y b))) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.4e+53) {
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	} else {
		tmp = (x / (y + (y * 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 <= 2.4d+53) then
        tmp = (x * ((1.0d0 / a) - (b / a))) / y
    else
        tmp = (x / (y + (y * 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 <= 2.4e+53) {
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	} else {
		tmp = (x / (y + (y * b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.4e+53:
		tmp = (x * ((1.0 / a) - (b / a))) / y
	else:
		tmp = (x / (y + (y * b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.4e+53)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) - Float64(b / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(y + Float64(y * b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.4e+53)
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	else
		tmp = (x / (y + (y * b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.4e+53], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.4e53

   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 y around 0 78.8%

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

   4. Taylor expanded in t around 0 58.0%

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

      1. *-commutative 58.0%

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

      2. mul-1-neg 58.0%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in b around 0 42.5%

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

      1. mul-1-neg 42.5%

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

      2. unsub-neg 42.5%

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

      3. log-rec 42.5%

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

      4. rem-exp-log 42.9%

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

      5. log-rec 42.9%

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

      6. rem-exp-log 42.9%

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

      7. associate-*r/ 42.9%

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

      8. *-rgt-identity 42.9%

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

   9. Simplified 42.9%

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

   if 2.4e53 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 90.2%

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

      2. *-commutative 90.2%

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

      3. +-commutative 90.2%

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

      4. associate--l+ 90.2%

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

      5. exp-sum 78.4%

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

      6. *-commutative 78.4%

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

      7. exp-to-pow 78.4%

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

      8. sub-neg 78.4%

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

      9. metadata-eval 78.4%

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

      10. exp-diff 58.8%

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

      11. *-commutative 58.8%

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

      12. exp-to-pow 58.8%

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

   3. Simplified 58.8%

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

   5. Taylor expanded in t around 0 72.6%

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

      1. times-frac 64.8%

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

   7. Simplified 64.8%

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

      1. associate-*l/ 72.6%

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

   9. Applied egg-rr 72.6%

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

   10. Taylor expanded in y around 0 84.6%

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

   11. Taylor expanded in b around 0 47.3%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.7% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.3 \cdot 10^{+79}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.3e+79) (/ (* (/ x a) (- 1.0 b)) y) (/ (/ x (+ y (* y b))) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.3e+79) {
		tmp = ((x / a) * (1.0 - b)) / y;
	} else {
		tmp = (x / (y + (y * 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 <= 2.3d+79) then
        tmp = ((x / a) * (1.0d0 - b)) / y
    else
        tmp = (x / (y + (y * 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 <= 2.3e+79) {
		tmp = ((x / a) * (1.0 - b)) / y;
	} else {
		tmp = (x / (y + (y * b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.3e+79:
		tmp = ((x / a) * (1.0 - b)) / y
	else:
		tmp = (x / (y + (y * b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.3e+79)
		tmp = Float64(Float64(Float64(x / a) * Float64(1.0 - b)) / y);
	else
		tmp = Float64(Float64(x / Float64(y + Float64(y * b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.3e+79)
		tmp = ((x / a) * (1.0 - b)) / y;
	else
		tmp = (x / (y + (y * b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.3e+79], N[(N[(N[(x / a), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.3e79

   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 y around 0 78.5%

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

   4. Taylor expanded in t around 0 58.2%

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

      1. *-commutative 58.2%

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

      2. mul-1-neg 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in b around 0 38.0%

