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

Percentage Accurate: 98.5% → 98.5%

Time: 52.3s

Alternatives: 22

Speedup: 1.0×

• 47.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

3. Final simplification 98.7%

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

Alternative 2: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+100} \lor \neg \left(t + -1 \leq -1\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -2e+100) (not (<= (+ t -1.0) -1.0)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -2e+100) || !((t + -1.0) <= -1.0)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-2d+100)) .or. (.not. ((t + (-1.0d0)) <= (-1.0d0)))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -2e+100) || !((t + -1.0) <= -1.0)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -2e+100) or not ((t + -1.0) <= -1.0):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -2e+100) || !(Float64(t + -1.0) <= -1.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -2e+100) || ~(((t + -1.0) <= -1.0)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -2e+100], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -1.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -2.00000000000000003e100 or -1 < (-.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. Add Preprocessing

   3. Taylor expanded in y around 0 96.2%

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

   if -2.00000000000000003e100 < (-.f64 t 1) < -1

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0 95.9%

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

      1. +-commutative 95.9%

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

      2. mul-1-neg 95.9%

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

      3. unsub-neg 95.9%

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

   5. Simplified 95.9%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+100} \lor \neg \left(t + -1 \leq -1\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+229} \lor \neg \left(y \leq 9.4 \cdot 10^{+138}\right):\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.3e+229) (not (<= y 9.4e+138)))
   (/ x (/ a (/ (pow z y) y)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e+229) || !(y <= 9.4e+138)) {
		tmp = x / (a / (pow(z, y) / y));
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.3d+229)) .or. (.not. (y <= 9.4d+138))) then
        tmp = x / (a / ((z ** y) / y))
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e+229) || !(y <= 9.4e+138)) {
		tmp = x / (a / (Math.pow(z, y) / y));
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.3e+229) or not (y <= 9.4e+138):
		tmp = x / (a / (math.pow(z, y) / y))
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.3e+229) || !(y <= 9.4e+138))
		tmp = Float64(x / Float64(a / Float64((z ^ y) / y)));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.3e+229) || ~((y <= 9.4e+138)))
		tmp = x / (a / ((z ^ y) / y));
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.3e+229], N[Not[LessEqual[y, 9.4e+138]], $MachinePrecision]], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e229 or 9.3999999999999996e138 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 78.3%

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

      2. *-commutative 78.3%

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

      3. exp-diff 56.5%

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

      4. +-commutative 56.5%

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

      5. exp-sum 50.0%

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

      6. associate-/l* 50.0%

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

      7. *-commutative 50.0%

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

      8. exp-to-pow 50.0%

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

      9. sub-neg 50.0%

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

      10. metadata-eval 50.0%

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

      11. *-commutative 50.0%

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

      12. exp-to-pow 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in b around 0 84.9%

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

      1. associate-/l* 84.9%

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

      2. *-commutative 84.9%

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

      3. exp-to-pow 84.9%

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

      4. *-commutative 84.9%

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

      5. exp-sum 95.7%

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

      6. exp-sum 84.9%

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

      7. *-commutative 84.9%

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

      8. exp-to-pow 84.9%

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

      9. exp-to-pow 84.9%

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

      10. sub-neg 84.9%

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

      11. metadata-eval 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in t around 0 80.5%

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

      1. associate-/l* 93.6%

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

   10. Simplified 93.6%

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

   if -1.3e229 < y < 9.3999999999999996e138

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 91.2%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+229} \lor \neg \left(y \leq 9.4 \cdot 10^{+138}\right):\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+229} \lor \neg \left(y \leq 5.4 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.3e+229) (not (<= y 5.4e+123)))
   (/ x (/ a (/ (pow z y) y)))
   (/ x (/ y (/ (pow a (+ t -1.0)) (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e+229) || !(y <= 5.4e+123)) {
		tmp = x / (a / (pow(z, y) / y));
	} else {
		tmp = x / (y / (pow(a, (t + -1.0)) / exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.3d+229)) .or. (.not. (y <= 5.4d+123))) then
        tmp = x / (a / ((z ** y) / y))
    else
        tmp = x / (y / ((a ** (t + (-1.0d0))) / exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.3e+229) || !(y <= 5.4e+123)) {
		tmp = x / (a / (Math.pow(z, y) / y));
	} else {
		tmp = x / (y / (Math.pow(a, (t + -1.0)) / Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.3e+229) or not (y <= 5.4e+123):
		tmp = x / (a / (math.pow(z, y) / y))
	else:
		tmp = x / (y / (math.pow(a, (t + -1.0)) / math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.3e+229) || !(y <= 5.4e+123))
		tmp = Float64(x / Float64(a / Float64((z ^ y) / y)));
	else
		tmp = Float64(x / Float64(y / Float64((a ^ Float64(t + -1.0)) / exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.3e+229) || ~((y <= 5.4e+123)))
		tmp = x / (a / ((z ^ y) / y));
	else
		tmp = x / (y / ((a ^ (t + -1.0)) / exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.3e+229], N[Not[LessEqual[y, 5.4e+123]], $MachinePrecision]], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y / N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e229 or 5.40000000000000026e123 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 79.2%

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

      2. *-commutative 79.2%

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

      3. exp-diff 56.3%

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

      4. +-commutative 56.3%

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

      5. exp-sum 50.0%

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

      6. associate-/l* 50.0%

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

      7. *-commutative 50.0%

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

      8. exp-to-pow 50.0%

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

      9. sub-neg 50.0%

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

      10. metadata-eval 50.0%

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

      11. *-commutative 50.0%

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

      12. exp-to-pow 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in b around 0 83.4%

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

      1. associate-/l* 83.4%

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

      2. *-commutative 83.4%

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

      3. exp-to-pow 83.4%

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

      4. *-commutative 83.4%

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

      5. exp-sum 93.8%

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

      6. exp-sum 83.4%

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

      7. *-commutative 83.4%

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

      8. exp-to-pow 83.4%

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

      9. exp-to-pow 83.4%

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

      10. sub-neg 83.4%

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

      11. metadata-eval 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in t around 0 79.3%

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

      1. associate-/l* 91.8%

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

   10. Simplified 91.8%

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

   if -1.3e229 < y < 5.40000000000000026e123

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 91.6%

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

      1. associate-/l* 92.0%

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

      2. div-exp 78.6%

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

      3. exp-to-pow 79.2%

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

      4. sub-neg 79.2%

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

      5. metadata-eval 79.2%

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

   5. Simplified 79.2%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+229} \lor \neg \left(y \leq 5.4 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ t_2 := y \cdot e^{b}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+122}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{t\_2}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)) (t_2 (* y (exp b))))
   (if (<= t -2.8e+122)
     t_1
     (if (<= t 3.6e-72)
       (* (/ x a) (/ (pow z y) t_2))
       (if (<= t 1.05e-31)
         (/ x (/ a (/ (pow z y) y)))
         (if (<= t 3.1e-17) (/ x t_2) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double t_2 = y * exp(b);
	double tmp;
	if (t <= -2.8e+122) {
		tmp = t_1;
	} else if (t <= 3.6e-72) {
		tmp = (x / a) * (pow(z, y) / t_2);
	} else if (t <= 1.05e-31) {
		tmp = x / (a / (pow(z, y) / y));
	} else if (t <= 3.1e-17) {
		tmp = x / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    t_2 = y * exp(b)
    if (t <= (-2.8d+122)) then
        tmp = t_1
    else if (t <= 3.6d-72) then
        tmp = (x / a) * ((z ** y) / t_2)
    else if (t <= 1.05d-31) then
        tmp = x / (a / ((z ** y) / y))
    else if (t <= 3.1d-17) then
        tmp = x / t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double t_2 = y * Math.exp(b);
	double tmp;
	if (t <= -2.8e+122) {
		tmp = t_1;
	} else if (t <= 3.6e-72) {
		tmp = (x / a) * (Math.pow(z, y) / t_2);
	} else if (t <= 1.05e-31) {
		tmp = x / (a / (Math.pow(z, y) / y));
	} else if (t <= 3.1e-17) {
		tmp = x / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	t_2 = y * math.exp(b)
	tmp = 0
	if t <= -2.8e+122:
		tmp = t_1
	elif t <= 3.6e-72:
		tmp = (x / a) * (math.pow(z, y) / t_2)
	elif t <= 1.05e-31:
		tmp = x / (a / (math.pow(z, y) / y))
	elif t <= 3.1e-17:
		tmp = x / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	t_2 = Float64(y * exp(b))
	tmp = 0.0
	if (t <= -2.8e+122)
		tmp = t_1;
	elseif (t <= 3.6e-72)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / t_2));
	elseif (t <= 1.05e-31)
		tmp = Float64(x / Float64(a / Float64((z ^ y) / y)));
	elseif (t <= 3.1e-17)
		tmp = Float64(x / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	t_2 = y * exp(b);
	tmp = 0.0;
	if (t <= -2.8e+122)
		tmp = t_1;
	elseif (t <= 3.6e-72)
		tmp = (x / a) * ((z ^ y) / t_2);
	elseif (t <= 1.05e-31)
		tmp = x / (a / ((z ^ y) / y));
	elseif (t <= 3.1e-17)
		tmp = x / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+122], t$95$1, If[LessEqual[t, 3.6e-72], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-31], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-17], N[(x / t$95$2), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.8e122 or 3.0999999999999998e-17 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.9%

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

   4. Taylor expanded in b around 0 87.8%

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

      1. *-commutative 87.8%

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

      2. exp-to-pow 87.8%

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

      3. sub-neg 87.8%

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

      4. metadata-eval 87.8%

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

      5. +-commutative 87.8%

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

   6. Simplified 87.8%

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

   if -2.8e122 < t < 3.6e-72

   1. Initial program 97.8%

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

      1. associate-*l/ 87.5%

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

      2. *-commutative 87.5%

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

      3. exp-diff 69.7%

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

      4. +-commutative 69.7%

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

      5. exp-sum 66.3%

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

      6. associate-/l* 66.3%

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

      7. *-commutative 66.3%

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

      8. exp-to-pow 67.1%

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

      9. sub-neg 67.1%

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

      10. metadata-eval 67.1%

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

      11. *-commutative 67.1%

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

      12. exp-to-pow 67.1%

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

   3. Simplified 67.1%

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

   5. Taylor expanded in t around 0 78.2%

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

      1. times-frac 78.2%

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

   7. Simplified 78.2%

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

   if 3.6e-72 < t < 1.04999999999999996e-31

   1. Initial program 98.6%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

      3. exp-diff 58.6%

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

      4. +-commutative 58.6%

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

      5. exp-sum 58.6%

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

      6. associate-/l* 58.6%

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

      7. *-commutative 58.6%

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

      8. exp-to-pow 59.8%

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

      9. sub-neg 59.8%

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

      10. metadata-eval 59.8%

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

      11. *-commutative 59.8%

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

      12. exp-to-pow 59.8%

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

   3. Simplified 59.8%

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

   5. Taylor expanded in b around 0 69.3%

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

      1. associate-/l* 78.9%

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

      2. *-commutative 78.9%

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

      3. exp-to-pow 78.9%

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

      4. *-commutative 78.9%

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

      5. exp-sum 78.9%

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

      6. exp-sum 78.9%

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

      7. *-commutative 78.9%

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

      8. exp-to-pow 78.9%

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

      9. exp-to-pow 80.3%

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

      10. sub-neg 80.3%

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

      11. metadata-eval 80.3%

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

   7. Simplified 80.3%

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

   8. Taylor expanded in t around 0 60.3%

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

      1. associate-/l* 80.3%

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

   10. Simplified 80.3%

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

   if 1.04999999999999996e-31 < t < 3.0999999999999998e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in b around inf 100.0%

