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

Percentage Accurate: 98.4% → 98.4%

Time: 11.1s

Alternatives: 14

Speedup: 1.0×

• 46.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

Alternative 2: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - 1 \leq -1 \cdot 10^{+103} \lor \neg \left(t - 1 \leq 20000000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (- t 1.0) -1e+103) (not (<= (- t 1.0) 20000000000.0)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (/ (* x (exp (- (fma (log z) y (- (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) <= -1e+103) || !((t - 1.0) <= 20000000000.0)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = (x * exp((fma(log(z), y, -log(a)) - b))) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t - 1.0) <= -1e+103) || !(Float64(t - 1.0) <= 20000000000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(fma(log(z), y, Float64(-log(a))) - b))) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t - 1.0), $MachinePrecision], -1e+103], N[Not[LessEqual[N[(t - 1.0), $MachinePrecision], 20000000000.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[z], $MachinePrecision] * y + (-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)) < -1e103 or 2e10 < (-.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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 96.6

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

   5. Applied rewrites 96.6%

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

   if -1e103 < (-.f64 t #s(literal 1 binary64)) < 2e10

   1. Initial program 97.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. rem-exp-log N/A

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

      8. lower-log.f64 N/A

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

      9. rem-exp-log 95.4

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

   5. Applied rewrites 95.4%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t - 1 \leq -1 \cdot 10^{+103} \lor \neg \left(t - 1 \leq 20000000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - 1 \leq -5000000000 \lor \neg \left(t - 1 \leq 20000000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{z}^{y}}{a}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (- t 1.0) -5000000000.0) (not (<= (- t 1.0) 20000000000.0)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (/ (* x (/ (/ (pow z y) a) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) <= -5000000000.0) || !((t - 1.0) <= 20000000000.0)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = (x * ((pow(z, y) / 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 - 1.0d0) <= (-5000000000.0d0)) .or. (.not. ((t - 1.0d0) <= 20000000000.0d0))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = (x * (((z ** y) / 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 - 1.0) <= -5000000000.0) || !((t - 1.0) <= 20000000000.0)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = (x * ((Math.pow(z, y) / a) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) <= -5000000000.0) or not ((t - 1.0) <= 20000000000.0):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = (x * ((math.pow(z, y) / a) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t - 1.0) <= -5000000000.0) || !(Float64(t - 1.0) <= 20000000000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(x * Float64(Float64((z ^ y) / a) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t - 1.0) <= -5000000000.0) || ~(((t - 1.0) <= 20000000000.0)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = (x * (((z ^ y) / a) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t - 1.0), $MachinePrecision], -5000000000.0], N[Not[LessEqual[N[(t - 1.0), $MachinePrecision], 20000000000.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -5e9 or 2e10 < (-.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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 94.3

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

   5. Applied rewrites 94.3%

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

   if -5e9 < (-.f64 t #s(literal 1 binary64)) < 2e10

   1. Initial program 96.7%

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

   3. Taylor expanded in t around 0

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

      1. exp-diff N/A

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

      2. lower-/.f64 N/A

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

      3. +-commutative N/A

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

      4. mul-1-neg N/A

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

      5. unsub-neg N/A

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

      6. exp-diff N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. exp-to-pow N/A