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

      1. associate-*r* 38.0%

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

      2. neg-mul-1 38.0%

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

      3. distribute-lft1-in 41.3%

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

      4. log-rec 41.3%

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

      5. rem-exp-log 41.7%

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

      6. associate-*r/ 41.7%

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

      7. *-rgt-identity 41.7%

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

   9. Simplified 41.7%

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

   if 2.3e79 < b

   1. Initial program 100.0%

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

      1. associate-*l/ 88.9%

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

      2. *-commutative 88.9%

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

      3. +-commutative 88.9%

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

      4. associate--l+ 88.9%

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

      5. exp-sum 77.8%

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

      6. *-commutative 77.8%

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

      7. exp-to-pow 77.8%

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

      8. sub-neg 77.8%

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

      9. metadata-eval 77.8%

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

      10. exp-diff 60.0%

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

      11. *-commutative 60.0%

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

      12. exp-to-pow 60.0%

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

   3. Simplified 60.0%

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

   5. Taylor expanded in t around 0 75.6%

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

      1. times-frac 66.7%

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

   7. Simplified 66.7%

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

      1. associate-*l/ 75.6%

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

   9. Applied egg-rr 75.6%

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

   10. Taylor expanded in y around 0 86.9%

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

   11. Taylor expanded in b around 0 53.2%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.3 \cdot 10^{+79}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(1 - b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 33.8% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.9e+43) (* (/ x a) (/ 1.0 y)) (/ x (/ y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.9e+43) {
		tmp = (x / a) * (1.0 / 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 (t <= 1.9d+43) then
        tmp = (x / a) * (1.0d0 / 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 (t <= 1.9e+43) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.9e+43:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = x / (y / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.9e+43)
		tmp = Float64(Float64(x / a) * Float64(1.0 / 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 (t <= 1.9e+43)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = x / (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.9e+43], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.90000000000000004e43

   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. Step-by-step derivation

      1. associate-*l/ 90.6%

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

      2. *-commutative 90.6%

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

      3. +-commutative 90.6%

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

      4. associate--l+ 90.6%

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

      5. exp-sum 79.6%

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

      6. *-commutative 79.6%

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

      7. exp-to-pow 80.1%

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

      8. sub-neg 80.1%

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

      9. metadata-eval 80.1%

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

      10. exp-diff 73.1%

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

      11. *-commutative 73.1%

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

      12. exp-to-pow 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in t around 0 77.4%

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

      1. times-frac 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in b around 0 58.5%

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

      1. times-frac 61.1%

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

   10. Simplified 61.1%

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

   11. Taylor expanded in y around 0 38.4%

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

   if 1.90000000000000004e43 < t

   1. Initial program 100.0%

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

      1. associate-*l/ 89.1%

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

      2. *-commutative 89.1%

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

      3. +-commutative 89.1%

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

      4. associate--l+ 89.1%

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

      5. exp-sum 54.5%

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

      6. *-commutative 54.5%

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

      7. exp-to-pow 54.5%

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

      8. sub-neg 54.5%

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

      9. metadata-eval 54.5%

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

      10. exp-diff 43.6%

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

      11. *-commutative 43.6%

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

      12. exp-to-pow 43.6%

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

   3. Simplified 43.6%

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

   5. Taylor expanded in t around 0 33.8%

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

      1. times-frac 33.9%

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

   7. Simplified 33.9%

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

   8. Taylor expanded in b around 0 32.2%

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

      1. times-frac 41.3%

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

   10. Simplified 41.3%

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

   11. Taylor expanded in y around 0 11.9%

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

       1. un-div-inv 11.9%

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

       2. div-inv 11.9%

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

       3. associate-/l* 11.9%

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

       4. rem-exp-log 11.9%

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

       5. neg-log 11.9%

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

       6. add-sqr-sqrt 7.2%

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

       7. sqrt-unprod 18.1%

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

       8. sqr-neg 18.1%

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

       9. sqrt-unprod 10.9%

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

       10. add-sqr-sqrt 35.3%

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

       11. add-exp-log 35.3%

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

   13. Applied egg-rr 35.3%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.9 \cdot 10^{+43}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 34.5% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 8.5e-7) (/ x (* y a)) (* x (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 8.5e-7) {
		tmp = x / (y * a);
	} 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 (t <= 8.5d-7) then
        tmp = x / (y * a)
    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 (t <= 8.5e-7) {
		tmp = x / (y * a);
	} else {
		tmp = x * (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 8.5e-7:
		tmp = x / (y * a)
	else:
		tmp = x * (a / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 8.5e-7)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x * Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 8.5e-7)
		tmp = x / (y * a);
	else
		tmp = x * (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 8.5e-7], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x * N[(a / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 8.50000000000000014e-7

   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/ 90.9%

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

      2. *-commutative 90.9%

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

      3. +-commutative 90.9%

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

      4. associate--l+ 90.9%

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

      5. exp-sum 82.9%

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

      6. *-commutative 82.9%

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

      7. exp-to-pow 83.4%

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

      8. sub-neg 83.4%

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

      9. metadata-eval 83.4%

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

      10. exp-diff 76.5%

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

      11. *-commutative 76.5%

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

      12. exp-to-pow 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in t around 0 77.4%

