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

Percentage Accurate: 98.4% → 98.4%

Time: 23.0s

Alternatives: 18

Speedup: 1.0×

• 21.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% 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: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

2. Final simplification 98.7%

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

Alternative 2: 93.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+79} \lor \neg \left(t \leq 450000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9.8e+79) (not (<= t 450000000.0)))
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9.8e+79) || !(t <= 450000000.0)) {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - 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 ((t <= (-9.8d+79)) .or. (.not. (t <= 450000000.0d0))) then
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - 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 ((t <= -9.8e+79) || !(t <= 450000000.0)) {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9.8e+79) or not (t <= 450000000.0):
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9.8e+79) || !(t <= 450000000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -9.8e+79) || ~((t <= 450000000.0)))
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9.8e+79], N[Not[LessEqual[t, 450000000.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.7999999999999997e79 or 4.5e8 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.1%

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

   if -9.7999999999999997e79 < t < 4.5e8

   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. Taylor expanded in t around 0 94.9%

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

      1. +-commutative 94.9%

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

      2. mul-1-neg 94.9%

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

      3. unsub-neg 94.9%

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

   4. Simplified 94.9%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+79} \lor \neg \left(t \leq 450000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]

Alternative 3: 78.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t + -1\right)}\\ t_2 := \frac{x}{\frac{y}{{z}^{y} \cdot t_1}}\\ t_3 := y \cdot e^{b}\\ t_4 := \frac{x}{a \cdot t_3}\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+127}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.6:\\ \;\;\;\;\frac{x \cdot t_1}{t_3}\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (+ t -1.0)))
        (t_2 (/ x (/ y (* (pow z y) t_1))))
        (t_3 (* y (exp b)))
        (t_4 (/ x (* a t_3))))
   (if (<= b -8.5e+127)
     t_4
     (if (<= b 5.5e-211)
       t_2
       (if (<= b 1.6) (/ (* x t_1) t_3) (if (<= b 1.65e+143) t_2 t_4))))))

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 / (y / (pow(z, y) * t_1));
	double t_3 = y * exp(b);
	double t_4 = x / (a * t_3);
	double tmp;
	if (b <= -8.5e+127) {
		tmp = t_4;
	} else if (b <= 5.5e-211) {
		tmp = t_2;
	} else if (b <= 1.6) {
		tmp = (x * t_1) / t_3;
	} else if (b <= 1.65e+143) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a ** (t + (-1.0d0))
    t_2 = x / (y / ((z ** y) * t_1))
    t_3 = y * exp(b)
    t_4 = x / (a * t_3)
    if (b <= (-8.5d+127)) then
        tmp = t_4
    else if (b <= 5.5d-211) then
        tmp = t_2
    else if (b <= 1.6d0) then
        tmp = (x * t_1) / t_3
    else if (b <= 1.65d+143) then
        tmp = t_2
    else
        tmp = t_4
    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 / (y / (Math.pow(z, y) * t_1));
	double t_3 = y * Math.exp(b);
	double t_4 = x / (a * t_3);
	double tmp;
	if (b <= -8.5e+127) {
		tmp = t_4;
	} else if (b <= 5.5e-211) {
		tmp = t_2;
	} else if (b <= 1.6) {
		tmp = (x * t_1) / t_3;
	} else if (b <= 1.65e+143) {
		tmp = t_2;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t + -1.0))
	t_2 = x / (y / (math.pow(z, y) * t_1))
	t_3 = y * math.exp(b)
	t_4 = x / (a * t_3)
	tmp = 0
	if b <= -8.5e+127:
		tmp = t_4
	elif b <= 5.5e-211:
		tmp = t_2
	elif b <= 1.6:
		tmp = (x * t_1) / t_3
	elif b <= 1.65e+143:
		tmp = t_2
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t + -1.0)
	t_2 = Float64(x / Float64(y / Float64((z ^ y) * t_1)))
	t_3 = Float64(y * exp(b))
	t_4 = Float64(x / Float64(a * t_3))
	tmp = 0.0
	if (b <= -8.5e+127)
		tmp = t_4;
	elseif (b <= 5.5e-211)
		tmp = t_2;
	elseif (b <= 1.6)
		tmp = Float64(Float64(x * t_1) / t_3);
	elseif (b <= 1.65e+143)
		tmp = t_2;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t + -1.0);
	t_2 = x / (y / ((z ^ y) * t_1));
	t_3 = y * exp(b);
	t_4 = x / (a * t_3);
	tmp = 0.0;
	if (b <= -8.5e+127)
		tmp = t_4;
	elseif (b <= 5.5e-211)
		tmp = t_2;
	elseif (b <= 1.6)
		tmp = (x * t_1) / t_3;
	elseif (b <= 1.65e+143)
		tmp = t_2;
	else
		tmp = t_4;
	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[(x / N[(y / N[(N[Power[z, y], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x / N[(a * t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.5e+127], t$95$4, If[LessEqual[b, 5.5e-211], t$95$2, If[LessEqual[b, 1.6], N[(N[(x * t$95$1), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[b, 1.65e+143], t$95$2, t$95$4]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.4999999999999997e127 or 1.65e143 < 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/ 88.6%

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

      2. *-commutative 88.6%

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

      3. exp-diff 54.3%

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

      4. exp-sum 48.6%

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

      5. *-commutative 48.6%

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

      6. exp-to-pow 48.6%

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

      7. *-commutative 48.6%

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

      8. exp-to-pow 48.6%

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

      9. sub-neg 48.6%

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

      10. metadata-eval 48.6%

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

   3. Simplified 48.6%

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

   4. Taylor expanded in t around 0 64.3%

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

      1. times-frac 55.7%

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

   6. Simplified 55.7%

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

   7. Taylor expanded in y around 0 93.0%

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

   if -8.4999999999999997e127 < b < 5.49999999999999973e-211 or 1.6000000000000001 < b < 1.65e143

   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/ 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. exp-diff 72.6%

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

      4. exp-sum 63.2%

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

      5. *-commutative 63.2%

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

      6. exp-to-pow 63.2%

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

      7. *-commutative 63.2%

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

      8. exp-to-pow 63.6%

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

      9. sub-neg 63.6%

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

      10. metadata-eval 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in b around 0 78.6%

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

      1. associate-/l* 78.6%

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

      2. *-commutative 78.6%

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

      3. exp-to-pow 79.2%

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

      4. sub-neg 79.2%

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

      5. metadata-eval 79.2%

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

   6. Simplified 79.2%

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

   if 5.49999999999999973e-211 < b < 1.6000000000000001

   1. Initial program 94.2%

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

      1. associate-*l/ 84.0%

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

      2. *-commutative 84.0%

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

      3. exp-diff 84.0%

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

      4. exp-sum 70.8%

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

      5. *-commutative 70.8%

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

      6. exp-to-pow 70.8%

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

      7. *-commutative 70.8%

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

      8. exp-to-pow 73.8%

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

      9. sub-neg 73.8%

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

      10. metadata-eval 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in y around 0 88.1%

