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

Percentage Accurate: 98.3% → 98.3%

Time: 29.0s

Alternatives: 17

Speedup: 1.0×

• 47.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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* 98.7%

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

   2. fma-def 98.7%

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

   3. sub-neg 98.7%

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

   4. metadata-eval 98.7%

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

3. Simplified 98.7%

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

5. Final simplification 98.7%

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

Alternative 2: 92.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+67} \lor \neg \left(t + -1 \leq 2 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{x}{\frac{y}{e^{\log a \cdot \left(t + -1\right) - b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -5e+67) (not (<= (+ t -1.0) 2e+61)))
   (/ x (/ y (exp (- (* (log a) (+ t -1.0)) b))))
   (/ (* 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 + -1.0) <= -5e+67) || !((t + -1.0) <= 2e+61)) {
		tmp = x / (y / exp(((log(a) * (t + -1.0)) - b)));
	} 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 + (-1.0d0)) <= (-5d+67)) .or. (.not. ((t + (-1.0d0)) <= 2d+61))) then
        tmp = x / (y / exp(((log(a) * (t + (-1.0d0))) - b)))
    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 + -1.0) <= -5e+67) || !((t + -1.0) <= 2e+61)) {
		tmp = x / (y / Math.exp(((Math.log(a) * (t + -1.0)) - b)));
	} 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 + -1.0) <= -5e+67) or not ((t + -1.0) <= 2e+61):
		tmp = x / (y / math.exp(((math.log(a) * (t + -1.0)) - b)))
	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 ((Float64(t + -1.0) <= -5e+67) || !(Float64(t + -1.0) <= 2e+61))
		tmp = Float64(x / Float64(y / exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))));
	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 + -1.0) <= -5e+67) || ~(((t + -1.0) <= 2e+61)))
		tmp = x / (y / exp(((log(a) * (t + -1.0)) - b)));
	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[N[(t + -1.0), $MachinePrecision], -5e+67], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+61]], $MachinePrecision]], N[(x / N[(y / N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $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 (-.f64 t 1) < -4.99999999999999976e67 or 1.9999999999999999e61 < (-.f64 t 1)

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 95.9%

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

   if -4.99999999999999976e67 < (-.f64 t 1) < 1.9999999999999999e61

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0 96.0%

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

      1. +-commutative 96.0%

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

      2. mul-1-neg 96.0%

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

      3. unsub-neg 96.0%

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

   5. Simplified 96.0%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+67} \lor \neg \left(t + -1 \leq 2 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{x}{\frac{y}{e^{\log a \cdot \left(t + -1\right) - b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Final simplification 98.3%

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

Alternative 4: 81.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+55} \lor \neg \left(t + -1 \leq 2 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y \cdot e^{b}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -5e+55) (not (<= (+ t -1.0) 2e+79)))
   (/ x (/ y (/ (pow a t) a)))
   (/ x (/ a (/ (pow z y) (* y (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -5e+55) || !((t + -1.0) <= 2e+79)) {
		tmp = x / (y / (pow(a, t) / a));
	} else {
		tmp = x / (a / (pow(z, y) / (y * exp(b))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-5d+55)) .or. (.not. ((t + (-1.0d0)) <= 2d+79))) then
        tmp = x / (y / ((a ** t) / a))
    else
        tmp = x / (a / ((z ** y) / (y * exp(b))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -5e+55) || !((t + -1.0) <= 2e+79)) {
		tmp = x / (y / (Math.pow(a, t) / a));
	} else {
		tmp = x / (a / (Math.pow(z, y) / (y * Math.exp(b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -5e+55) or not ((t + -1.0) <= 2e+79):
		tmp = x / (y / (math.pow(a, t) / a))
	else:
		tmp = x / (a / (math.pow(z, y) / (y * math.exp(b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -5e+55) || !(Float64(t + -1.0) <= 2e+79))
		tmp = Float64(x / Float64(y / Float64((a ^ t) / a)));
	else
		tmp = Float64(x / Float64(a / Float64((z ^ y) / Float64(y * exp(b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -5e+55) || ~(((t + -1.0) <= 2e+79)))
		tmp = x / (y / ((a ^ t) / a));
	else
		tmp = x / (a / ((z ^ y) / (y * exp(b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+55], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+79]], $MachinePrecision]], N[(x / N[(y / N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -5.00000000000000046e55 or 1.99999999999999993e79 < (-.f64 t 1)

