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

Percentage Accurate: 98.5% → 98.5%

Time: 18.3s

Alternatives: 21

Speedup: 1.0×

• Could not converge on a ground truth

  1. x = 1.626097232675537e+75
  2. y = -2.450499820829281e+44
  3. z = 2.9465694046472513e-236
  4. t = -4.2148823547500386e-204
  5. a = 3.4447699534483324e+72
  6. b = -4.199400172543493e+171

• 47.7% 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 98.9%

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

3. Final simplification 98.9%

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

Alternative 2: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+106} \lor \neg \left(y \leq 66000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.3e+106) (not (<= y 66000.0)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) 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+106) || !(y <= 66000.0)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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+106)) .or. (.not. (y <= 66000.0d0))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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+106) || !(y <= 66000.0)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / 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+106) or not (y <= 66000.0):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / 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+106) || !(y <= 66000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / 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+106) || ~((y <= 66000.0)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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+106], N[Not[LessEqual[y, 66000.0]], $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], 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 < -1.3000000000000001e106 or 66000 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 94.5%

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

      1. +-commutative 94.5%

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

      2. mul-1-neg 94.5%

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

      3. unsub-neg 94.5%

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

   5. Simplified 94.5%

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

   if -1.3000000000000001e106 < y < 66000

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 97.1%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+106} \lor \neg \left(y \leq 66000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+106} \lor \neg \left(y \leq 3.3 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.85e+106) (not (<= y 3.3e+43)))
   (/ (/ (* x (pow z y)) a) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.85e+106) || !(y <= 3.3e+43)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.85d+106)) .or. (.not. (y <= 3.3d+43))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.85e+106) || !(y <= 3.3e+43)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.85e+106) or not (y <= 3.3e+43):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.85e+106) || !(y <= 3.3e+43))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.85e+106) || ~((y <= 3.3e+43)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.85e+106], N[Not[LessEqual[y, 3.3e+43]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.84999999999999997e106 or 3.3000000000000001e43 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 93.8%

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

      1. exp-sum 76.9%

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

      2. *-commutative 76.9%

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

      3. exp-to-pow 76.9%

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

      4. exp-to-pow 76.9%

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

      5. sub-neg 76.9%

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

      6. metadata-eval 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in t around 0 89.6%

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

   if -1.84999999999999997e106 < y < 3.3000000000000001e43

   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 96.7%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+106} \lor \neg \left(y \leq 3.3 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+106} \lor \neg \left(y \leq 8.8 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.5e+106) (not (<= y 8.8e+42)))
   (/ (/ (* x (pow z y)) a) y)
   (/ (* x (/ (pow a (+ t -1.0)) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.5e+106) || !(y <= 8.8e+42)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = (x * (pow(a, (t + -1.0)) / exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.5d+106)) .or. (.not. (y <= 8.8d+42))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = (x * ((a ** (t + (-1.0d0))) / exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.5e+106) || !(y <= 8.8e+42)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.5e+106) or not (y <= 8.8e+42):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = (x * (math.pow(a, (t + -1.0)) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.5e+106) || !(y <= 8.8e+42))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.5e+106) || ~((y <= 8.8e+42)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = (x * ((a ^ (t + -1.0)) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.5e+106], N[Not[LessEqual[y, 8.8e+42]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.49999999999999981e106 or 8.8000000000000005e42 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 93.8%

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

      1. exp-sum 76.9%

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

      2. *-commutative 76.9%

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

      3. exp-to-pow 76.9%

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

      4. exp-to-pow 76.9%

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

      5. sub-neg 76.9%

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

      6. metadata-eval 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in t around 0 89.6%

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

   if -3.49999999999999981e106 < y < 8.8000000000000005e42

   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 96.7%

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

      1. div-exp 91.2%

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

      2. exp-to-pow 92.1%

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

      3. sub-neg 92.1%

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

      4. metadata-eval 92.1%

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

   5. Simplified 92.1%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+106} \lor \neg \left(y \leq 8.8 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+106} \lor \neg \left(y \leq 1.3 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.3e+106) (not (<= y 1.3e+42)))
   (/ (/ (* x (pow z y)) a) y)
   (* x (/ (/ (pow a (+ t -1.0)) y) (exp b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e+106) || !(y <= 1.3e+42)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = x * ((pow(a, (t + -1.0)) / y) / exp(b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.3d+106)) .or. (.not. (y <= 1.3d+42))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = x * (((a ** (t + (-1.0d0))) / y) / exp(b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e+106) || !(y <= 1.3e+42)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = x * ((Math.pow(a, (t + -1.0)) / y) / Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.3e+106) or not (y <= 1.3e+42):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = x * ((math.pow(a, (t + -1.0)) / y) / math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.3e+106) || !(y <= 1.3e+42))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(x * Float64(Float64((a ^ Float64(t + -1.0)) / y) / exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.3e+106) || ~((y <= 1.3e+42)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = x * (((a ^ (t + -1.0)) / y) / exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.3e+106], N[Not[LessEqual[y, 1.3e+42]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.30000000000000008e106 or 1.29999999999999995e42 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 93.8%

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

      1. exp-sum 76.9%

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

      2. *-commutative 76.9%

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

      3. exp-to-pow 76.9%

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

      4. exp-to-pow 76.9%

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

      5. sub-neg 76.9%

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

      6. metadata-eval 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in t around 0 89.6%

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

   if -3.30000000000000008e106 < y < 1.29999999999999995e42

   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* 95.6%

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

      2. associate--l+ 95.6%

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

      3. exp-sum 85.1%

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

      4. associate-/l* 84.5%

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

      5. *-commutative 84.5%

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

      6. exp-to-pow 84.5%

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

      7. exp-diff 78.9%

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

      8. *-commutative 78.9%

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

      9. exp-to-pow 79.6%

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

      10. sub-neg 79.6%

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

      11. metadata-eval 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in y around 0 88.7%