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

      1. exp-to-pow 91.0%

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

      2. sub-neg 91.0%

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

      3. metadata-eval 91.0%

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

   6. Simplified 91.0%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+127}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-211}:\\ \;\;\;\;\frac{x}{\frac{y}{{z}^{y} \cdot {a}^{\left(t + -1\right)}}}\\ \mathbf{elif}\;b \leq 1.6:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{\frac{y}{{z}^{y} \cdot {a}^{\left(t + -1\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 4: 81.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ t_2 := \frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{t_1}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{a \cdot t_1}\\ \mathbf{elif}\;t \leq 105000000000:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{z}^{y}}{y}}{e^{b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))) (t_2 (/ x (/ y (/ (pow a t) a)))))
   (if (<= t -1.35e+66)
     t_2
     (if (<= t -6.6e-23)
       (* (/ x a) (/ (pow z y) t_1))
       (if (<= t -2.9e-63)
         (/ x (* a t_1))
         (if (<= t 105000000000.0)
           (/ (* x (/ (/ (pow z y) y) (exp b))) a)
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * exp(b);
	double t_2 = x / (y / (pow(a, t) / a));
	double tmp;
	if (t <= -1.35e+66) {
		tmp = t_2;
	} else if (t <= -6.6e-23) {
		tmp = (x / a) * (pow(z, y) / t_1);
	} else if (t <= -2.9e-63) {
		tmp = x / (a * t_1);
	} else if (t <= 105000000000.0) {
		tmp = (x * ((pow(z, y) / y) / exp(b))) / a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * exp(b)
    t_2 = x / (y / ((a ** t) / a))
    if (t <= (-1.35d+66)) then
        tmp = t_2
    else if (t <= (-6.6d-23)) then
        tmp = (x / a) * ((z ** y) / t_1)
    else if (t <= (-2.9d-63)) then
        tmp = x / (a * t_1)
    else if (t <= 105000000000.0d0) then
        tmp = (x * (((z ** y) / y) / exp(b))) / a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * Math.exp(b);
	double t_2 = x / (y / (Math.pow(a, t) / a));
	double tmp;
	if (t <= -1.35e+66) {
		tmp = t_2;
	} else if (t <= -6.6e-23) {
		tmp = (x / a) * (Math.pow(z, y) / t_1);
	} else if (t <= -2.9e-63) {
		tmp = x / (a * t_1);
	} else if (t <= 105000000000.0) {
		tmp = (x * ((Math.pow(z, y) / y) / Math.exp(b))) / a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * math.exp(b)
	t_2 = x / (y / (math.pow(a, t) / a))
	tmp = 0
	if t <= -1.35e+66:
		tmp = t_2
	elif t <= -6.6e-23:
		tmp = (x / a) * (math.pow(z, y) / t_1)
	elif t <= -2.9e-63:
		tmp = x / (a * t_1)
	elif t <= 105000000000.0:
		tmp = (x * ((math.pow(z, y) / y) / math.exp(b))) / a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * exp(b))
	t_2 = Float64(x / Float64(y / Float64((a ^ t) / a)))
	tmp = 0.0
	if (t <= -1.35e+66)
		tmp = t_2;
	elseif (t <= -6.6e-23)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / t_1));
	elseif (t <= -2.9e-63)
		tmp = Float64(x / Float64(a * t_1));
	elseif (t <= 105000000000.0)
		tmp = Float64(Float64(x * Float64(Float64((z ^ y) / y) / exp(b))) / a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * exp(b);
	t_2 = x / (y / ((a ^ t) / a));
	tmp = 0.0;
	if (t <= -1.35e+66)
		tmp = t_2;
	elseif (t <= -6.6e-23)
		tmp = (x / a) * ((z ^ y) / t_1);
	elseif (t <= -2.9e-63)
		tmp = x / (a * t_1);
	elseif (t <= 105000000000.0)
		tmp = (x * (((z ^ y) / y) / exp(b))) / a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y / N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.35e+66], t$95$2, If[LessEqual[t, -6.6e-23], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e-63], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 105000000000.0], N[(N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.35e66 or 1.05e11 < 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/ 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. exp-diff 65.0%

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

      4. exp-sum 48.5%

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

      5. *-commutative 48.5%

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

      6. exp-to-pow 48.5%

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

      7. *-commutative 48.5%

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

      8. exp-to-pow 48.5%

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

      9. sub-neg 48.5%

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

      10. metadata-eval 48.5%

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

   3. Simplified 48.5%

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

   4. Taylor expanded in y around 0 69.9%

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

      1. exp-to-pow 69.9%

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

      2. sub-neg 69.9%

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

      3. metadata-eval 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in b around 0 84.7%

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

   9. Simplified 84.7%

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

       1. +-commutative 84.7%

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

       2. unpow-prod-up 84.7%

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

       3. unpow-1 84.7%

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

   11. Applied egg-rr 84.7%

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

       1. associate-*r/ 84.7%

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

       2. *-rgt-identity 84.7%

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

   13. Simplified 84.7%

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

   if -1.35e66 < t < -6.60000000000000041e-23

   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/ 95.0%

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

      2. *-commutative 95.0%

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

      3. exp-diff 85.0%

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

      4. exp-sum 65.0%

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

      5. *-commutative 65.0%

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

      6. exp-to-pow 65.0%

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

      7. *-commutative 65.0%

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

      8. exp-to-pow 65.0%

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

      9. sub-neg 65.0%

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

      10. metadata-eval 65.0%

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

   3. Simplified 65.0%

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

   4. Taylor expanded in t around 0 80.7%

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

      1. times-frac 85.7%

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

   6. Simplified 85.7%

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

   if -6.60000000000000041e-23 < t < -2.89999999999999975e-63

   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/ 91.7%

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

      2. *-commutative 91.7%

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

      3. exp-diff 37.8%

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

      4. exp-sum 37.8%

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

      5. *-commutative 37.8%

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

      6. exp-to-pow 37.8%

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

      7. *-commutative 37.8%

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

      8. exp-to-pow 38.8%

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

      9. sub-neg 38.8%

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

      10. metadata-eval 38.8%

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

   3. Simplified 38.8%

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

   4. Taylor expanded in t around 0 46.2%

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

      1. times-frac 46.0%

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

   6. Simplified 46.0%

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

   7. Taylor expanded in y around 0 81.2%

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

   if -2.89999999999999975e-63 < t < 1.05e11

   1. Initial program 97.4%

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

      1. associate-*l/ 85.4%

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

      2. *-commutative 85.4%

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

      3. exp-diff 73.8%

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

      4. exp-sum 72.1%

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

      5. *-commutative 72.1%

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

      6. exp-to-pow 72.1%

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

      7. *-commutative 72.1%

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

      8. exp-to-pow 73.5%

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

      9. sub-neg 73.5%

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

      10. metadata-eval 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in t around 0 79.6%

