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

Percentage Accurate: 98.3% → 98.3%

Time: 18.1s

Alternatives: 25

Speedup: 1.0×

• Could not converge on a ground truth

  1. x = 1.1180316464842415e-63
  2. y = -3.2915214761589543e-106
  3. z = 2.485572689707247e-81
  4. t = -2.3663055844036068e-57
  5. a = 4.936366843960936e+246
  6. b = -7.426353223127531e+77

• 48.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 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 99.0%

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

3. Final simplification 99.0%

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

Alternative 2: 91.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+162} \lor \neg \left(t + -1 \leq -0.5\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -5e+162) (not (<= (+ t -1.0) -0.5)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -5e+162) || !((t + -1.0) <= -0.5)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-5d+162)) .or. (.not. ((t + (-1.0d0)) <= (-0.5d0)))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -5e+162) || !((t + -1.0) <= -0.5)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -5e+162) or not ((t + -1.0) <= -0.5):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -5e+162) || !(Float64(t + -1.0) <= -0.5))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -5e+162) || ~(((t + -1.0) <= -0.5)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+162], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -0.5]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -4.9999999999999997e162 or -0.5 < (-.f64 t #s(literal 1 binary64))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.0%

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

   if -4.9999999999999997e162 < (-.f64 t #s(literal 1 binary64)) < -0.5

   1. Initial program 98.4%

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

   3. Taylor expanded in 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%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+162} \lor \neg \left(t + -1 \leq -0.5\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+161} \lor \neg \left(y \leq 2 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.4e+161) (not (<= y 2e+53)))
   (/ (* 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 <= -3.4e+161) || !(y <= 2e+53)) {
		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 <= (-3.4d+161)) .or. (.not. (y <= 2d+53))) 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 <= -3.4e+161) || !(y <= 2e+53)) {
		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 <= -3.4e+161) or not (y <= 2e+53):
		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 <= -3.4e+161) || !(y <= 2e+53))
		tmp = Float64(Float64(x * Float64((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 <= -3.4e+161) || ~((y <= 2e+53)))
		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, -3.4e+161], N[Not[LessEqual[y, 2e+53]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $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 < -3.39999999999999993e161 or 2e53 < 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 96.3%

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

      1. +-commutative 96.3%

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

      2. mul-1-neg 96.3%

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

      3. unsub-neg 96.3%

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

   5. Simplified 96.3%

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

   6. Taylor expanded in b around 0 90.2%

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

      1. div-exp 90.2%

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

      2. *-commutative 90.2%

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

      3. exp-to-pow 90.2%

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

      4. rem-exp-log 90.2%

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

   8. Simplified 90.2%

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

   if -3.39999999999999993e161 < y < 2e53

   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 y around 0 95.0%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+161} \lor \neg \left(y \leq 2 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11000000000000 \lor \neg \left(y \leq 7.4 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -11000000000000.0) (not (<= y 7.4e+52)))
   (/ (* 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 <= -11000000000000.0) || !(y <= 7.4e+52)) {
		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 <= (-11000000000000.0d0)) .or. (.not. (y <= 7.4d+52))) 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 <= -11000000000000.0) || !(y <= 7.4e+52)) {
		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 <= -11000000000000.0) or not (y <= 7.4e+52):
		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 <= -11000000000000.0) || !(y <= 7.4e+52))
		tmp = Float64(Float64(x * Float64((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 <= -11000000000000.0) || ~((y <= 7.4e+52)))
		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, -11000000000000.0], N[Not[LessEqual[y, 7.4e+52]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $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 < -1.1e13 or 7.3999999999999999e52 < 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 93.1%

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

      1. +-commutative 93.1%

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

      2. mul-1-neg 93.1%

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

      3. unsub-neg 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in b around 0 85.3%

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

      1. div-exp 85.3%

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

      2. *-commutative 85.3%

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

      3. exp-to-pow 85.3%

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

      4. rem-exp-log 85.3%

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

   8. Simplified 85.3%

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

   if -1.1e13 < y < 7.3999999999999999e52

   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 98.0%

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

      1. div-exp 86.0%

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

      2. exp-to-pow 86.9%

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

      3. sub-neg 86.9%

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

      4. metadata-eval 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11000000000000 \lor \neg \left(y \leq 7.4 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+14} \lor \neg \left(y \leq 3.6 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.3e+14) (not (<= y 3.6e+29)))
   (/ (* x (/ (pow z y) a)) y)
   (* x (/ (pow a t) (* a (* y (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e+14) || !(y <= 3.6e+29)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = x * (pow(a, t) / (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 ((y <= (-3.3d+14)) .or. (.not. (y <= 3.6d+29))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = x * ((a ** t) / (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 ((y <= -3.3e+14) || !(y <= 3.6e+29)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = x * (Math.pow(a, t) / (a * (y * Math.exp(b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.3e+14) or not (y <= 3.6e+29):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = x * (math.pow(a, t) / (a * (y * math.exp(b))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.3e+14) || !(y <= 3.6e+29))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(x * Float64((a ^ t) / 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 ((y <= -3.3e+14) || ~((y <= 3.6e+29)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = x * ((a ^ t) / (a * (y * exp(b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.3e+14], N[Not[LessEqual[y, 3.6e+29]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e14 or 3.59999999999999976e29 < 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 92.1%

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

      1. +-commutative 92.1%

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

      2. mul-1-neg 92.1%

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

      3. unsub-neg 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in b around 0 84.1%

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

      1. div-exp 84.1%

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

      2. *-commutative 84.1%

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

      3. exp-to-pow 84.1%

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

      4. rem-exp-log 84.1%

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

   8. Simplified 84.1%

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

   if -3.3e14 < y < 3.59999999999999976e29

   1. Initial program 98.1%

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

      1. associate-/l* 96.7%

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

      2. associate--l+ 96.7%

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

      3. exp-sum 94.5%

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

      4. associate-/l* 94.5%

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

      5. *-commutative 94.5%

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

      6. exp-to-pow 94.5%

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

      7. exp-diff 83.9%

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

      8. *-commutative 83.9%

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

      9. exp-to-pow 84.8%

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

      10. sub-neg 84.8%

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

      11. metadata-eval 84.8%

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

   3. Simplified 84.8%

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

      1. associate-/l/ 84.8%

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

      2. unpow-prod-up 84.9%

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

      3. associate-/l* 81.1%

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

      4. unpow-1 81.1%

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

   6. Applied egg-rr 81.1%

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

      1. associate-/r* 81.1%

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

      2. associate-*r/ 81.9%

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

      3. *-rgt-identity 81.9%

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

      4. associate-*r* 75.8%

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

   8. Simplified 75.8%

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

   9. Taylor expanded in y around 0 83.1%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+14} \lor \neg \left(y \leq 3.6 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -900 \lor \neg \left(b \leq 2100000\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -900.0) (not (<= b 2100000.0)))
   (/ x (* a (* y (exp b))))
   (/ (* x (pow a (+ t -1.0))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -900.0) || !(b <= 2100000.0)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (x * pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-900.0d0)) .or. (.not. (b <= 2100000.0d0))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -900.0) || !(b <= 2100000.0)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -900.0) or not (b <= 2100000.0):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -900.0) || !(b <= 2100000.0))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -900.0) || ~((b <= 2100000.0)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (x * (a ^ (t + -1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -900.0], N[Not[LessEqual[b, 2100000.0]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -900 or 2.1e6 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 86.8%