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 93.8%

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

      1. exp-diff 85.5%

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

      2. exp-to-pow 85.5%

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

      3. sub-neg 85.5%

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

      4. metadata-eval 85.5%

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

   7. Simplified 85.5%

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

      1. unpow-prod-up 85.5%

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

      2. unpow-1 85.5%

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

   9. Applied egg-rr 85.5%

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

       1. associate-*r/ 85.5%

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

       2. *-rgt-identity 85.5%

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

   11. Simplified 85.5%

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

   12. Taylor expanded in b around 0 92.8%

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

   if -5.00000000000000046e55 < (-.f64 t 1) < 1.99999999999999993e79

   1. Initial program 97.3%

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

      1. associate-/l* 97.9%

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

      2. associate--l+ 97.9%

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

      3. exp-sum 82.9%

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

      4. associate-/r* 82.9%

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

      5. *-commutative 82.9%

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

      6. exp-to-pow 82.9%

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

      7. exp-diff 78.5%

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

      8. *-commutative 78.5%

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

      9. exp-to-pow 79.3%

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

      10. sub-neg 79.3%

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

      11. metadata-eval 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in t around 0 82.5%

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

      1. associate-/l* 84.3%

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

   7. Simplified 84.3%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+55} \lor \neg \left(t + -1 \leq 2 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y \cdot e^{b}}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+16} \lor \neg \left(y \leq 2.65 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{e^{\log a \cdot \left(t + -1\right) - b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8e+16) (not (<= y 2.65e+95)))
   (/ (* x (/ (pow z y) a)) y)
   (/ x (/ y (exp (- (* (log a) (+ t -1.0)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e+16) || !(y <= 2.65e+95)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = x / (y / exp(((log(a) * (t + -1.0)) - b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8d+16)) .or. (.not. (y <= 2.65d+95))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = x / (y / exp(((log(a) * (t + (-1.0d0))) - b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8e+16) || !(y <= 2.65e+95)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = x / (y / Math.exp(((Math.log(a) * (t + -1.0)) - b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8e+16) or not (y <= 2.65e+95):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = x / (y / math.exp(((math.log(a) * (t + -1.0)) - b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8e+16) || !(y <= 2.65e+95))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(x / Float64(y / exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8e+16) || ~((y <= 2.65e+95)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = x / (y / exp(((log(a) * (t + -1.0)) - b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8e+16], N[Not[LessEqual[y, 2.65e+95]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y / N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8e16 or 2.6500000000000001e95 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 91.2%

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

      1. +-commutative 91.2%

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

      2. mul-1-neg 91.2%

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

      3. unsub-neg 91.2%

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

   5. Simplified 91.2%

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

   6. Taylor expanded in b around 0 81.5%

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

      1. *-commutative 81.5%

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

      2. exp-diff 81.5%

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

      3. *-commutative 81.5%

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

      4. exp-to-pow 81.5%

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

      5. rem-exp-log 81.5%

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

   8. Simplified 81.5%

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

   if -8e16 < y < 2.6500000000000001e95

   1. Initial program 97.2%

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

      1. associate-/l* 97.9%

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

      2. fma-def 97.9%

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

      3. sub-neg 97.9%

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

      4. metadata-eval 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around 0 96.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+16} \lor \neg \left(y \leq 2.65 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{e^{\log a \cdot \left(t + -1\right) - b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+55} \lor \neg \left(t + -1 \leq 4 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -5e+55) (not (<= (+ t -1.0) 4e+105)))
   (/ x (/ y (/ (pow a t) a)))
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -5e+55) || !((t + -1.0) <= 4e+105)) {
		tmp = x / (y / (pow(a, t) / a));
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-5d+55)) .or. (.not. ((t + (-1.0d0)) <= 4d+105))) then
        tmp = x / (y / ((a ** t) / a))
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -5e+55) || !((t + -1.0) <= 4e+105)) {
		tmp = x / (y / (Math.pow(a, t) / a));
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -5e+55) or not ((t + -1.0) <= 4e+105):
		tmp = x / (y / (math.pow(a, t) / a))
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -5e+55) || !(Float64(t + -1.0) <= 4e+105))
		tmp = Float64(x / Float64(y / Float64((a ^ t) / a)));
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -5e+55) || ~(((t + -1.0) <= 4e+105)))
		tmp = x / (y / ((a ^ t) / a));
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+55], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 4e+105]], $MachinePrecision]], N[(x / N[(y / N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -5.00000000000000046e55 or 3.9999999999999998e105 < (-.f64 t 1)