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

      1. times-frac 73.6%

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

   6. Simplified 73.6%

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

      1. associate-*l/ 82.1%

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

      2. associate-/r* 82.1%

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

   8. Applied egg-rr 82.1%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 105000000000:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{z}^{y}}{y}}{e^{b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \end{array} \]

Alternative 5: 81.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ t_2 := \frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{t_1}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{a \cdot t_1}\\ \mathbf{elif}\;t \leq 80000000000:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{z}^{y}}{y}}{e^{b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))) (t_2 (/ x (/ y (/ (pow a t) a)))))
   (if (<= t -5.2e+69)
     t_2
     (if (<= t -2.4e+14)
       (* (/ x a) (/ (pow z y) t_1))
       (if (<= t -2.6e-63)
         (/ (* x (pow a t)) (* a t_1))
         (if (<= t 80000000000.0)
           (/ (* x (/ (/ (pow z y) y) (exp b))) a)
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * exp(b);
	double t_2 = x / (y / (pow(a, t) / a));
	double tmp;
	if (t <= -5.2e+69) {
		tmp = t_2;
	} else if (t <= -2.4e+14) {
		tmp = (x / a) * (pow(z, y) / t_1);
	} else if (t <= -2.6e-63) {
		tmp = (x * pow(a, t)) / (a * t_1);
	} else if (t <= 80000000000.0) {
		tmp = (x * ((pow(z, y) / y) / exp(b))) / a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * exp(b)
    t_2 = x / (y / ((a ** t) / a))
    if (t <= (-5.2d+69)) then
        tmp = t_2
    else if (t <= (-2.4d+14)) then
        tmp = (x / a) * ((z ** y) / t_1)
    else if (t <= (-2.6d-63)) then
        tmp = (x * (a ** t)) / (a * t_1)
    else if (t <= 80000000000.0d0) then
        tmp = (x * (((z ** y) / y) / exp(b))) / a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * Math.exp(b);
	double t_2 = x / (y / (Math.pow(a, t) / a));
	double tmp;
	if (t <= -5.2e+69) {
		tmp = t_2;
	} else if (t <= -2.4e+14) {
		tmp = (x / a) * (Math.pow(z, y) / t_1);
	} else if (t <= -2.6e-63) {
		tmp = (x * Math.pow(a, t)) / (a * t_1);
	} else if (t <= 80000000000.0) {
		tmp = (x * ((Math.pow(z, y) / y) / Math.exp(b))) / a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * math.exp(b)
	t_2 = x / (y / (math.pow(a, t) / a))
	tmp = 0
	if t <= -5.2e+69:
		tmp = t_2
	elif t <= -2.4e+14:
		tmp = (x / a) * (math.pow(z, y) / t_1)
	elif t <= -2.6e-63:
		tmp = (x * math.pow(a, t)) / (a * t_1)
	elif t <= 80000000000.0:
		tmp = (x * ((math.pow(z, y) / y) / math.exp(b))) / a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * exp(b))
	t_2 = Float64(x / Float64(y / Float64((a ^ t) / a)))
	tmp = 0.0
	if (t <= -5.2e+69)
		tmp = t_2;
	elseif (t <= -2.4e+14)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / t_1));
	elseif (t <= -2.6e-63)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(a * t_1));
	elseif (t <= 80000000000.0)
		tmp = Float64(Float64(x * Float64(Float64((z ^ y) / y) / exp(b))) / a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * exp(b);
	t_2 = x / (y / ((a ^ t) / a));
	tmp = 0.0;
	if (t <= -5.2e+69)
		tmp = t_2;
	elseif (t <= -2.4e+14)
		tmp = (x / a) * ((z ^ y) / t_1);
	elseif (t <= -2.6e-63)
		tmp = (x * (a ^ t)) / (a * t_1);
	elseif (t <= 80000000000.0)
		tmp = (x * (((z ^ y) / y) / exp(b))) / a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y / N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+69], t$95$2, If[LessEqual[t, -2.4e+14], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e-63], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 80000000000.0], N[(N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.2000000000000004e69 or 8e10 < 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/ 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. exp-diff 65.0%

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

      4. exp-sum 48.5%

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

      5. *-commutative 48.5%

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

      6. exp-to-pow 48.5%

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

      7. *-commutative 48.5%

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

      8. exp-to-pow 48.5%

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

      9. sub-neg 48.5%

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

      10. metadata-eval 48.5%

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

   3. Simplified 48.5%

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

   4. Taylor expanded in y around 0 69.9%

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

      1. exp-to-pow 69.9%

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

      2. sub-neg 69.9%

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

      3. metadata-eval 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in b around 0 84.7%

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

   9. Simplified 84.7%

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

       1. +-commutative 84.7%

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

       2. unpow-prod-up 84.7%

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

       3. unpow-1 84.7%

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

   11. Applied egg-rr 84.7%

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

       1. associate-*r/ 84.7%

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

       2. *-rgt-identity 84.7%

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

   13. Simplified 84.7%

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

   if -5.2000000000000004e69 < t < -2.4e14

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

      3. exp-diff 81.8%

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

      4. exp-sum 45.5%

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

      5. *-commutative 45.5%

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

      6. exp-to-pow 45.5%

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

      7. *-commutative 45.5%

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

      8. exp-to-pow 45.5%

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

      9. sub-neg 45.5%

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

      10. metadata-eval 45.5%

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

   3. Simplified 45.5%

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

   4. Taylor expanded in t around 0 91.6%

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

      1. times-frac 91.6%

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

   6. Simplified 91.6%

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

   if -2.4e14 < t < -2.6000000000000001e-63

   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/ 90.5%

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

      2. *-commutative 90.5%

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

      3. exp-diff 58.7%

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

      4. exp-sum 58.7%

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

      5. *-commutative 58.7%

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

      6. exp-to-pow 58.7%

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

      7. *-commutative 58.7%

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

      8. exp-to-pow 59.3%

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

      9. sub-neg 59.3%

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

      10. metadata-eval 59.3%

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

   3. Simplified 59.3%

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

      1. unpow-prod-up 59.3%

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

      2. unpow-1 59.3%

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

   5. Applied egg-rr 59.3%

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

      1. associate-*r/ 59.3%

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

      2. *-rgt-identity 59.3%

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

   7. Simplified 59.3%

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

   8. Taylor expanded in y around 0 80.1%

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

   if -2.6000000000000001e-63 < t < 8e10

   1. Initial program 97.4%

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

      1. associate-*l/ 85.4%

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

      2. *-commutative 85.4%

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

      3. exp-diff 73.8%

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

      4. exp-sum 72.1%

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

      5. *-commutative 72.1%

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

      6. exp-to-pow 72.1%

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

      7. *-commutative 72.1%

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

      8. exp-to-pow 73.5%

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

      9. sub-neg 73.5%

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

      10. metadata-eval 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in t around 0 79.6%