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

      10. lower-pow.f64 N/A

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

      11. rem-exp-log N/A

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

      12. lower-exp.f64 86.4

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

   5. Applied rewrites 86.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t - 1 \leq -5000000000 \lor \neg \left(t - 1 \leq 20000000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{z}^{y}}{a}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+46} \lor \neg \left(b \leq 1.26 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({a}^{t} \cdot \frac{{z}^{y}}{a}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.4e+46) (not (<= b 1.26e-38)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (/ (* x (* (pow a t) (/ (pow z y) a))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -5.4e+46) || !(b <= 1.26e-38)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = (x * (pow(a, t) * (pow(z, y) / 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 <= (-5.4d+46)) .or. (.not. (b <= 1.26d-38))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = (x * ((a ** t) * ((z ** y) / 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 <= -5.4e+46) || !(b <= 1.26e-38)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = (x * (Math.pow(a, t) * (Math.pow(z, y) / a))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.4e+46) or not (b <= 1.26e-38):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = (x * (math.pow(a, t) * (math.pow(z, y) / a))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.4e+46) || !(b <= 1.26e-38))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ t) * Float64((z ^ y) / a))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -5.4e+46) || ~((b <= 1.26e-38)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = (x * ((a ^ t) * ((z ^ y) / a))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.4e+46], N[Not[LessEqual[b, 1.26e-38]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.4000000000000003e46 or 1.26e-38 < 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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 91.2

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

   5. Applied rewrites 91.2%

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

   if -5.4000000000000003e46 < b < 1.26e-38

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

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

      3. distribute-rgt-in N/A

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

      4. associate-+l+ N/A

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

      5. +-commutative N/A

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

      6. associate-+l+ N/A

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

      7. +-commutative N/A

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

      8. exp-sum N/A

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

      9. lower-*.f64 N/A

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

      10. *-commutative N/A

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

      11. exp-prod N/A

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

      12. lower-pow.f64 N/A

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

      13. rem-exp-log N/A

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

      14. +-commutative N/A

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

      15. mul-1-neg N/A

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

   5. Applied rewrites 88.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+46} \lor \neg \left(b \leq 1.26 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({a}^{t} \cdot \frac{{z}^{y}}{a}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+46} \lor \neg \left(b \leq 1.26 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.4e+46) (not (<= b 1.26e-38)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (/ (* (* x (pow z y)) (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 <= -5.4e+46) || !(b <= 1.26e-38)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = ((x * pow(z, y)) * 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 <= (-5.4d+46)) .or. (.not. (b <= 1.26d-38))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = ((x * (z ** y)) * (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 <= -5.4e+46) || !(b <= 1.26e-38)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = ((x * Math.pow(z, y)) * Math.pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.4e+46) or not (b <= 1.26e-38):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = ((x * math.pow(z, y)) * math.pow(a, (t - 1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.4e+46) || !(b <= 1.26e-38))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(Float64(x * (z ^ y)) * (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 <= -5.4e+46) || ~((b <= 1.26e-38)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = ((x * (z ^ y)) * (a ^ (t - 1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.4e+46], N[Not[LessEqual[b, 1.26e-38]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.4000000000000003e46 or 1.26e-38 < 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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 91.2

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

   5. Applied rewrites 91.2%

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

   if -5.4000000000000003e46 < b < 1.26e-38

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 88.5

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

   5. Applied rewrites 88.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{+46} \lor \neg \left(b \leq 1.26 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+47} \lor \neg \left(b \leq 1.26 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.3e+47) (not (<= b 1.26e-38)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (* (* x (pow z y)) (/ (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 <= -4.3e+47) || !(b <= 1.26e-38)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = (x * pow(z, y)) * (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 <= (-4.3d+47)) .or. (.not. (b <= 1.26d-38))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = (x * (z ** y)) * ((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 <= -4.3e+47) || !(b <= 1.26e-38)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = (x * Math.pow(z, y)) * (Math.pow(a, (t - 1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.3e+47) or not (b <= 1.26e-38):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = (x * math.pow(z, y)) * (math.pow(a, (t - 1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.3e+47) || !(b <= 1.26e-38))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(x * (z ^ y)) * Float64((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 <= -4.3e+47) || ~((b <= 1.26e-38)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = (x * (z ^ y)) * ((a ^ (t - 1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.3e+47], N[Not[LessEqual[b, 1.26e-38]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.29999999999999995e47 or 1.26e-38 < 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 t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 91.2