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

      1. associate-/l* 88.5%

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

      2. associate-/r* 85.4%

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

      3. exp-to-pow 86.0%

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

      4. sub-neg 86.0%

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

      5. metadata-eval 86.0%

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

   7. Simplified 86.0%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+106} \lor \neg \left(y \leq 1.3 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ t_2 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -1100000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-114}:\\ \;\;\;\;\frac{\frac{x}{a}}{t\_1}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-247}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{a \cdot \frac{t\_1}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))) (t_2 (* x (/ (pow a t) y))))
   (if (<= t -1100000000.0)
     t_2
     (if (<= t -4.8e-114)
       (/ (/ x a) t_1)
       (if (<= t 9.8e-247)
         (/ (/ (* x (pow z y)) a) y)
         (if (<= t 1.46e+35) (/ 1.0 (* a (/ t_1 x))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * exp(b);
	double t_2 = x * (pow(a, t) / y);
	double tmp;
	if (t <= -1100000000.0) {
		tmp = t_2;
	} else if (t <= -4.8e-114) {
		tmp = (x / a) / t_1;
	} else if (t <= 9.8e-247) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else if (t <= 1.46e+35) {
		tmp = 1.0 / (a * (t_1 / x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * exp(b)
    t_2 = x * ((a ** t) / y)
    if (t <= (-1100000000.0d0)) then
        tmp = t_2
    else if (t <= (-4.8d-114)) then
        tmp = (x / a) / t_1
    else if (t <= 9.8d-247) then
        tmp = ((x * (z ** y)) / a) / y
    else if (t <= 1.46d+35) then
        tmp = 1.0d0 / (a * (t_1 / x))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * Math.exp(b);
	double t_2 = x * (Math.pow(a, t) / y);
	double tmp;
	if (t <= -1100000000.0) {
		tmp = t_2;
	} else if (t <= -4.8e-114) {
		tmp = (x / a) / t_1;
	} else if (t <= 9.8e-247) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else if (t <= 1.46e+35) {
		tmp = 1.0 / (a * (t_1 / x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * math.exp(b)
	t_2 = x * (math.pow(a, t) / y)
	tmp = 0
	if t <= -1100000000.0:
		tmp = t_2
	elif t <= -4.8e-114:
		tmp = (x / a) / t_1
	elif t <= 9.8e-247:
		tmp = ((x * math.pow(z, y)) / a) / y
	elif t <= 1.46e+35:
		tmp = 1.0 / (a * (t_1 / x))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * exp(b))
	t_2 = Float64(x * Float64((a ^ t) / y))
	tmp = 0.0
	if (t <= -1100000000.0)
		tmp = t_2;
	elseif (t <= -4.8e-114)
		tmp = Float64(Float64(x / a) / t_1);
	elseif (t <= 9.8e-247)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	elseif (t <= 1.46e+35)
		tmp = Float64(1.0 / Float64(a * Float64(t_1 / x)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * exp(b);
	t_2 = x * ((a ^ t) / y);
	tmp = 0.0;
	if (t <= -1100000000.0)
		tmp = t_2;
	elseif (t <= -4.8e-114)
		tmp = (x / a) / t_1;
	elseif (t <= 9.8e-247)
		tmp = ((x * (z ^ y)) / a) / y;
	elseif (t <= 1.46e+35)
		tmp = 1.0 / (a * (t_1 / x));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1100000000.0], t$95$2, If[LessEqual[t, -4.8e-114], N[(N[(x / a), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 9.8e-247], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.46e+35], N[(1.0 / N[(a * N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1e9 or 1.4599999999999999e35 < t

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 78.8%

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

      4. associate-/l* 78.8%

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

      5. *-commutative 78.8%

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

      6. exp-to-pow 78.8%

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

      7. exp-diff 69.5%

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

      8. *-commutative 69.5%

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

      9. exp-to-pow 69.5%

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

      10. sub-neg 69.5%

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

      11. metadata-eval 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in y around 0 81.5%

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

      1. associate-/l* 81.5%

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

      2. associate-/r* 81.5%

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

      3. exp-to-pow 81.5%

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

      4. sub-neg 81.5%

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

      5. metadata-eval 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in b around 0 90.0%

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

      1. sub-neg 90.0%

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

      2. metadata-eval 90.0%

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

      3. exp-to-pow 90.0%

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

      4. associate-*r/ 90.0%

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

      5. +-commutative 90.0%

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

   10. Simplified 90.0%

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

   11. Taylor expanded in t around inf 90.0%

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

   if -1.1e9 < t < -4.8000000000000002e-114

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. mul-1-neg 97.5%

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

      3. unsub-neg 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in x around 0 97.5%

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

      1. associate-/l* 91.0%

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

      2. associate--r+ 91.0%

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

      3. remove-double-neg 91.0%

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

      4. log-rec 91.0%

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

      5. mul-1-neg 91.0%

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

      6. associate--r+ 91.0%

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

   8. Simplified 76.7%

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

   9. Taylor expanded in y around 0 81.4%

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

       1. associate-/r* 96.1%

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

   11. Simplified 96.1%

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

   if -4.8000000000000002e-114 < t < 9.8e-247

   1. Initial program 96.8%

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

   3. Taylor expanded in b around 0 80.0%

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

      1. exp-sum 80.1%

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

      2. *-commutative 80.1%

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

      3. exp-to-pow 80.1%

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

      4. exp-to-pow 81.1%

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

      5. sub-neg 81.1%

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

      6. metadata-eval 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around 0 81.2%

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

   if 9.8e-247 < t < 1.4599999999999999e35

   1. Initial program 99.3%

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

      1. associate-/l* 96.5%

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

      2. associate--l+ 96.5%

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

      3. exp-sum 84.8%

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

      4. associate-/l* 81.5%

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

      5. *-commutative 81.5%

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

      6. exp-to-pow 81.5%

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

      7. exp-diff 78.2%

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

      8. *-commutative 78.2%

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

      9. exp-to-pow 78.4%

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

      10. sub-neg 78.4%

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

      11. metadata-eval 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in t around 0 81.3%