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

      1. times-frac 73.6%

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

   6. Simplified 73.6%

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

      1. associate-*l/ 82.1%

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

      2. associate-/r* 82.1%

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

   8. Applied egg-rr 82.1%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 80000000000:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{z}^{y}}{y}}{e^{b}}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \end{array} \]

Alternative 6: 76.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.42 \cdot 10^{-176}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+115}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -4.2e-10)
     t_1
     (if (<= y 3.42e-176)
       (/ x (/ y (/ (pow a t) a)))
       (if (<= y 5.5e+115) (* (/ (pow a (+ t -1.0)) (exp b)) (/ x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -4.2e-10) {
		tmp = t_1;
	} else if (y <= 3.42e-176) {
		tmp = x / (y / (pow(a, t) / a));
	} else if (y <= 5.5e+115) {
		tmp = (pow(a, (t + -1.0)) / exp(b)) * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * ((z ** y) / a)) / y
    if (y <= (-4.2d-10)) then
        tmp = t_1
    else if (y <= 3.42d-176) then
        tmp = x / (y / ((a ** t) / a))
    else if (y <= 5.5d+115) then
        tmp = ((a ** (t + (-1.0d0))) / exp(b)) * (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (Math.pow(z, y) / a)) / y;
	double tmp;
	if (y <= -4.2e-10) {
		tmp = t_1;
	} else if (y <= 3.42e-176) {
		tmp = x / (y / (Math.pow(a, t) / a));
	} else if (y <= 5.5e+115) {
		tmp = (Math.pow(a, (t + -1.0)) / Math.exp(b)) * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -4.2e-10:
		tmp = t_1
	elif y <= 3.42e-176:
		tmp = x / (y / (math.pow(a, t) / a))
	elif y <= 5.5e+115:
		tmp = (math.pow(a, (t + -1.0)) / math.exp(b)) * (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -4.2e-10)
		tmp = t_1;
	elseif (y <= 3.42e-176)
		tmp = Float64(x / Float64(y / Float64((a ^ t) / a)));
	elseif (y <= 5.5e+115)
		tmp = Float64(Float64((a ^ Float64(t + -1.0)) / exp(b)) * Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -4.2e-10)
		tmp = t_1;
	elseif (y <= 3.42e-176)
		tmp = x / (y / ((a ^ t) / a));
	elseif (y <= 5.5e+115)
		tmp = ((a ^ (t + -1.0)) / exp(b)) * (x / 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[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -4.2e-10], t$95$1, If[LessEqual[y, 3.42e-176], N[(x / N[(y / N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+115], N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2e-10 or 5.5e115 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 89.1%

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

      1. +-commutative 89.1%

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

      2. mul-1-neg 89.1%

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

      3. unsub-neg 89.1%

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

   4. Simplified 89.1%

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

   5. Taylor expanded in b around 0 79.9%

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

      1. *-commutative 79.9%

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

      2. div-exp 79.9%

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

      3. *-commutative 79.9%

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

      4. exp-to-pow 79.9%

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

      5. rem-exp-log 80.0%

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

   7. Simplified 80.0%

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

   if -4.2e-10 < y < 3.4199999999999999e-176

   1. Initial program 96.7%

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

      1. associate-*l/ 87.2%

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

      2. *-commutative 87.2%

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

      3. exp-diff 76.8%

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

      4. exp-sum 76.8%

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

      5. *-commutative 76.8%

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

      6. exp-to-pow 76.8%

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

      7. *-commutative 76.8%

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

      8. exp-to-pow 78.2%

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

      9. sub-neg 78.2%

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

      10. metadata-eval 78.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in y around 0 81.4%

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

      1. exp-to-pow 83.2%

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

      2. sub-neg 83.2%

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

      3. metadata-eval 83.2%

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

   6. Simplified 83.2%

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

   7. Taylor expanded in b around 0 81.0%

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

   9. Simplified 83.9%

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

       1. +-commutative 83.9%

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

       2. unpow-prod-up 84.0%

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

       3. unpow-1 84.0%

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

   11. Applied egg-rr 84.0%

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

       1. associate-*r/ 84.0%

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

       2. *-rgt-identity 84.0%

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

   13. Simplified 84.0%

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

   if 3.4199999999999999e-176 < y < 5.5e115

   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/ 92.5%

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

      2. *-commutative 92.5%

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

      3. exp-diff 74.5%

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

      4. exp-sum 63.0%

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

      5. *-commutative 63.0%

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

      6. exp-to-pow 63.0%

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

      7. *-commutative 63.0%

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

      8. exp-to-pow 64.0%

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

      9. sub-neg 64.0%

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

      10. metadata-eval 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in y around 0 75.0%

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

      1. exp-to-pow 76.0%

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

      2. sub-neg 76.0%

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

      3. metadata-eval 76.0%

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

   6. Simplified 76.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 3.42 \cdot 10^{-176}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+115}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{e^{b}} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 7: 87.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+82} \lor \neg \left(y \leq 2.05 \cdot 10^{+214}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.3e+82) (not (<= y 2.05e+214)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.3e+82) || !(y <= 2.05e+214)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5.3d+82)) .or. (.not. (y <= 2.05d+214))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.3e+82) || !(y <= 2.05e+214)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.3e+82) or not (y <= 2.05e+214):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.3e+82) || !(y <= 2.05e+214))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.3e+82) || ~((y <= 2.05e+214)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.3e+82], N[Not[LessEqual[y, 2.05e+214]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.29999999999999977e82 or 2.05e214 < 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. Taylor expanded in t around 0 94.4%

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

      1. +-commutative 94.4%

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

      2. mul-1-neg 94.4%

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

      3. unsub-neg 94.4%

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

   4. Simplified 94.4%

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

   5. Taylor expanded in b around 0 90.2%

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

      1. *-commutative 90.2%

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

      2. div-exp 90.2%

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

      3. *-commutative 90.2%

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

      4. exp-to-pow 90.2%

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

      5. rem-exp-log 90.2%

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

   7. Simplified 90.2%

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

   if -5.29999999999999977e82 < y < 2.05e214

   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. Taylor expanded in y around 0 89.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+82} \lor \neg \left(y \leq 2.05 \cdot 10^{+214}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]