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

      1. neg-mul-1 100.0%

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

   6. Simplified 100.0%

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

      1. associate-/l* 100.0%

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

      2. div-inv 100.0%

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

      3. div-inv 100.0%

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

      4. add-sqr-sqrt 66.7%

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

      5. sqrt-unprod 67.2%

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

      6. sqr-neg 67.2%

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

      7. sqrt-unprod 0.5%

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

      8. add-sqr-sqrt 1.6%

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

      9. exp-neg 1.6%

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

      10. add-sqr-sqrt 1.0%

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

      11. sqrt-unprod 34.4%

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

      12. sqr-neg 34.4%

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

      13. sqrt-unprod 33.3%

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

      14. add-sqr-sqrt 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. associate-*r/ 100.0%

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

      2. *-rgt-identity 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+122}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-72}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ t_2 := \frac{x}{y \cdot e^{b}}\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{+182}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -220000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)) (t_2 (/ x (* y (exp b)))))
   (if (<= b -2.45e+182)
     t_2
     (if (<= b -5e+106)
       t_1
       (if (<= b -220000.0)
         t_2
         (if (<= b -6e-255)
           t_1
           (if (<= b 4.1e-165)
             (/ x (/ a (/ (pow z y) y)))
             (if (<= b 2.1e+28) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double t_2 = x / (y * exp(b));
	double tmp;
	if (b <= -2.45e+182) {
		tmp = t_2;
	} else if (b <= -5e+106) {
		tmp = t_1;
	} else if (b <= -220000.0) {
		tmp = t_2;
	} else if (b <= -6e-255) {
		tmp = t_1;
	} else if (b <= 4.1e-165) {
		tmp = x / (a / (pow(z, y) / y));
	} else if (b <= 2.1e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    t_2 = x / (y * exp(b))
    if (b <= (-2.45d+182)) then
        tmp = t_2
    else if (b <= (-5d+106)) then
        tmp = t_1
    else if (b <= (-220000.0d0)) then
        tmp = t_2
    else if (b <= (-6d-255)) then
        tmp = t_1
    else if (b <= 4.1d-165) then
        tmp = x / (a / ((z ** y) / y))
    else if (b <= 2.1d+28) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double t_2 = x / (y * Math.exp(b));
	double tmp;
	if (b <= -2.45e+182) {
		tmp = t_2;
	} else if (b <= -5e+106) {
		tmp = t_1;
	} else if (b <= -220000.0) {
		tmp = t_2;
	} else if (b <= -6e-255) {
		tmp = t_1;
	} else if (b <= 4.1e-165) {
		tmp = x / (a / (Math.pow(z, y) / y));
	} else if (b <= 2.1e+28) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	t_2 = x / (y * math.exp(b))
	tmp = 0
	if b <= -2.45e+182:
		tmp = t_2
	elif b <= -5e+106:
		tmp = t_1
	elif b <= -220000.0:
		tmp = t_2
	elif b <= -6e-255:
		tmp = t_1
	elif b <= 4.1e-165:
		tmp = x / (a / (math.pow(z, y) / y))
	elif b <= 2.1e+28:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	t_2 = Float64(x / Float64(y * exp(b)))
	tmp = 0.0
	if (b <= -2.45e+182)
		tmp = t_2;
	elseif (b <= -5e+106)
		tmp = t_1;
	elseif (b <= -220000.0)
		tmp = t_2;
	elseif (b <= -6e-255)
		tmp = t_1;
	elseif (b <= 4.1e-165)
		tmp = Float64(x / Float64(a / Float64((z ^ y) / y)));
	elseif (b <= 2.1e+28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	t_2 = x / (y * exp(b));
	tmp = 0.0;
	if (b <= -2.45e+182)
		tmp = t_2;
	elseif (b <= -5e+106)
		tmp = t_1;
	elseif (b <= -220000.0)
		tmp = t_2;
	elseif (b <= -6e-255)
		tmp = t_1;
	elseif (b <= 4.1e-165)
		tmp = x / (a / ((z ^ y) / y));
	elseif (b <= 2.1e+28)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.45e+182], t$95$2, If[LessEqual[b, -5e+106], t$95$1, If[LessEqual[b, -220000.0], t$95$2, If[LessEqual[b, -6e-255], t$95$1, If[LessEqual[b, 4.1e-165], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+28], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.45e182 or -4.9999999999999998e106 < b < -2.2e5 or 2.09999999999999989e28 < 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 93.6%

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

   4. Taylor expanded in b around inf 89.1%

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

      1. neg-mul-1 89.1%

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

   6. Simplified 89.1%

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

      1. associate-/l* 89.1%

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

      2. div-inv 89.1%

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

      3. div-inv 89.1%

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

      4. add-sqr-sqrt 44.5%

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

      5. sqrt-unprod 49.9%

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

      6. sqr-neg 49.9%

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

      7. sqrt-unprod 5.3%

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

      8. add-sqr-sqrt 12.5%

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

      9. exp-neg 12.5%

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

      10. add-sqr-sqrt 7.2%

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

      11. sqrt-unprod 51.7%

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

      12. sqr-neg 51.7%

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

      13. sqrt-unprod 44.5%

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

      14. add-sqr-sqrt 89.1%

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

   8. Applied egg-rr 89.1%

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

      1. associate-*r/ 89.1%

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

      2. *-rgt-identity 89.1%

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

   10. Simplified 89.1%

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

   if -2.45e182 < b < -4.9999999999999998e106 or -2.2e5 < b < -6.00000000000000004e-255 or 4.1000000000000002e-165 < b < 2.09999999999999989e28

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 79.6%

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

   4. Taylor expanded in b around 0 77.5%

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

      1. *-commutative 77.5%

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

      2. exp-to-pow 78.2%

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

      3. sub-neg 78.2%

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

      4. metadata-eval 78.2%

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

      5. +-commutative 78.2%

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

   6. Simplified 78.2%

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

   if -6.00000000000000004e-255 < b < 4.1000000000000002e-165

   1. Initial program 94.5%

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

      1. associate-*l/ 88.7%

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

      2. *-commutative 88.7%

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

      3. exp-diff 88.7%

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

      4. +-commutative 88.7%

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

      5. exp-sum 81.2%

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

      6. associate-/l* 81.2%

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

      7. *-commutative 81.2%

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

      8. exp-to-pow 82.4%

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

      9. sub-neg 82.4%

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

      10. metadata-eval 82.4%

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

      11. *-commutative 82.4%

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

      12. exp-to-pow 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in b around 0 82.0%

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

      1. associate-/l* 86.2%

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

      2. *-commutative 86.2%

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

      3. exp-to-pow 86.2%

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

      4. *-commutative 86.2%

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

      5. exp-sum 98.7%

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

      6. exp-sum 86.2%

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

      7. *-commutative 86.2%

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

      8. exp-to-pow 86.2%

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

      9. exp-to-pow 87.5%

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

      10. sub-neg 87.5%

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

      11. metadata-eval 87.5%

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

   7. Simplified 87.5%

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

   8. Taylor expanded in t around 0 82.8%

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

      1. associate-/l* 85.3%

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

   10. Simplified 85.3%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+182}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+106}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq -220000:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-255}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+28}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot e^{b}}\\ \mathbf{if}\;b \leq -450:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-285}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-219}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{elif}\;b \leq 230000:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y (exp b)))))
   (if (<= b -450.0)
     t_1
     (if (<= b -3.4e-285)
       (- (/ x (* y a)) (* (/ x a) (/ b y)))
       (if (<= b 3.3e-219)
         (/ (- x) (/ y b))
         (if (<= b 230000.0) (* (/ x a) (/ 1.0 y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * exp(b));
	double tmp;
	if (b <= -450.0) {
		tmp = t_1;
	} else if (b <= -3.4e-285) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= 3.3e-219) {
		tmp = -x / (y / b);
	} else if (b <= 230000.0) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y * exp(b))
    if (b <= (-450.0d0)) then
        tmp = t_1
    else if (b <= (-3.4d-285)) then
        tmp = (x / (y * a)) - ((x / a) * (b / y))
    else if (b <= 3.3d-219) then
        tmp = -x / (y / b)
    else if (b <= 230000.0d0) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * Math.exp(b));
	double tmp;
	if (b <= -450.0) {
		tmp = t_1;
	} else if (b <= -3.4e-285) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= 3.3e-219) {
		tmp = -x / (y / b);
	} else if (b <= 230000.0) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * math.exp(b))
	tmp = 0
	if b <= -450.0:
		tmp = t_1
	elif b <= -3.4e-285:
		tmp = (x / (y * a)) - ((x / a) * (b / y))
	elif b <= 3.3e-219:
		tmp = -x / (y / b)
	elif b <= 230000.0:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * exp(b)))
	tmp = 0.0
	if (b <= -450.0)
		tmp = t_1;
	elseif (b <= -3.4e-285)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x / a) * Float64(b / y)));
	elseif (b <= 3.3e-219)
		tmp = Float64(Float64(-x) / Float64(y / b));
	elseif (b <= 230000.0)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * exp(b));
	tmp = 0.0;
	if (b <= -450.0)
		tmp = t_1;
	elseif (b <= -3.4e-285)
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	elseif (b <= 3.3e-219)
		tmp = -x / (y / b);
	elseif (b <= 230000.0)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -450.0], t$95$1, If[LessEqual[b, -3.4e-285], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e-219], N[((-x) / N[(y / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 230000.0], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -450 or 2.3e5 < 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 91.3%

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

   4. Taylor expanded in b around inf 81.9%

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

      1. neg-mul-1 81.9%

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

   6. Simplified 81.9%

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

      1. associate-/l* 81.9%

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

      2. div-inv 81.9%

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

      3. div-inv 81.9%

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

      4. add-sqr-sqrt 45.1%

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

      5. sqrt-unprod 50.1%

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

      6. sqr-neg 50.1%

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

      7. sqrt-unprod 5.0%

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

      8. add-sqr-sqrt 19.7%

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

      9. exp-neg 19.7%

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

      10. add-sqr-sqrt 14.7%

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

      11. sqrt-unprod 51.5%

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

      12. sqr-neg 51.5%

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

      13. sqrt-unprod 36.8%

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

      14. add-sqr-sqrt 81.9%

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

   8. Applied egg-rr 81.9%

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

      1. associate-*r/ 81.9%

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

      2. *-rgt-identity 81.9%

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

   10. Simplified 81.9%

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

   if -450 < b < -3.3999999999999999e-285

   1. Initial program 97.0%

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

      1. associate-*l/ 94.6%

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

      2. *-commutative 94.6%

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

      3. exp-diff 94.7%

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

      4. +-commutative 94.7%

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

      5. exp-sum 75.5%

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

      6. associate-/l* 75.5%

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

      7. *-commutative 75.5%

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

      8. exp-to-pow 76.5%

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

      9. sub-neg 76.5%

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

      10. metadata-eval 76.5%

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

      11. *-commutative 76.5%

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

      12. exp-to-pow 76.5%

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

   3. Simplified 76.5%

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

   5. Taylor expanded in t around 0 64.6%

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

      1. times-frac 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in y around 0 38.6%