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

      1. clear-num 81.3%

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

      2. inv-pow 81.3%

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

   7. Applied egg-rr 81.3%

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

      1. unpow-1 81.3%

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

      2. associate-/l* 87.7%

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

   9. Simplified 87.7%

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

   10. Taylor expanded in y around 0 78.2%

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

Alternative 7: 74.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.92 \cdot 10^{-112}:\\ \;\;\;\;\frac{\frac{x}{a}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))))
   (if (<= t -8.2e+14)
     t_1
     (if (<= t -1.92e-112)
       (/ (/ x a) (* y (exp b)))
       (if (<= t 6.2e+33) (/ (/ (* x (pow z y)) a) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(a, t) / y);
	double tmp;
	if (t <= -8.2e+14) {
		tmp = t_1;
	} else if (t <= -1.92e-112) {
		tmp = (x / a) / (y * exp(b));
	} else if (t <= 6.2e+33) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((a ** t) / y)
    if (t <= (-8.2d+14)) then
        tmp = t_1
    else if (t <= (-1.92d-112)) then
        tmp = (x / a) / (y * exp(b))
    else if (t <= 6.2d+33) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.pow(a, t) / y);
	double tmp;
	if (t <= -8.2e+14) {
		tmp = t_1;
	} else if (t <= -1.92e-112) {
		tmp = (x / a) / (y * Math.exp(b));
	} else if (t <= 6.2e+33) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(a, t) / y)
	tmp = 0
	if t <= -8.2e+14:
		tmp = t_1
	elif t <= -1.92e-112:
		tmp = (x / a) / (y * math.exp(b))
	elif t <= 6.2e+33:
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ t) / y))
	tmp = 0.0
	if (t <= -8.2e+14)
		tmp = t_1;
	elseif (t <= -1.92e-112)
		tmp = Float64(Float64(x / a) / Float64(y * exp(b)));
	elseif (t <= 6.2e+33)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((a ^ t) / y);
	tmp = 0.0;
	if (t <= -8.2e+14)
		tmp = t_1;
	elseif (t <= -1.92e-112)
		tmp = (x / a) / (y * exp(b));
	elseif (t <= 6.2e+33)
		tmp = ((x * (z ^ y)) / a) / 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[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.2e+14], t$95$1, If[LessEqual[t, -1.92e-112], N[(N[(x / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+33], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.2e14 or 6.2e33 < t

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 78.8%

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

      4. associate-/l* 78.8%

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

      5. *-commutative 78.8%

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

      6. exp-to-pow 78.8%

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

      7. exp-diff 69.5%

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

      8. *-commutative 69.5%

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

      9. exp-to-pow 69.5%

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

      10. sub-neg 69.5%

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

      11. metadata-eval 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in y around 0 81.5%

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

      1. associate-/l* 81.5%

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

      2. associate-/r* 81.5%

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

      3. exp-to-pow 81.5%

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

      4. sub-neg 81.5%

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

      5. metadata-eval 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in b around 0 90.0%

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

      1. sub-neg 90.0%

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

      2. metadata-eval 90.0%

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

      3. exp-to-pow 90.0%

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

      4. associate-*r/ 90.0%

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

      5. +-commutative 90.0%

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

   10. Simplified 90.0%

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

   11. Taylor expanded in t around inf 90.0%

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

   if -8.2e14 < t < -1.9200000000000001e-112

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. mul-1-neg 97.5%

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

      3. unsub-neg 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in x around 0 97.5%

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

      1. associate-/l* 91.0%

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

      2. associate--r+ 91.0%

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

      3. remove-double-neg 91.0%

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

      4. log-rec 91.0%

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

      5. mul-1-neg 91.0%

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

      6. associate--r+ 91.0%

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

   8. Simplified 76.7%

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

   9. Taylor expanded in y around 0 81.4%

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

       1. associate-/r* 96.1%

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

   11. Simplified 96.1%

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

   if -1.9200000000000001e-112 < t < 6.2e33

   1. Initial program 98.1%

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

   3. Taylor expanded in b around 0 74.7%

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

      1. exp-sum 72.9%

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

      2. *-commutative 72.9%

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

      3. exp-to-pow 72.9%

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

      4. exp-to-pow 73.6%

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

      5. sub-neg 73.6%

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

      6. metadata-eval 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in t around 0 75.3%

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

Alternative 8: 69.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -80000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-173}:\\ \;\;\;\;\frac{\frac{x}{a}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))))
   (if (<= t -80000000.0)
     t_1
     (if (<= t 1.1e-173)
       (/ (/ x a) (* y (exp b)))
       (if (<= t 4.7e+33) (/ (* x (exp (- b))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(a, t) / y);
	double tmp;
	if (t <= -80000000.0) {
		tmp = t_1;
	} else if (t <= 1.1e-173) {
		tmp = (x / a) / (y * exp(b));
	} else if (t <= 4.7e+33) {
		tmp = (x * exp(-b)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((a ** t) / y)
    if (t <= (-80000000.0d0)) then
        tmp = t_1
    else if (t <= 1.1d-173) then
        tmp = (x / a) / (y * exp(b))
    else if (t <= 4.7d+33) then
        tmp = (x * exp(-b)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.pow(a, t) / y);
	double tmp;
	if (t <= -80000000.0) {
		tmp = t_1;
	} else if (t <= 1.1e-173) {
		tmp = (x / a) / (y * Math.exp(b));
	} else if (t <= 4.7e+33) {
		tmp = (x * Math.exp(-b)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(a, t) / y)
	tmp = 0
	if t <= -80000000.0:
		tmp = t_1
	elif t <= 1.1e-173:
		tmp = (x / a) / (y * math.exp(b))
	elif t <= 4.7e+33:
		tmp = (x * math.exp(-b)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ t) / y))
	tmp = 0.0
	if (t <= -80000000.0)
		tmp = t_1;
	elseif (t <= 1.1e-173)
		tmp = Float64(Float64(x / a) / Float64(y * exp(b)));
	elseif (t <= 4.7e+33)
		tmp = Float64(Float64(x * exp(Float64(-b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((a ^ t) / y);
	tmp = 0.0;
	if (t <= -80000000.0)
		tmp = t_1;
	elseif (t <= 1.1e-173)
		tmp = (x / a) / (y * exp(b));
	elseif (t <= 4.7e+33)
		tmp = (x * exp(-b)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -80000000.0], t$95$1, If[LessEqual[t, 1.1e-173], N[(N[(x / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.7e+33], N[(N[(x * N[Exp[(-b)], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8e7 or 4.6999999999999998e33 < t