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

      1. div-exp 65.8%

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

      2. exp-to-pow 65.8%

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

      3. sub-neg 65.8%

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

      4. metadata-eval 65.8%

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

   5. Simplified 65.8%

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

   6. Taylor expanded in t around 0 81.6%

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

   if -900 < b < 2.1e6

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 81.0%

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

      1. div-exp 81.0%

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

      2. exp-to-pow 82.1%

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

      3. sub-neg 82.1%

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

      4. metadata-eval 82.1%

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

   5. Simplified 82.1%

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

   6. Taylor expanded in b around 0 81.0%

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

   8. Simplified 82.1%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -900 \lor \neg \left(b \leq 2100000\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -320000000000 \lor \neg \left(y \leq 1.05 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -320000000000.0) (not (<= y 1.05e+44)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (/ x (* a (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -320000000000.0) || !(y <= 1.05e+44)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-320000000000.0d0)) .or. (.not. (y <= 1.05d+44))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -320000000000.0) || !(y <= 1.05e+44)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -320000000000.0) or not (y <= 1.05e+44):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -320000000000.0) || !(y <= 1.05e+44))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -320000000000.0) || ~((y <= 1.05e+44)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -320000000000.0], N[Not[LessEqual[y, 1.05e+44]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e11 or 1.04999999999999993e44 < 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 92.6%

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

      1. +-commutative 92.6%

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

      2. mul-1-neg 92.6%

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

      3. unsub-neg 92.6%

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

   5. Simplified 92.6%

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

   6. Taylor expanded in b around 0 85.2%

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

      1. div-exp 85.2%

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

      2. *-commutative 85.2%

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

      3. exp-to-pow 85.2%

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

      4. rem-exp-log 85.2%

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

   8. Simplified 85.2%

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

   if -3.2e11 < y < 1.04999999999999993e44

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 97.9%

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

      1. div-exp 85.4%

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

      2. exp-to-pow 86.4%

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

      3. sub-neg 86.4%

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

      4. metadata-eval 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in t around 0 77.6%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -320000000000 \lor \neg \left(y \leq 1.05 \cdot 10^{+44}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+113} \lor \neg \left(t \leq 6 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.8e+113) (not (<= t 6e-9)))
   (/ (* x (pow a t)) y)
   (/ (/ x (* a (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.8e+113) || !(t <= 6e-9)) {
		tmp = (x * pow(a, t)) / y;
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.8d+113)) .or. (.not. (t <= 6d-9))) then
        tmp = (x * (a ** t)) / y
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.8e+113) || !(t <= 6e-9)) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.8e+113) or not (t <= 6e-9):
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.8e+113) || !(t <= 6e-9))
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.8e+113) || ~((t <= 6e-9)))
		tmp = (x * (a ^ t)) / y;
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.8e+113], N[Not[LessEqual[t, 6e-9]], $MachinePrecision]], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.79999999999999968e113 or 5.99999999999999996e-9 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.7%

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

      1. div-exp 75.6%

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

      2. exp-to-pow 75.6%

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

      3. sub-neg 75.6%

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

      4. metadata-eval 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in b around 0 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in t around inf 85.2%

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

   if -5.79999999999999968e113 < t < 5.99999999999999996e-9

   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 78.7%

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

      1. div-exp 71.3%

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

      2. exp-to-pow 72.2%

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

      3. sub-neg 72.2%

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

      4. metadata-eval 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in t around 0 77.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+113} \lor \neg \left(t \leq 6 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+116} \lor \neg \left(t \leq 6 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.1e+116) (not (<= t 6e-9)))
   (/ (* 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 <= -3.1e+116) || !(t <= 6e-9)) {
		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 <= (-3.1d+116)) .or. (.not. (t <= 6d-9))) 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 <= -3.1e+116) || !(t <= 6e-9)) {
		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 <= -3.1e+116) or not (t <= 6e-9):
		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 <= -3.1e+116) || !(t <= 6e-9))
		tmp = Float64(Float64(x * (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 <= -3.1e+116) || ~((t <= 6e-9)))
		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, -3.1e+116], N[Not[LessEqual[t, 6e-9]], $MachinePrecision]], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.09999999999999996e116 or 5.99999999999999996e-9 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.5%

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

      1. div-exp 76.3%

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

      2. exp-to-pow 76.3%

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

      3. sub-neg 76.3%

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

      4. metadata-eval 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in b around 0 86.0%

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

   8. Simplified 86.0%

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

   9. Taylor expanded in t around inf 86.0%

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

   if -3.09999999999999996e116 < t < 5.99999999999999996e-9

   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 78.1%

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

      1. div-exp 70.9%

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

      2. exp-to-pow 71.7%

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

      3. sub-neg 71.7%

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

      4. metadata-eval 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around 0 75.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+116} \lor \neg \left(t \leq 6 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+117} \lor \neg \left(t \leq 5.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7e+117) (not (<= t 5.2e-13)))
   (/ (* x (pow a t)) y)
   (/
    (/ x (* a (- 1.0 (* b (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))
    y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7e+117) || !(t <= 5.2e-13)) {
		tmp = (x * pow(a, t)) / y;
	} else {
		tmp = (x / (a * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))))))) / 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 <= (-7d+117)) .or. (.not. (t <= 5.2d-13))) then
        tmp = (x * (a ** t)) / y
    else
        tmp = (x / (a * (1.0d0 - (b * ((-1.0d0) - (b * (0.5d0 + (b * 0.16666666666666666d0)))))))) / 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 <= -7e+117) || !(t <= 5.2e-13)) {
		tmp = (x * Math.pow(a, t)) / y;
	} else {
		tmp = (x / (a * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7e+117) or not (t <= 5.2e-13):
		tmp = (x * math.pow(a, t)) / y
	else:
		tmp = (x / (a * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7e+117) || !(t <= 5.2e-13))
		tmp = Float64(Float64(x * (a ^ t)) / y);
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7e+117) || ~((t <= 5.2e-13)))
		tmp = (x * (a ^ t)) / y;
	else
		tmp = (x / (a * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7e+117], N[Not[LessEqual[t, 5.2e-13]], $MachinePrecision]], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * N[(1.0 - N[(b * N[(-1.0 - N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.99999999999999965e117 or 5.2000000000000001e-13 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.5%

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

      1. div-exp 77.2%

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

      2. exp-to-pow 77.2%

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

      3. sub-neg 77.2%

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

      4. metadata-eval 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in b around 0 86.0%