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

      1. associate-*r* 38.6%

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

   10. Simplified 38.6%

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

   11. Taylor expanded in b around 0 38.6%

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

       1. +-commutative 38.6%

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

       2. mul-1-neg 38.6%

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

       3. unsub-neg 38.6%

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

       4. *-commutative 38.6%

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

       5. times-frac 42.6%

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

   13. Simplified 42.6%

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

   if -3.3999999999999999e-285 < b < 3.3000000000000002e-219

   1. Initial program 99.1%

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

   3. Taylor expanded in y around 0 70.9%

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

   4. Taylor expanded in b around inf 20.7%

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

      1. neg-mul-1 20.7%

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

   6. Simplified 20.7%

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

   7. Taylor expanded in b around 0 20.7%

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

   8. Taylor expanded in b around inf 40.5%

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

      1. mul-1-neg 40.5%

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

      2. associate-*r/ 40.5%

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

      3. *-commutative 40.5%

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

      4. associate-/r/ 54.9%

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

      5. distribute-neg-frac 54.9%

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

   10. Simplified 54.9%

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

   if 3.3000000000000002e-219 < b < 2.3e5

   1. Initial program 96.4%

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

      1. associate-*l/ 86.5%

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

      2. *-commutative 86.5%

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

      3. exp-diff 84.5%

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

      4. +-commutative 84.5%

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

      5. exp-sum 74.3%

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

      6. associate-/l* 74.3%

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

      7. *-commutative 74.3%

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

      8. exp-to-pow 75.6%

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

      9. sub-neg 75.6%

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

      10. metadata-eval 75.6%

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

      11. *-commutative 75.6%

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

      12. exp-to-pow 75.6%

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

   3. Simplified 75.6%

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

   5. Taylor expanded in t around 0 64.0%

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

      1. times-frac 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in b around 0 63.0%

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

      1. times-frac 67.0%

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

   10. Simplified 67.0%

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

   11. Taylor expanded in y around 0 36.3%

       \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{1}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -450:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-285}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-219}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{elif}\;b \leq 230000:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6600000000 \lor \neg \left(b \leq 1400000000\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6600000000.0) (not (<= b 1400000000.0)))
   (/ x (* y (exp b)))
   (* (/ (pow z y) y) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6600000000.0) || !(b <= 1400000000.0)) {
		tmp = x / (y * exp(b));
	} else {
		tmp = (pow(z, y) / y) * (x / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6600000000.0d0)) .or. (.not. (b <= 1400000000.0d0))) then
        tmp = x / (y * exp(b))
    else
        tmp = ((z ** y) / y) * (x / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6600000000.0) || !(b <= 1400000000.0)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = (Math.pow(z, y) / y) * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6600000000.0) or not (b <= 1400000000.0):
		tmp = x / (y * math.exp(b))
	else:
		tmp = (math.pow(z, y) / y) * (x / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6600000000.0) || !(b <= 1400000000.0))
		tmp = Float64(x / Float64(y * exp(b)));
	else
		tmp = Float64(Float64((z ^ y) / y) * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6600000000.0) || ~((b <= 1400000000.0)))
		tmp = x / (y * exp(b));
	else
		tmp = ((z ^ y) / y) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6600000000.0], N[Not[LessEqual[b, 1400000000.0]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.6e9 or 1.4e9 < 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 91.1%

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

   4. Taylor expanded in b around inf 82.2%

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

      1. neg-mul-1 82.2%

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

   6. Simplified 82.2%

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

      1. associate-/l* 82.2%

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

      2. div-inv 82.2%

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

      3. div-inv 82.2%

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

      4. add-sqr-sqrt 44.6%

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

      5. sqrt-unprod 49.7%

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

      6. sqr-neg 49.7%

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

      7. sqrt-unprod 5.1%

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

      8. add-sqr-sqrt 19.3%

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

      9. exp-neg 19.3%

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

      10. add-sqr-sqrt 14.2%

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

      11. sqrt-unprod 51.9%

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

      12. sqr-neg 51.9%

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

      13. sqrt-unprod 37.7%

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

      14. add-sqr-sqrt 82.2%

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

   8. Applied egg-rr 82.2%

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

      1. associate-*r/ 82.2%

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

      2. *-rgt-identity 82.2%

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

   10. Simplified 82.2%

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

   if -6.6e9 < b < 1.4e9

   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/ 89.9%

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

      2. *-commutative 89.9%

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

      3. exp-diff 88.4%

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

      4. +-commutative 88.4%

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

      5. exp-sum 75.4%

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

      6. associate-/l* 75.4%

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

      7. *-commutative 75.4%

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

      8. exp-to-pow 76.4%

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

      9. sub-neg 76.4%

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

      10. metadata-eval 76.4%

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

      11. *-commutative 76.4%

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

      12. exp-to-pow 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in t around 0 66.5%

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

      1. times-frac 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in b around 0 65.9%

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

      1. times-frac 68.4%

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

   10. Simplified 68.4%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6600000000 \lor \neg \left(b \leq 1400000000\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1550000000 \lor \neg \left(b \leq 14000000\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1550000000.0) (not (<= b 14000000.0)))
   (/ x (* y (exp b)))
   (/ x (/ a (/ (pow z y) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1550000000.0) || !(b <= 14000000.0)) {
		tmp = x / (y * exp(b));
	} else {
		tmp = x / (a / (pow(z, y) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1550000000.0d0)) .or. (.not. (b <= 14000000.0d0))) then
        tmp = x / (y * exp(b))
    else
        tmp = x / (a / ((z ** y) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1550000000.0) || !(b <= 14000000.0)) {
		tmp = x / (y * Math.exp(b));
	} else {
		tmp = x / (a / (Math.pow(z, y) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1550000000.0) or not (b <= 14000000.0):
		tmp = x / (y * math.exp(b))
	else:
		tmp = x / (a / (math.pow(z, y) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1550000000.0) || !(b <= 14000000.0))
		tmp = Float64(x / Float64(y * exp(b)));
	else
		tmp = Float64(x / Float64(a / Float64((z ^ y) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1550000000.0) || ~((b <= 14000000.0)))
		tmp = x / (y * exp(b));
	else
		tmp = x / (a / ((z ^ y) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1550000000.0], N[Not[LessEqual[b, 14000000.0]], $MachinePrecision]], N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.55e9 or 1.4e7 < 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 91.1%

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

   4. Taylor expanded in b around inf 82.2%

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

      1. neg-mul-1 82.2%

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

   6. Simplified 82.2%

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

      1. associate-/l* 82.2%

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

      2. div-inv 82.2%

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

      3. div-inv 82.2%

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

      4. add-sqr-sqrt 44.6%

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

      5. sqrt-unprod 49.7%

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

      6. sqr-neg 49.7%

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

      7. sqrt-unprod 5.1%

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

      8. add-sqr-sqrt 19.3%

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

      9. exp-neg 19.3%

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

      10. add-sqr-sqrt 14.2%

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

      11. sqrt-unprod 51.9%

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

      12. sqr-neg 51.9%

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

      13. sqrt-unprod 37.7%

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

      14. add-sqr-sqrt 82.2%

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

   8. Applied egg-rr 82.2%

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

      1. associate-*r/ 82.2%

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

      2. *-rgt-identity 82.2%

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

   10. Simplified 82.2%

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

   if -1.55e9 < b < 1.4e7

   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/ 89.9%

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

      2. *-commutative 89.9%

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

      3. exp-diff 88.4%

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

      4. +-commutative 88.4%

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

      5. exp-sum 75.4%

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

      6. associate-/l* 75.4%

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

      7. *-commutative 75.4%

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

      8. exp-to-pow 76.4%

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

      9. sub-neg 76.4%

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

      10. metadata-eval 76.4%

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

      11. *-commutative 76.4%

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

      12. exp-to-pow 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in b around 0 80.6%

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

      1. associate-/l* 81.3%

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

      2. *-commutative 81.3%

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

      3. exp-to-pow 81.3%

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

      4. *-commutative 81.3%

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

      5. exp-sum 96.7%

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

      6. exp-sum 81.3%

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

      7. *-commutative 81.3%

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

      8. exp-to-pow 81.3%

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

      9. exp-to-pow 82.3%

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

      10. sub-neg 82.3%

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

      11. metadata-eval 82.3%

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

   7. Simplified 82.3%

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

   8. Taylor expanded in t around 0 65.9%

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

      1. associate-/l* 70.8%

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

   10. Simplified 70.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1550000000 \lor \neg \left(b \leq 14000000\right):\\ \;\;\;\;\frac{x}{y \cdot e^{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.9% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-164}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{elif}\;b \leq 0.038:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \left(\frac{y}{x} + \frac{b}{\frac{x}{y}}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.45e-284)
   (- (/ x (* y a)) (* (/ x a) (/ b y)))
   (if (<= b 9.5e-164)
     (/ (- x) (/ y b))
     (if (<= b 0.038)
       (* (/ x a) (/ 1.0 y))
       (/ 1.0 (* a (+ (/ y x) (/ b (/ x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.45e-284) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= 9.5e-164) {
		tmp = -x / (y / b);
	} else if (b <= 0.038) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = 1.0 / (a * ((y / x) + (b / (x / y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.45d-284)) then
        tmp = (x / (y * a)) - ((x / a) * (b / y))
    else if (b <= 9.5d-164) then
        tmp = -x / (y / b)
    else if (b <= 0.038d0) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = 1.0d0 / (a * ((y / x) + (b / (x / y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.45e-284) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= 9.5e-164) {
		tmp = -x / (y / b);
	} else if (b <= 0.038) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = 1.0 / (a * ((y / x) + (b / (x / y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.45e-284:
		tmp = (x / (y * a)) - ((x / a) * (b / y))
	elif b <= 9.5e-164:
		tmp = -x / (y / b)
	elif b <= 0.038:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = 1.0 / (a * ((y / x) + (b / (x / y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.45e-284)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x / a) * Float64(b / y)));
	elseif (b <= 9.5e-164)
		tmp = Float64(Float64(-x) / Float64(y / b));
	elseif (b <= 0.038)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(1.0 / Float64(a * Float64(Float64(y / x) + Float64(b / Float64(x / y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.45e-284)
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	elseif (b <= 9.5e-164)
		tmp = -x / (y / b);
	elseif (b <= 0.038)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = 1.0 / (a * ((y / x) + (b / (x / y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.45e-284], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-164], N[((-x) / N[(y / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.038], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a * N[(N[(y / x), $MachinePrecision] + N[(b / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.4500000000000001e-284

   1. Initial program 98.9%

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

      1. associate-*l/ 94.1%

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

      2. *-commutative 94.1%

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

      3. exp-diff 66.5%

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

      4. +-commutative 66.5%

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

      5. exp-sum 58.7%

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

      6. associate-/l* 58.7%

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

      7. *-commutative 58.7%

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

      8. exp-to-pow 59.0%

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

      9. sub-neg 59.0%

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

      10. metadata-eval 59.0%

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

      11. *-commutative 59.0%

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

      12. exp-to-pow 59.0%

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

   3. Simplified 59.0%

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

   5. Taylor expanded in t around 0 61.0%

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

      1. times-frac 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in y around 0 62.5%