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 78.8%

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

      4. associate-/l* 78.8%

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

      5. *-commutative 78.8%

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

      6. exp-to-pow 78.8%

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

      7. exp-diff 69.5%

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

      8. *-commutative 69.5%

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

      9. exp-to-pow 69.5%

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

      10. sub-neg 69.5%

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

      11. metadata-eval 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in y around 0 81.5%

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

      1. associate-/l* 81.5%

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

      2. associate-/r* 81.5%

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

      3. exp-to-pow 81.5%

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

      4. sub-neg 81.5%

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

      5. metadata-eval 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in b around 0 90.0%

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

      1. sub-neg 90.0%

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

      2. metadata-eval 90.0%

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

      3. exp-to-pow 90.0%

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

      4. associate-*r/ 90.0%

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

      5. +-commutative 90.0%

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

   10. Simplified 90.0%

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

   11. Taylor expanded in t around inf 90.0%

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

   if -8e7 < t < 1.1e-173

   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. Add Preprocessing

   3. Taylor expanded in t around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. mul-1-neg 97.3%

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

      3. unsub-neg 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in x around 0 97.3%

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

      1. associate-/l* 93.6%

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

      2. associate--r+ 93.6%

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

      3. remove-double-neg 93.6%

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

      4. log-rec 93.6%

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

      5. mul-1-neg 93.6%

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

      6. associate--r+ 93.6%

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

   8. Simplified 79.7%

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

   9. Taylor expanded in y around 0 67.5%

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

       1. associate-/r* 73.3%

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

   11. Simplified 73.3%

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

   if 1.1e-173 < t < 4.6999999999999998e33

   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. Add Preprocessing

   3. Taylor expanded in t around 0 99.0%

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

      1. +-commutative 99.0%

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

      2. mul-1-neg 99.0%

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

      3. unsub-neg 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in b around inf 69.3%

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

      1. neg-mul-1 69.3%

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

   8. Simplified 69.3%

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

Alternative 9: 63.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-97}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;t \leq 9.3 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot e^{-b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))))
   (if (<= t -9.5e-5)
     t_1
     (if (<= t -1.85e-97)
       (/ (/ x a) y)
       (if (<= t 9.3e+33) (/ (* x (exp (- b))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(a, t) / y);
	double tmp;
	if (t <= -9.5e-5) {
		tmp = t_1;
	} else if (t <= -1.85e-97) {
		tmp = (x / a) / y;
	} else if (t <= 9.3e+33) {
		tmp = (x * exp(-b)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((a ** t) / y)
    if (t <= (-9.5d-5)) then
        tmp = t_1
    else if (t <= (-1.85d-97)) then
        tmp = (x / a) / y
    else if (t <= 9.3d+33) then
        tmp = (x * exp(-b)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.pow(a, t) / y);
	double tmp;
	if (t <= -9.5e-5) {
		tmp = t_1;
	} else if (t <= -1.85e-97) {
		tmp = (x / a) / y;
	} else if (t <= 9.3e+33) {
		tmp = (x * Math.exp(-b)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(a, t) / y)
	tmp = 0
	if t <= -9.5e-5:
		tmp = t_1
	elif t <= -1.85e-97:
		tmp = (x / a) / y
	elif t <= 9.3e+33:
		tmp = (x * math.exp(-b)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ t) / y))
	tmp = 0.0
	if (t <= -9.5e-5)
		tmp = t_1;
	elseif (t <= -1.85e-97)
		tmp = Float64(Float64(x / a) / y);
	elseif (t <= 9.3e+33)
		tmp = Float64(Float64(x * exp(Float64(-b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((a ^ t) / y);
	tmp = 0.0;
	if (t <= -9.5e-5)
		tmp = t_1;
	elseif (t <= -1.85e-97)
		tmp = (x / a) / y;
	elseif (t <= 9.3e+33)
		tmp = (x * exp(-b)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e-5], t$95$1, If[LessEqual[t, -1.85e-97], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 9.3e+33], N[(N[(x * N[Exp[(-b)], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.5000000000000005e-5 or 9.30000000000000001e33 < t

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 77.0%

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

      4. associate-/l* 77.0%

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

      5. *-commutative 77.0%

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

      6. exp-to-pow 77.0%

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

      7. exp-diff 68.0%

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

      8. *-commutative 68.0%

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

      9. exp-to-pow 68.0%

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

      10. sub-neg 68.0%

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

      11. metadata-eval 68.0%

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

   3. Simplified 68.0%

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

   5. Taylor expanded in y around 0 81.3%

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

      1. associate-/l* 81.3%

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

      2. associate-/r* 80.4%

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

      3. exp-to-pow 80.4%

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

      4. sub-neg 80.4%

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

      5. metadata-eval 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in b around 0 88.7%