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-def 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 94.7%

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

      1. exp-diff 87.0%

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

      2. exp-to-pow 87.0%

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

      3. sub-neg 87.0%

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

      4. metadata-eval 87.0%

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

   7. Simplified 87.0%

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

      1. unpow-prod-up 87.0%

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

      2. unpow-1 87.0%

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

   9. Applied egg-rr 87.0%

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

       1. associate-*r/ 87.0%

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

       2. *-rgt-identity 87.0%

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

   11. Simplified 87.0%

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

   12. Taylor expanded in b around 0 94.7%

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

   if -5.00000000000000046e55 < (-.f64 t 1) < 3.9999999999999998e105

   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* 98.0%

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

      2. associate--l+ 98.0%

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

      3. exp-sum 81.5%

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

      4. associate-/r* 81.5%

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

      5. *-commutative 81.5%

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

      6. exp-to-pow 81.5%

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

      7. exp-diff 77.2%

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

      8. *-commutative 77.2%

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

      9. exp-to-pow 78.0%

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

      10. sub-neg 78.0%

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

      11. metadata-eval 78.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in t around 0 81.1%

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

      1. associate-/l* 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in y around 0 72.1%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+55} \lor \neg \left(t + -1 \leq 4 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{t}}{a}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.0% 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 98.3%

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

   1. associate-/l* 98.7%

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

   2. associate--l+ 98.7%

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

   3. exp-sum 80.0%

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

   4. associate-/r* 80.0%

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

   5. *-commutative 80.0%

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

   6. exp-to-pow 80.0%

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

   7. exp-diff 75.7%

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

   8. *-commutative 75.7%

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

   9. exp-to-pow 76.1%

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

   10. sub-neg 76.1%

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

   11. metadata-eval 76.1%

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

3. Simplified 76.1%

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

5. Taylor expanded in t around 0 67.2%

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

   1. associate-/l* 69.5%

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

7. Simplified 69.5%

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

8. Taylor expanded in y around 0 62.3%

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

9. Final simplification 62.3%

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

Alternative 8: 39.6% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{x \cdot \left(-b\right)}{a}}{y}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y \cdot \left(b + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.5e+133)
   (/ (/ (* x (- b)) a) y)
   (if (<= b 4.8e-244)
     (* x (/ 1.0 (* y a)))
     (if (<= b 8.5e+190)
       (/ (/ x (+ a (* a b))) y)
       (* (/ 1.0 a) (/ x (* y (+ b 1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+133) {
		tmp = ((x * -b) / a) / y;
	} else if (b <= 4.8e-244) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 8.5e+190) {
		tmp = (x / (a + (a * b))) / y;
	} else {
		tmp = (1.0 / a) * (x / (y * (b + 1.0)));
	}
	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 <= (-9.5d+133)) then
        tmp = ((x * -b) / a) / y
    else if (b <= 4.8d-244) then
        tmp = x * (1.0d0 / (y * a))
    else if (b <= 8.5d+190) then
        tmp = (x / (a + (a * b))) / y
    else
        tmp = (1.0d0 / a) * (x / (y * (b + 1.0d0)))
    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 <= -9.5e+133) {
		tmp = ((x * -b) / a) / y;
	} else if (b <= 4.8e-244) {
		tmp = x * (1.0 / (y * a));
	} else if (b <= 8.5e+190) {
		tmp = (x / (a + (a * b))) / y;
	} else {
		tmp = (1.0 / a) * (x / (y * (b + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e+133:
		tmp = ((x * -b) / a) / y
	elif b <= 4.8e-244:
		tmp = x * (1.0 / (y * a))
	elif b <= 8.5e+190:
		tmp = (x / (a + (a * b))) / y
	else:
		tmp = (1.0 / a) * (x / (y * (b + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e+133)
		tmp = Float64(Float64(Float64(x * Float64(-b)) / a) / y);
	elseif (b <= 4.8e-244)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	elseif (b <= 8.5e+190)
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	else
		tmp = Float64(Float64(1.0 / a) * Float64(x / Float64(y * Float64(b + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.5e+133)
		tmp = ((x * -b) / a) / y;
	elseif (b <= 4.8e-244)
		tmp = x * (1.0 / (y * a));
	elseif (b <= 8.5e+190)
		tmp = (x / (a + (a * b))) / y;
	else
		tmp = (1.0 / a) * (x / (y * (b + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e+133], N[(N[(N[(x * (-b)), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.8e-244], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e+190], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(1.0 / a), $MachinePrecision] * N[(x / N[(y * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.49999999999999996e133