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

      1. associate-*r* 55.4%

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

   10. Simplified 55.4%

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

   11. Taylor expanded in b around 0 39.1%

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

       1. +-commutative 39.1%

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

       2. mul-1-neg 39.1%

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

       3. unsub-neg 39.1%

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

       4. *-commutative 39.1%

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

       5. times-frac 39.7%

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

   13. Simplified 39.7%

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

   if -1.4500000000000001e-284 < b < 9.5000000000000001e-164

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0 67.2%

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

   4. Taylor expanded in b around inf 22.0%

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

      1. neg-mul-1 22.0%

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

   6. Simplified 22.0%

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

   7. Taylor expanded in b around 0 22.0%

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

   8. Taylor expanded in b around inf 39.1%

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

      1. mul-1-neg 39.1%

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

      2. associate-*r/ 36.2%

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

      3. *-commutative 36.2%

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

      4. associate-/r/ 49.6%

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

      5. distribute-neg-frac 49.6%

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

   10. Simplified 49.6%

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

   if 9.5000000000000001e-164 < b < 0.0379999999999999991

   1. Initial program 98.2%

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

      1. associate-*l/ 84.9%

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

      2. *-commutative 84.9%

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

      3. exp-diff 84.9%

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

      4. +-commutative 84.9%

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

      5. exp-sum 73.4%

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

      6. associate-/l* 73.4%

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

      7. *-commutative 73.4%

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

      8. exp-to-pow 74.5%

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

      9. sub-neg 74.5%

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

      10. metadata-eval 74.5%

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

      11. *-commutative 74.5%

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

      12. exp-to-pow 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in t around 0 58.1%

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

      1. times-frac 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in b around 0 58.1%

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

      1. times-frac 66.5%

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

   10. Simplified 66.5%

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

   11. Taylor expanded in y around 0 42.6%

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

   if 0.0379999999999999991 < b

   1. Initial program 99.6%

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

      1. associate-*l/ 86.5%

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

      2. *-commutative 86.5%

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

      3. exp-diff 58.7%

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

      4. +-commutative 58.7%

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

      5. exp-sum 57.1%

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

      6. associate-/l* 57.1%

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

      7. *-commutative 57.1%

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

      8. exp-to-pow 57.3%

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

      9. sub-neg 57.3%

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

      10. metadata-eval 57.3%

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

      11. *-commutative 57.3%

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

      12. exp-to-pow 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in t around 0 80.4%

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

      1. times-frac 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in y around 0 85.5%

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

      1. associate-*r* 74.0%

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

   10. Simplified 74.0%

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

       1. clear-num 74.0%

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

       2. inv-pow 74.0%

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

   12. Applied egg-rr 74.0%

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

       1. unpow-1 74.0%

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

       2. associate-*r* 85.5%

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

       3. *-lft-identity 85.5%

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

       4. times-frac 85.5%

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

       5. /-rgt-identity 85.5%

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

       6. *-commutative 85.5%

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

       7. associate-*r/ 75.6%

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

   14. Simplified 75.6%

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

   15. Taylor expanded in b around 0 34.6%

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

       1. associate-/l* 34.6%

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

   17. Simplified 34.6%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{-284}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-164}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{elif}\;b \leq 0.038:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \left(\frac{y}{x} + \frac{b}{\frac{x}{y}}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.8% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.08 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-165}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{elif}\;b \leq 0.038:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \left(\frac{y}{x} + \frac{b}{\frac{x}{y}}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.08e-296)
   (- (/ x (* y a)) (/ (* x b) (* y a)))
   (if (<= b 4.2e-165)
     (/ (- x) (/ y b))
     (if (<= b 0.038)
       (* (/ x a) (/ 1.0 y))
       (/ 1.0 (* a (+ (/ y x) (/ b (/ x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.08e-296) {
		tmp = (x / (y * a)) - ((x * b) / (y * a));
	} else if (b <= 4.2e-165) {
		tmp = -x / (y / b);
	} else if (b <= 0.038) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = 1.0 / (a * ((y / x) + (b / (x / y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.08d-296) then
        tmp = (x / (y * a)) - ((x * b) / (y * a))
    else if (b <= 4.2d-165) then
        tmp = -x / (y / b)
    else if (b <= 0.038d0) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = 1.0d0 / (a * ((y / x) + (b / (x / y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.08e-296) {
		tmp = (x / (y * a)) - ((x * b) / (y * a));
	} else if (b <= 4.2e-165) {
		tmp = -x / (y / b);
	} else if (b <= 0.038) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = 1.0 / (a * ((y / x) + (b / (x / y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.08e-296:
		tmp = (x / (y * a)) - ((x * b) / (y * a))
	elif b <= 4.2e-165:
		tmp = -x / (y / b)
	elif b <= 0.038:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = 1.0 / (a * ((y / x) + (b / (x / y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.08e-296)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x * b) / Float64(y * a)));
	elseif (b <= 4.2e-165)
		tmp = Float64(Float64(-x) / Float64(y / b));
	elseif (b <= 0.038)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(1.0 / Float64(a * Float64(Float64(y / x) + Float64(b / Float64(x / y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.08e-296)
		tmp = (x / (y * a)) - ((x * b) / (y * a));
	elseif (b <= 4.2e-165)
		tmp = -x / (y / b);
	elseif (b <= 0.038)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = 1.0 / (a * ((y / x) + (b / (x / y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.08e-296], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-165], N[((-x) / N[(y / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 0.038], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a * N[(N[(y / x), $MachinePrecision] + N[(b / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < 1.08e-296

   1. Initial program 98.9%

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

      1. associate-*l/ 93.0%

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

      2. *-commutative 93.0%

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

      3. exp-diff 67.5%

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

      4. +-commutative 67.5%

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

      5. exp-sum 60.2%

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

      6. associate-/l* 60.2%

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

      7. *-commutative 60.2%

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

      8. exp-to-pow 60.5%

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

      9. sub-neg 60.5%

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

      10. metadata-eval 60.5%

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

      11. *-commutative 60.5%

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

      12. exp-to-pow 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in t around 0 60.2%

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

      1. times-frac 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in y around 0 61.0%

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

      1. associate-*r* 54.3%

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

   10. Simplified 54.3%

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

   11. Taylor expanded in b around 0 39.2%

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

   if 1.08e-296 < b < 4.1999999999999999e-165

   1. Initial program 95.3%

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

   3. Taylor expanded in y around 0 61.7%

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

   4. Taylor expanded in b around inf 25.6%

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

      1. neg-mul-1 25.6%

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

   6. Simplified 25.6%

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

   7. Taylor expanded in b around 0 25.6%

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

   8. Taylor expanded in b around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. associate-*r/ 45.8%

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

      3. *-commutative 45.8%

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

      4. associate-/r/ 57.5%

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

      5. distribute-neg-frac 57.5%

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

   10. Simplified 57.5%

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

   if 4.1999999999999999e-165 < b < 0.0379999999999999991

   1. Initial program 98.2%

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

      1. associate-*l/ 84.9%

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

      2. *-commutative 84.9%

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

      3. exp-diff 84.9%

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

      4. +-commutative 84.9%

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

      5. exp-sum 73.4%

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

      6. associate-/l* 73.4%

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

      7. *-commutative 73.4%

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

      8. exp-to-pow 74.5%

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

      9. sub-neg 74.5%

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

      10. metadata-eval 74.5%

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

      11. *-commutative 74.5%

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

      12. exp-to-pow 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in t around 0 58.1%

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

      1. times-frac 66.5%

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

   7. Simplified 66.5%

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

   8. Taylor expanded in b around 0 58.1%

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

      1. times-frac 66.5%

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

   10. Simplified 66.5%

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

   11. Taylor expanded in y around 0 42.6%

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

   if 0.0379999999999999991 < b

   1. Initial program 99.6%

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

      1. associate-*l/ 86.5%

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

      2. *-commutative 86.5%

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

      3. exp-diff 58.7%

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

      4. +-commutative 58.7%

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

      5. exp-sum 57.1%

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

      6. associate-/l* 57.1%

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

      7. *-commutative 57.1%

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

      8. exp-to-pow 57.3%

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

      9. sub-neg 57.3%

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

      10. metadata-eval 57.3%

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

      11. *-commutative 57.3%

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

      12. exp-to-pow 57.3%

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

   3. Simplified 57.3%

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

   5. Taylor expanded in t around 0 80.4%

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

      1. times-frac 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in y around 0 85.5%

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

      1. associate-*r* 74.0%

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

   10. Simplified 74.0%

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

       1. clear-num 74.0%

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

       2. inv-pow 74.0%

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

   12. Applied egg-rr 74.0%

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

       1. unpow-1 74.0%

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

       2. associate-*r* 85.5%

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

       3. *-lft-identity 85.5%

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

       4. times-frac 85.5%

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

       5. /-rgt-identity 85.5%

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

       6. *-commutative 85.5%

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

       7. associate-*r/ 75.6%

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

   14. Simplified 75.6%

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

   15. Taylor expanded in b around 0 34.6%

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

       1. associate-/l* 34.6%

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

   17. Simplified 34.6%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.08 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-165}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{elif}\;b \leq 0.038:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \left(\frac{y}{x} + \frac{b}{\frac{x}{y}}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.2% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5000:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-277}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-222}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5000.0)
   (/ (* x (- b)) y)
   (if (<= b -5e-277)
     (/ 1.0 (* a (/ y x)))
     (if (<= b 1.7e-222)
       (/ (- x) (/ y b))
       (if (<= b 7.5e+91) (* (/ x a) (/ 1.0 y)) (/ x (+ y (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5000.0) {
		tmp = (x * -b) / y;
	} else if (b <= -5e-277) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 1.7e-222) {
		tmp = -x / (y / b);
	} else if (b <= 7.5e+91) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5000.0d0)) then
        tmp = (x * -b) / y
    else if (b <= (-5d-277)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 1.7d-222) then
        tmp = -x / (y / b)
    else if (b <= 7.5d+91) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = x / (y + (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5000.0) {
		tmp = (x * -b) / y;
	} else if (b <= -5e-277) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 1.7e-222) {
		tmp = -x / (y / b);
	} else if (b <= 7.5e+91) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5000.0:
		tmp = (x * -b) / y
	elif b <= -5e-277:
		tmp = 1.0 / (a * (y / x))
	elif b <= 1.7e-222:
		tmp = -x / (y / b)
	elif b <= 7.5e+91:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = x / (y + (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5000.0)
		tmp = Float64(Float64(x * Float64(-b)) / y);
	elseif (b <= -5e-277)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 1.7e-222)
		tmp = Float64(Float64(-x) / Float64(y / b));
	elseif (b <= 7.5e+91)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(x / Float64(y + Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5000.0)
		tmp = (x * -b) / y;
	elseif (b <= -5e-277)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 1.7e-222)
		tmp = -x / (y / b);
	elseif (b <= 7.5e+91)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = x / (y + (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5000.0], N[(N[(x * (-b)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -5e-277], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-222], N[((-x) / N[(y / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e+91], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -5e3

   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 88.9%

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

   4. Taylor expanded in b around inf 76.6%

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

      1. neg-mul-1 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in b around 0 37.4%