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

      1. sub-neg 88.7%

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

      2. metadata-eval 88.7%

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

      3. exp-to-pow 88.7%

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

      4. associate-*r/ 88.7%

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

      5. +-commutative 88.7%

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

   10. Simplified 88.7%

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

   11. Taylor expanded in t around inf 88.7%

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

   if -9.5000000000000005e-5 < t < -1.84999999999999988e-97

   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 b around 0 77.2%

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

      1. exp-sum 77.2%

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

      2. *-commutative 77.2%

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

      3. exp-to-pow 77.2%

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

      4. exp-to-pow 80.4%

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

      5. sub-neg 80.4%

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

      6. metadata-eval 80.4%

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

   5. Simplified 80.4%

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

   6. Taylor expanded in t around 0 80.5%

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

   7. Taylor expanded in y around 0 74.1%

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

   if -1.84999999999999988e-97 < t < 9.30000000000000001e33

   1. Initial program 98.1%

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

   3. Taylor expanded in t around 0 97.9%

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

      1. +-commutative 97.9%

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

      2. mul-1-neg 97.9%

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

      3. unsub-neg 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in b around inf 53.6%

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

      1. neg-mul-1 53.6%

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

   8. Simplified 53.6%

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

Alternative 10: 56.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y}\\ \mathbf{if}\;t \leq -0.00038:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-201}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) y))))
   (if (<= t -0.00038)
     t_1
     (if (<= t 3.2e-201)
       (/ (/ x a) y)
       (if (<= t 4.2e+33) (/ (* x (+ 1.0 (* b (+ -1.0 (* b 0.5))))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(a, t) / y);
	double tmp;
	if (t <= -0.00038) {
		tmp = t_1;
	} else if (t <= 3.2e-201) {
		tmp = (x / a) / y;
	} else if (t <= 4.2e+33) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((a ** t) / y)
    if (t <= (-0.00038d0)) then
        tmp = t_1
    else if (t <= 3.2d-201) then
        tmp = (x / a) / y
    else if (t <= 4.2d+33) then
        tmp = (x * (1.0d0 + (b * ((-1.0d0) + (b * 0.5d0))))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.pow(a, t) / y);
	double tmp;
	if (t <= -0.00038) {
		tmp = t_1;
	} else if (t <= 3.2e-201) {
		tmp = (x / a) / y;
	} else if (t <= 4.2e+33) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(a, t) / y)
	tmp = 0
	if t <= -0.00038:
		tmp = t_1
	elif t <= 3.2e-201:
		tmp = (x / a) / y
	elif t <= 4.2e+33:
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ t) / y))
	tmp = 0.0
	if (t <= -0.00038)
		tmp = t_1;
	elseif (t <= 3.2e-201)
		tmp = Float64(Float64(x / a) / y);
	elseif (t <= 4.2e+33)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * 0.5))))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((a ^ t) / y);
	tmp = 0.0;
	if (t <= -0.00038)
		tmp = t_1;
	elseif (t <= 3.2e-201)
		tmp = (x / a) / y;
	elseif (t <= 4.2e+33)
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / 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[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.00038], t$95$1, If[LessEqual[t, 3.2e-201], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4.2e+33], N[(N[(x * N[(1.0 + N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.8000000000000002e-4 or 4.2000000000000001e33 < t

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 77.0%

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

      4. associate-/l* 77.0%

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

      5. *-commutative 77.0%

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

      6. exp-to-pow 77.0%

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

      7. exp-diff 68.0%

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

      8. *-commutative 68.0%

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

      9. exp-to-pow 68.0%

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

      10. sub-neg 68.0%

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

      11. metadata-eval 68.0%

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

   3. Simplified 68.0%

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

   5. Taylor expanded in y around 0 81.3%

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

      1. associate-/l* 81.3%

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

      2. associate-/r* 80.4%

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

      3. exp-to-pow 80.4%

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

      4. sub-neg 80.4%

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

      5. metadata-eval 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in b around 0 88.7%

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

      1. sub-neg 88.7%

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

      2. metadata-eval 88.7%

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

      3. exp-to-pow 88.7%

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

      4. associate-*r/ 88.7%

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

      5. +-commutative 88.7%

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

   10. Simplified 88.7%

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

   11. Taylor expanded in t around inf 88.7%

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

   if -3.8000000000000002e-4 < t < 3.2000000000000001e-201

   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. Add Preprocessing

   3. Taylor expanded in b around 0 73.3%

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

      1. exp-sum 73.3%

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

      2. *-commutative 73.3%

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

      3. exp-to-pow 73.3%

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

      4. exp-to-pow 74.8%

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

      5. sub-neg 74.8%

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

      6. metadata-eval 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in t around 0 74.8%

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

   7. Taylor expanded in y around 0 42.5%

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

   if 3.2000000000000001e-201 < t < 4.2000000000000001e33

   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. Add Preprocessing

   3. Taylor expanded in t around 0 99.1%

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

      1. +-commutative 99.1%

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

      2. mul-1-neg 99.1%

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

      3. unsub-neg 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in b around inf 67.8%

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

      1. neg-mul-1 67.8%

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

   8. Simplified 67.8%

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

   9. Taylor expanded in b around 0 49.6%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(0.5 \cdot b - 1\right)\right)}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00038:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-201}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+14} \lor \neg \left(t \leq 4.4 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.6e+14) (not (<= t 4.4e+33)))
   (* x (/ (pow a t) y))
   (/ (* x (/ (exp (- b)) a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.6e+14) || !(t <= 4.4e+33)) {
		tmp = x * (pow(a, t) / y);
	} else {
		tmp = (x * (exp(-b) / a)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.6d+14)) .or. (.not. (t <= 4.4d+33))) then
        tmp = x * ((a ** t) / y)
    else
        tmp = (x * (exp(-b) / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.6e+14) || !(t <= 4.4e+33)) {
		tmp = x * (Math.pow(a, t) / y);
	} else {
		tmp = (x * (Math.exp(-b) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.6e+14) or not (t <= 4.4e+33):
		tmp = x * (math.pow(a, t) / y)
	else:
		tmp = (x * (math.exp(-b) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.6e+14) || !(t <= 4.4e+33))
		tmp = Float64(x * Float64((a ^ t) / y));
	else
		tmp = Float64(Float64(x * Float64(exp(Float64(-b)) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.6e+14) || ~((t <= 4.4e+33)))
		tmp = x * ((a ^ t) / y);
	else
		tmp = (x * (exp(-b) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.6e+14], N[Not[LessEqual[t, 4.4e+33]], $MachinePrecision]], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6e14 or 4.39999999999999988e33 < t