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

   8. Simplified 86.0%

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

   9. Taylor expanded in t around inf 86.0%

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

   if -6.99999999999999965e117 < t < 5.2000000000000001e-13

   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 77.5%

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

      1. div-exp 70.2%

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

      2. exp-to-pow 71.1%

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

      3. sub-neg 71.1%

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

      4. metadata-eval 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in t around 0 76.0%

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

   7. Taylor expanded in b around 0 54.5%

      \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}}}{y} \]
   8. Step-by-step derivation

      1. *-commutative 54.5%

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

   9. Simplified 54.5%

      \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+117} \lor \neg \left(t \leq 5.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.9% accurate, 6.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{a}\\ t_2 := 1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+129}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \left(\frac{x}{a} + b \cdot \left(\left(t\_1 - \frac{x}{a}\right) + b \cdot \left(\left(\frac{x}{a} - t\_1\right) + \left(-0.5 \cdot \frac{x}{a} + 0.16666666666666666 \cdot \frac{x}{a}\right)\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot t\_2\right)}\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-188}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot t\_2}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ x a)))
        (t_2 (- 1.0 (* b (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))
   (if (<= b -3.1e+129)
     (/
      (-
       (/ x a)
       (*
        b
        (+
         (/ x a)
         (*
          b
          (+
           (- t_1 (/ x a))
           (*
            b
            (+
             (- (/ x a) t_1)
             (+ (* -0.5 (/ x a)) (* 0.16666666666666666 (/ x a))))))))))
      y)
     (if (<= b -3.7e+85)
       (/ x (* a (* y t_2)))
       (if (<= b -4.6e-188)
         (/ (* b (- (/ x (* a b)) (/ x a))) y)
         (/ (/ x (* a t_2)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (x / a);
	double t_2 = 1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))));
	double tmp;
	if (b <= -3.1e+129) {
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((-0.5 * (x / a)) + (0.16666666666666666 * (x / a)))))))))) / y;
	} else if (b <= -3.7e+85) {
		tmp = x / (a * (y * t_2));
	} else if (b <= -4.6e-188) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a * t_2)) / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.5d0 * (x / a)
    t_2 = 1.0d0 - (b * ((-1.0d0) - (b * (0.5d0 + (b * 0.16666666666666666d0)))))
    if (b <= (-3.1d+129)) then
        tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + (((-0.5d0) * (x / a)) + (0.16666666666666666d0 * (x / a)))))))))) / y
    else if (b <= (-3.7d+85)) then
        tmp = x / (a * (y * t_2))
    else if (b <= (-4.6d-188)) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a * t_2)) / 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 t_1 = 0.5 * (x / a);
	double t_2 = 1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))));
	double tmp;
	if (b <= -3.1e+129) {
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((-0.5 * (x / a)) + (0.16666666666666666 * (x / a)))))))))) / y;
	} else if (b <= -3.7e+85) {
		tmp = x / (a * (y * t_2));
	} else if (b <= -4.6e-188) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a * t_2)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.5 * (x / a)
	t_2 = 1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))))
	tmp = 0
	if b <= -3.1e+129:
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((-0.5 * (x / a)) + (0.16666666666666666 * (x / a)))))))))) / y
	elif b <= -3.7e+85:
		tmp = x / (a * (y * t_2))
	elif b <= -4.6e-188:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a * t_2)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.5 * Float64(x / a))
	t_2 = Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666))))))
	tmp = 0.0
	if (b <= -3.1e+129)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(Float64(x / a) + Float64(b * Float64(Float64(t_1 - Float64(x / a)) + Float64(b * Float64(Float64(Float64(x / a) - t_1) + Float64(Float64(-0.5 * Float64(x / a)) + Float64(0.16666666666666666 * Float64(x / a)))))))))) / y);
	elseif (b <= -3.7e+85)
		tmp = Float64(x / Float64(a * Float64(y * t_2)));
	elseif (b <= -4.6e-188)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a * t_2)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.5 * (x / a);
	t_2 = 1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))));
	tmp = 0.0;
	if (b <= -3.1e+129)
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((-0.5 * (x / a)) + (0.16666666666666666 * (x / a)))))))))) / y;
	elseif (b <= -3.7e+85)
		tmp = x / (a * (y * t_2));
	elseif (b <= -4.6e-188)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a * t_2)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(b * N[(-1.0 - N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+129], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(t$95$1 - N[(x / a), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(N[(x / a), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(-0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision] + N[(0.16666666666666666 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -3.7e+85], N[(x / N[(a * N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.6e-188], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * t$95$2), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.1e129

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.6%

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

      1. div-exp 60.6%

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

      2. exp-to-pow 60.6%

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

      3. sub-neg 60.6%

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

      4. metadata-eval 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in t around 0 92.2%

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

   7. Taylor expanded in b around 0 74.0%

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

   if -3.1e129 < b < -3.7000000000000002e85

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.2%

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

      1. div-exp 37.9%

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

      2. exp-to-pow 37.9%

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

      3. sub-neg 37.9%

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

      4. metadata-eval 37.9%

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

   5. Simplified 37.9%

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

   6. Taylor expanded in t around 0 38.5%

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

   7. Taylor expanded in b around 0 63.0%

      \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}\right)} \]
   8. Step-by-step derivation

      1. *-commutative 51.2%

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

   9. Simplified 63.0%

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

   if -3.7000000000000002e85 < b < -4.6e-188

   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 y around 0 83.0%

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

      1. div-exp 79.9%

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

      2. exp-to-pow 80.3%

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

      3. sub-neg 80.3%

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

      4. metadata-eval 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in t around 0 49.0%

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

   7. Taylor expanded in b around 0 35.8%

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

      1. +-commutative 35.8%

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

      2. mul-1-neg 35.8%

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

      3. unsub-neg 35.8%

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

      4. associate-/l* 35.8%

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

   9. Simplified 35.8%

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

   10. Taylor expanded in b around inf 42.8%

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

   if -4.6e-188 < b

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 84.7%

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

      1. div-exp 77.4%

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

      2. exp-to-pow 78.1%

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

      3. sub-neg 78.1%

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

      4. metadata-eval 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in t around 0 64.3%

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

   7. Taylor expanded in b around 0 61.5%

      \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}}}{y} \]
   8. Step-by-step derivation