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

   8. Taylor expanded in b around inf 37.4%

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

   if -5e3 < b < -5e-277

   1. Initial program 99.0%

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

      1. associate-*l/ 94.6%

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

      2. *-commutative 94.6%

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

      3. exp-diff 94.7%

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

      4. +-commutative 94.7%

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

      5. exp-sum 74.7%

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

      6. associate-/l* 74.7%

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

      7. *-commutative 74.7%

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

      8. exp-to-pow 75.5%

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

      9. sub-neg 75.5%

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

      10. metadata-eval 75.5%

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

      11. *-commutative 75.5%

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

      12. exp-to-pow 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in t around 0 63.0%

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

      1. times-frac 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in y around 0 35.9%

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

      1. associate-*r* 35.9%

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

   10. Simplified 35.9%

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

       1. clear-num 35.8%

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

       2. inv-pow 35.8%

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

   12. Applied egg-rr 35.8%

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

       1. unpow-1 35.8%

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

       2. associate-*r* 35.8%

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

       3. *-lft-identity 35.8%

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

       4. times-frac 42.3%

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

       5. /-rgt-identity 42.3%

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

       6. *-commutative 42.3%

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

       7. associate-*r/ 42.3%

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

   14. Simplified 42.3%

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

   15. Taylor expanded in b around 0 35.4%

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

       1. associate-*r/ 41.7%

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

   17. Simplified 41.7%

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

   if -5e-277 < b < 1.7000000000000001e-222

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0 65.8%

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

   4. Taylor expanded in b around inf 19.4%

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

      1. neg-mul-1 19.4%

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

   6. Simplified 19.4%

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

   7. Taylor expanded in b around 0 19.4%

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

   8. Taylor expanded in b around inf 38.1%

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

      1. mul-1-neg 38.1%

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

      2. associate-*r/ 38.1%

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

      3. *-commutative 38.1%

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

      4. associate-/r/ 54.9%

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

      5. distribute-neg-frac 54.9%

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

   10. Simplified 54.9%

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

   if 1.7000000000000001e-222 < b < 7.50000000000000033e91

   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/ 89.6%

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

      2. *-commutative 89.6%

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

      3. exp-diff 80.3%

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

      4. +-commutative 80.3%

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

      5. exp-sum 72.5%

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

      6. associate-/l* 72.5%

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

      7. *-commutative 72.5%

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

      8. exp-to-pow 73.5%

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

      9. sub-neg 73.5%

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

      10. metadata-eval 73.5%

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

      11. *-commutative 73.5%

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

      12. exp-to-pow 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in t around 0 66.2%

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

      1. times-frac 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in b around 0 58.0%

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

      1. times-frac 62.6%

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

   10. Simplified 62.6%

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

   11. Taylor expanded in y around 0 31.6%

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

   if 7.50000000000000033e91 < 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 97.6%

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

   4. Taylor expanded in b around inf 92.8%

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

      1. neg-mul-1 92.8%

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

   6. Simplified 92.8%

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

      1. associate-/l* 92.8%

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

      2. div-inv 92.8%

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

      3. div-inv 92.8%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 8.8%

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

      6. sqr-neg 8.8%

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

      7. sqrt-unprod 8.8%

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

      8. add-sqr-sqrt 8.8%

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

      9. exp-neg 8.8%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 92.8%

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

      12. sqr-neg 92.8%

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

      13. sqrt-unprod 92.8%

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

      14. add-sqr-sqrt 92.8%

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

   8. Applied egg-rr 92.8%

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

      1. associate-*r/ 92.8%

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

      2. *-rgt-identity 92.8%

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

   10. Simplified 92.8%

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

   11. Taylor expanded in b around 0 36.1%

       \[\leadsto \frac{x}{\color{blue}{y + b \cdot y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5000:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-277}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-222}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.2% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1300:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-275}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-222}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1300.0)
   (/ (- x (* x b)) y)
   (if (<= b -1.95e-275)
     (/ 1.0 (* a (/ y x)))
     (if (<= b 2.65e-222)
       (/ (- x) (/ y b))
       (if (<= b 3.2e+91) (* (/ x a) (/ 1.0 y)) (/ x (+ y (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1300.0) {
		tmp = (x - (x * b)) / y;
	} else if (b <= -1.95e-275) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 2.65e-222) {
		tmp = -x / (y / b);
	} else if (b <= 3.2e+91) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1300.0d0)) then
        tmp = (x - (x * b)) / y
    else if (b <= (-1.95d-275)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 2.65d-222) then
        tmp = -x / (y / b)
    else if (b <= 3.2d+91) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = x / (y + (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1300.0) {
		tmp = (x - (x * b)) / y;
	} else if (b <= -1.95e-275) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 2.65e-222) {
		tmp = -x / (y / b);
	} else if (b <= 3.2e+91) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1300.0:
		tmp = (x - (x * b)) / y
	elif b <= -1.95e-275:
		tmp = 1.0 / (a * (y / x))
	elif b <= 2.65e-222:
		tmp = -x / (y / b)
	elif b <= 3.2e+91:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = x / (y + (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1300.0)
		tmp = Float64(Float64(x - Float64(x * b)) / y);
	elseif (b <= -1.95e-275)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 2.65e-222)
		tmp = Float64(Float64(-x) / Float64(y / b));
	elseif (b <= 3.2e+91)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(x / Float64(y + Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1300.0)
		tmp = (x - (x * b)) / y;
	elseif (b <= -1.95e-275)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 2.65e-222)
		tmp = -x / (y / b);
	elseif (b <= 3.2e+91)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = x / (y + (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1300.0], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.95e-275], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.65e-222], N[((-x) / N[(y / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+91], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1300

   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 88.9%

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

   4. Taylor expanded in b around inf 76.6%

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

      1. neg-mul-1 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in b around 0 37.4%

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

   8. Taylor expanded in y around 0 37.4%

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

      1. mul-1-neg 37.4%

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

      2. distribute-rgt-neg-out 37.4%

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

   10. Simplified 37.4%

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

   if -1300 < b < -1.94999999999999986e-275

   1. Initial program 99.0%

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

      1. associate-*l/ 94.6%

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

      2. *-commutative 94.6%

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

      3. exp-diff 94.7%

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

      4. +-commutative 94.7%

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

      5. exp-sum 74.7%

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

      6. associate-/l* 74.7%

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

      7. *-commutative 74.7%

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

      8. exp-to-pow 75.5%

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

      9. sub-neg 75.5%

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

      10. metadata-eval 75.5%

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

      11. *-commutative 75.5%

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

      12. exp-to-pow 75.5%

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

   3. Simplified 75.5%

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

   5. Taylor expanded in t around 0 63.0%

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

      1. times-frac 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in y around 0 35.9%

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

      1. associate-*r* 35.9%

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

   10. Simplified 35.9%

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

       1. clear-num 35.8%

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

       2. inv-pow 35.8%

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

   12. Applied egg-rr 35.8%

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

       1. unpow-1 35.8%

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

       2. associate-*r* 35.8%

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

       3. *-lft-identity 35.8%

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

       4. times-frac 42.3%

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

       5. /-rgt-identity 42.3%

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

       6. *-commutative 42.3%

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

       7. associate-*r/ 42.3%

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

   14. Simplified 42.3%

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

   15. Taylor expanded in b around 0 35.4%

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

       1. associate-*r/ 41.7%

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

   17. Simplified 41.7%

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

   if -1.94999999999999986e-275 < b < 2.6499999999999999e-222

   1. Initial program 95.6%

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

   3. Taylor expanded in y around 0 65.8%

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

   4. Taylor expanded in b around inf 19.4%

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

      1. neg-mul-1 19.4%

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

   6. Simplified 19.4%

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

   7. Taylor expanded in b around 0 19.4%

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

   8. Taylor expanded in b around inf 38.1%

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

      1. mul-1-neg 38.1%

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

      2. associate-*r/ 38.1%

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

      3. *-commutative 38.1%

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

      4. associate-/r/ 54.9%

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

      5. distribute-neg-frac 54.9%

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

   10. Simplified 54.9%

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

   if 2.6499999999999999e-222 < b < 3.19999999999999989e91

   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/ 89.6%

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

      2. *-commutative 89.6%

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

      3. exp-diff 80.3%

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

      4. +-commutative 80.3%

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

      5. exp-sum 72.5%

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

      6. associate-/l* 72.5%

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

      7. *-commutative 72.5%

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

      8. exp-to-pow 73.5%

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

      9. sub-neg 73.5%

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

      10. metadata-eval 73.5%

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

      11. *-commutative 73.5%

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

      12. exp-to-pow 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in t around 0 66.2%

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

      1. times-frac 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in b around 0 58.0%

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

      1. times-frac 62.6%

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

   10. Simplified 62.6%

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

   11. Taylor expanded in y around 0 31.6%

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

   if 3.19999999999999989e91 < 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 97.6%

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

   4. Taylor expanded in b around inf 92.8%

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

      1. neg-mul-1 92.8%

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

   6. Simplified 92.8%

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

      1. associate-/l* 92.8%

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

      2. div-inv 92.8%

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

      3. div-inv 92.8%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 8.8%

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

      6. sqr-neg 8.8%

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

      7. sqrt-unprod 8.8%

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

      8. add-sqr-sqrt 8.8%

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

      9. exp-neg 8.8%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 92.8%

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

      12. sqr-neg 92.8%

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

      13. sqrt-unprod 92.8%

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

      14. add-sqr-sqrt 92.8%

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

   8. Applied egg-rr 92.8%

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

      1. associate-*r/ 92.8%

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

      2. *-rgt-identity 92.8%

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

   10. Simplified 92.8%

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

   11. Taylor expanded in b around 0 36.1%

       \[\leadsto \frac{x}{\color{blue}{y + b \cdot y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1300:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-275}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{-222}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 37.5% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3100:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-277}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-223}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3100.0)
   (/ (- x (* x b)) y)
   (if (<= b -8.8e-277)
     (/ 1.0 (* a (/ y x)))
     (if (<= b 5.8e-223) (/ (- x) (/ y b)) (/ x (* a (+ y (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3100.0) {
		tmp = (x - (x * b)) / y;
	} else if (b <= -8.8e-277) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 5.8e-223) {
		tmp = -x / (y / b);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3100.0d0)) then
        tmp = (x - (x * b)) / y
    else if (b <= (-8.8d-277)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 5.8d-223) then
        tmp = -x / (y / b)
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3100.0) {
		tmp = (x - (x * b)) / y;
	} else if (b <= -8.8e-277) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 5.8e-223) {
		tmp = -x / (y / b);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3100.0:
		tmp = (x - (x * b)) / y
	elif b <= -8.8e-277:
		tmp = 1.0 / (a * (y / x))
	elif b <= 5.8e-223:
		tmp = -x / (y / b)
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3100.0)
		tmp = Float64(Float64(x - Float64(x * b)) / y);
	elseif (b <= -8.8e-277)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 5.8e-223)
		tmp = Float64(Float64(-x) / Float64(y / b));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3100.0)
		tmp = (x - (x * b)) / y;
	elseif (b <= -8.8e-277)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 5.8e-223)
		tmp = -x / (y / b);
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3100.0], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -8.8e-277], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e-223], N[((-x) / N[(y / b), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3100

