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

Percentage Accurate: 98.6% → 98.6%

Time: 11.2s

Alternatives: 13

Speedup: 1.0×

• 48.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.6% 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: 98.6% 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 98.3%

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

Alternative 2: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - 1 \leq -1 \cdot 10^{+104} \lor \neg \left(t - 1 \leq -0.998\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (- t 1.0) -1e+104) (not (<= (- t 1.0) -0.998)))
   (/ (* 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+104) || !((t - 1.0) <= -0.998)) {
		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+104) || !(Float64(t - 1.0) <= -0.998))
		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+104], N[Not[LessEqual[N[(t - 1.0), $MachinePrecision], -0.998]], $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)) < -1e104 or -0.998 < (-.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 93.3

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

   5. Applied rewrites 93.3%

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

   if -1e104 < (-.f64 t #s(literal 1 binary64)) < -0.998

   1. Initial program 97.0%

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

   3. Taylor expanded in 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%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t - 1 \leq -1 \cdot 10^{+104} \lor \neg \left(t - 1 \leq -0.998\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\mathsf{fma}\left(\log z, y, -\log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+95}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{z}^{y}}{a}}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -4e+95)
   (/ (* x (exp (- (* (log a) t) b))) y)
   (if (<= t 1.6e-19)
     (/ (* x (/ (/ (pow z y) a) (exp b))) y)
     (/ (* x (exp (- (* (- t 1.0) (log a)) b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4e+95) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else if (t <= 1.6e-19) {
		tmp = (x * ((pow(z, y) / a) / exp(b))) / y;
	} else {
		tmp = (x * exp((((t - 1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-4d+95)) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else if (t <= 1.6d-19) then
        tmp = (x * (((z ** y) / a) / exp(b))) / y
    else
        tmp = (x * exp((((t - 1.0d0) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -4e+95) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else if (t <= 1.6e-19) {
		tmp = (x * ((Math.pow(z, y) / a) / Math.exp(b))) / y;
	} else {
		tmp = (x * Math.exp((((t - 1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -4e+95:
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	elif t <= 1.6e-19:
		tmp = (x * ((math.pow(z, y) / a) / math.exp(b))) / y
	else:
		tmp = (x * math.exp((((t - 1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -4e+95)
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	elseif (t <= 1.6e-19)
		tmp = Float64(Float64(x * Float64(Float64((z ^ y) / a) / exp(b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t - 1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -4e+95)
		tmp = (x * exp(((log(a) * t) - b))) / y;
	elseif (t <= 1.6e-19)
		tmp = (x * (((z ^ y) / a) / exp(b))) / y;
	else
		tmp = (x * exp((((t - 1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -4e+95], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.6e-19], N[(N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.00000000000000008e95

   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 96.7

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

   5. Applied rewrites 96.7%

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

   if -4.00000000000000008e95 < t < 1.59999999999999991e-19

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0

      \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   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 89.8

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

   5. Applied rewrites 89.8%

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

   if 1.59999999999999991e-19 < t

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. rem-exp-log N/A

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

      5. lower-log.f64 N/A

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

      6. rem-exp-log 87.2

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

   5. Applied rewrites 87.2%

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

Alternative 4: 79.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - 1 \leq -2 \cdot 10^{+44} \lor \neg \left(t - 1 \leq -0.998\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{-1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (- t 1.0) -2e+44) (not (<= (- t 1.0) -0.998)))
   (/ (* x (exp (- (* (log a) t) b))) y)
   (/ (* (* x (pow z y)) (pow a -1.0)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) <= -2e+44) || !((t - 1.0) <= -0.998)) {
		tmp = (x * exp(((log(a) * t) - b))) / y;
	} else {
		tmp = ((x * pow(z, y)) * pow(a, -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 (((t - 1.0d0) <= (-2d+44)) .or. (.not. ((t - 1.0d0) <= (-0.998d0)))) then
        tmp = (x * exp(((log(a) * t) - b))) / y
    else
        tmp = ((x * (z ** y)) * (a ** (-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 (((t - 1.0) <= -2e+44) || !((t - 1.0) <= -0.998)) {
		tmp = (x * Math.exp(((Math.log(a) * t) - b))) / y;
	} else {
		tmp = ((x * Math.pow(z, y)) * Math.pow(a, -1.0)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) <= -2e+44) or not ((t - 1.0) <= -0.998):
		tmp = (x * math.exp(((math.log(a) * t) - b))) / y
	else:
		tmp = ((x * math.pow(z, y)) * math.pow(a, -1.0)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t - 1.0) <= -2e+44) || !(Float64(t - 1.0) <= -0.998))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * t) - b))) / y);
	else
		tmp = Float64(Float64(Float64(x * (z ^ y)) * (a ^ -1.0)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t - 1.0) <= -2e+44) || ~(((t - 1.0) <= -0.998)))
		tmp = (x * exp(((log(a) * t) - b))) / y;
	else
		tmp = ((x * (z ^ y)) * (a ^ -1.0)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t - 1.0), $MachinePrecision], -2e+44], N[Not[LessEqual[N[(t - 1.0), $MachinePrecision], -0.998]], $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, -1.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -2.0000000000000002e44 or -0.998 < (-.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 92.2