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

      1. times-frac 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in b around 0 59.0%

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

      1. times-frac 62.4%

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

   10. Simplified 62.4%

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

   11. Taylor expanded in y around 0 38.7%

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

       1. *-commutative 38.7%

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

   13. Simplified 38.7%

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

   if 8.50000000000000014e-7 < t

   1. Initial program 100.0%

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

      1. associate-*l/ 88.4%

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

      2. *-commutative 88.4%

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

      3. +-commutative 88.4%

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

      4. associate--l+ 88.4%

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

      5. exp-sum 50.7%

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

      6. *-commutative 50.7%

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

      7. exp-to-pow 50.7%

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

      8. sub-neg 50.7%

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

      9. metadata-eval 50.7%

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

      10. exp-diff 40.6%

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

      11. *-commutative 40.6%

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

      12. exp-to-pow 40.6%

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

   3. Simplified 40.6%

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

   5. Taylor expanded in t around 0 42.9%

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

      1. times-frac 41.5%

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

   7. Simplified 41.5%

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

   8. Taylor expanded in b around 0 36.1%

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

      1. times-frac 41.9%

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

   10. Simplified 41.9%

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

   11. Taylor expanded in y around 0 14.3%

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

       1. expm1-log1p-u 10.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{a} \cdot \frac{1}{y}\right)\right)} \]

       2. expm1-udef 28.6%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{a} \cdot \frac{1}{y}\right)} - 1} \]

       3. associate-*l/ 28.5%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x \cdot \frac{1}{y}}{a}}\right)} - 1 \]

       4. div-inv 28.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\frac{x}{y}}}{a}\right)} - 1 \]

       5. div-inv 28.5%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{y} \cdot \frac{1}{a}}\right)} - 1 \]

       6. rem-exp-log 28.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \color{blue}{e^{\log \left(\frac{1}{a}\right)}}\right)} - 1 \]

       7. neg-log 28.5%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{-\log a}}\right)} - 1 \]

       8. add-sqr-sqrt 19.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{\sqrt{-\log a} \cdot \sqrt{-\log a}}}\right)} - 1 \]

       9. sqrt-unprod 30.0%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{\sqrt{\left(-\log a\right) \cdot \left(-\log a\right)}}}\right)} - 1 \]

       10. sqr-neg 30.0%

           \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\sqrt{\color{blue}{\log a \cdot \log a}}}\right)} - 1 \]

       11. sqrt-unprod 10.8%

           \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{\sqrt{\log a} \cdot \sqrt{\log a}}}\right)} - 1 \]

       12. add-sqr-sqrt 35.7%

           \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{\log a}}\right)} - 1 \]

       13. add-exp-log 35.7%

           \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \color{blue}{a}\right)} - 1 \]

   13. Applied egg-rr 35.7%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{y} \cdot a\right)} - 1} \]
   14. Step-by-step derivation

       1. expm1-def 24.7%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y} \cdot a\right)\right)} \]

       2. expm1-log1p 28.4%

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

       3. *-commutative 28.4%

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

       4. *-rgt-identity 28.4%

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

       5. associate-*r/ 28.4%

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

       6. associate-*l* 31.7%

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

       7. *-commutative 31.7%

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

       8. associate-*l* 30.3%

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

       9. associate-*r/ 30.3%

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

       10. *-rgt-identity 30.3%

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

   15. Simplified 30.3%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 34.4% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{a}}\\ \end{array} \end{array} \]

FPCore

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

C

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

Python

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

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 7e-7)
		tmp = Float64(x / Float64(y * a));
	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 (t <= 7e-7)
		tmp = x / (y * a);
	else
		tmp = x / (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 7e-7], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.99999999999999968e-7

   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/ 90.9%

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

      2. *-commutative 90.9%

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

      3. +-commutative 90.9%

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

      4. associate--l+ 90.9%

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

      5. exp-sum 82.9%

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

      6. *-commutative 82.9%

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

      7. exp-to-pow 83.4%

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

      8. sub-neg 83.4%

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

      9. metadata-eval 83.4%

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

      10. exp-diff 76.5%

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

      11. *-commutative 76.5%

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

      12. exp-to-pow 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in t around 0 77.4%

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

      1. times-frac 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in b around 0 59.0%