Alternative 8: 74.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-169}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (/ (pow z y) a)) y)))
   (if (<= y -4.2e-10)
     t_1
     (if (<= y 1.02e-169)
       (/ x (/ y (/ (pow a t) a)))
       (if (<= y 2.9e+113) (/ (/ x (* a (exp b))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * (pow(z, y) / a)) / y;
	double tmp;
	if (y <= -4.2e-10) {
		tmp = t_1;
	} else if (y <= 1.02e-169) {
		tmp = x / (y / (pow(a, t) / a));
	} else if (y <= 2.9e+113) {
		tmp = (x / (a * exp(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 * ((z ** y) / a)) / y
    if (y <= (-4.2d-10)) then
        tmp = t_1
    else if (y <= 1.02d-169) then
        tmp = x / (y / ((a ** t) / a))
    else if (y <= 2.9d+113) then
        tmp = (x / (a * exp(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(z, y) / a)) / y;
	double tmp;
	if (y <= -4.2e-10) {
		tmp = t_1;
	} else if (y <= 1.02e-169) {
		tmp = x / (y / (Math.pow(a, t) / a));
	} else if (y <= 2.9e+113) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * (math.pow(z, y) / a)) / y
	tmp = 0
	if y <= -4.2e-10:
		tmp = t_1
	elif y <= 1.02e-169:
		tmp = x / (y / (math.pow(a, t) / a))
	elif y <= 2.9e+113:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	tmp = 0.0
	if (y <= -4.2e-10)
		tmp = t_1;
	elseif (y <= 1.02e-169)
		tmp = Float64(x / Float64(y / Float64((a ^ t) / a)));
	elseif (y <= 2.9e+113)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * ((z ^ y) / a)) / y;
	tmp = 0.0;
	if (y <= -4.2e-10)
		tmp = t_1;
	elseif (y <= 1.02e-169)
		tmp = x / (y / ((a ^ t) / a));
	elseif (y <= 2.9e+113)
		tmp = (x / (a * exp(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[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -4.2e-10], t$95$1, If[LessEqual[y, 1.02e-169], N[(x / N[(y / N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+113], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2e-10 or 2.89999999999999984e113 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 89.1%

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

      1. +-commutative 89.1%

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

      2. mul-1-neg 89.1%

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

      3. unsub-neg 89.1%

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

   4. Simplified 89.1%

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

   5. Taylor expanded in b around 0 79.9%

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

      1. *-commutative 79.9%

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

      2. div-exp 79.9%

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

      3. *-commutative 79.9%

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

      4. exp-to-pow 79.9%

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

      5. rem-exp-log 80.0%

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

   7. Simplified 80.0%

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

   if -4.2e-10 < y < 1.01999999999999996e-169

   1. Initial program 96.8%

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

      1. associate-*l/ 87.5%

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

      2. *-commutative 87.5%

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

      3. exp-diff 77.4%

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

      4. exp-sum 77.4%

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

      5. *-commutative 77.4%

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

      6. exp-to-pow 77.4%

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

      7. *-commutative 77.4%

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

      8. exp-to-pow 78.7%

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

      9. sub-neg 78.7%

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

      10. metadata-eval 78.7%

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

   3. Simplified 78.7%

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

   4. Taylor expanded in y around 0 81.9%

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

      1. exp-to-pow 83.6%

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

      2. sub-neg 83.6%

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

      3. metadata-eval 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in b around 0 80.3%

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

   9. Simplified 83.1%

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

       1. +-commutative 83.1%

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

       2. unpow-prod-up 83.1%

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

       3. unpow-1 83.1%

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

   11. Applied egg-rr 83.1%

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

       1. associate-*r/ 83.1%

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

       2. *-rgt-identity 83.1%

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

   13. Simplified 83.1%

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

   if 1.01999999999999996e-169 < y < 2.89999999999999984e113

   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. Taylor expanded in t around 0 80.5%

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

      1. +-commutative 80.5%

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

      2. mul-1-neg 80.5%

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

      3. unsub-neg 80.5%

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

   4. Simplified 80.5%

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

   5. Taylor expanded in y around 0 70.9%

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

      1. exp-neg 70.9%

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

      2. associate-*r/ 70.9%

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

      3. *-rgt-identity 70.9%

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

      4. +-commutative 70.9%

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

      5. exp-sum 70.9%

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

      6. rem-exp-log 72.1%

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

   7. Simplified 72.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-169}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 9: 70.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+108} \lor \neg \left(b \leq 9 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.35e+108) (not (<= b 9e+60)))
   (/ x (* a (* y (exp b))))
   (* (pow a (+ t -1.0)) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.35e+108) || !(b <= 9e+60)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = pow(a, (t + -1.0)) * (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 ((b <= (-1.35d+108)) .or. (.not. (b <= 9d+60))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (a ** (t + (-1.0d0))) * (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 ((b <= -1.35e+108) || !(b <= 9e+60)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = Math.pow(a, (t + -1.0)) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.35e+108) or not (b <= 9e+60):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = math.pow(a, (t + -1.0)) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.35e+108) || !(b <= 9e+60))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64((a ^ Float64(t + -1.0)) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.35e+108) || ~((b <= 9e+60)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (a ^ (t + -1.0)) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.35e+108], N[Not[LessEqual[b, 9e+60]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.35e108 or 9.00000000000000026e60 < 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/ 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. exp-diff 57.1%

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

      4. exp-sum 52.7%

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

      5. *-commutative 52.7%

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

      6. exp-to-pow 52.7%

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

      7. *-commutative 52.7%

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

      8. exp-to-pow 52.7%

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

      9. sub-neg 52.7%

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

      10. metadata-eval 52.7%

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

   3. Simplified 52.7%

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

   4. Taylor expanded in t around 0 66.0%

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

      1. times-frac 53.9%

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

   6. Simplified 53.9%

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

   7. Taylor expanded in y around 0 88.1%

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

   if -1.35e108 < b < 9.00000000000000026e60

   1. Initial program 97.9%

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

      1. associate-*l/ 86.9%

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

      2. *-commutative 86.9%

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

      3. exp-diff 76.0%

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

      4. exp-sum 64.5%

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

      5. *-commutative 64.5%

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

      6. exp-to-pow 64.5%

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

      7. *-commutative 64.5%

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

      8. exp-to-pow 65.6%

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

      9. sub-neg 65.6%

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

      10. metadata-eval 65.6%

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

   3. Simplified 65.6%

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

   4. Taylor expanded in y around 0 62.9%

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

      1. exp-to-pow 64.1%

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

      2. sub-neg 64.1%

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

      3. metadata-eval 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in b around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-*r/ 64.6%

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

      3. exp-to-pow 65.6%

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

      4. sub-neg 65.6%

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

      5. metadata-eval 65.6%

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

      6. +-commutative 65.6%

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

   9. Simplified 65.6%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+108} \lor \neg \left(b \leq 9 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;{a}^{\left(t + -1\right)} \cdot \frac{x}{y}\\ \end{array} \]