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

   5. Applied rewrites 91.2%

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

   if -4.29999999999999995e47 < b < 1.26e-38

   1. Initial program 97.4%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 86.1

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

   5. Applied rewrites 86.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.3 \cdot 10^{+47} \lor \neg \left(b \leq 1.26 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-50} \lor \neg \left(t \leq 16500000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.6e-50) (not (<= t 16500000000.0)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (/ (/ (* (pow z y) x) a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.6e-50) || !(t <= 16500000000.0)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = ((pow(z, y) * 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 ((t <= (-4.6d-50)) .or. (.not. (t <= 16500000000.0d0))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = (((z ** y) * 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 ((t <= -4.6e-50) || !(t <= 16500000000.0)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = ((Math.pow(z, y) * x) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.6e-50) or not (t <= 16500000000.0):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = ((math.pow(z, y) * x) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.6e-50) || !(t <= 16500000000.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(Float64((z ^ y) * x) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.6e-50) || ~((t <= 16500000000.0)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = (((z ^ y) * x) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.6e-50], N[Not[LessEqual[t, 16500000000.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.60000000000000039e-50 or 1.65e10 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. rem-exp-log N/A

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

      4. lower-log.f64 N/A

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

      5. rem-exp-log 93.2

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

   5. Applied rewrites 93.2%

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

   if -4.60000000000000039e-50 < t < 1.65e10

   1. Initial program 96.7%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 76.3

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

   5. Applied rewrites 76.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 78.1%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-50} \lor \neg \left(t \leq 16500000000\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+102} \lor \neg \left(t \leq 260000000000\right):\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.4e+102) (not (<= t 260000000000.0)))
   (/ (* (pow a (- t 1.0)) x) y)
   (/ (/ (* (pow z y) x) a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.4e+102) || !(t <= 260000000000.0)) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else {
		tmp = ((pow(z, y) * 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 ((t <= (-4.4d+102)) .or. (.not. (t <= 260000000000.0d0))) then
        tmp = ((a ** (t - 1.0d0)) * x) / y
    else
        tmp = (((z ** y) * 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 ((t <= -4.4e+102) || !(t <= 260000000000.0)) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	} else {
		tmp = ((Math.pow(z, y) * x) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.4e+102) or not (t <= 260000000000.0):
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	else:
		tmp = ((math.pow(z, y) * x) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.4e+102) || !(t <= 260000000000.0))
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	else
		tmp = Float64(Float64(Float64((z ^ y) * x) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.4e+102) || ~((t <= 260000000000.0)))
		tmp = ((a ^ (t - 1.0)) * x) / y;
	else
		tmp = (((z ^ y) * x) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.4e+102], N[Not[LessEqual[t, 260000000000.0]], $MachinePrecision]], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.40000000000000015e102 or 2.6e11 < 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 b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 77.0

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

   5. Applied rewrites 77.0%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 91.6%

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

   if -4.40000000000000015e102 < t < 2.6e11

   1. Initial program 97.2%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 72.8

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

   5. Applied rewrites 72.8%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 77.5%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+102} \lor \neg \left(t \leq 260000000000\right):\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+110} \lor \neg \left(b \leq 2.65 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 1\right) \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.6e+110) (not (<= b 2.65e+66)))
   (* (/ (exp (- b)) y) x)
   (* (* x 1.0) (/ (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 <= -5.6e+110) || !(b <= 2.65e+66)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (x * 1.0) * (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 <= (-5.6d+110)) .or. (.not. (b <= 2.65d+66))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (x * 1.0d0) * ((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 <= -5.6e+110) || !(b <= 2.65e+66)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (x * 1.0) * (Math.pow(a, (t - 1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -5.6e+110) or not (b <= 2.65e+66):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (x * 1.0) * (math.pow(a, (t - 1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -5.6e+110) || !(b <= 2.65e+66))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x * 1.0) * Float64((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 <= -5.6e+110) || ~((b <= 2.65e+66)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (x * 1.0) * ((a ^ (t - 1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -5.6e+110], N[Not[LessEqual[b, 2.65e+66]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x * 1.0), $MachinePrecision] * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.59999999999999973e110 or 2.6499999999999998e66 < 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 t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. rem-exp-log N/A