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

      1. exp-diff 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 94.5%

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

   7. Taylor expanded in b around 0 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. associate-/l* 46.7%

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

   9. Simplified 46.7%

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

   10. Taylor expanded in b around inf 57.4%

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

   if -9.49999999999999996e133 < b < 4.80000000000000032e-244

   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* 98.4%

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

      2. associate--l+ 98.4%

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

      3. exp-sum 80.8%

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

      4. associate-/r* 80.8%

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

      5. *-commutative 80.8%

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

      6. exp-to-pow 80.8%

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

      7. exp-diff 76.8%

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

      8. *-commutative 76.8%

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

      9. exp-to-pow 77.3%

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

      10. sub-neg 77.3%

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

      11. metadata-eval 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in t around 0 59.8%

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

      1. associate-/l* 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in y around 0 50.7%

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

   9. Taylor expanded in b around 0 39.4%

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

       1. div-inv 41.3%

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

   11. Applied egg-rr 41.3%

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

   if 4.80000000000000032e-244 < b < 8.50000000000000022e190

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 77.2%

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

      1. exp-diff 75.1%

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

      2. exp-to-pow 75.9%

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

      3. sub-neg 75.9%

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

      4. metadata-eval 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in t around 0 57.1%

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

   7. Taylor expanded in b around 0 39.6%

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

   if 8.50000000000000022e190 < 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* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 70.8%

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

      4. associate-/r* 70.8%

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

      5. *-commutative 70.8%

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

      6. exp-to-pow 70.8%

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

      7. exp-diff 70.8%

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

      8. *-commutative 70.8%

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

      9. exp-to-pow 70.8%

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

      10. sub-neg 70.8%

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

      11. metadata-eval 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in t around 0 70.8%

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

      1. associate-/l* 70.8%

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

   7. Simplified 70.8%

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

   8. Taylor expanded in y around 0 91.8%

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

   9. Taylor expanded in b around 0 72.0%

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

       1. distribute-lft-out 72.0%

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

       2. distribute-rgt1-in 72.0%

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

   11. Simplified 72.0%

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

       1. *-un-lft-identity 72.0%

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

       2. times-frac 83.8%

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

       3. *-commutative 83.8%

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

   13. Applied egg-rr 83.8%

       \[\leadsto \color{blue}{\frac{1}{a} \cdot \frac{x}{y \cdot \left(b + 1\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{x \cdot \left(-b\right)}{a}}{y}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+190}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a} \cdot \frac{x}{y \cdot \left(b + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 39.9% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{\frac{x \cdot \left(-b\right)}{a}}{y}\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e+128)
   (/ (/ (* x (- b)) a) y)
   (if (<= b 4.6e-250) (* x (/ 1.0 (* y a))) (/ (/ x (+ a (* a b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+128) {
		tmp = ((x * -b) / a) / y;
	} else if (b <= 4.6e-250) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.5d+128)) then
        tmp = ((x * -b) / a) / y
    else if (b <= 4.6d-250) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e+128) {
		tmp = ((x * -b) / a) / y;
	} else if (b <= 4.6e-250) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e+128:
		tmp = ((x * -b) / a) / y
	elif b <= 4.6e-250:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e+128)
		tmp = Float64(Float64(Float64(x * Float64(-b)) / a) / y);
	elseif (b <= 4.6e-250)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.5e+128)
		tmp = ((x * -b) / a) / y;
	elseif (b <= 4.6e-250)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e+128], N[(N[(N[(x * (-b)), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.6e-250], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.49999999999999969e128

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

      1. exp-diff 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 94.5%

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

   7. Taylor expanded in b around 0 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. associate-/l* 46.7%

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

   9. Simplified 46.7%

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

   10. Taylor expanded in b around inf 57.4%

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

   if -3.49999999999999969e128 < b < 4.5999999999999999e-250

   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* 98.4%

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

      2. associate--l+ 98.4%

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

      3. exp-sum 80.8%

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

      4. associate-/r* 80.8%

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

      5. *-commutative 80.8%

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

      6. exp-to-pow 80.8%

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

      7. exp-diff 76.8%

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

      8. *-commutative 76.8%

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

      9. exp-to-pow 77.3%

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

      10. sub-neg 77.3%

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

      11. metadata-eval 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in t around 0 59.8%