      1. *-commutative 61.5%

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

   9. Simplified 61.5%

      \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+129}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \left(\frac{x}{a} + b \cdot \left(\left(0.5 \cdot \frac{x}{a} - \frac{x}{a}\right) + b \cdot \left(\left(\frac{x}{a} - 0.5 \cdot \frac{x}{a}\right) + \left(-0.5 \cdot \frac{x}{a} + 0.16666666666666666 \cdot \frac{x}{a}\right)\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-188}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.3% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{+86} \lor \neg \left(b \leq -4.9 \cdot 10^{-262}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.16e+125)
   (* x (/ (- (/ 1.0 a) (/ b a)) y))
   (if (or (<= b -6.8e+86) (not (<= b -4.9e-262)))
     (/
      x
      (*
       a
       (* y (- 1.0 (* b (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))))
     (/ (* b (- (/ x (* a b)) (/ x a))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.16e+125) {
		tmp = x * (((1.0 / a) - (b / a)) / y);
	} else if ((b <= -6.8e+86) || !(b <= -4.9e-262)) {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	} else {
		tmp = (b * ((x / (a * b)) - (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 <= (-1.16d+125)) then
        tmp = x * (((1.0d0 / a) - (b / a)) / y)
    else if ((b <= (-6.8d+86)) .or. (.not. (b <= (-4.9d-262)))) then
        tmp = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * (0.5d0 + (b * 0.16666666666666666d0))))))))
    else
        tmp = (b * ((x / (a * b)) - (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 <= -1.16e+125) {
		tmp = x * (((1.0 / a) - (b / a)) / y);
	} else if ((b <= -6.8e+86) || !(b <= -4.9e-262)) {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	} else {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.16e+125:
		tmp = x * (((1.0 / a) - (b / a)) / y)
	elif (b <= -6.8e+86) or not (b <= -4.9e-262):
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))))
	else:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.16e+125)
		tmp = Float64(x * Float64(Float64(Float64(1.0 / a) - Float64(b / a)) / y));
	elseif ((b <= -6.8e+86) || !(b <= -4.9e-262))
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	else
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.16e+125)
		tmp = x * (((1.0 / a) - (b / a)) / y);
	elseif ((b <= -6.8e+86) || ~((b <= -4.9e-262)))
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	else
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.16e+125], N[(x * N[(N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -6.8e+86], N[Not[LessEqual[b, -4.9e-262]], $MachinePrecision]], N[(x / N[(a * N[(y * N[(1.0 - N[(b * N[(-1.0 - N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.16000000000000009e125

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.9%

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

      1. div-exp 61.6%

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

      2. exp-to-pow 61.6%

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

      3. sub-neg 61.6%

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

      4. metadata-eval 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in t around 0 92.4%

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

   7. Taylor expanded in b around 0 55.5%

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

      1. +-commutative 55.5%

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

      2. mul-1-neg 55.5%

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

      3. unsub-neg 55.5%

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

      4. associate-/l* 50.6%

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

   9. Simplified 50.6%

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

   10. Taylor expanded in x around 0 62.9%

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

       1. associate-/l* 62.9%

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

   12. Simplified 62.9%

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

   if -1.16000000000000009e125 < b < -6.7999999999999995e86 or -4.9000000000000003e-262 < b

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 82.9%

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

      1. div-exp 72.5%

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

      2. exp-to-pow 73.2%

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

      3. sub-neg 73.2%

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

      4. metadata-eval 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in t around 0 62.2%

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

   7. Taylor expanded in b around 0 63.0%

      \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}\right)} \]
   8. Step-by-step derivation

      1. *-commutative 61.7%

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

   9. Simplified 63.0%

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

   if -6.7999999999999995e86 < b < -4.9000000000000003e-262

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 83.2%

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

      1. div-exp 80.4%

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

      2. exp-to-pow 80.8%

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

      3. sub-neg 80.8%

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

      4. metadata-eval 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in t around 0 48.5%

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

   7. Taylor expanded in b around 0 36.6%

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

      1. +-commutative 36.6%

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

      2. mul-1-neg 36.6%

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

      3. unsub-neg 36.6%

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

      4. associate-/l* 36.6%

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

   9. Simplified 36.6%

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

   10. Taylor expanded in b around inf 42.9%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq -6.8 \cdot 10^{+86} \lor \neg \left(b \leq -4.9 \cdot 10^{-262}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.9% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\\ \mathbf{if}\;b \leq -5.4 \cdot 10^{+130}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(b \cdot \left(\frac{x}{a} - 0.5 \cdot \frac{x}{a}\right) - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot t\_1\right)}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-187}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot t\_1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (* b (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))
   (if (<= b -5.4e+130)
     (/ (+ (/ x a) (* b (- (* b (- (/ x a) (* 0.5 (/ x a)))) (/ x a)))) y)
     (if (<= b -4.5e+86)
       (/ x (* a (* y t_1)))
       (if (<= b -5e-187)
         (/ (* b (- (/ x (* a b)) (/ x a))) y)
         (/ (/ x (* a t_1)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))));
	double tmp;
	if (b <= -5.4e+130) {
		tmp = ((x / a) + (b * ((b * ((x / a) - (0.5 * (x / a)))) - (x / a)))) / y;
	} else if (b <= -4.5e+86) {
		tmp = x / (a * (y * t_1));
	} else if (b <= -5e-187) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a * t_1)) / 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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - (b * ((-1.0d0) - (b * (0.5d0 + (b * 0.16666666666666666d0)))))
    if (b <= (-5.4d+130)) then
        tmp = ((x / a) + (b * ((b * ((x / a) - (0.5d0 * (x / a)))) - (x / a)))) / y
    else if (b <= (-4.5d+86)) then
        tmp = x / (a * (y * t_1))
    else if (b <= (-5d-187)) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a * t_1)) / 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 t_1 = 1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))));
	double tmp;
	if (b <= -5.4e+130) {
		tmp = ((x / a) + (b * ((b * ((x / a) - (0.5 * (x / a)))) - (x / a)))) / y;
	} else if (b <= -4.5e+86) {
		tmp = x / (a * (y * t_1));
	} else if (b <= -5e-187) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a * t_1)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))))
	tmp = 0
	if b <= -5.4e+130:
		tmp = ((x / a) + (b * ((b * ((x / a) - (0.5 * (x / a)))) - (x / a)))) / y
	elif b <= -4.5e+86:
		tmp = x / (a * (y * t_1))
	elif b <= -5e-187:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a * t_1)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666))))))
	tmp = 0.0
	if (b <= -5.4e+130)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(Float64(b * Float64(Float64(x / a) - Float64(0.5 * Float64(x / a)))) - Float64(x / a)))) / y);
	elseif (b <= -4.5e+86)
		tmp = Float64(x / Float64(a * Float64(y * t_1)));
	elseif (b <= -5e-187)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a * t_1)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))));
	tmp = 0.0;
	if (b <= -5.4e+130)
		tmp = ((x / a) + (b * ((b * ((x / a) - (0.5 * (x / a)))) - (x / a)))) / y;
	elseif (b <= -4.5e+86)
		tmp = x / (a * (y * t_1));
	elseif (b <= -5e-187)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a * t_1)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 - N[(b * N[(-1.0 - N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.4e+130], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(x / a), $MachinePrecision] - N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -4.5e+86], N[(x / N[(a * N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5e-187], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.3999999999999997e130

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.6%

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

      1. div-exp 60.6%

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

      2. exp-to-pow 60.6%

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

      3. sub-neg 60.6%

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

      4. metadata-eval 60.6%

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

   5. Simplified 60.6%

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

   6. Taylor expanded in t around 0 92.2%

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

   7. Taylor expanded in b around 0 69.0%

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

   if -5.3999999999999997e130 < b < -4.49999999999999993e86

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.2%

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

      1. div-exp 37.9%

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

      2. exp-to-pow 37.9%

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

      3. sub-neg 37.9%

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

      4. metadata-eval 37.9%

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

   5. Simplified 37.9%

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

   6. Taylor expanded in t around 0 38.5%

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

   7. Taylor expanded in b around 0 63.0%

      \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}\right)} \]
   8. Step-by-step derivation