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

      1. times-frac 62.4%

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

   10. Simplified 62.4%

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

   11. Taylor expanded in y around 0 38.7%

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

       1. *-commutative 38.7%

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

   13. Simplified 38.7%

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

   if 6.99999999999999968e-7 < t

   1. Initial program 100.0%

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

      1. associate-*l/ 88.4%

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

      2. *-commutative 88.4%

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

      3. +-commutative 88.4%

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

      4. associate--l+ 88.4%

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

      5. exp-sum 50.7%

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

      6. *-commutative 50.7%

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

      7. exp-to-pow 50.7%

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

      8. sub-neg 50.7%

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

      9. metadata-eval 50.7%

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

      10. exp-diff 40.6%

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

      11. *-commutative 40.6%

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

      12. exp-to-pow 40.6%

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

   3. Simplified 40.6%

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

   5. Taylor expanded in t around 0 42.9%

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

      1. times-frac 41.5%

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

   7. Simplified 41.5%

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

   8. Taylor expanded in b around 0 36.1%

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

      1. times-frac 41.9%

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

   10. Simplified 41.9%

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

   11. Taylor expanded in y around 0 14.3%

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

       1. un-div-inv 14.3%

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

       2. div-inv 14.3%

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

       3. associate-/l* 12.9%

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

       4. rem-exp-log 12.9%

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

       5. neg-log 12.9%

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

       6. add-sqr-sqrt 5.9%

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

       7. sqrt-unprod 17.9%

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

       8. sqr-neg 17.9%

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

       9. sqrt-unprod 12.0%

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

       10. add-sqr-sqrt 31.7%

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

       11. add-exp-log 31.7%

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

   13. Applied egg-rr 31.7%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 34.6% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1.25e-6) (/ x (* y a)) (/ (* x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1.25e-6) {
		tmp = x / (y * a);
	} 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 (t <= 1.25d-6) then
        tmp = x / (y * a)
    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 (t <= 1.25e-6) {
		tmp = x / (y * a);
	} else {
		tmp = (x * a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1.25e-6:
		tmp = x / (y * a)
	else:
		tmp = (x * a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1.25e-6)
		tmp = Float64(x / Float64(y * a));
	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 (t <= 1.25e-6)
		tmp = x / (y * a);
	else
		tmp = (x * a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1.25e-6], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x * a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.2500000000000001e-6

   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/ 90.9%

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

      2. *-commutative 90.9%

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

      3. +-commutative 90.9%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 90.9%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 82.9%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 82.9%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 83.4%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 83.4%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 83.4%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 76.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 76.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 76.5%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 77.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 75.0%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 75.0%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in b around 0 59.0%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   9. Step-by-step derivation

      1. times-frac 62.4%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

   10. Simplified 62.4%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

   11. Taylor expanded in y around 0 38.7%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. *-commutative 38.7%

          \[\leadsto \frac{x}{\color{blue}{y \cdot a}} \]

   13. Simplified 38.7%

       \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

   if 1.2500000000000001e-6 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 88.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 88.4%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 88.4%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 50.7%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 50.7%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 50.7%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 50.7%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 50.7%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 40.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 40.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 40.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 40.6%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 42.9%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 41.5%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 41.5%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in b around 0 36.1%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   9. Step-by-step derivation

      1. times-frac 41.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

   10. Simplified 41.9%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

   11. Taylor expanded in y around 0 14.3%

       \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{1}{y}} \]
   12. Step-by-step derivation

       1. un-div-inv 14.3%

          \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

       2. clear-num 14.3%

          \[\leadsto \frac{\color{blue}{\frac{1}{\frac{a}{x}}}}{y} \]

       3. associate-/r/ 14.3%

          \[\leadsto \frac{\color{blue}{\frac{1}{a} \cdot x}}{y} \]

       4. rem-exp-log 14.3%

          \[\leadsto \frac{\color{blue}{e^{\log \left(\frac{1}{a}\right)}} \cdot x}{y} \]

       5. neg-log 14.3%

          \[\leadsto \frac{e^{\color{blue}{-\log a}} \cdot x}{y} \]

       6. add-sqr-sqrt 8.7%

          \[\leadsto \frac{e^{\color{blue}{\sqrt{-\log a} \cdot \sqrt{-\log a}}} \cdot x}{y} \]