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

      8. lower-log.f64 N/A

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

      9. rem-exp-log 96.3

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

   5. Applied rewrites 96.3%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 90.2

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

   8. Applied rewrites 90.2%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 90.2

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

   10. Applied rewrites 90.2%

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

   if -5.59999999999999973e110 < b < 2.6499999999999998e66

   1. Initial program 97.8%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. *-commutative N/A

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

      7. exp-to-pow N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. exp-prod N/A

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

      11. lower-pow.f64 N/A

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

      12. rem-exp-log N/A

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

      13. lower--.f64 83.5

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

   5. Applied rewrites 83.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 71.8%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+110} \lor \neg \left(b \leq 2.65 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 1\right) \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+108} \lor \neg \left(b \leq 2.65 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.2e+108) (not (<= b 2.65e+66)))
   (* (/ (exp (- b)) y) x)
   (/ (* (pow a (- t 1.0)) x) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.2e+108) || !(b <= 2.65e+66)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-6.2d+108)) .or. (.not. (b <= 2.65d+66))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = ((a ** (t - 1.0d0)) * x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.2e+108) || !(b <= 2.65e+66)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.2e+108) or not (b <= 2.65e+66):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.2e+108) || !(b <= 2.65e+66))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.2e+108) || ~((b <= 2.65e+66)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = ((a ^ (t - 1.0)) * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.2e+108], N[Not[LessEqual[b, 2.65e+66]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.2000000000000003e108 or 2.6499999999999998e66 < 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 t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. rem-exp-log N/A

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

      8. lower-log.f64 N/A

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

      9. rem-exp-log 96.4

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

   5. Applied rewrites 96.4%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 90.3

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

   8. Applied rewrites 90.3%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 90.3

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

   10. Applied rewrites 90.3%

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

   if -6.2000000000000003e108 < b < 2.6499999999999998e66

   1. Initial program 97.8%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 85.3

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

   5. Applied rewrites 85.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 70.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+108} \lor \neg \left(b \leq 2.65 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-19} \lor \neg \left(b \leq 1.8 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot {y}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.5e-19) (not (<= b 1.8e+14)))
   (* (/ (exp (- b)) y) x)
   (* (/ x a) (pow y -1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.5e-19) || !(b <= 1.8e+14)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (x / a) * pow(y, -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1.5d-19)) .or. (.not. (b <= 1.8d+14))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (x / a) * (y ** (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.5e-19) || !(b <= 1.8e+14)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (x / a) * Math.pow(y, -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.5e-19) or not (b <= 1.8e+14):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (x / a) * math.pow(y, -1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.5e-19) || !(b <= 1.8e+14))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x / a) * (y ^ -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.5e-19) || ~((b <= 1.8e+14)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (x / a) * (y ^ -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.5e-19], N[Not[LessEqual[b, 1.8e+14]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * N[Power[y, -1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.49999999999999996e-19 or 1.8e14 < 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 t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-log.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. rem-exp-log N/A

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

      8. lower-log.f64 N/A

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

      9. rem-exp-log 89.6

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

   5. Applied rewrites 89.6%

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

   6. Taylor expanded in b around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 78.1

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

   8. Applied rewrites 78.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 78.1

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

   10. Applied rewrites 78.1%

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

   if -1.49999999999999996e-19 < b < 1.8e14

   1. Initial program 97.2%

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

   3. Taylor expanded in b around 0

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

      1. exp-sum N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. exp-to-pow N/A