      1. *-commutative 51.2%

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

   9. Simplified 63.0%

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

   if -4.49999999999999993e86 < b < -4.9999999999999996e-187

   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 y around 0 83.0%

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

      1. div-exp 79.9%

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

      2. exp-to-pow 80.3%

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

      3. sub-neg 80.3%

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

      4. metadata-eval 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in t around 0 49.0%

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

   7. Taylor expanded in b around 0 35.8%

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

      1. +-commutative 35.8%

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

      2. mul-1-neg 35.8%

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

      3. unsub-neg 35.8%

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

      4. associate-/l* 35.8%

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

   9. Simplified 35.8%

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

   10. Taylor expanded in b around inf 42.8%

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

   if -4.9999999999999996e-187 < b

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 84.7%

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

      1. div-exp 77.4%

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

      2. exp-to-pow 78.1%

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

      3. sub-neg 78.1%

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

      4. metadata-eval 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in t around 0 64.3%

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

   7. Taylor expanded in b around 0 61.5%

      \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}}}{y} \]
   8. Step-by-step derivation

      1. *-commutative 61.5%

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

   9. Simplified 61.5%

      \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+130}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(b \cdot \left(\frac{x}{a} - 0.5 \cdot \frac{x}{a}\right) - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{+86}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-187}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.3% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\\ \mathbf{if}\;b \leq -2.15 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot t\_1\right)}\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-190}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot t\_1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- 1.0 (* b (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))
   (if (<= b -2.15e+127)
     (* x (/ (- (/ 1.0 a) (/ b a)) y))
     (if (<= b -9.2e+85)
       (/ x (* a (* y t_1)))
       (if (<= b -1.5e-190)
         (/ (* b (- (/ x (* a b)) (/ x a))) y)
         (/ (/ x (* a t_1)) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))));
	double tmp;
	if (b <= -2.15e+127) {
		tmp = x * (((1.0 / a) - (b / a)) / y);
	} else if (b <= -9.2e+85) {
		tmp = x / (a * (y * t_1));
	} else if (b <= -1.5e-190) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a * t_1)) / 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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - (b * ((-1.0d0) - (b * (0.5d0 + (b * 0.16666666666666666d0)))))
    if (b <= (-2.15d+127)) then
        tmp = x * (((1.0d0 / a) - (b / a)) / y)
    else if (b <= (-9.2d+85)) then
        tmp = x / (a * (y * t_1))
    else if (b <= (-1.5d-190)) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a * t_1)) / 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 t_1 = 1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))));
	double tmp;
	if (b <= -2.15e+127) {
		tmp = x * (((1.0 / a) - (b / a)) / y);
	} else if (b <= -9.2e+85) {
		tmp = x / (a * (y * t_1));
	} else if (b <= -1.5e-190) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a * t_1)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))))
	tmp = 0
	if b <= -2.15e+127:
		tmp = x * (((1.0 / a) - (b / a)) / y)
	elif b <= -9.2e+85:
		tmp = x / (a * (y * t_1))
	elif b <= -1.5e-190:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a * t_1)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666))))))
	tmp = 0.0
	if (b <= -2.15e+127)
		tmp = Float64(x * Float64(Float64(Float64(1.0 / a) - Float64(b / a)) / y));
	elseif (b <= -9.2e+85)
		tmp = Float64(x / Float64(a * Float64(y * t_1)));
	elseif (b <= -1.5e-190)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a * t_1)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666)))));
	tmp = 0.0;
	if (b <= -2.15e+127)
		tmp = x * (((1.0 / a) - (b / a)) / y);
	elseif (b <= -9.2e+85)
		tmp = x / (a * (y * t_1));
	elseif (b <= -1.5e-190)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a * t_1)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 - N[(b * N[(-1.0 - N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.15e+127], N[(x * N[(N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.2e+85], N[(x / N[(a * N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.5e-190], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.14999999999999992e127

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.9%

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

      1. div-exp 61.6%

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

      2. exp-to-pow 61.6%

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

      3. sub-neg 61.6%

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

      4. metadata-eval 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in t around 0 92.4%

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

   7. Taylor expanded in b around 0 55.5%

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

      1. +-commutative 55.5%

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

      2. mul-1-neg 55.5%

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

      3. unsub-neg 55.5%

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

      4. associate-/l* 50.6%

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

   9. Simplified 50.6%

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

   10. Taylor expanded in x around 0 62.9%

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

       1. associate-/l* 62.9%

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

   12. Simplified 62.9%

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

   if -2.14999999999999992e127 < b < -9.1999999999999996e85

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.2%

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

      1. div-exp 33.8%

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

      2. exp-to-pow 33.8%

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

      3. sub-neg 33.8%

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

      4. metadata-eval 33.8%

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

   5. Simplified 33.8%

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

   6. Taylor expanded in t around 0 34.4%

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

   7. Taylor expanded in b around 0 67.1%

      \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}\right)} \]
   8. Step-by-step derivation

      1. *-commutative 54.5%

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

   9. Simplified 67.1%

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

   if -9.1999999999999996e85 < b < -1.4999999999999999e-190

   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 y around 0 83.3%

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

      1. div-exp 80.2%

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

      2. exp-to-pow 80.6%

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

      3. sub-neg 80.6%

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

      4. metadata-eval 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in t around 0 48.3%

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

   7. Taylor expanded in b around 0 35.2%

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

      1. +-commutative 35.2%

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

      2. mul-1-neg 35.2%

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

      3. unsub-neg 35.2%

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

      4. associate-/l* 35.2%

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

   9. Simplified 35.2%

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

   10. Taylor expanded in b around inf 42.2%

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

   if -1.4999999999999999e-190 < b

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 84.6%

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

      1. div-exp 77.2%

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

      2. exp-to-pow 78.0%

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

      3. sub-neg 78.0%

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

      4. metadata-eval 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in t around 0 64.8%

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

   7. Taylor expanded in b around 0 62.0%

      \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}}}{y} \]
   8. Step-by-step derivation