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

      1. associate-/l* 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in y around 0 50.7%

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

   9. Taylor expanded in b around 0 39.4%

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

       1. div-inv 41.3%

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

   11. Applied egg-rr 41.3%

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

   if 4.5999999999999999e-250 < b

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 80.2%

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

      1. exp-diff 76.8%

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

      2. exp-to-pow 77.5%

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

      3. sub-neg 77.5%

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

      4. metadata-eval 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in t around 0 64.1%

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

   7. Taylor expanded in b around 0 45.9%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{\frac{x \cdot \left(-b\right)}{a}}{y}\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-250}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.1% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+129}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+129)
   (* (/ x y) (/ (- b) a))
   (if (<= b 3e+55) (* x (/ 1.0 (* 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 <= -1.25e+129) {
		tmp = (x / y) * (-b / a);
	} else if (b <= 3e+55) {
		tmp = x * (1.0 / (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 <= (-1.25d+129)) then
        tmp = (x / y) * (-b / a)
    else if (b <= 3d+55) then
        tmp = x * (1.0d0 / (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 <= -1.25e+129) {
		tmp = (x / y) * (-b / a);
	} else if (b <= 3e+55) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+129:
		tmp = (x / y) * (-b / a)
	elif b <= 3e+55:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+129)
		tmp = Float64(Float64(x / y) * Float64(Float64(-b) / a));
	elseif (b <= 3e+55)
		tmp = Float64(x * Float64(1.0 / 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 <= -1.25e+129)
		tmp = (x / y) * (-b / a);
	elseif (b <= 3e+55)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+129], N[(N[(x / y), $MachinePrecision] * N[((-b) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e+55], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.2500000000000001e129

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

      1. exp-diff 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 94.5%

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

   7. Taylor expanded in b around 0 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. associate-/l* 46.7%

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

   9. Simplified 46.7%

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

   10. Taylor expanded in b around inf 49.3%

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

       1. mul-1-neg 49.3%

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

       2. times-frac 49.3%

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

       3. distribute-rgt-neg-in 49.3%

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

   12. Simplified 49.3%

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

   if -1.2500000000000001e129 < b < 3.00000000000000017e55

   1. Initial program 97.5%

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

      1. associate-/l* 98.1%

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

      2. associate--l+ 98.1%

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

      3. exp-sum 83.5%

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

      4. associate-/r* 83.5%

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

      5. *-commutative 83.5%

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

      6. exp-to-pow 83.5%

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

      7. exp-diff 80.6%

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

      8. *-commutative 80.6%

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

      9. exp-to-pow 81.3%

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

      10. sub-neg 81.3%

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

      11. metadata-eval 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in t around 0 65.1%

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

      1. associate-/l* 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in y around 0 48.5%

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

   9. Taylor expanded in b around 0 40.1%

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

       1. div-inv 41.2%

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

   11. Applied egg-rr 41.2%

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

   if 3.00000000000000017e55 < 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* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 72.9%

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

      4. associate-/r* 72.9%

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

      5. *-commutative 72.9%

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

      6. exp-to-pow 72.9%

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

      7. exp-diff 70.8%

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

      8. *-commutative 70.8%

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

      9. exp-to-pow 70.8%

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

      10. sub-neg 70.8%

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

      11. metadata-eval 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in t around 0 72.9%

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

      1. associate-/l* 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in y around 0 87.7%

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

   9. Taylor expanded in b around 0 47.5%

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

       1. distribute-lft-out 47.5%

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

       2. distribute-rgt1-in 47.5%

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

   11. Simplified 47.5%

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

   12. Taylor expanded in b around inf 47.5%

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

       1. *-commutative 47.5%

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

   14. Simplified 47.5%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+129}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.9% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e+128)
   (/ (* x (/ (- b) a)) y)
   (if (<= b 2.85e+54) (* x (/ 1.0 (* 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 <= -3.5e+128) {
		tmp = (x * (-b / a)) / y;
	} else if (b <= 2.85e+54) {
		tmp = x * (1.0 / (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 <= (-3.5d+128)) then
        tmp = (x * (-b / a)) / y
    else if (b <= 2.85d+54) then
        tmp = x * (1.0d0 / (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 <= -3.5e+128) {
		tmp = (x * (-b / a)) / y;
	} else if (b <= 2.85e+54) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e+128:
		tmp = (x * (-b / a)) / y
	elif b <= 2.85e+54:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e+128)
		tmp = Float64(Float64(x * Float64(Float64(-b) / a)) / y);
	elseif (b <= 2.85e+54)
		tmp = Float64(x * Float64(1.0 / 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 <= -3.5e+128)
		tmp = (x * (-b / a)) / y;
	elseif (b <= 2.85e+54)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e+128], N[(N[(x * N[((-b) / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.85e+54], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.49999999999999969e128