   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 88.9%

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

   4. Taylor expanded in b around inf 76.6%

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

      1. neg-mul-1 76.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   6. Simplified 76.6%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   7. Taylor expanded in b around 0 37.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]

   8. Taylor expanded in y around 0 37.4%

      \[\leadsto \color{blue}{\frac{x + -1 \cdot \left(b \cdot x\right)}{y}} \]
   9. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto \frac{x + \color{blue}{\left(-b \cdot x\right)}}{y} \]

      2. distribute-rgt-neg-out 37.4%

         \[\leadsto \frac{x + \color{blue}{b \cdot \left(-x\right)}}{y} \]

   10. Simplified 37.4%

       \[\leadsto \color{blue}{\frac{x + b \cdot \left(-x\right)}{y}} \]

   if -3100 < b < -8.79999999999999983e-277

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 94.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. exp-diff 94.7%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}} \cdot \frac{x}{y} \]

      4. +-commutative 94.7%

         \[\leadsto \frac{e^{\color{blue}{\left(t - 1\right) \cdot \log a + y \cdot \log z}}}{e^{b}} \cdot \frac{x}{y} \]

      5. exp-sum 74.7%

         \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z}}}{e^{b}} \cdot \frac{x}{y} \]

      6. associate-/l* 74.7%

         \[\leadsto \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{\frac{e^{b}}{e^{y \cdot \log z}}}} \cdot \frac{x}{y} \]

      7. *-commutative 74.7%

         \[\leadsto \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      8. exp-to-pow 75.5%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      9. sub-neg 75.5%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      10. metadata-eval 75.5%

          \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      11. *-commutative 75.5%

          \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{e^{\color{blue}{\log z \cdot y}}}} \cdot \frac{x}{y} \]

      12. exp-to-pow 75.5%

          \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{\color{blue}{{z}^{y}}}} \cdot \frac{x}{y} \]

   3. Simplified 75.5%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{{z}^{y}}} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 63.0%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 67.4%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 35.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 35.9%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 35.9%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]
   11. Step-by-step derivation

       1. clear-num 35.8%

          \[\leadsto \color{blue}{\frac{1}{\frac{\left(a \cdot y\right) \cdot e^{b}}{x}}} \]

       2. inv-pow 35.8%

          \[\leadsto \color{blue}{{\left(\frac{\left(a \cdot y\right) \cdot e^{b}}{x}\right)}^{-1}} \]

   12. Applied egg-rr 35.8%

       \[\leadsto \color{blue}{{\left(\frac{\left(a \cdot y\right) \cdot e^{b}}{x}\right)}^{-1}} \]
   13. Step-by-step derivation

       1. unpow-1 35.8%

          \[\leadsto \color{blue}{\frac{1}{\frac{\left(a \cdot y\right) \cdot e^{b}}{x}}} \]

       2. associate-*r* 35.8%

          \[\leadsto \frac{1}{\frac{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}}{x}} \]

       3. *-lft-identity 35.8%

          \[\leadsto \frac{1}{\frac{a \cdot \left(y \cdot e^{b}\right)}{\color{blue}{1 \cdot x}}} \]

       4. times-frac 42.3%

          \[\leadsto \frac{1}{\color{blue}{\frac{a}{1} \cdot \frac{y \cdot e^{b}}{x}}} \]

       5. /-rgt-identity 42.3%

          \[\leadsto \frac{1}{\color{blue}{a} \cdot \frac{y \cdot e^{b}}{x}} \]

       6. *-commutative 42.3%

          \[\leadsto \frac{1}{a \cdot \frac{\color{blue}{e^{b} \cdot y}}{x}} \]

       7. associate-*r/ 42.3%

          \[\leadsto \frac{1}{a \cdot \color{blue}{\left(e^{b} \cdot \frac{y}{x}\right)}} \]

   14. Simplified 42.3%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \left(e^{b} \cdot \frac{y}{x}\right)}} \]

   15. Taylor expanded in b around 0 35.4%

       \[\leadsto \frac{1}{\color{blue}{\frac{a \cdot y}{x}}} \]
   16. Step-by-step derivation

       1. associate-*r/ 41.7%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   17. Simplified 41.7%

       \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   if -8.79999999999999983e-277 < b < 5.8000000000000001e-223

   1. Initial program 95.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 65.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around inf 19.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   5. Step-by-step derivation

      1. neg-mul-1 19.4%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   6. Simplified 19.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   7. Taylor expanded in b around 0 19.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]

   8. Taylor expanded in b around inf 38.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y}} \]
   9. Step-by-step derivation

      1. mul-1-neg 38.1%

         \[\leadsto \color{blue}{-\frac{b \cdot x}{y}} \]

      2. associate-*r/ 38.1%

         \[\leadsto -\color{blue}{b \cdot \frac{x}{y}} \]

      3. *-commutative 38.1%

         \[\leadsto -\color{blue}{\frac{x}{y} \cdot b} \]

      4. associate-/r/ 54.9%

         \[\leadsto -\color{blue}{\frac{x}{\frac{y}{b}}} \]

      5. distribute-neg-frac 54.9%

         \[\leadsto \color{blue}{\frac{-x}{\frac{y}{b}}} \]

   10. Simplified 54.9%

       \[\leadsto \color{blue}{\frac{-x}{\frac{y}{b}}} \]

   if 5.8000000000000001e-223 < b

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 86.1%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 86.1%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. exp-diff 69.9%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}} \cdot \frac{x}{y} \]

      4. +-commutative 69.9%

         \[\leadsto \frac{e^{\color{blue}{\left(t - 1\right) \cdot \log a + y \cdot \log z}}}{e^{b}} \cdot \frac{x}{y} \]

      5. exp-sum 64.2%

         \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z}}}{e^{b}} \cdot \frac{x}{y} \]

      6. associate-/l* 64.2%

         \[\leadsto \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{\frac{e^{b}}{e^{y \cdot \log z}}}} \cdot \frac{x}{y} \]

      7. *-commutative 64.2%

         \[\leadsto \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      8. exp-to-pow 64.8%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      9. sub-neg 64.8%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      10. metadata-eval 64.8%

          \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      11. *-commutative 64.8%

          \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{e^{\color{blue}{\log z \cdot y}}}} \cdot \frac{x}{y} \]

      12. exp-to-pow 64.8%

          \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{\color{blue}{{z}^{y}}}} \cdot \frac{x}{y} \]

   3. Simplified 64.8%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{{z}^{y}}} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 73.7%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 70.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 70.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 64.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 57.6%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 57.6%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   11. Taylor expanded in b around 0 31.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   12. Step-by-step derivation

       1. distribute-lft-out 31.0%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 31.0%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   13. Simplified 31.0%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3100:\\ \;\;\;\;\frac{x - x \cdot b}{y}\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-277}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-223}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.1% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-287}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-164}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.05e-287)
   (- (/ x (* y a)) (* (/ x a) (/ b y)))
   (if (<= b 5e-164)
     (/ (- x) (/ y b))
     (if (<= b 2.9e+91) (* (/ x a) (/ 1.0 y)) (/ x (+ y (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05e-287) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= 5e-164) {
		tmp = -x / (y / b);
	} else if (b <= 2.9e+91) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.05d-287)) then
        tmp = (x / (y * a)) - ((x / a) * (b / y))
    else if (b <= 5d-164) then
        tmp = -x / (y / b)
    else if (b <= 2.9d+91) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = x / (y + (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05e-287) {
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	} else if (b <= 5e-164) {
		tmp = -x / (y / b);
	} else if (b <= 2.9e+91) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y + (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.05e-287:
		tmp = (x / (y * a)) - ((x / a) * (b / y))
	elif b <= 5e-164:
		tmp = -x / (y / b)
	elif b <= 2.9e+91:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = x / (y + (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.05e-287)
		tmp = Float64(Float64(x / Float64(y * a)) - Float64(Float64(x / a) * Float64(b / y)));
	elseif (b <= 5e-164)
		tmp = Float64(Float64(-x) / Float64(y / b));
	elseif (b <= 2.9e+91)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(x / Float64(y + Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.05e-287)
		tmp = (x / (y * a)) - ((x / a) * (b / y));
	elseif (b <= 5e-164)
		tmp = -x / (y / b);
	elseif (b <= 2.9e+91)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = x / (y + (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.05e-287], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e-164], N[((-x) / N[(y / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e+91], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.0499999999999999e-287

   1. Initial program 98.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 94.1%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 94.1%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. exp-diff 66.5%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}} \cdot \frac{x}{y} \]

      4. +-commutative 66.5%

         \[\leadsto \frac{e^{\color{blue}{\left(t - 1\right) \cdot \log a + y \cdot \log z}}}{e^{b}} \cdot \frac{x}{y} \]

      5. exp-sum 58.7%

         \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z}}}{e^{b}} \cdot \frac{x}{y} \]

      6. associate-/l* 58.7%

         \[\leadsto \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{\frac{e^{b}}{e^{y \cdot \log z}}}} \cdot \frac{x}{y} \]

      7. *-commutative 58.7%

         \[\leadsto \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      8. exp-to-pow 59.0%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      9. sub-neg 59.0%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      10. metadata-eval 59.0%

          \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      11. *-commutative 59.0%

          \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{e^{\color{blue}{\log z \cdot y}}}} \cdot \frac{x}{y} \]

      12. exp-to-pow 59.0%

          \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{\color{blue}{{z}^{y}}}} \cdot \frac{x}{y} \]

   3. Simplified 59.0%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{{z}^{y}}} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 61.0%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 58.7%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 58.7%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 62.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 55.4%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 55.4%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   11. Taylor expanded in b around 0 39.1%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. +-commutative 39.1%

          \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{a \cdot y}} \]

       2. mul-1-neg 39.1%

          \[\leadsto \frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} \]

       3. unsub-neg 39.1%

          \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{b \cdot x}{a \cdot y}} \]

       4. *-commutative 39.1%

          \[\leadsto \frac{x}{a \cdot y} - \frac{\color{blue}{x \cdot b}}{a \cdot y} \]

       5. times-frac 39.7%

          \[\leadsto \frac{x}{a \cdot y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

   13. Simplified 39.7%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{x}{a} \cdot \frac{b}{y}} \]

   if -1.0499999999999999e-287 < b < 4.99999999999999962e-164

   1. Initial program 96.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 67.2%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around inf 22.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   5. Step-by-step derivation

      1. neg-mul-1 22.0%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   6. Simplified 22.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   7. Taylor expanded in b around 0 22.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]

   8. Taylor expanded in b around inf 39.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y}} \]
   9. Step-by-step derivation

      1. mul-1-neg 39.1%

         \[\leadsto \color{blue}{-\frac{b \cdot x}{y}} \]

      2. associate-*r/ 36.2%

         \[\leadsto -\color{blue}{b \cdot \frac{x}{y}} \]

      3. *-commutative 36.2%

         \[\leadsto -\color{blue}{\frac{x}{y} \cdot b} \]

      4. associate-/r/ 49.6%

         \[\leadsto -\color{blue}{\frac{x}{\frac{y}{b}}} \]

      5. distribute-neg-frac 49.6%

         \[\leadsto \color{blue}{\frac{-x}{\frac{y}{b}}} \]