      1. *-commutative 62.0%

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

   9. Simplified 62.0%

      \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.15 \cdot 10^{+127}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-190}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.7% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-188}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e+112)
   (* x (/ (- (/ 1.0 a) (/ b a)) y))
   (if (<= b -9.2e-188)
     (/ (* b (- (/ x (* a b)) (/ x a))) y)
     (/ (/ x (* a (- 1.0 (* b (- -1.0 (* b 0.5)))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+112) {
		tmp = x * (((1.0 / a) - (b / a)) / y);
	} else if (b <= -9.2e-188) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a * (1.0 - (b * (-1.0 - (b * 0.5)))))) / 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 <= (-2d+112)) then
        tmp = x * (((1.0d0 / a) - (b / a)) / y)
    else if (b <= (-9.2d-188)) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a * (1.0d0 - (b * ((-1.0d0) - (b * 0.5d0)))))) / 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 <= -2e+112) {
		tmp = x * (((1.0 / a) - (b / a)) / y);
	} else if (b <= -9.2e-188) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a * (1.0 - (b * (-1.0 - (b * 0.5)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e+112:
		tmp = x * (((1.0 / a) - (b / a)) / y)
	elif b <= -9.2e-188:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a * (1.0 - (b * (-1.0 - (b * 0.5)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e+112)
		tmp = Float64(x * Float64(Float64(Float64(1.0 / a) - Float64(b / a)) / y));
	elseif (b <= -9.2e-188)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * 0.5)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e+112)
		tmp = x * (((1.0 / a) - (b / a)) / y);
	elseif (b <= -9.2e-188)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a * (1.0 - (b * (-1.0 - (b * 0.5)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e+112], N[(x * N[(N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9.2e-188], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * N[(1.0 - N[(b * N[(-1.0 - N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9999999999999999e112

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.2%

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

      1. div-exp 56.7%

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

      2. exp-to-pow 56.7%

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

      3. sub-neg 56.7%

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

      4. metadata-eval 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in t around 0 82.9%

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

   7. Taylor expanded in b around 0 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. associate-/l* 43.5%

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

   9. Simplified 43.5%

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

   10. Taylor expanded in x around 0 53.9%

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

       1. associate-/l* 55.9%

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

   12. Simplified 55.9%

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

   if -1.9999999999999999e112 < b < -9.1999999999999999e-188

   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 y around 0 80.8%

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

      1. div-exp 75.3%

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

      2. exp-to-pow 75.6%

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

      3. sub-neg 75.6%

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

      4. metadata-eval 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in t around 0 47.9%

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

   7. Taylor expanded in b around 0 36.2%

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

      1. +-commutative 36.2%

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

      2. mul-1-neg 36.2%

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

      3. unsub-neg 36.2%

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

      4. associate-/l* 36.2%

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

   9. Simplified 36.2%

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

   10. Taylor expanded in b around inf 42.5%

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

   if -9.1999999999999999e-188 < b

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 84.7%

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

      1. div-exp 77.4%

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

      2. exp-to-pow 78.1%

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

      3. sub-neg 78.1%

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

      4. metadata-eval 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in t around 0 64.3%

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

   7. Taylor expanded in b around 0 57.4%

      \[\leadsto \frac{\frac{x}{a \cdot \color{blue}{\left(1 + b \cdot \left(1 + 0.5 \cdot b\right)\right)}}}{y} \]
   8. Step-by-step derivation

      1. *-commutative 57.4%

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

   9. Simplified 57.4%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-188}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 44.4% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-259}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e+112)
   (* x (/ (- (/ 1.0 a) (/ b a)) y))
   (if (<= b -6.6e-259)
     (/ (* b (- (/ x (* a b)) (/ x a))) y)
     (/ x (* a (+ y (* b (+ y (* 0.5 (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+112) {
		tmp = x * (((1.0 / a) - (b / a)) / y);
	} else if (b <= -6.6e-259) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2d+112)) then
        tmp = x * (((1.0d0 / a) - (b / a)) / y)
    else if (b <= (-6.6d-259)) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = x / (a * (y + (b * (y + (0.5d0 * (y * b))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+112) {
		tmp = x * (((1.0 / a) - (b / a)) / y);
	} else if (b <= -6.6e-259) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e+112:
		tmp = x * (((1.0 / a) - (b / a)) / y)
	elif b <= -6.6e-259:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e+112)
		tmp = Float64(x * Float64(Float64(Float64(1.0 / a) - Float64(b / a)) / y));
	elseif (b <= -6.6e-259)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(0.5 * Float64(y * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e+112)
		tmp = x * (((1.0 / a) - (b / a)) / y);
	elseif (b <= -6.6e-259)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e+112], N[(x * N[(N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -6.6e-259], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(0.5 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.9999999999999999e112

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.2%

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

      1. div-exp 56.7%

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

      2. exp-to-pow 56.7%

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

      3. sub-neg 56.7%

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

      4. metadata-eval 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in t around 0 82.9%

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

   7. Taylor expanded in b around 0 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. associate-/l* 43.5%

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

   9. Simplified 43.5%

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

   10. Taylor expanded in x around 0 53.9%

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

       1. associate-/l* 55.9%

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

   12. Simplified 55.9%

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

   if -1.9999999999999999e112 < b < -6.6e-259

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 81.2%

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

      1. div-exp 76.1%

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

      2. exp-to-pow 76.6%

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

      3. sub-neg 76.6%

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

      4. metadata-eval 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in t around 0 47.5%

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

   7. Taylor expanded in b around 0 36.8%

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

      1. +-commutative 36.8%

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

      2. mul-1-neg 36.8%

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

      3. unsub-neg 36.8%

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

      4. associate-/l* 36.9%

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

   9. Simplified 36.9%

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

   10. Taylor expanded in b around inf 42.6%

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

   if -6.6e-259 < b

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 84.7%

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

      1. div-exp 77.0%

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

      2. exp-to-pow 77.7%

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

      3. sub-neg 77.7%

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

      4. metadata-eval 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in t around 0 65.4%

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

   7. Taylor expanded in b around 0 55.8%

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

      1. *-commutative 55.8%

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

   9. Simplified 55.8%

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

Alternative 17: 40.4% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-264}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7e+110)
   (* x (/ (- (/ 1.0 a) (/ b a)) y))
   (if (<= b -7e-264)
     (/ (* b (- (/ x (* a b)) (/ x a))) y)
     (/ x (* a (* y (+ 1.0 b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e+110) {
		tmp = x * (((1.0 / a) - (b / a)) / y);
	} else if (b <= -7e-264) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7d+110)) then
        tmp = x * (((1.0d0 / a) - (b / a)) / y)
    else if (b <= (-7d-264)) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = x / (a * (y * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7e+110) {
		tmp = x * (((1.0 / a) - (b / a)) / y);
	} else if (b <= -7e-264) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7e+110:
		tmp = x * (((1.0 / a) - (b / a)) / y)
	elif b <= -7e-264:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7e+110)
		tmp = Float64(x * Float64(Float64(Float64(1.0 / a) - Float64(b / a)) / y));
	elseif (b <= -7e-264)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7e+110)
		tmp = x * (((1.0 / a) - (b / a)) / y);
	elseif (b <= -7e-264)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7e+110], N[(x * N[(N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7e-264], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.9999999999999998e110