Alternative 10: 74.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+55} \lor \neg \left(b \leq 8.4 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2e+55) (not (<= b 8.4e+60)))
   (/ x (* a (* y (exp b))))
   (/ x (/ y (/ (pow a t) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2e+55) || !(b <= 8.4e+60)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x / (y / (pow(a, t) / 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 <= (-2d+55)) .or. (.not. (b <= 8.4d+60))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x / (y / ((a ** t) / 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 <= -2e+55) || !(b <= 8.4e+60)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x / (y / (Math.pow(a, t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2e+55) or not (b <= 8.4e+60):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x / (y / (math.pow(a, t) / a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2e+55) || !(b <= 8.4e+60))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x / Float64(y / Float64((a ^ t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2e+55) || ~((b <= 8.4e+60)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x / (y / ((a ^ t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2e+55], N[Not[LessEqual[b, 8.4e+60]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y / N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.00000000000000002e55 or 8.4000000000000004e60 < 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/ 91.5%

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

      2. *-commutative 91.5%

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

      3. exp-diff 57.5%

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

      4. exp-sum 52.8%

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

      5. *-commutative 52.8%

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

      6. exp-to-pow 52.8%

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

      7. *-commutative 52.8%

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

      8. exp-to-pow 52.8%

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

      9. sub-neg 52.8%

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

      10. metadata-eval 52.8%

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

   3. Simplified 52.8%

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

   4. Taylor expanded in t around 0 65.2%

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

      1. times-frac 51.9%

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

   6. Simplified 51.9%

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

   7. Taylor expanded in y around 0 85.1%

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

   if -2.00000000000000002e55 < b < 8.4000000000000004e60

   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. Step-by-step derivation

      1. associate-*l/ 86.3%

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

      2. *-commutative 86.3%

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

      3. exp-diff 77.6%

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

      4. exp-sum 65.6%

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

      5. *-commutative 65.6%

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

      6. exp-to-pow 65.6%

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

      7. *-commutative 65.6%

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

      8. exp-to-pow 66.8%

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

      9. sub-neg 66.8%

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

      10. metadata-eval 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in y around 0 63.1%

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

      1. exp-to-pow 64.5%

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

      2. sub-neg 64.5%

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

      3. metadata-eval 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in b around 0 68.8%

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

   9. Simplified 70.9%

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

       1. +-commutative 70.9%

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

       2. unpow-prod-up 70.9%

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

       3. unpow-1 70.9%

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

   11. Applied egg-rr 70.9%

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

       1. associate-*r/ 70.9%

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

       2. *-rgt-identity 70.9%

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

   13. Simplified 70.9%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+55} \lor \neg \left(b \leq 8.4 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \end{array} \]

Alternative 11: 59.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \frac{x}{a \cdot \left(y \cdot e^{b}\right)} \end{array} \]

FPCore

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

C

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

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 * exp(b)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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/ 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. exp-diff 69.3%

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

   4. exp-sum 60.3%

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

   5. *-commutative 60.3%

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

   6. exp-to-pow 60.3%

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

   7. *-commutative 60.3%

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

   8. exp-to-pow 61.0%

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

   9. sub-neg 61.0%

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

   10. metadata-eval 61.0%

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

3. Simplified 61.0%

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

4. Taylor expanded in t around 0 62.7%

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

   1. times-frac 57.2%

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

6. Simplified 57.2%

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

7. Taylor expanded in y around 0 58.7%

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

8. Final simplification 58.7%

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

Alternative 12: 39.5% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{a}\\ \mathbf{if}\;b \leq -27:\\ \;\;\;\;t_1 - \frac{x}{y} \cdot \frac{b}{a}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-233}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-209}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x y) a)))
   (if (<= b -27.0)
     (- t_1 (* (/ x y) (/ b a)))
     (if (<= b 5.5e-233)
       (/ x (* a (+ y (* y b))))
       (if (<= b 1.02e-209)
         (/ (/ x (* a b)) y)
         (if (<= b 8e+57) t_1 (/ x (* a (* y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) / a;
	double tmp;
	if (b <= -27.0) {
		tmp = t_1 - ((x / y) * (b / a));
	} else if (b <= 5.5e-233) {
		tmp = x / (a * (y + (y * b)));
	} else if (b <= 1.02e-209) {
		tmp = (x / (a * b)) / y;
	} else if (b <= 8e+57) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) / a
    if (b <= (-27.0d0)) then
        tmp = t_1 - ((x / y) * (b / a))
    else if (b <= 5.5d-233) then
        tmp = x / (a * (y + (y * b)))
    else if (b <= 1.02d-209) then
        tmp = (x / (a * b)) / y
    else if (b <= 8d+57) then
        tmp = t_1
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / y) / a;
	double tmp;
	if (b <= -27.0) {
		tmp = t_1 - ((x / y) * (b / a));
	} else if (b <= 5.5e-233) {
		tmp = x / (a * (y + (y * b)));
	} else if (b <= 1.02e-209) {
		tmp = (x / (a * b)) / y;
	} else if (b <= 8e+57) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / y) / a
	tmp = 0
	if b <= -27.0:
		tmp = t_1 - ((x / y) * (b / a))
	elif b <= 5.5e-233:
		tmp = x / (a * (y + (y * b)))
	elif b <= 1.02e-209:
		tmp = (x / (a * b)) / y
	elif b <= 8e+57:
		tmp = t_1
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / y) / a)
	tmp = 0.0
	if (b <= -27.0)
		tmp = Float64(t_1 - Float64(Float64(x / y) * Float64(b / a)));
	elseif (b <= 5.5e-233)
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	elseif (b <= 1.02e-209)
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	elseif (b <= 8e+57)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / y) / a;
	tmp = 0.0;
	if (b <= -27.0)
		tmp = t_1 - ((x / y) * (b / a));
	elseif (b <= 5.5e-233)
		tmp = x / (a * (y + (y * b)));
	elseif (b <= 1.02e-209)
		tmp = (x / (a * b)) / y;
	elseif (b <= 8e+57)
		tmp = t_1;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[b, -27.0], N[(t$95$1 - N[(N[(x / y), $MachinePrecision] * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-233], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.02e-209], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 8e+57], t$95$1, N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -27

   1. Initial program 99.8%

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

      1. associate-*l/ 92.4%

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

      2. *-commutative 92.4%

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

      3. exp-diff 55.5%

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

      4. exp-sum 47.8%

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

      5. *-commutative 47.8%

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

      6. exp-to-pow 47.8%

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

      7. *-commutative 47.8%

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

      8. exp-to-pow 47.8%

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

      9. sub-neg 47.8%

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

      10. metadata-eval 47.8%

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

   3. Simplified 47.8%

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

   4. Taylor expanded in t around 0 60.3%

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

      1. times-frac 49.5%

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

   6. Simplified 49.5%

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

   7. Taylor expanded in y around 0 75.9%

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

   8. Taylor expanded in b around 0 36.2%

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

      1. +-commutative 36.2%

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

      2. mul-1-neg 36.2%

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

      3. unsub-neg 36.2%

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

      4. associate-/r* 37.6%

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

      5. *-rgt-identity 37.6%

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

      6. associate-*r/ 37.6%

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

      7. associate-*l/ 39.1%

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

      8. associate-*r/ 39.1%

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

      9. *-rgt-identity 39.1%

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

      10. times-frac 43.5%

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

   10. Simplified 43.5%

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

   if -27 < b < 5.50000000000000005e-233

   1. Initial program 98.6%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

      3. exp-diff 86.8%

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

      4. exp-sum 73.0%

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

      5. *-commutative 73.0%

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

      6. exp-to-pow 73.0%

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

      7. *-commutative 73.0%

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

      8. exp-to-pow 73.9%

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

      9. sub-neg 73.9%

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

      10. metadata-eval 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in t around 0 63.5%