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

      1. exp-diff 77.8%

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

      2. exp-to-pow 77.8%

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

      3. sub-neg 77.8%

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

      4. metadata-eval 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in t around 0 94.5%

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

   7. Taylor expanded in b around 0 57.4%

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

      1. +-commutative 57.4%

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

      2. mul-1-neg 57.4%

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

      3. unsub-neg 57.4%

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

      4. associate-/l* 46.7%

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

   9. Simplified 46.7%

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

   10. Taylor expanded in b around inf 57.4%

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

       1. mul-1-neg 57.4%

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

       2. associate-*l/ 52.0%

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

       3. distribute-rgt-neg-out 52.0%

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

   12. Simplified 52.0%

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

   if -3.49999999999999969e128 < b < 2.8499999999999998e54

   1. Initial program 97.5%

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

      1. associate-/l* 98.1%

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

      2. associate--l+ 98.1%

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

      3. exp-sum 83.5%

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

      4. associate-/r* 83.5%

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

      5. *-commutative 83.5%

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

      6. exp-to-pow 83.5%

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

      7. exp-diff 80.6%

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

      8. *-commutative 80.6%

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

      9. exp-to-pow 81.3%

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

      10. sub-neg 81.3%

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

      11. metadata-eval 81.3%

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

   3. Simplified 81.3%

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

   5. Taylor expanded in t around 0 65.1%

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

      1. associate-/l* 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in y around 0 48.5%

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

   9. Taylor expanded in b around 0 40.1%

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

       1. div-inv 41.2%

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

   11. Applied egg-rr 41.2%

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

   if 2.8499999999999998e54 < 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* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 72.9%

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

      4. associate-/r* 72.9%

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

      5. *-commutative 72.9%

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

      6. exp-to-pow 72.9%

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

      7. exp-diff 70.8%

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

      8. *-commutative 70.8%

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

      9. exp-to-pow 70.8%

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

      10. sub-neg 70.8%

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

      11. metadata-eval 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in t around 0 72.9%

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

      1. associate-/l* 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in y around 0 87.7%

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

   9. Taylor expanded in b around 0 47.5%

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

       1. distribute-lft-out 47.5%

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

       2. distribute-rgt1-in 47.5%

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

   11. Simplified 47.5%

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

   12. Taylor expanded in b around inf 47.5%

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

       1. *-commutative 47.5%

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

   14. Simplified 47.5%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.2% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(b + 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.3e-6) (/ (* x (/ (- b) a)) y) (/ x (* a (* y (+ b 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.3e-6) {
		tmp = (x * (-b / a)) / y;
	} else {
		tmp = x / (a * (y * (b + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.3d-6)) then
        tmp = (x * (-b / a)) / y
    else
        tmp = x / (a * (y * (b + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.3e-6) {
		tmp = (x * (-b / a)) / y;
	} else {
		tmp = x / (a * (y * (b + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.3e-6:
		tmp = (x * (-b / a)) / y
	else:
		tmp = x / (a * (y * (b + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.3e-6)
		tmp = Float64(Float64(x * Float64(Float64(-b) / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(b + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.3e-6)
		tmp = (x * (-b / a)) / y;
	else
		tmp = x / (a * (y * (b + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.3e-6], N[(N[(x * N[((-b) / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.30000000000000017e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.9%

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

      1. exp-diff 67.4%

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

      2. exp-to-pow 67.4%

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

      3. sub-neg 67.4%

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

      4. metadata-eval 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in t around 0 78.1%