       7. sqrt-unprod 24.8%

          \[\leadsto \frac{e^{\color{blue}{\sqrt{\left(-\log a\right) \cdot \left(-\log a\right)}}} \cdot x}{y} \]

       8. sqr-neg 24.8%

          \[\leadsto \frac{e^{\sqrt{\color{blue}{\log a \cdot \log a}}} \cdot x}{y} \]

       9. sqrt-unprod 16.1%

          \[\leadsto \frac{e^{\color{blue}{\sqrt{\log a} \cdot \sqrt{\log a}}} \cdot x}{y} \]

       10. add-sqr-sqrt 31.7%

           \[\leadsto \frac{e^{\color{blue}{\log a}} \cdot x}{y} \]

       11. add-exp-log 31.7%

           \[\leadsto \frac{\color{blue}{a} \cdot x}{y} \]

   13. Applied egg-rr 31.7%

       \[\leadsto \color{blue}{\frac{a \cdot x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.25 \cdot 10^{-6}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.8% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.26 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 2.26e+46) (/ (/ x a) y) (/ x (/ y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 2.26e+46) {
		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 (t <= 2.26d+46) 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 (t <= 2.26e+46) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 2.26e+46:
		tmp = (x / a) / y
	else:
		tmp = x / (y / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 2.26e+46)
		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 (t <= 2.26e+46)
		tmp = (x / a) / y;
	else
		tmp = x / (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 2.26e+46], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.2599999999999999e46

   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 y around 0 77.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around 0 54.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y}} \]
   5. Step-by-step derivation

      1. *-commutative 54.4%

         \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y} \]

      2. exp-to-pow 54.8%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}} \cdot x}{y} \]

      3. sub-neg 54.8%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot x}{y} \]

      4. metadata-eval 54.8%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)} \cdot x}{y} \]

      5. +-commutative 54.8%

         \[\leadsto \frac{{a}^{\color{blue}{\left(-1 + t\right)}} \cdot x}{y} \]

   6. Simplified 54.8%

      \[\leadsto \color{blue}{\frac{{a}^{\left(-1 + t\right)} \cdot x}{y}} \]

   7. Taylor expanded in t around 0 38.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 2.2599999999999999e46 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.1%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 89.1%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 89.1%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 89.1%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 54.5%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 54.5%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 54.5%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 54.5%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 54.5%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 43.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 43.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 43.6%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 43.6%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 33.8%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 33.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 33.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in b around 0 32.2%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   9. Step-by-step derivation

      1. times-frac 41.3%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

   10. Simplified 41.3%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

   11. Taylor expanded in y around 0 11.9%

       \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{1}{y}} \]
   12. Step-by-step derivation

       1. un-div-inv 11.9%

          \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

       2. div-inv 11.9%

          \[\leadsto \frac{\color{blue}{x \cdot \frac{1}{a}}}{y} \]

       3. associate-/l* 11.9%

          \[\leadsto \color{blue}{\frac{x}{\frac{y}{\frac{1}{a}}}} \]

       4. rem-exp-log 11.9%

          \[\leadsto \frac{x}{\frac{y}{\color{blue}{e^{\log \left(\frac{1}{a}\right)}}}} \]

       5. neg-log 11.9%

          \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{-\log a}}}} \]

       6. add-sqr-sqrt 7.2%

          \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\sqrt{-\log a} \cdot \sqrt{-\log a}}}}} \]

       7. sqrt-unprod 18.1%

          \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\sqrt{\left(-\log a\right) \cdot \left(-\log a\right)}}}}} \]

       8. sqr-neg 18.1%

          \[\leadsto \frac{x}{\frac{y}{e^{\sqrt{\color{blue}{\log a \cdot \log a}}}}} \]

       9. sqrt-unprod 10.9%

          \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\sqrt{\log a} \cdot \sqrt{\log a}}}}} \]

       10. add-sqr-sqrt 35.3%

           \[\leadsto \frac{x}{\frac{y}{e^{\color{blue}{\log a}}}} \]

       11. add-exp-log 35.3%

           \[\leadsto \frac{x}{\frac{y}{\color{blue}{a}}} \]

   13. Applied egg-rr 35.3%

       \[\leadsto \color{blue}{\frac{x}{\frac{y}{a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.26 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.3% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ a \cdot \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* a (/ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return a * (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 = a * (x / y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a * (x / y);
}