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.2%

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

      1. div-exp 56.7%

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

      2. exp-to-pow 56.7%

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

      3. sub-neg 56.7%

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

      4. metadata-eval 56.7%

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

   5. Simplified 56.7%

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

   6. Taylor expanded in t around 0 82.9%

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

   7. Taylor expanded in b around 0 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

      4. associate-/l* 43.5%

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

   9. Simplified 43.5%

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

   10. Taylor expanded in x around 0 53.9%

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

       1. associate-/l* 55.9%

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

   12. Simplified 55.9%

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

   if -6.9999999999999998e110 < b < -7.0000000000000001e-264

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 81.2%

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

      1. div-exp 76.1%

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

      2. exp-to-pow 76.6%

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

      3. sub-neg 76.6%

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

      4. metadata-eval 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in t around 0 47.5%

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

   7. Taylor expanded in b around 0 36.8%

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

      1. +-commutative 36.8%

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

      2. mul-1-neg 36.8%

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

      3. unsub-neg 36.8%

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

      4. associate-/l* 36.9%

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

   9. Simplified 36.9%

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

   10. Taylor expanded in b around inf 42.6%

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

   if -7.0000000000000001e-264 < b

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 84.7%

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

      1. div-exp 77.0%

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

      2. exp-to-pow 77.7%

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

      3. sub-neg 77.7%

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

      4. metadata-eval 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in t around 0 65.4%

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

   7. Taylor expanded in b around 0 42.6%

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

      1. distribute-lft-out 42.6%

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

      2. distribute-rgt1-in 42.6%

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

   9. Simplified 42.6%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-264}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.2% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.2e+110)
   (* x (/ (- (/ 1.0 a) (/ b a)) y))
   (if (<= b 9.2e-42) (/ (/ x a) y) (/ x (* a (* y (+ 1.0 b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+110) {
		tmp = x * (((1.0 / a) - (b / a)) / y);
	} else if (b <= 9.2e-42) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.2d+110)) then
        tmp = x * (((1.0d0 / a) - (b / a)) / y)
    else if (b <= 9.2d-42) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+110) {
		tmp = x * (((1.0 / a) - (b / a)) / y);
	} else if (b <= 9.2e-42) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.2e+110:
		tmp = x * (((1.0 / a) - (b / a)) / y)
	elif b <= 9.2e-42:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.2e+110)
		tmp = Float64(x * Float64(Float64(Float64(1.0 / a) - Float64(b / a)) / y));
	elseif (b <= 9.2e-42)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.2e+110)
		tmp = x * (((1.0 / a) - (b / a)) / y);
	elseif (b <= 9.2e-42)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.2e+110], N[(x * N[(N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.2e-42], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.19999999999999992e110

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.4%

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

      1. div-exp 57.6%

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

      2. exp-to-pow 57.6%

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

      3. sub-neg 57.6%

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

      4. metadata-eval 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in t around 0 83.2%

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

   7. Taylor expanded in b around 0 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

      4. associate-/l* 44.7%

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

   9. Simplified 44.7%

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

   10. Taylor expanded in x around 0 54.8%

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

       1. associate-/l* 56.9%

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

   12. Simplified 56.9%

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

   if -2.19999999999999992e110 < b < 9.20000000000000015e-42

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 80.2%

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

      1. div-exp 77.3%

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

      2. exp-to-pow 78.2%

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

      3. sub-neg 78.2%

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

      4. metadata-eval 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in t around 0 48.0%

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

   7. Taylor expanded in b around 0 42.4%

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

   if 9.20000000000000015e-42 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.1%

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

      1. div-exp 75.2%

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

      2. exp-to-pow 75.2%

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

      3. sub-neg 75.2%

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

      4. metadata-eval 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in t around 0 79.6%

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

   7. Taylor expanded in b around 0 38.3%

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

      1. distribute-lft-out 38.3%

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

      2. distribute-rgt1-in 38.3%

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

   9. Simplified 38.3%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 39.1% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.2e+110)
   (/ (/ (* x b) a) (- y))
   (if (<= b 2.2e-47) (/ (/ x a) y) (/ x (* a (* y (+ 1.0 b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+110) {
		tmp = ((x * b) / a) / -y;
	} else if (b <= 2.2e-47) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.2d+110)) then
        tmp = ((x * b) / a) / -y
    else if (b <= 2.2d-47) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+110) {
		tmp = ((x * b) / a) / -y;
	} else if (b <= 2.2e-47) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.2e+110:
		tmp = ((x * b) / a) / -y
	elif b <= 2.2e-47:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.2e+110)
		tmp = Float64(Float64(Float64(x * b) / a) / Float64(-y));
	elseif (b <= 2.2e-47)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.2e+110)
		tmp = ((x * b) / a) / -y;
	elseif (b <= 2.2e-47)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.2e+110], N[(N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[b, 2.2e-47], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.19999999999999992e110

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.4%

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

      1. div-exp 57.6%

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

      2. exp-to-pow 57.6%

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

      3. sub-neg 57.6%

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

      4. metadata-eval 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in t around 0 83.2%

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

   7. Taylor expanded in b around 0 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

      4. associate-/l* 44.7%

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

   9. Simplified 44.7%

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

   10. Taylor expanded in b around inf 48.7%

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

   if -2.19999999999999992e110 < b < 2.20000000000000019e-47

   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 80.0%

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

      1. div-exp 77.0%

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

      2. exp-to-pow 77.9%

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

      3. sub-neg 77.9%

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

      4. metadata-eval 77.9%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in t around 0 47.9%

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

   7. Taylor expanded in b around 0 42.3%

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

   if 2.20000000000000019e-47 < b

   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 y around 0 89.3%

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

      1. div-exp 75.8%

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

      2. exp-to-pow 75.9%

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

      3. sub-neg 75.9%

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

      4. metadata-eval 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in t around 0 78.8%

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

   7. Taylor expanded in b around 0 38.6%

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

      1. distribute-lft-out 38.6%

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

      2. distribute-rgt1-in 38.6%

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

   9. Simplified 38.6%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{x \cdot b}{a}}{-y}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 38.2% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-a}}{y}\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.2e+110)
   (/ (* b (/ x (- a))) y)
   (if (<= b 6.8e-43) (/ (/ x a) y) (/ x (* a (* y (+ 1.0 b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+110) {
		tmp = (b * (x / -a)) / y;
	} else if (b <= 6.8e-43) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.2d+110)) then
        tmp = (b * (x / -a)) / y
    else if (b <= 6.8d-43) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+110) {
		tmp = (b * (x / -a)) / y;
	} else if (b <= 6.8e-43) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.2e+110:
		tmp = (b * (x / -a)) / y
	elif b <= 6.8e-43:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.2e+110)
		tmp = Float64(Float64(b * Float64(x / Float64(-a))) / y);
	elseif (b <= 6.8e-43)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.2e+110)
		tmp = (b * (x / -a)) / y;
	elseif (b <= 6.8e-43)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.2e+110], N[(N[(b * N[(x / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6.8e-43], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.19999999999999992e110

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.4%

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

      1. div-exp 57.6%

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

      2. exp-to-pow 57.6%

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

      3. sub-neg 57.6%

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

      4. metadata-eval 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in t around 0 83.2%