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

   7. Taylor expanded in b around 0 40.9%

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

      1. +-commutative 40.9%

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

      2. mul-1-neg 40.9%

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

      3. unsub-neg 40.9%

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

      4. associate-/l* 35.2%

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

   9. Simplified 35.2%

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

   10. Taylor expanded in b around inf 40.9%

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

       1. mul-1-neg 40.9%

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

       2. associate-*l/ 38.1%

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

       3. distribute-rgt-neg-out 38.1%

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

   12. Simplified 38.1%

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

   if -3.30000000000000017e-6 < b

   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* 98.2%

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

      2. associate--l+ 98.2%

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

      3. exp-sum 84.0%

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

      4. associate-/r* 84.0%

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

      5. *-commutative 84.0%

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

      6. exp-to-pow 84.0%

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

      7. exp-diff 82.9%

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

      8. *-commutative 82.9%

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

      9. exp-to-pow 83.5%

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

      10. sub-neg 83.5%

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

      11. metadata-eval 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in t around 0 68.2%

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

      1. associate-/l* 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in y around 0 56.7%

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

   9. Taylor expanded in b around 0 41.8%

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

       1. distribute-lft-out 44.5%

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

       2. distribute-rgt1-in 44.5%

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

   11. Simplified 44.5%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot \frac{-b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(b + 1\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.3% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x \cdot \left(-b\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(b + 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.5e-5) (/ (/ (* x (- b)) a) y) (/ x (* a (* y (+ b 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.5e-5) {
		tmp = ((x * -b) / a) / y;
	} else {
		tmp = x / (a * (y * (b + 1.0)));
	}
	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-5)) then
        tmp = ((x * -b) / a) / y
    else
        tmp = x / (a * (y * (b + 1.0d0)))
    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-5) {
		tmp = ((x * -b) / a) / y;
	} else {
		tmp = x / (a * (y * (b + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.5e-5:
		tmp = ((x * -b) / a) / y
	else:
		tmp = x / (a * (y * (b + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.5e-5)
		tmp = Float64(Float64(Float64(x * Float64(-b)) / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(b + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.5e-5)
		tmp = ((x * -b) / a) / y;
	else
		tmp = x / (a * (y * (b + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.5e-5], N[(N[(N[(x * (-b)), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(b + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.5000000000000002e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.9%

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

      1. exp-diff 67.4%

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

      2. exp-to-pow 67.4%

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

      3. sub-neg 67.4%

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

      4. metadata-eval 67.4%

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

   5. Simplified 67.4%

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

   6. Taylor expanded in t around 0 78.1%

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

   7. Taylor expanded in b around 0 40.9%

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

      1. +-commutative 40.9%

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

      2. mul-1-neg 40.9%

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

      3. unsub-neg 40.9%

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

      4. associate-/l* 35.2%

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

   9. Simplified 35.2%

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

   10. Taylor expanded in b around inf 40.9%

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

   if -5.5000000000000002e-5 < b

   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* 98.2%

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

      2. associate--l+ 98.2%

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

      3. exp-sum 84.0%

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

      4. associate-/r* 84.0%

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

      5. *-commutative 84.0%

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

      6. exp-to-pow 84.0%

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

      7. exp-diff 82.9%

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

      8. *-commutative 82.9%

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

      9. exp-to-pow 83.5%

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

      10. sub-neg 83.5%

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

      11. metadata-eval 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in t around 0 68.2%

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

      1. associate-/l* 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in y around 0 56.7%

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

   9. Taylor expanded in b around 0 41.8%

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

       1. distribute-lft-out 44.5%

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

       2. distribute-rgt1-in 44.5%

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

   11. Simplified 44.5%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x \cdot \left(-b\right)}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(b + 1\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.8% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.8 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.8e-244) (* x (/ 1.0 (* y a))) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.8e-244) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 4.8d-244) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.8e-244) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 4.8e-244:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.8e-244)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 4.8e-244)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4.8e-244], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.80000000000000032e-244

   1. Initial program 97.6%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 78.5%

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

      4. associate-/r* 78.5%

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

      5. *-commutative 78.5%

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

      6. exp-to-pow 78.5%

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

      7. exp-diff 72.0%

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

      8. *-commutative 72.0%

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

      9. exp-to-pow 72.4%

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

      10. sub-neg 72.4%

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

      11. metadata-eval 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in t around 0 62.3%

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

      1. associate-/l* 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in y around 0 62.1%

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

   9. Taylor expanded in b around 0 35.6%

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

       1. div-inv 37.0%

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

   11. Applied egg-rr 37.0%

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

   if 4.80000000000000032e-244 < b

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 80.2%

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

      1. exp-diff 76.8%

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

      2. exp-to-pow 77.5%

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

      3. sub-neg 77.5%

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

      4. metadata-eval 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in t around 0 64.1%