Python

def code(x, y, z, t, a, b):
	return a * (x / y)

Julia

function code(x, y, z, t, a, b)
	return Float64(a * Float64(x / y))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a * (x / y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 90.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

   2. *-commutative 90.2%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. +-commutative 90.2%

      \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

   4. associate--l+ 90.2%

      \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

   5. exp-sum 74.2%

      \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

   6. *-commutative 74.2%

      \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   7. exp-to-pow 74.6%

      \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   8. sub-neg 74.6%

      \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   9. metadata-eval 74.6%

      \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   10. exp-diff 66.8%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

   11. *-commutative 66.8%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   12. exp-to-pow 66.8%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

3. Simplified 66.8%

   \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in t around 0 68.1%

   \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
6. Step-by-step derivation

   1. times-frac 66.0%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

7. Simplified 66.0%

   \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

8. Taylor expanded in b around 0 52.8%

   \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
9. Step-by-step derivation

   1. times-frac 56.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

10. Simplified 56.9%

    \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

11. Taylor expanded in y around 0 32.7%

    \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{1}{y}} \]
12. Step-by-step derivation

    1. expm1-log1p-u 22.3%

       \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{a} \cdot \frac{1}{y}\right)\right)} \]

    2. expm1-udef 34.8%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{a} \cdot \frac{1}{y}\right)} - 1} \]

    3. associate-*l/ 33.5%

       \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x \cdot \frac{1}{y}}{a}}\right)} - 1 \]

    4. div-inv 33.5%

       \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\frac{x}{y}}}{a}\right)} - 1 \]

    5. div-inv 33.5%

       \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{y} \cdot \frac{1}{a}}\right)} - 1 \]

    6. rem-exp-log 33.5%

       \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \color{blue}{e^{\log \left(\frac{1}{a}\right)}}\right)} - 1 \]

    7. neg-log 33.5%

       \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{-\log a}}\right)} - 1 \]

    8. add-sqr-sqrt 11.7%

       \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{\sqrt{-\log a} \cdot \sqrt{-\log a}}}\right)} - 1 \]

    9. sqrt-unprod 24.3%

       \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{\sqrt{\left(-\log a\right) \cdot \left(-\log a\right)}}}\right)} - 1 \]

    10. sqr-neg 24.3%

        \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\sqrt{\color{blue}{\log a \cdot \log a}}}\right)} - 1 \]

    11. sqrt-unprod 12.6%

        \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{\sqrt{\log a} \cdot \sqrt{\log a}}}\right)} - 1 \]

    12. add-sqr-sqrt 28.7%

        \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{\log a}}\right)} - 1 \]

    13. add-exp-log 28.7%

        \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \color{blue}{a}\right)} - 1 \]

13. Applied egg-rr 28.7%

    \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{y} \cdot a\right)} - 1} \]
14. Step-by-step derivation

    1. expm1-def 17.6%

       \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y} \cdot a\right)\right)} \]

    2. expm1-log1p 21.4%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot a} \]

    3. *-commutative 21.4%

       \[\leadsto \color{blue}{a \cdot \frac{x}{y}} \]

15. Simplified 21.4%

    \[\leadsto \color{blue}{a \cdot \frac{x}{y}} \]

16. Final simplification 21.4%

    \[\leadsto a \cdot \frac{x}{y} \]
17. Add Preprocessing

Alternative 23: 21.2% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{a}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* x (/ a y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * (a / 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 * (a / y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * (a / y);
}

Python

def code(x, y, z, t, a, b):
	return x * (a / y)

Julia

function code(x, y, z, t, a, b)
	return Float64(x * Float64(a / y))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * (a / y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[(a / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 90.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

   2. *-commutative 90.2%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. +-commutative 90.2%

      \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

   4. associate--l+ 90.2%

      \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

   5. exp-sum 74.2%

      \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

   6. *-commutative 74.2%

      \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   7. exp-to-pow 74.6%

      \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   8. sub-neg 74.6%

      \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   9. metadata-eval 74.6%

      \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   10. exp-diff 66.8%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

   11. *-commutative 66.8%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   12. exp-to-pow 66.8%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

3. Simplified 66.8%

   \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]
4. Add Preprocessing

5. Taylor expanded in t around 0 68.1%

   \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
6. Step-by-step derivation