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 78.8%

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

      4. associate-/l* 78.8%

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

      5. *-commutative 78.8%

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

      6. exp-to-pow 78.8%

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

      7. exp-diff 69.5%

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

      8. *-commutative 69.5%

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

      9. exp-to-pow 69.5%

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

      10. sub-neg 69.5%

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

      11. metadata-eval 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in y around 0 81.5%

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

      1. associate-/l* 81.5%

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

      2. associate-/r* 81.5%

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

      3. exp-to-pow 81.5%

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

      4. sub-neg 81.5%

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

      5. metadata-eval 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in b around 0 90.0%

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

      1. sub-neg 90.0%

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

      2. metadata-eval 90.0%

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

      3. exp-to-pow 90.0%

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

      4. associate-*r/ 90.0%

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

      5. +-commutative 90.0%

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

   10. Simplified 90.0%

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

   11. Taylor expanded in t around inf 90.0%

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

   if -1.6e14 < t < 4.39999999999999988e33

   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 t around 0 97.8%

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

      1. +-commutative 97.8%

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

      2. mul-1-neg 97.8%

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

      3. unsub-neg 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in y around 0 70.9%

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

      1. distribute-neg-in 70.9%

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

      2. sub-neg 70.9%

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

      3. exp-diff 71.0%

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

      4. rem-exp-log 72.0%

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

   8. Simplified 72.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+14} \lor \neg \left(t \leq 4.4 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{e^{-b}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -190000000000 \lor \neg \left(t \leq 4.2 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -190000000000.0) (not (<= t 4.2e+33)))
   (* x (/ (pow a t) y))
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -190000000000.0) || !(t <= 4.2e+33)) {
		tmp = x * (pow(a, t) / y);
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-190000000000.0d0)) .or. (.not. (t <= 4.2d+33))) then
        tmp = x * ((a ** t) / y)
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -190000000000.0) || !(t <= 4.2e+33)) {
		tmp = x * (Math.pow(a, t) / y);
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -190000000000.0) or not (t <= 4.2e+33):
		tmp = x * (math.pow(a, t) / y)
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -190000000000.0) || !(t <= 4.2e+33))
		tmp = Float64(x * Float64((a ^ t) / y));
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -190000000000.0) || ~((t <= 4.2e+33)))
		tmp = x * ((a ^ t) / y);
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -190000000000.0], N[Not[LessEqual[t, 4.2e+33]], $MachinePrecision]], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9e11 or 4.2000000000000001e33 < t

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 78.8%

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

      4. associate-/l* 78.8%

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

      5. *-commutative 78.8%

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

      6. exp-to-pow 78.8%

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

      7. exp-diff 69.5%

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

      8. *-commutative 69.5%

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

      9. exp-to-pow 69.5%

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

      10. sub-neg 69.5%

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

      11. metadata-eval 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in y around 0 81.5%

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

      1. associate-/l* 81.5%

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

      2. associate-/r* 81.5%

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

      3. exp-to-pow 81.5%

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

      4. sub-neg 81.5%

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

      5. metadata-eval 81.5%

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

   7. Simplified 81.5%

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

   8. Taylor expanded in b around 0 90.0%

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

      1. sub-neg 90.0%

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

      2. metadata-eval 90.0%

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

      3. exp-to-pow 90.0%

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

      4. associate-*r/ 90.0%

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

      5. +-commutative 90.0%

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

   10. Simplified 90.0%

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

   11. Taylor expanded in t around inf 90.0%

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

   if -1.9e11 < t < 4.2000000000000001e33

   1. Initial program 98.0%

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

      1. associate-/l* 94.9%

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

      2. associate--l+ 94.9%

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

      3. exp-sum 81.2%

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

      4. associate-/l* 77.5%

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

      5. *-commutative 77.5%

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

      6. exp-to-pow 77.5%

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

      7. exp-diff 76.1%

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

      8. *-commutative 76.1%

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

      9. exp-to-pow 77.0%

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

      10. sub-neg 77.0%

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

      11. metadata-eval 77.0%

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

   3. Simplified 77.0%

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

   5. Taylor expanded in y around 0 65.4%

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

      1. associate-/l* 64.5%

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

      2. associate-/r* 59.4%

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

      3. exp-to-pow 60.2%

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

      4. sub-neg 60.2%

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

      5. metadata-eval 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in t around 0 67.5%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -190000000000 \lor \neg \left(t \leq 4.2 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 41.2% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -550000:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -550000.0)
   (/ (* x (+ 1.0 (* b (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666))))))) y)
   (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -550000.0) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-550000.0d0)) then
        tmp = (x * (1.0d0 + (b * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0)))))))) / y
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -550000.0) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -550000.0:
		tmp = (x * (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -550000.0)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))))))) / y);
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -550000.0)
		tmp = (x * (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -550000.0], N[(N[(x * N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.5e5

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 90.2%

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

      1. +-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in b around inf 83.6%

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

      1. neg-mul-1 83.6%

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

   8. Simplified 83.6%

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

   9. Taylor expanded in b around 0 77.3%

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

   if -5.5e5 < b

   1. Initial program 98.6%

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

   3. Taylor expanded in b around 0 89.6%

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

      1. exp-sum 80.4%

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

      2. *-commutative 80.4%

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

      3. exp-to-pow 80.4%

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

      4. exp-to-pow 81.1%

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

      5. sub-neg 81.1%

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

      6. metadata-eval 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around 0 65.5%