   10. Simplified 49.6%

       \[\leadsto \color{blue}{\frac{-x}{\frac{y}{b}}} \]

   if 4.99999999999999962e-164 < b < 2.90000000000000014e91

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 90.0%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. exp-diff 79.1%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}} \cdot \frac{x}{y} \]

      4. +-commutative 79.1%

         \[\leadsto \frac{e^{\color{blue}{\left(t - 1\right) \cdot \log a + y \cdot \log z}}}{e^{b}} \cdot \frac{x}{y} \]

      5. exp-sum 71.8%

         \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z}}}{e^{b}} \cdot \frac{x}{y} \]

      6. associate-/l* 71.8%

         \[\leadsto \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{\frac{e^{b}}{e^{y \cdot \log z}}}} \cdot \frac{x}{y} \]

      7. *-commutative 71.8%

         \[\leadsto \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      8. exp-to-pow 72.8%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      9. sub-neg 72.8%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      10. metadata-eval 72.8%

          \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      11. *-commutative 72.8%

          \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{e^{\color{blue}{\log z \cdot y}}}} \cdot \frac{x}{y} \]

      12. exp-to-pow 72.8%

          \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{\color{blue}{{z}^{y}}}} \cdot \frac{x}{y} \]

   3. Simplified 72.8%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{{z}^{y}}} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 62.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 69.6%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 69.6%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in b around 0 52.9%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   9. Step-by-step derivation

      1. times-frac 61.8%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

   10. Simplified 61.8%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

   11. Taylor expanded in y around 0 32.6%

       \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{1}{y}} \]

   if 2.90000000000000014e91 < 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 97.6%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around inf 92.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   5. Step-by-step derivation

      1. neg-mul-1 92.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   6. Simplified 92.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   7. Step-by-step derivation

      1. associate-/l* 92.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{e^{-b}}}} \]

      2. div-inv 92.8%

         \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{y}{e^{-b}}}} \]

      3. div-inv 92.8%

         \[\leadsto x \cdot \frac{1}{\color{blue}{y \cdot \frac{1}{e^{-b}}}} \]

      4. add-sqr-sqrt 0.0%

         \[\leadsto x \cdot \frac{1}{y \cdot \frac{1}{e^{\color{blue}{\sqrt{-b} \cdot \sqrt{-b}}}}} \]

      5. sqrt-unprod 8.8%

         \[\leadsto x \cdot \frac{1}{y \cdot \frac{1}{e^{\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}}}} \]

      6. sqr-neg 8.8%

         \[\leadsto x \cdot \frac{1}{y \cdot \frac{1}{e^{\sqrt{\color{blue}{b \cdot b}}}}} \]

      7. sqrt-unprod 8.8%

         \[\leadsto x \cdot \frac{1}{y \cdot \frac{1}{e^{\color{blue}{\sqrt{b} \cdot \sqrt{b}}}}} \]

      8. add-sqr-sqrt 8.8%

         \[\leadsto x \cdot \frac{1}{y \cdot \frac{1}{e^{\color{blue}{b}}}} \]

      9. exp-neg 8.8%

         \[\leadsto x \cdot \frac{1}{y \cdot \color{blue}{e^{-b}}} \]

      10. add-sqr-sqrt 0.0%

          \[\leadsto x \cdot \frac{1}{y \cdot e^{\color{blue}{\sqrt{-b} \cdot \sqrt{-b}}}} \]

      11. sqrt-unprod 92.8%

          \[\leadsto x \cdot \frac{1}{y \cdot e^{\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}}}} \]

      12. sqr-neg 92.8%

          \[\leadsto x \cdot \frac{1}{y \cdot e^{\sqrt{\color{blue}{b \cdot b}}}} \]

      13. sqrt-unprod 92.8%

          \[\leadsto x \cdot \frac{1}{y \cdot e^{\color{blue}{\sqrt{b} \cdot \sqrt{b}}}} \]

      14. add-sqr-sqrt 92.8%

          \[\leadsto x \cdot \frac{1}{y \cdot e^{\color{blue}{b}}} \]

   8. Applied egg-rr 92.8%

      \[\leadsto \color{blue}{x \cdot \frac{1}{y \cdot e^{b}}} \]
   9. Step-by-step derivation

      1. associate-*r/ 92.8%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{y \cdot e^{b}}} \]

      2. *-rgt-identity 92.8%

         \[\leadsto \frac{\color{blue}{x}}{y \cdot e^{b}} \]

   10. Simplified 92.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot e^{b}}} \]

   11. Taylor expanded in b around 0 36.1%

       \[\leadsto \frac{x}{\color{blue}{y + b \cdot y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{-287}:\\ \;\;\;\;\frac{x}{y \cdot a} - \frac{x}{a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-164}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 32.8% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-163}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 9:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.5e-242)
   (* (/ x a) (/ 1.0 y))
   (if (<= t 2.4e-163)
     (/ 1.0 (* a (/ y x)))
     (if (<= t 9.0) (/ x (* y a)) (/ (* x (- b)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.5e-242) {
		tmp = (x / a) * (1.0 / y);
	} else if (t <= 2.4e-163) {
		tmp = 1.0 / (a * (y / x));
	} else if (t <= 9.0) {
		tmp = x / (y * a);
	} else {
		tmp = (x * -b) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-5.5d-242)) then
        tmp = (x / a) * (1.0d0 / y)
    else if (t <= 2.4d-163) then
        tmp = 1.0d0 / (a * (y / x))
    else if (t <= 9.0d0) then
        tmp = x / (y * a)
    else
        tmp = (x * -b) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.5e-242) {
		tmp = (x / a) * (1.0 / y);
	} else if (t <= 2.4e-163) {
		tmp = 1.0 / (a * (y / x));
	} else if (t <= 9.0) {
		tmp = x / (y * a);
	} else {
		tmp = (x * -b) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.5e-242:
		tmp = (x / a) * (1.0 / y)
	elif t <= 2.4e-163:
		tmp = 1.0 / (a * (y / x))
	elif t <= 9.0:
		tmp = x / (y * a)
	else:
		tmp = (x * -b) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.5e-242)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	elseif (t <= 2.4e-163)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (t <= 9.0)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x * Float64(-b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.5e-242)
		tmp = (x / a) * (1.0 / y);
	elseif (t <= 2.4e-163)
		tmp = 1.0 / (a * (y / x));
	elseif (t <= 9.0)
		tmp = x / (y * a);
	else
		tmp = (x * -b) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.5e-242], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-163], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.0], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x * (-b)), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.4999999999999998e-242

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 88.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 88.3%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. exp-diff 69.9%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}} \cdot \frac{x}{y} \]

      4. +-commutative 69.9%

         \[\leadsto \frac{e^{\color{blue}{\left(t - 1\right) \cdot \log a + y \cdot \log z}}}{e^{b}} \cdot \frac{x}{y} \]

      5. exp-sum 58.7%

         \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z}}}{e^{b}} \cdot \frac{x}{y} \]

      6. associate-/l* 58.7%

         \[\leadsto \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{\frac{e^{b}}{e^{y \cdot \log z}}}} \cdot \frac{x}{y} \]

      7. *-commutative 58.7%

         \[\leadsto \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      8. exp-to-pow 59.2%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      9. sub-neg 59.2%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      10. metadata-eval 59.2%

          \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      11. *-commutative 59.2%

          \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{e^{\color{blue}{\log z \cdot y}}}} \cdot \frac{x}{y} \]

      12. exp-to-pow 59.2%

          \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{\color{blue}{{z}^{y}}}} \cdot \frac{x}{y} \]

   3. Simplified 59.2%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{{z}^{y}}} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 70.0%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 69.2%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 69.2%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in b around 0 58.1%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot y}} \]
   9. Step-by-step derivation

      1. times-frac 59.7%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

   10. Simplified 59.7%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y}} \]

   11. Taylor expanded in y around 0 36.2%

       \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{1}{y}} \]

   if -5.4999999999999998e-242 < t < 2.4000000000000001e-163

   1. Initial program 97.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 91.4%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. exp-diff 70.3%

         \[\leadsto \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}} \cdot \frac{x}{y} \]

      4. +-commutative 70.3%

         \[\leadsto \frac{e^{\color{blue}{\left(t - 1\right) \cdot \log a + y \cdot \log z}}}{e^{b}} \cdot \frac{x}{y} \]

      5. exp-sum 70.3%

         \[\leadsto \frac{\color{blue}{e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z}}}{e^{b}} \cdot \frac{x}{y} \]

      6. associate-/l* 70.3%

         \[\leadsto \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{\frac{e^{b}}{e^{y \cdot \log z}}}} \cdot \frac{x}{y} \]

      7. *-commutative 70.3%

         \[\leadsto \frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      8. exp-to-pow 71.0%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      9. sub-neg 71.0%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      10. metadata-eval 71.0%

          \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{\frac{e^{b}}{e^{y \cdot \log z}}} \cdot \frac{x}{y} \]

      11. *-commutative 71.0%

          \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{e^{\color{blue}{\log z \cdot y}}}} \cdot \frac{x}{y} \]

      12. exp-to-pow 71.0%

          \[\leadsto \frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{\color{blue}{{z}^{y}}}} \cdot \frac{x}{y} \]

   3. Simplified 71.0%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t + -1\right)}}{\frac{e^{b}}{{z}^{y}}} \cdot \frac{x}{y}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 73.6%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 73.8%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 73.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 67.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 61.7%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 61.7%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]
   11. Step-by-step derivation

       1. clear-num 61.7%

          \[\leadsto \color{blue}{\frac{1}{\frac{\left(a \cdot y\right) \cdot e^{b}}{x}}} \]

       2. inv-pow 61.7%

          \[\leadsto \color{blue}{{\left(\frac{\left(a \cdot y\right) \cdot e^{b}}{x}\right)}^{-1}} \]

   12. Applied egg-rr 61.7%

       \[\leadsto \color{blue}{{\left(\frac{\left(a \cdot y\right) \cdot e^{b}}{x}\right)}^{-1}} \]
   13. Step-by-step derivation

       1. unpow-1 61.7%

          \[\leadsto \color{blue}{\frac{1}{\frac{\left(a \cdot y\right) \cdot e^{b}}{x}}} \]

       2. associate-*r* 67.1%

          \[\leadsto \frac{1}{\frac{\color{blue}{a \cdot \left(y \cdot e^{b}\right)}}{x}} \]

       3. *-lft-identity 67.1%

          \[\leadsto \frac{1}{\frac{a \cdot \left(y \cdot e^{b}\right)}{\color{blue}{1 \cdot x}}} \]

       4. times-frac 69.7%

          \[\leadsto \frac{1}{\color{blue}{\frac{a}{1} \cdot \frac{y \cdot e^{b}}{x}}} \]

       5. /-rgt-identity 69.7%

          \[\leadsto \frac{1}{\color{blue}{a} \cdot \frac{y \cdot e^{b}}{x}} \]

       6. *-commutative 69.7%

          \[\leadsto \frac{1}{a \cdot \frac{\color{blue}{e^{b} \cdot y}}{x}} \]

       7. associate-*r/ 61.6%

          \[\leadsto \frac{1}{a \cdot \color{blue}{\left(e^{b} \cdot \frac{y}{x}\right)}} \]

   14. Simplified 61.6%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \left(e^{b} \cdot \frac{y}{x}\right)}} \]

   15. Taylor expanded in b around 0 29.2%

       \[\leadsto \frac{1}{\color{blue}{\frac{a \cdot y}{x}}} \]
   16. Step-by-step derivation