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

      7. lower-pow.f64 N/A

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

      8. exp-prod N/A

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

      9. lower-pow.f64 N/A

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

      10. rem-exp-log N/A

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

      11. lower--.f64 86.1

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

   5. Applied rewrites 86.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 71.1%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 37.3%

       \[\leadsto \frac{\frac{x}{a}}{y} \]
   12. Step-by-step derivation

       1. lift-/.f64 N/A

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

       2. frac-2neg N/A

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

       3. div-inv N/A

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

       4. metadata-eval N/A

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

       5. frac-2neg N/A

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

       6. lift-/.f64 N/A

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

       7. lower-*.f64 N/A

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

   13. Applied rewrites 37.3%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-19} \lor \neg \left(b \leq 1.8 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot {y}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ {\left(\frac{y}{\frac{x}{a}}\right)}^{-1} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (pow (/ y (/ x a)) -1.0))

C

double code(double x, double y, double z, double t, double a, double b) {
	return pow((y / (x / a)), -1.0);
}

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 = (y / (x / a)) ** (-1.0d0)
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return math.pow((y / (x / a)), -1.0)

Julia

function code(x, y, z, t, a, b)
	return Float64(y / Float64(x / a)) ^ -1.0
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (y / (x / a)) ^ -1.0;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[Power[N[(y / N[(x / a), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]

Derivation

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 b around 0

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

   1. exp-sum N/A

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

   2. associate-*r* N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. *-commutative N/A

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

   6. exp-to-pow N/A

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

   7. lower-pow.f64 N/A

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

   8. exp-prod N/A

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

   9. lower-pow.f64 N/A

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

   10. rem-exp-log N/A

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

   11. lower--.f64 74.7

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

5. Applied rewrites 74.7%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 60.1%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 29.8%

    \[\leadsto \frac{\frac{x}{a}}{y} \]
12. Step-by-step derivation

    1. lift-/.f64 N/A

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

    2. clear-num N/A

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

    3. lower-/.f64 N/A

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

    4. lower-/.f64 30.0

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

13. Applied rewrites 30.0%

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

14. Final simplification 30.0%

    \[\leadsto {\left(\frac{y}{\frac{x}{a}}\right)}^{-1} \]
15. Add Preprocessing

Alternative 13: 30.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{a} \cdot {y}^{-1} \end{array} \]

FPCore

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

C

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

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 ** (-1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x / a), $MachinePrecision] * N[Power[y, -1.0], $MachinePrecision]), $MachinePrecision]

Derivation

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 b around 0

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

   1. exp-sum N/A

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

   2. associate-*r* N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. *-commutative N/A

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

   6. exp-to-pow N/A

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

   7. lower-pow.f64 N/A

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

   8. exp-prod N/A

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

   9. lower-pow.f64 N/A

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

   10. rem-exp-log N/A

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

   11. lower--.f64 74.7

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

5. Applied rewrites 74.7%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 60.1%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 29.8%

    \[\leadsto \frac{\frac{x}{a}}{y} \]
12. Step-by-step derivation

    1. lift-/.f64 N/A

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

    2. frac-2neg N/A

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

    3. div-inv N/A

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

    4. metadata-eval N/A

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

    5. frac-2neg N/A

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

    6. lift-/.f64 N/A

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

    7. lower-*.f64 N/A

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

13. Applied rewrites 29.8%

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

14. Final simplification 29.8%

    \[\leadsto \frac{x}{a} \cdot {y}^{-1} \]
15. Add Preprocessing

Alternative 14: 30.5% accurate, 14.6× 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 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 b around 0

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

   1. exp-sum N/A

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

   2. associate-*r* N/A

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

   3. lower-*.f64 N/A

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

   4. lower-*.f64 N/A

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

   5. *-commutative N/A

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

   6. exp-to-pow N/A

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

   7. lower-pow.f64 N/A

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

   8. exp-prod N/A

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

   9. lower-pow.f64 N/A

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

   10. rem-exp-log N/A

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

   11. lower--.f64 74.7

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

5. Applied rewrites 74.7%

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

6. Taylor expanded in t around 0

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

8. Applied rewrites 60.1%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 29.8%

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

Developer Target 1: 71.8% 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 2024318 
(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))