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

   7. Taylor expanded in y around 0 35.6%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -550000:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.6% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -370:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -370.0) (/ (* x (+ 1.0 (* b (+ -1.0 (* b 0.5))))) y) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -370.0) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-370.0d0)) then
        tmp = (x * (1.0d0 + (b * ((-1.0d0) + (b * 0.5d0))))) / y
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -370.0) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -370.0:
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -370.0)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * 0.5))))) / y);
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -370.0)
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -370.0], N[(N[(x * N[(1.0 + N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -370

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 90.2%

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

      1. +-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in b around inf 83.6%

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

      1. neg-mul-1 83.6%

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

   8. Simplified 83.6%

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

   9. Taylor expanded in b around 0 70.9%

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

   if -370 < b

   1. Initial program 98.6%

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

   3. Taylor expanded in b around 0 89.6%

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

      1. exp-sum 80.4%

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

      2. *-commutative 80.4%

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

      3. exp-to-pow 80.4%

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

      4. exp-to-pow 81.1%

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

      5. sub-neg 81.1%

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

      6. metadata-eval 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around 0 65.5%

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

   7. Taylor expanded in y around 0 35.6%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -370:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 37.0% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -310:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(\left(b \cdot 0.5\right) \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -310.0) (+ (/ x y) (* b (* (* b 0.5) (/ x y)))) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -310.0) {
		tmp = (x / y) + (b * ((b * 0.5) * (x / y)));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-310.0d0)) then
        tmp = (x / y) + (b * ((b * 0.5d0) * (x / y)))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -310.0) {
		tmp = (x / y) + (b * ((b * 0.5) * (x / y)));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -310.0:
		tmp = (x / y) + (b * ((b * 0.5) * (x / y)))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -310.0)
		tmp = Float64(Float64(x / y) + Float64(b * Float64(Float64(b * 0.5) * Float64(x / y))));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -310.0)
		tmp = (x / y) + (b * ((b * 0.5) * (x / y)));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -310.0], N[(N[(x / y), $MachinePrecision] + N[(b * N[(N[(b * 0.5), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -310

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 90.2%

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

      1. +-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in b around inf 83.6%

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

      1. neg-mul-1 83.6%

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

   8. Simplified 83.6%

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

   9. Taylor expanded in b around 0 55.2%

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

   10. Taylor expanded in b around inf 55.2%

       \[\leadsto b \cdot \color{blue}{\left(0.5 \cdot \frac{b \cdot x}{y}\right)} + \frac{x}{y} \]
   11. Step-by-step derivation

       1. associate-*r/ 53.7%

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

       2. associate-*r* 53.7%

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

   12. Simplified 53.7%

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

   if -310 < b

   1. Initial program 98.6%

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

   3. Taylor expanded in b around 0 89.6%

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

      1. exp-sum 80.4%

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

      2. *-commutative 80.4%

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

      3. exp-to-pow 80.4%

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

      4. exp-to-pow 81.1%

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

      5. sub-neg 81.1%

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

      6. metadata-eval 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around 0 65.5%

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

   7. Taylor expanded in y around 0 35.6%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -310:\\ \;\;\;\;\frac{x}{y} + b \cdot \left(\left(b \cdot 0.5\right) \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.9% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.4 \cdot 10^{+116}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{b} - x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 7.4e+116) (/ (/ x a) y) (/ (* b (- (/ x b) x)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 7.4e+116) {
		tmp = (x / a) / y;
	} else {
		tmp = (b * ((x / b) - x)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 7.4d+116) then
        tmp = (x / a) / y
    else
        tmp = (b * ((x / b) - x)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 7.4e+116) {
		tmp = (x / a) / y;
	} else {
		tmp = (b * ((x / b) - x)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 7.4e+116:
		tmp = (x / a) / y
	else:
		tmp = (b * ((x / b) - x)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 7.4e+116)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(b * Float64(Float64(x / b) - x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 7.4e+116)
		tmp = (x / a) / y;
	else
		tmp = (b * ((x / b) - x)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 7.4e+116], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(b * N[(N[(x / b), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.4000000000000003e116

   1. Initial program 98.8%

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

   3. Taylor expanded in b around 0 81.8%

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

      1. exp-sum 72.6%

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

      2. *-commutative 72.6%

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

      3. exp-to-pow 72.6%

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

      4. exp-to-pow 73.2%

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

      5. sub-neg 73.2%

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

      6. metadata-eval 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in t around 0 61.4%

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

   7. Taylor expanded in y around 0 31.9%

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

   if 7.4000000000000003e116 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 76.9%

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

      1. +-commutative 76.9%

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

      2. mul-1-neg 76.9%

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

      3. unsub-neg 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in b around inf 56.8%

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

      1. neg-mul-1 56.8%

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

   8. Simplified 56.8%

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

   9. Taylor expanded in b around 0 43.9%

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

       1. mul-1-neg 43.9%

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

       2. unsub-neg 43.9%

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

   11. Simplified 43.9%

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

   12. Taylor expanded in b around inf 48.8%

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

       1. neg-mul-1 48.8%

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

       2. +-commutative 48.8%

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

       3. unsub-neg 48.8%

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

   14. Simplified 48.8%

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

Alternative 17: 33.8% accurate, 28.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -460000:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -460000.0) (/ (* x (- b)) y) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -460000.0) {
		tmp = (x * -b) / y;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-460000.0d0)) then
        tmp = (x * -b) / y
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -460000.0) {
		tmp = (x * -b) / y;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -460000.0:
		tmp = (x * -b) / y
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -460000.0)
		tmp = Float64(Float64(x * Float64(-b)) / y);
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -460000.0)
		tmp = (x * -b) / y;
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -460000.0], N[(N[(x * (-b)), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.6e5