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

   7. Taylor expanded in b around 0 39.5%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.8 \cdot 10^{-244}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.4% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3e+54) (* x (/ 1.0 (* 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 <= 3e+54) {
		tmp = x * (1.0 / (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 <= 3d+54) then
        tmp = x * (1.0d0 / (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 <= 3e+54) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3e+54:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3e+54)
		tmp = Float64(x * Float64(1.0 / 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 <= 3e+54)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3e+54], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.9999999999999999e54

   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* 98.4%

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

      2. associate--l+ 98.4%

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

      3. exp-sum 81.6%

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

      4. associate-/r* 81.6%

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

      5. *-commutative 81.6%

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

      6. exp-to-pow 81.6%

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

      7. exp-diff 76.8%

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

      8. *-commutative 76.8%

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

      9. exp-to-pow 77.3%

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

      10. sub-neg 77.3%

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

      11. metadata-eval 77.3%

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

   3. Simplified 77.3%

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

   5. Taylor expanded in t around 0 65.9%

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

      1. associate-/l* 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in y around 0 56.4%

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

   9. Taylor expanded in b around 0 37.5%

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

       1. div-inv 38.4%

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

   11. Applied egg-rr 38.4%

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

   if 2.9999999999999999e54 < 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* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 72.9%

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

      4. associate-/r* 72.9%

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

      5. *-commutative 72.9%

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

      6. exp-to-pow 72.9%

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

      7. exp-diff 70.8%

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

      8. *-commutative 70.8%

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

      9. exp-to-pow 70.8%

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

      10. sub-neg 70.8%

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

      11. metadata-eval 70.8%

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

   3. Simplified 70.8%

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

   5. Taylor expanded in t around 0 72.9%

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

      1. associate-/l* 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in y around 0 87.7%

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

   9. Taylor expanded in b around 0 47.5%

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

       1. distribute-lft-out 47.5%

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

       2. distribute-rgt1-in 47.5%

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

   11. Simplified 47.5%

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

   12. Taylor expanded in b around inf 47.5%

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

       1. *-commutative 47.5%

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

   14. Simplified 47.5%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.6% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.2e+49) (/ x (* y a)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.2e+49) {
		tmp = x / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.2d+49) then
        tmp = x / (y * a)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.2e+49) {
		tmp = x / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.2e+49:
		tmp = x / (y * a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.2e+49)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.2e+49)
		tmp = x / (y * a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.2e+49], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.20000000000000014e49

   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* 98.4%

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

      2. associate--l+ 98.4%

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

      3. exp-sum 81.4%

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

      4. associate-/r* 81.4%

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

      5. *-commutative 81.4%

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

      6. exp-to-pow 81.4%

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

      7. exp-diff 77.0%

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

      8. *-commutative 77.0%

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

      9. exp-to-pow 77.6%

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

      10. sub-neg 77.6%

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

      11. metadata-eval 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in t around 0 66.0%

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

      1. associate-/l* 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in y around 0 56.5%

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

   9. Taylor expanded in b around 0 37.3%

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

   if 3.20000000000000014e49 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.2%

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

      1. exp-diff 80.2%

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

      2. exp-to-pow 80.2%

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

      3. sub-neg 80.2%

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

      4. metadata-eval 80.2%

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

   5. Simplified 80.2%

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

   6. Taylor expanded in t around 0 86.2%

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

   7. Taylor expanded in b around 0 37.7%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.2% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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* 98.7%

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

   2. associate--l+ 98.7%

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

   3. exp-sum 80.0%

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

   4. associate-/r* 80.0%

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

   5. *-commutative 80.0%

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

   6. exp-to-pow 80.0%

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

   7. exp-diff 75.7%

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

   8. *-commutative 75.7%

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

   9. exp-to-pow 76.1%

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

   10. sub-neg 76.1%

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

   11. metadata-eval 76.1%

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

3. Simplified 76.1%

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

5. Taylor expanded in t around 0 67.2%

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

   1. associate-/l* 69.5%

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

7. Simplified 69.5%

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

8. Taylor expanded in y around 0 62.3%

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

9. Taylor expanded in b around 0 34.8%

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

10. Final simplification 34.8%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Developer target: 72.7% 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 2024096 
(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))