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

      1. times-frac 63.5%

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

   6. Simplified 63.5%

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

   7. Taylor expanded in y around 0 34.4%

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

   8. Taylor expanded in b around 0 34.4%

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

   if 5.50000000000000005e-233 < b < 1.01999999999999999e-209

   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. Taylor expanded in t around 0 98.4%

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

      1. +-commutative 98.4%

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

      2. mul-1-neg 98.4%

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

      3. unsub-neg 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in y around 0 26.0%

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

      1. exp-neg 26.0%

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

      2. associate-*r/ 26.0%

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

      3. *-rgt-identity 26.0%

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

      4. +-commutative 26.0%

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

      5. exp-sum 26.0%

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

      6. rem-exp-log 27.6%

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

   7. Simplified 27.6%

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

   8. Taylor expanded in b around 0 27.6%

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

   9. Taylor expanded in b around inf 51.8%

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

   if 1.01999999999999999e-209 < b < 8.00000000000000039e57

   1. Initial program 95.4%

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

      1. associate-*l/ 82.3%

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

      2. *-commutative 82.3%

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

      3. exp-diff 71.2%

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

      4. exp-sum 60.1%

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

      5. *-commutative 60.1%

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

      6. exp-to-pow 60.1%

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

      7. *-commutative 60.1%

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

      8. exp-to-pow 62.3%

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

      9. sub-neg 62.3%

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

      10. metadata-eval 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in t around 0 58.8%

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

      1. times-frac 56.3%

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

   6. Simplified 56.3%

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

   7. Taylor expanded in y around 0 51.5%

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

   8. Taylor expanded in b around 0 50.1%

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

      1. associate-/r* 49.9%

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

      2. *-rgt-identity 49.9%

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

      3. associate-*r/ 49.9%

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

      4. associate-*l/ 53.5%

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

      5. associate-*r/ 53.6%

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

      6. *-rgt-identity 53.6%

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

   10. Simplified 53.6%

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

   if 8.00000000000000039e57 < 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. Taylor expanded in t around 0 94.9%

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

      1. +-commutative 94.9%

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

      2. mul-1-neg 94.9%

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

      3. unsub-neg 94.9%

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

   4. Simplified 94.9%

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

   5. Taylor expanded in y around 0 84.7%

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

      1. exp-neg 84.7%

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

      2. associate-*r/ 84.7%

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

      3. *-rgt-identity 84.7%

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

      4. +-commutative 84.7%

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

      5. exp-sum 84.7%

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

      6. rem-exp-log 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in b around 0 44.9%

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

   9. Taylor expanded in b around inf 53.1%

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

       1. *-commutative 53.1%

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

   11. Simplified 53.1%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -27:\\ \;\;\;\;\frac{\frac{x}{y}}{a} - \frac{x}{y} \cdot \frac{b}{a}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-233}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-209}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+57}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 13: 40.8% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.6e-65)
   (/ (- (/ x a) (* x (/ b a))) y)
   (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.6e-65) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.6d-65)) then
        tmp = ((x / a) - (x * (b / a))) / y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.6e-65) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.6e-65:
		tmp = ((x / a) - (x * (b / a))) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.6e-65)
		tmp = Float64(Float64(Float64(x / a) - Float64(x * Float64(b / a))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.6e-65)
		tmp = ((x / a) - (x * (b / a))) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.6e-65], N[(N[(N[(x / a), $MachinePrecision] - N[(x * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.6000000000000003e-65

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 87.4%

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

      1. +-commutative 87.4%

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

      2. mul-1-neg 87.4%

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

      3. unsub-neg 87.4%

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

   4. Simplified 87.4%

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

   5. Taylor expanded in y around 0 70.2%

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

      1. exp-neg 70.2%

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

      2. associate-*r/ 70.2%

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

      3. *-rgt-identity 70.2%

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

      4. +-commutative 70.2%

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

      5. exp-sum 70.2%

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

      6. rem-exp-log 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in b around 0 17.9%

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

   9. Taylor expanded in b around 0 45.0%

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

       1. +-commutative 45.0%

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

       2. mul-1-neg 45.0%

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

       3. unsub-neg 45.0%

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

       4. associate-/l* 40.1%

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

       5. associate-/r/ 40.2%

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

   11. Simplified 40.2%

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

   if -7.6000000000000003e-65 < b

   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/ 86.6%

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

      2. *-commutative 86.6%

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

      3. exp-diff 72.5%

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

      4. exp-sum 63.5%

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

      5. *-commutative 63.5%

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

      6. exp-to-pow 63.5%

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

      7. *-commutative 63.5%

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

      8. exp-to-pow 64.5%

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

      9. sub-neg 64.5%

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

      10. metadata-eval 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in t around 0 62.9%

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

      1. times-frac 59.4%

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

   6. Simplified 59.4%

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

   7. Taylor expanded in y around 0 54.6%

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

   8. Taylor expanded in b around 0 44.0%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 14: 40.8% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.35e-62)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.35e-62) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.35d-62)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.35e-62) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.35e-62:
		tmp = ((x / a) - ((x * b) / a)) / y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.35e-62)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.35e-62)
		tmp = ((x / a) - ((x * b) / a)) / y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.35e-62], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.3500000000000001e-62

   1. Initial program 99.9%

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

   2. Taylor expanded in t around 0 87.4%

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

      1. +-commutative 87.4%

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

      2. mul-1-neg 87.4%

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

      3. unsub-neg 87.4%

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

   4. Simplified 87.4%

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

   5. Taylor expanded in y around 0 70.2%

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

      1. exp-neg 70.2%

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

      2. associate-*r/ 70.2%

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

      3. *-rgt-identity 70.2%

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

      4. +-commutative 70.2%

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

      5. exp-sum 70.2%

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

      6. rem-exp-log 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in b around 0 17.9%

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

   9. Taylor expanded in b around 0 45.0%

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

   if -1.3500000000000001e-62 < b

   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/ 86.6%

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

      2. *-commutative 86.6%

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

      3. exp-diff 72.5%

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

      4. exp-sum 63.5%

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

      5. *-commutative 63.5%

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

      6. exp-to-pow 63.5%

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

      7. *-commutative 63.5%

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

      8. exp-to-pow 64.5%

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

      9. sub-neg 64.5%

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

      10. metadata-eval 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in t around 0 62.9%