       1. associate-*r/ 39.1%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   17. Simplified 39.1%

       \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   if 2.4000000000000001e-163 < t < 9

   1. Initial program 98.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around 0 34.3%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right)}}}{y} \]
   5. Step-by-step derivation

      1. *-commutative 34.3%

         \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y} \]

      2. exp-to-pow 35.6%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}} \cdot x}{y} \]

      3. sub-neg 35.6%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot x}{y} \]

      4. metadata-eval 35.6%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)} \cdot x}{y} \]

      5. +-commutative 35.6%

         \[\leadsto \frac{{a}^{\color{blue}{\left(-1 + t\right)}} \cdot x}{y} \]

   6. Simplified 35.6%

      \[\leadsto \frac{\color{blue}{{a}^{\left(-1 + t\right)} \cdot x}}{y} \]

   7. Taylor expanded in t around 0 41.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 9 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around inf 42.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   5. Step-by-step derivation

      1. neg-mul-1 42.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   6. Simplified 42.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   7. Taylor expanded in b around 0 13.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]

   8. Taylor expanded in b around inf 26.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-163}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq 9:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 32.5% accurate, 28.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 0.0033:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{-x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 0.0033) (/ x (* y a)) (* b (/ (- x) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 0.0033) {
		tmp = x / (y * a);
	} else {
		tmp = b * (-x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 0.0033d0) then
        tmp = x / (y * a)
    else
        tmp = b * (-x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 0.0033) {
		tmp = x / (y * a);
	} else {
		tmp = b * (-x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 0.0033:
		tmp = x / (y * a)
	else:
		tmp = b * (-x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 0.0033)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(b * Float64(Float64(-x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 0.0033)
		tmp = x / (y * a);
	else
		tmp = b * (-x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 0.0033], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(b * N[((-x) / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 0.0033

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around 0 50.4%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right)}}}{y} \]
   5. Step-by-step derivation

      1. *-commutative 50.4%

         \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y} \]

      2. exp-to-pow 50.9%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}} \cdot x}{y} \]

      3. sub-neg 50.9%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot x}{y} \]

      4. metadata-eval 50.9%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)} \cdot x}{y} \]

      5. +-commutative 50.9%

         \[\leadsto \frac{{a}^{\color{blue}{\left(-1 + t\right)}} \cdot x}{y} \]

   6. Simplified 50.9%

      \[\leadsto \frac{\color{blue}{{a}^{\left(-1 + t\right)} \cdot x}}{y} \]

   7. Taylor expanded in t around 0 34.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 0.0033 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around inf 42.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   5. Step-by-step derivation

      1. neg-mul-1 42.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   6. Simplified 42.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   7. Taylor expanded in b around 0 13.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]

   8. Taylor expanded in b around inf 26.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y}} \]
   9. Step-by-step derivation

      1. mul-1-neg 26.8%

         \[\leadsto \color{blue}{-\frac{b \cdot x}{y}} \]

      2. associate-*r/ 20.7%

         \[\leadsto -\color{blue}{b \cdot \frac{x}{y}} \]

      3. distribute-rgt-neg-in 20.7%

         \[\leadsto \color{blue}{b \cdot \left(-\frac{x}{y}\right)} \]

      4. distribute-frac-neg 20.7%

         \[\leadsto b \cdot \color{blue}{\frac{-x}{y}} \]

   10. Simplified 20.7%

       \[\leadsto \color{blue}{b \cdot \frac{-x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 0.0033:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{-x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.5% accurate, 28.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.3:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 5.3) (/ x (* y a)) (/ (- x) (/ y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 5.3) {
		tmp = x / (y * a);
	} else {
		tmp = -x / (y / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 5.3d0) then
        tmp = x / (y * a)
    else
        tmp = -x / (y / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 5.3) {
		tmp = x / (y * a);
	} else {
		tmp = -x / (y / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 5.3:
		tmp = x / (y * a)
	else:
		tmp = -x / (y / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 5.3)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(-x) / Float64(y / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 5.3)
		tmp = x / (y * a);
	else
		tmp = -x / (y / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 5.3], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[((-x) / N[(y / b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.29999999999999982

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around 0 50.4%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right)}}}{y} \]
   5. Step-by-step derivation

      1. *-commutative 50.4%

         \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y} \]

      2. exp-to-pow 50.9%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}} \cdot x}{y} \]

      3. sub-neg 50.9%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot x}{y} \]

      4. metadata-eval 50.9%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)} \cdot x}{y} \]

      5. +-commutative 50.9%

         \[\leadsto \frac{{a}^{\color{blue}{\left(-1 + t\right)}} \cdot x}{y} \]

   6. Simplified 50.9%

      \[\leadsto \frac{\color{blue}{{a}^{\left(-1 + t\right)} \cdot x}}{y} \]

   7. Taylor expanded in t around 0 34.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 5.29999999999999982 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around inf 42.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   5. Step-by-step derivation

      1. neg-mul-1 42.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   6. Simplified 42.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   7. Taylor expanded in b around 0 13.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]

   8. Taylor expanded in b around inf 26.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y}} \]
   9. Step-by-step derivation

      1. mul-1-neg 26.8%

         \[\leadsto \color{blue}{-\frac{b \cdot x}{y}} \]

      2. associate-*r/ 20.7%

         \[\leadsto -\color{blue}{b \cdot \frac{x}{y}} \]

      3. *-commutative 20.7%

         \[\leadsto -\color{blue}{\frac{x}{y} \cdot b} \]

      4. associate-/r/ 20.7%

         \[\leadsto -\color{blue}{\frac{x}{\frac{y}{b}}} \]

      5. distribute-neg-frac 20.7%

         \[\leadsto \color{blue}{\frac{-x}{\frac{y}{b}}} \]

   10. Simplified 20.7%

       \[\leadsto \color{blue}{\frac{-x}{\frac{y}{b}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.3:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{y}{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 32.5% accurate, 28.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 0.03:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 0.03) (/ x (* y a)) (/ (* x (- b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 0.03) {
		tmp = x / (y * a);
	} else {
		tmp = (x * -b) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 0.03d0) then
        tmp = x / (y * a)
    else
        tmp = (x * -b) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 0.03) {
		tmp = x / (y * a);
	} else {
		tmp = (x * -b) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 0.03:
		tmp = x / (y * a)
	else:
		tmp = (x * -b) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 0.03)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x * Float64(-b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 0.03)
		tmp = x / (y * a);
	else
		tmp = (x * -b) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 0.03], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x * (-b)), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 0.029999999999999999

   1. Initial program 98.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around 0 50.4%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right)}}}{y} \]
   5. Step-by-step derivation

      1. *-commutative 50.4%

         \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y} \]

      2. exp-to-pow 50.9%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}} \cdot x}{y} \]

      3. sub-neg 50.9%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot x}{y} \]

      4. metadata-eval 50.9%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)} \cdot x}{y} \]

      5. +-commutative 50.9%

         \[\leadsto \frac{{a}^{\color{blue}{\left(-1 + t\right)}} \cdot x}{y} \]

   6. Simplified 50.9%

      \[\leadsto \frac{\color{blue}{{a}^{\left(-1 + t\right)} \cdot x}}{y} \]

   7. Taylor expanded in t around 0 34.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 0.029999999999999999 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around inf 42.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   5. Step-by-step derivation

      1. neg-mul-1 42.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   6. Simplified 42.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   7. Taylor expanded in b around 0 13.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y} + \frac{x}{y}} \]

   8. Taylor expanded in b around inf 26.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 0.03:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.3% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.8 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.8e-161) (/ 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 <= 3.8e-161) {
		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 <= 3.8d-161) 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 <= 3.8e-161) {
		tmp = x / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.8e-161:
		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 <= 3.8e-161)
		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 <= 3.8e-161)
		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, 3.8e-161], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.8000000000000001e-161

   1. Initial program 98.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.6%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around 0 60.3%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right)}}}{y} \]
   5. Step-by-step derivation

      1. *-commutative 60.3%

         \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y} \]

      2. exp-to-pow 60.6%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}} \cdot x}{y} \]

      3. sub-neg 60.6%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot x}{y} \]

      4. metadata-eval 60.6%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)} \cdot x}{y} \]

      5. +-commutative 60.6%

         \[\leadsto \frac{{a}^{\color{blue}{\left(-1 + t\right)}} \cdot x}{y} \]

   6. Simplified 60.6%

      \[\leadsto \frac{\color{blue}{{a}^{\left(-1 + t\right)} \cdot x}}{y} \]

   7. Taylor expanded in t around 0 34.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

   if 3.8000000000000001e-161 < b

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 89.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

   4. Taylor expanded in b around 0 55.7%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right)}}}{y} \]
   5. Step-by-step derivation

      1. *-commutative 55.7%

         \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y} \]

      2. exp-to-pow 56.2%

         \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}} \cdot x}{y} \]

      3. sub-neg 56.2%

         \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot x}{y} \]

      4. metadata-eval 56.2%

         \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)} \cdot x}{y} \]

      5. +-commutative 56.2%

         \[\leadsto \frac{{a}^{\color{blue}{\left(-1 + t\right)}} \cdot x}{y} \]

   6. Simplified 56.2%

      \[\leadsto \frac{\color{blue}{{a}^{\left(-1 + t\right)} \cdot x}}{y} \]

   7. Taylor expanded in t around 0 22.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.8 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.5% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.7%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 83.3%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

4. Taylor expanded in b around 0 58.6%

   \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right)}}}{y} \]
5. Step-by-step derivation

   1. *-commutative 58.6%

      \[\leadsto \frac{\color{blue}{e^{\log a \cdot \left(t - 1\right)} \cdot x}}{y} \]

   2. exp-to-pow 59.0%

      \[\leadsto \frac{\color{blue}{{a}^{\left(t - 1\right)}} \cdot x}{y} \]

   3. sub-neg 59.0%

      \[\leadsto \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot x}{y} \]

   4. metadata-eval 59.0%

      \[\leadsto \frac{{a}^{\left(t + \color{blue}{-1}\right)} \cdot x}{y} \]

   5. +-commutative 59.0%

      \[\leadsto \frac{{a}^{\color{blue}{\left(-1 + t\right)}} \cdot x}{y} \]

6. Simplified 59.0%

   \[\leadsto \frac{\color{blue}{{a}^{\left(-1 + t\right)} \cdot x}}{y} \]

7. Taylor expanded in t around 0 28.0%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

8. Final simplification 28.0%

   \[\leadsto \frac{x}{y \cdot a} \]
9. Add Preprocessing

Alternative 22: 16.5% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Python

def code(x, y, z, t, a, b):
	return x / y

Julia

function code(x, y, z, t, a, b)
	return Float64(x / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 98.7%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 83.3%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

4. Taylor expanded in b around inf 51.8%

   \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
5. Step-by-step derivation

   1. neg-mul-1 51.8%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

6. Simplified 51.8%

   \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

7. Taylor expanded in b around 0 17.0%

   \[\leadsto \color{blue}{\frac{x}{y}} \]

8. Final simplification 17.0%

   \[\leadsto \frac{x}{y} \]
9. Add Preprocessing

Developer target: 73.2% 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 2024034 
(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))