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 90.2%

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

      1. +-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in b around inf 83.6%

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

      1. neg-mul-1 83.6%

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

   8. Simplified 83.6%

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

   9. Taylor expanded in b around 0 39.3%

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

       1. mul-1-neg 39.3%

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

       2. unsub-neg 39.3%

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

   11. Simplified 39.3%

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

   12. Taylor expanded in b around inf 39.3%

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

       1. associate-*r/ 39.3%

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

       2. mul-1-neg 39.3%

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

       3. *-commutative 39.3%

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

       4. distribute-rgt-neg-in 39.3%

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

   14. Simplified 39.3%

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

   if -4.6e5 < b

   1. Initial program 98.6%

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

   3. Taylor expanded in b around 0 89.6%

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

      1. exp-sum 80.4%

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

      2. *-commutative 80.4%

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

      3. exp-to-pow 80.4%

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

      4. exp-to-pow 81.1%

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

      5. sub-neg 81.1%

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

      6. metadata-eval 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around 0 65.5%

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

   7. Taylor expanded in y around 0 35.6%

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

Alternative 18: 33.0% accurate, 28.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -370000:\\ \;\;\;\;b \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -370000.0) (* b (/ x (- y))) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -370000.0) {
		tmp = b * (x / -y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-370000.0d0)) then
        tmp = b * (x / -y)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -370000.0) {
		tmp = b * (x / -y);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -370000.0:
		tmp = b * (x / -y)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -370000.0)
		tmp = Float64(b * Float64(x / Float64(-y)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -370000.0)
		tmp = b * (x / -y);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -370000.0], N[(b * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.7e5

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 90.2%

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

      1. +-commutative 90.2%

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

      2. mul-1-neg 90.2%

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

      3. unsub-neg 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in b around inf 83.6%

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

      1. neg-mul-1 83.6%

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

   8. Simplified 83.6%

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

   9. Taylor expanded in b around 0 39.3%

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

       1. mul-1-neg 39.3%

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

       2. unsub-neg 39.3%

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

   11. Simplified 39.3%

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

   12. Taylor expanded in b around inf 39.3%

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

       1. mul-1-neg 39.3%

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

       2. associate-*r/ 33.1%

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

       3. *-commutative 33.1%

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

       4. distribute-rgt-neg-in 33.1%

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

   14. Simplified 33.1%

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

   if -3.7e5 < b

   1. Initial program 98.6%

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

   3. Taylor expanded in b around 0 89.6%

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

      1. exp-sum 80.4%

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

      2. *-commutative 80.4%

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

      3. exp-to-pow 80.4%

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

      4. exp-to-pow 81.1%

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

      5. sub-neg 81.1%

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

      6. metadata-eval 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in t around 0 65.5%

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

   7. Taylor expanded in y around 0 35.6%

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

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -370000:\\ \;\;\;\;b \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.6% accurate, 31.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1e+88) (/ (/ x a) y) (/ x y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1e+88) {
		tmp = (x / a) / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 1d+88) then
        tmp = (x / a) / y
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1e+88) {
		tmp = (x / a) / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1e+88:
		tmp = (x / a) / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1e+88)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1e+88)
		tmp = (x / a) / y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1e+88], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.99999999999999959e87

   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 b around 0 78.7%

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

      1. exp-sum 71.6%

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

      2. *-commutative 71.6%

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

      3. exp-to-pow 71.6%

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

      4. exp-to-pow 72.2%

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

      5. sub-neg 72.2%

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

      6. metadata-eval 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in t around 0 65.5%

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

   7. Taylor expanded in y around 0 37.7%

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

   if 9.99999999999999959e87 < 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 t around 0 53.4%

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

      1. +-commutative 53.4%

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

      2. mul-1-neg 53.4%

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

      3. unsub-neg 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in b around inf 41.3%

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

      1. neg-mul-1 41.3%

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

   8. Simplified 41.3%

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

   9. Taylor expanded in b around 0 14.2%

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

Alternative 20: 30.7% 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 98.9%

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

   1. associate-/l* 97.3%

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

   2. associate--l+ 97.3%

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

   3. exp-sum 80.1%

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

   4. associate-/l* 78.1%

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

   5. *-commutative 78.1%

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

   6. exp-to-pow 78.1%

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

   7. exp-diff 73.1%

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

   8. *-commutative 73.1%

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

   9. exp-to-pow 73.5%

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

   10. sub-neg 73.5%

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

   11. metadata-eval 73.5%

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

3. Simplified 73.5%

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

5. Taylor expanded in y around 0 72.8%

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

   1. associate-/l* 72.3%

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

   2. associate-/r* 69.6%

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

   3. exp-to-pow 70.0%

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

   4. sub-neg 70.0%

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

   5. metadata-eval 70.0%

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

7. Simplified 70.0%

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

8. Taylor expanded in b around 0 61.6%

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

   1. sub-neg 61.6%

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

   2. metadata-eval 61.6%

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

   3. exp-to-pow 62.1%

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

   4. associate-*r/ 60.6%

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

   5. +-commutative 60.6%

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

10. Simplified 60.6%

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

11. Taylor expanded in t around 0 30.7%

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

    1. *-commutative 30.7%

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

13. Simplified 30.7%

    \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
14. Add Preprocessing

Alternative 21: 15.5% 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 98.9%

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

3. Taylor expanded in t around 0 81.4%

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

   1. +-commutative 81.4%

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

   2. mul-1-neg 81.4%

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

   3. unsub-neg 81.4%

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

5. Simplified 81.4%

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

6. Taylor expanded in b around inf 48.3%

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

   1. neg-mul-1 48.3%

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

8. Simplified 48.3%

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

9. Taylor expanded in b around 0 16.5%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
10. Add Preprocessing

Developer Target 1: 71.5% 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 2024165 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8845848504127471/10000000000000000) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 8520312288374073/10000000000) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))