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

   7. Taylor expanded in b around 0 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

      4. associate-/l* 44.7%

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

   9. Simplified 44.7%

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

   10. Taylor expanded in b around inf 48.7%

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

       1. neg-mul-1 48.7%

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

       2. associate-/l* 44.7%

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

       3. distribute-lft-neg-out 44.7%

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

       4. *-commutative 44.7%

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

   12. Simplified 44.7%

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

   if -2.19999999999999992e110 < b < 6.8000000000000001e-43

   1. Initial program 98.1%

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

   3. Taylor expanded in y around 0 80.2%

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

      1. div-exp 77.3%

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

      2. exp-to-pow 78.2%

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

      3. sub-neg 78.2%

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

      4. metadata-eval 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in t around 0 48.0%

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

   7. Taylor expanded in b around 0 42.4%

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

   if 6.8000000000000001e-43 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.1%

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

      1. div-exp 75.2%

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

      2. exp-to-pow 75.2%

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

      3. sub-neg 75.2%

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

      4. metadata-eval 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in t around 0 79.6%

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

   7. Taylor expanded in b around 0 38.3%

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

      1. distribute-lft-out 38.3%

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

      2. distribute-rgt1-in 38.3%

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

   9. Simplified 38.3%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-a}}{y}\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 33.8% accurate, 24.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.2e+110) (/ (* b (/ x (- a))) y) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+110) {
		tmp = (b * (x / -a)) / 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 <= (-2.2d+110)) then
        tmp = (b * (x / -a)) / 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 <= -2.2e+110) {
		tmp = (b * (x / -a)) / y;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.2e+110:
		tmp = (b * (x / -a)) / y
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.2e+110)
		tmp = Float64(Float64(b * Float64(x / Float64(-a))) / 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 <= -2.2e+110)
		tmp = (b * (x / -a)) / y;
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.2e+110], N[(N[(b * N[(x / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.19999999999999992e110

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.4%

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

      1. div-exp 57.6%

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

      2. exp-to-pow 57.6%

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

      3. sub-neg 57.6%

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

      4. metadata-eval 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in t around 0 83.2%

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

   7. Taylor expanded in b around 0 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

      4. associate-/l* 44.7%

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

   9. Simplified 44.7%

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

   10. Taylor expanded in b around inf 48.7%

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

       1. neg-mul-1 48.7%

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

       2. associate-/l* 44.7%

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

       3. distribute-lft-neg-out 44.7%

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

       4. *-commutative 44.7%

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

   12. Simplified 44.7%

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

   if -2.19999999999999992e110 < b

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 83.3%

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

      1. div-exp 76.6%

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

      2. exp-to-pow 77.2%

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

      3. sub-neg 77.2%

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

      4. metadata-eval 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in t around 0 58.4%

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

   7. Taylor expanded in b around 0 34.5%

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

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{b \cdot \frac{x}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 33.9% accurate, 24.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.2e+110) (/ (* x b) (* y (- a))) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+110) {
		tmp = (x * b) / (y * -a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.2d+110)) then
        tmp = (x * b) / (y * -a)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.2e+110) {
		tmp = (x * b) / (y * -a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.2e+110:
		tmp = (x * b) / (y * -a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.2e+110)
		tmp = Float64(Float64(x * b) / Float64(y * Float64(-a)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.2e+110)
		tmp = (x * b) / (y * -a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.2e+110], N[(N[(x * b), $MachinePrecision] / N[(y * (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.19999999999999992e110

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.4%

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

      1. div-exp 57.6%

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

      2. exp-to-pow 57.6%

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

      3. sub-neg 57.6%

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

      4. metadata-eval 57.6%

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

   5. Simplified 57.6%

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

   6. Taylor expanded in t around 0 83.2%

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

   7. Taylor expanded in b around 0 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

      4. associate-/l* 44.7%

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

   9. Simplified 44.7%

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

   10. Taylor expanded in b around inf 42.6%

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

       1. associate-*r/ 42.6%

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

       2. associate-*r* 42.6%

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

       3. neg-mul-1 42.6%

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

   12. Simplified 42.6%

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

   if -2.19999999999999992e110 < b

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 83.3%

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

      1. div-exp 76.6%

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

      2. exp-to-pow 77.2%

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

      3. sub-neg 77.2%

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

      4. metadata-eval 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in t around 0 58.4%

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

   7. Taylor expanded in b around 0 34.5%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+110}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 33.7% accurate, 24.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.3e+31) (* b (/ x (* y (- a)))) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.3e+31) {
		tmp = b * (x / (y * -a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.3d+31)) then
        tmp = b * (x / (y * -a))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.3e+31) {
		tmp = b * (x / (y * -a));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.3e+31:
		tmp = b * (x / (y * -a))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.3e+31)
		tmp = Float64(b * Float64(x / Float64(y * Float64(-a))));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.3e+31)
		tmp = b * (x / (y * -a));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.3e+31], N[(b * N[(x / N[(y * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.29999999999999992e31

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.1%

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

      1. div-exp 56.4%

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

      2. exp-to-pow 56.4%

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

      3. sub-neg 56.4%

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

      4. metadata-eval 56.4%

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

   5. Simplified 56.4%

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

   6. Taylor expanded in t around 0 76.9%

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

   7. Taylor expanded in b around 0 44.2%

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

      1. +-commutative 44.2%

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

      2. mul-1-neg 44.2%

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

      3. unsub-neg 44.2%

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

      4. associate-/l* 41.2%

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

   9. Simplified 41.2%

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

   10. Taylor expanded in b around inf 39.7%

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

       1. mul-1-neg 39.7%

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

       2. associate-/l* 41.1%

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

       3. distribute-rgt-neg-in 41.1%

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

       4. distribute-neg-frac2 41.1%

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

       5. distribute-rgt-neg-out 41.1%

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

   12. Simplified 41.1%

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

   if -3.29999999999999992e31 < b

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 84.4%

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

      1. div-exp 78.6%

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

      2. exp-to-pow 79.3%

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

      3. sub-neg 79.3%

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

      4. metadata-eval 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in t around 0 58.3%

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

   7. Taylor expanded in b around 0 34.3%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.0% accurate, 63.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

3. Taylor expanded in y around 0 84.0%

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

   1. div-exp 73.1%

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

   2. exp-to-pow 73.6%

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

   3. sub-neg 73.6%

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

   4. metadata-eval 73.6%

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

5. Simplified 73.6%

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

6. Taylor expanded in t around 0 63.0%

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

7. Taylor expanded in b around 0 32.6%

   \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]
8. Add Preprocessing

Alternative 25: 30.8% 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 99.0%

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

3. Taylor expanded in y around 0 84.0%

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

   1. div-exp 73.1%

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

   2. exp-to-pow 73.6%

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

   3. sub-neg 73.6%

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

   4. metadata-eval 73.6%

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

5. Simplified 73.6%

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

6. Taylor expanded in t around 0 61.4%

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

7. Taylor expanded in b around 0 29.1%

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

8. Final simplification 29.1%

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

Developer Target 1: 71.3% 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 2024170 
(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))