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

      1. times-frac 59.4%

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

   6. Simplified 59.4%

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

   7. Taylor expanded in y around 0 54.6%

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

   8. Taylor expanded in b around 0 44.0%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 15: 36.2% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -24.5:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -24.5) (/ (/ x y) a) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -24.5) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-24.5d0)) then
        tmp = (x / y) / a
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -24.5) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -24.5:
		tmp = (x / y) / a
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -24.5)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -24.5)
		tmp = (x / y) / a;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -24.5], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -24.5

   1. Initial program 99.8%

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

      1. associate-*l/ 92.4%

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

      2. *-commutative 92.4%

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

      3. exp-diff 55.5%

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

      4. exp-sum 47.8%

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

      5. *-commutative 47.8%

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

      6. exp-to-pow 47.8%

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

      7. *-commutative 47.8%

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

      8. exp-to-pow 47.8%

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

      9. sub-neg 47.8%

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

      10. metadata-eval 47.8%

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

   3. Simplified 47.8%

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

   4. Taylor expanded in t around 0 60.3%

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

      1. times-frac 49.5%

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

   6. Simplified 49.5%

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

   7. Taylor expanded in y around 0 75.9%

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

   8. Taylor expanded in b around 0 29.0%

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

      1. associate-/r* 31.9%

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

      2. *-rgt-identity 31.9%

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

      3. associate-*r/ 31.9%

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

      4. associate-*l/ 34.4%

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

      5. associate-*r/ 34.4%

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

      6. *-rgt-identity 34.4%

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

   10. Simplified 34.4%

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

   if -24.5 < b

   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/ 87.1%

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

      2. *-commutative 87.1%

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

      3. exp-diff 74.0%

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

      4. exp-sum 64.6%

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

      5. *-commutative 64.6%

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

      6. exp-to-pow 64.6%

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

      7. *-commutative 64.6%

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

      8. exp-to-pow 65.5%

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

      9. sub-neg 65.5%

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

      10. metadata-eval 65.5%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in t around 0 63.6%

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

      1. times-frac 59.8%

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

   6. Simplified 59.8%

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

   7. Taylor expanded in y around 0 52.9%

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

   8. Taylor expanded in b around 0 43.1%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -24.5:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 16: 35.8% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 5.5e-42) (/ x (* y a)) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.5e-42) {
		tmp = x / (y * a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 5.5d-42) then
        tmp = x / (y * a)
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5.5e-42) {
		tmp = x / (y * a);
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5.5e-42:
		tmp = x / (y * a)
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5.5e-42)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5.5e-42)
		tmp = x / (y * a);
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5.5e-42], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.5e-42

   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/ 88.8%

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

      2. *-commutative 88.8%

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

      3. exp-diff 75.7%

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

      4. exp-sum 63.6%

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

      5. *-commutative 63.6%

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

      6. exp-to-pow 63.6%

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

      7. *-commutative 63.6%

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

      8. exp-to-pow 64.6%

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

      9. sub-neg 64.6%

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

      10. metadata-eval 64.6%

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

   3. Simplified 64.6%

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

   4. Taylor expanded in t around 0 63.5%

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

      1. times-frac 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in y around 0 52.4%

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

   8. Taylor expanded in b around 0 35.7%

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

   if 5.5e-42 < b

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 87.7%

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

      1. +-commutative 87.7%

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

      2. mul-1-neg 87.7%

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

      3. unsub-neg 87.7%

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

   4. Simplified 87.7%

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

   5. Taylor expanded in y around 0 75.5%

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

      1. exp-neg 75.5%

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

      2. associate-*r/ 75.5%

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

      3. *-rgt-identity 75.5%

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

      4. +-commutative 75.5%

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

      5. exp-sum 75.6%

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

      6. rem-exp-log 75.8%

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

   7. Simplified 75.8%

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

   8. Taylor expanded in b around 0 43.5%

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

   9. Taylor expanded in b around inf 49.8%

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

       1. *-commutative 49.8%

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

   11. Simplified 49.8%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 17: 31.7% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{+136}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1e+136) (/ (/ x y) a) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1e+136) {
		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 (x <= 1d+136) 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 (x <= 1e+136) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1e+136:
		tmp = (x / y) / a
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1e+136)
		tmp = Float64(Float64(x / 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 (x <= 1e+136)
		tmp = (x / y) / a;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1e+136], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.00000000000000006e136

   1. Initial program 98.6%

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

      1. associate-*l/ 90.5%

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

      2. *-commutative 90.5%

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

      3. exp-diff 70.9%

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

      4. exp-sum 62.2%

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

      5. *-commutative 62.2%

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

      6. exp-to-pow 62.2%

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

      7. *-commutative 62.2%

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

      8. exp-to-pow 63.0%

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

      9. sub-neg 63.0%

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

      10. metadata-eval 63.0%

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

   3. Simplified 63.0%

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

   4. Taylor expanded in t around 0 61.8%

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

      1. times-frac 56.2%

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

   6. Simplified 56.2%

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

   7. Taylor expanded in y around 0 58.4%

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

   8. Taylor expanded in b around 0 33.6%

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

      1. associate-/r* 34.4%

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

      2. *-rgt-identity 34.4%

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

      3. associate-*r/ 34.4%

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

      4. associate-*l/ 36.5%

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

      5. associate-*r/ 36.5%

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

      6. *-rgt-identity 36.5%

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

   10. Simplified 36.5%

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

   if 1.00000000000000006e136 < x

   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/ 76.3%

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

      2. *-commutative 76.3%

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

      3. exp-diff 60.1%

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

      4. exp-sum 49.3%

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

      5. *-commutative 49.3%

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

      6. exp-to-pow 49.3%

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

      7. *-commutative 49.3%

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

      8. exp-to-pow 49.3%

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

      9. sub-neg 49.3%

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

      10. metadata-eval 49.3%

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

   3. Simplified 49.3%

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

   4. Taylor expanded in t around 0 68.1%

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

      1. times-frac 62.6%

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

   6. Simplified 62.6%

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

   7. Taylor expanded in y around 0 60.6%

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

   8. Taylor expanded in b around 0 34.4%

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

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 10^{+136}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 18: 31.5% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

   1. associate-*l/ 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. exp-diff 69.3%

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

   4. exp-sum 60.3%

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

   5. *-commutative 60.3%

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

   6. exp-to-pow 60.3%

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

   7. *-commutative 60.3%

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

   8. exp-to-pow 61.0%

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

   9. sub-neg 61.0%

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

   10. metadata-eval 61.0%

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

3. Simplified 61.0%

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

4. Taylor expanded in t around 0 62.7%

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

   1. times-frac 57.2%

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

6. Simplified 57.2%

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

7. Taylor expanded in y around 0 58.7%

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

8. Taylor expanded in b around 0 33.7%

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

9. Final simplification 33.7%

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

Developer target: 72.1% 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 2023318 
(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))