   1. times-frac 66.0%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

7. Simplified 66.0%

   \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

8. Taylor expanded in b around 0 52.8%

   \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
9. Step-by-step derivation

   1. times-frac 56.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

10. Simplified 56.9%

    \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

11. Taylor expanded in y around 0 32.7%

    \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{1}{y}} \]
12. Step-by-step derivation

    1. expm1-log1p-u 22.3%

       \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{a} \cdot \frac{1}{y}\right)\right)} \]

    2. expm1-udef 34.8%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{a} \cdot \frac{1}{y}\right)} - 1} \]

    3. associate-*l/ 33.5%

       \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x \cdot \frac{1}{y}}{a}}\right)} - 1 \]

    4. div-inv 33.5%

       \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\frac{x}{y}}}{a}\right)} - 1 \]

    5. div-inv 33.5%

       \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x}{y} \cdot \frac{1}{a}}\right)} - 1 \]

    6. rem-exp-log 33.5%

       \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \color{blue}{e^{\log \left(\frac{1}{a}\right)}}\right)} - 1 \]

    7. neg-log 33.5%

       \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{-\log a}}\right)} - 1 \]

    8. add-sqr-sqrt 11.7%

       \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{\sqrt{-\log a} \cdot \sqrt{-\log a}}}\right)} - 1 \]

    9. sqrt-unprod 24.3%

       \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{\sqrt{\left(-\log a\right) \cdot \left(-\log a\right)}}}\right)} - 1 \]

    10. sqr-neg 24.3%

        \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\sqrt{\color{blue}{\log a \cdot \log a}}}\right)} - 1 \]

    11. sqrt-unprod 12.6%

        \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{\sqrt{\log a} \cdot \sqrt{\log a}}}\right)} - 1 \]

    12. add-sqr-sqrt 28.7%

        \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot e^{\color{blue}{\log a}}\right)} - 1 \]

    13. add-exp-log 28.7%

        \[\leadsto e^{\mathsf{log1p}\left(\frac{x}{y} \cdot \color{blue}{a}\right)} - 1 \]

13. Applied egg-rr 28.7%

    \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{y} \cdot a\right)} - 1} \]
14. Step-by-step derivation

    1. expm1-def 17.6%

       \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y} \cdot a\right)\right)} \]

    2. expm1-log1p 21.4%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot a} \]

    3. *-commutative 21.4%

       \[\leadsto \color{blue}{a \cdot \frac{x}{y}} \]

    4. *-rgt-identity 21.4%

       \[\leadsto a \cdot \frac{\color{blue}{x \cdot 1}}{y} \]

    5. associate-*r/ 21.4%

       \[\leadsto a \cdot \color{blue}{\left(x \cdot \frac{1}{y}\right)} \]

    6. associate-*l* 21.9%

       \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot \frac{1}{y}} \]

    7. *-commutative 21.9%

       \[\leadsto \color{blue}{\left(x \cdot a\right)} \cdot \frac{1}{y} \]

    8. associate-*l* 21.5%

       \[\leadsto \color{blue}{x \cdot \left(a \cdot \frac{1}{y}\right)} \]

    9. associate-*r/ 21.5%

       \[\leadsto x \cdot \color{blue}{\frac{a \cdot 1}{y}} \]

    10. *-rgt-identity 21.5%

        \[\leadsto x \cdot \frac{\color{blue}{a}}{y} \]

15. Simplified 21.5%

    \[\leadsto \color{blue}{x \cdot \frac{a}{y}} \]

16. Final simplification 21.5%

    \[\leadsto x \cdot \frac{a}{y} \]
17. Add Preprocessing

Alternative 24: 15.7% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Python

def code(x, y, z, t, a, b):
	return x / y

Julia

function code(x, y, z, t, a, b)
	return Float64(x / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 81.1%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

4. Taylor expanded in b around inf 52.3%

   \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
5. Step-by-step derivation

   1. neg-mul-1 52.3%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

6. Simplified 52.3%

   \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

7. Taylor expanded in b around 0 16.0%

   \[\leadsto \frac{\color{blue}{x}}{y} \]

8. Final simplification 16.0%

   \[\leadsto \frac{x}{y} \]
9. Add Preprocessing

Developer target: 70.6% 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 2024024 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))