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

   5. Applied rewrites 92.2%

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

   if -2.0000000000000002e44 < (-.f64 t #s(literal 1 binary64)) < -0.998

   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 70.6

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

   5. Applied rewrites 70.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t - 1 \leq -2 \cdot 10^{+44} \lor \neg \left(t - 1 \leq -0.998\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{-1}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - 1 \leq -2 \cdot 10^{+44} \lor \neg \left(t - 1 \leq 40\right):\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{-1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (- t 1.0) -2e+44) (not (<= (- t 1.0) 40.0)))
   (/ (* (pow a (- t 1.0)) x) y)
   (/ (* (* x (pow z y)) (pow a -1.0)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) <= -2e+44) || !((t - 1.0) <= 40.0)) {
		tmp = (pow(a, (t - 1.0)) * x) / y;
	} else {
		tmp = ((x * pow(z, y)) * pow(a, -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 (((t - 1.0d0) <= (-2d+44)) .or. (.not. ((t - 1.0d0) <= 40.0d0))) then
        tmp = ((a ** (t - 1.0d0)) * x) / y
    else
        tmp = ((x * (z ** y)) * (a ** (-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 (((t - 1.0) <= -2e+44) || !((t - 1.0) <= 40.0)) {
		tmp = (Math.pow(a, (t - 1.0)) * x) / y;
	} else {
		tmp = ((x * Math.pow(z, y)) * Math.pow(a, -1.0)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) <= -2e+44) or not ((t - 1.0) <= 40.0):
		tmp = (math.pow(a, (t - 1.0)) * x) / y
	else:
		tmp = ((x * math.pow(z, y)) * math.pow(a, -1.0)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t - 1.0) <= -2e+44) || !(Float64(t - 1.0) <= 40.0))
		tmp = Float64(Float64((a ^ Float64(t - 1.0)) * x) / y);
	else
		tmp = Float64(Float64(Float64(x * (z ^ y)) * (a ^ -1.0)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t - 1.0) <= -2e+44) || ~(((t - 1.0) <= 40.0)))
		tmp = ((a ^ (t - 1.0)) * x) / y;
	else
		tmp = ((x * (z ^ y)) * (a ^ -1.0)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t - 1.0), $MachinePrecision], -2e+44], N[Not[LessEqual[N[(t - 1.0), $MachinePrecision], 40.0]], $MachinePrecision]], N[(N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] * N[Power[a, -1.0], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -2.0000000000000002e44 or 40 < (-.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 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 64.9

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

   5. Applied rewrites 64.9%

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

   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 82.7%

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

   if -2.0000000000000002e44 < (-.f64 t #s(literal 1 binary64)) < 40

   1. Initial program 96.8%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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 70.3

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

   5. Applied rewrites 70.3%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 75.6%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t - 1 \leq -2 \cdot 10^{+44} \lor \neg \left(t - 1 \leq 40\right):\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{-1}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+115} \lor \neg \left(y \leq 8.8 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.5e+115) (not (<= y 8.8e+76)))
   (/ (/ (* (pow z y) x) a) y)
   (/ (* x (exp (- (* (- t 1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.5e+115) || !(y <= 8.8e+76)) {
		tmp = ((pow(z, y) * x) / a) / y;
	} else {
		tmp = (x * exp((((t - 1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.5d+115)) .or. (.not. (y <= 8.8d+76))) then
        tmp = (((z ** y) * x) / a) / y
    else
        tmp = (x * exp((((t - 1.0d0) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.5e+115) || !(y <= 8.8e+76)) {
		tmp = ((Math.pow(z, y) * x) / a) / y;
	} else {
		tmp = (x * Math.exp((((t - 1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.5e+115) or not (y <= 8.8e+76):
		tmp = ((math.pow(z, y) * x) / a) / y
	else:
		tmp = (x * math.exp((((t - 1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.5e+115) || !(y <= 8.8e+76))
		tmp = Float64(Float64(Float64((z ^ y) * x) / a) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t - 1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.5e+115) || ~((y <= 8.8e+76)))
		tmp = (((z ^ y) * x) / a) / y;
	else
		tmp = (x * exp((((t - 1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.5e+115], N[Not[LessEqual[y, 8.8e+76]], $MachinePrecision]], N[(N[(N[(N[Power[z, y], $MachinePrecision] * x), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e115 or 8.8000000000000002e76 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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 63.8

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

   5. Applied rewrites 63.8%

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

   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 84.9%

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

   if -1.5e115 < y < 8.8000000000000002e76

   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 y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. rem-exp-log N/A

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

      5. lower-log.f64 N/A

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

      6. rem-exp-log 93.5

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

   5. Applied rewrites 93.5%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+115} \lor \neg \left(y \leq 8.8 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-27} \lor \neg \left(b \leq 640\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.5e-27) (not (<= b 640.0)))
   (/ (* 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 <= -5.5e-27) || !(b <= 640.0)) {
		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 <= (-5.5d-27)) .or. (.not. (b <= 640.0d0))) 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 <= -5.5e-27) || !(b <= 640.0)) {
		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 <= -5.5e-27) or not (b <= 640.0):
		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 <= -5.5e-27) || !(b <= 640.0))
		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 <= -5.5e-27) || ~((b <= 640.0)))
		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, -5.5e-27], N[Not[LessEqual[b, 640.0]], $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 < -5.5000000000000002e-27 or 640 < 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 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 93.9

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

   5. Applied rewrites 93.9%

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

   if -5.5000000000000002e-27 < b < 640

   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 80.9

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

   5. Applied rewrites 80.9%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-27} \lor \neg \left(b \leq 640\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-27} \lor \neg \left(b \leq 640\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -5.5e-27) (not (<= b 640.0)))
   (/ (* 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 <= -5.5e-27) || !(b <= 640.0)) {
		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 <= (-5.5d-27)) .or. (.not. (b <= 640.0d0))) 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 <= -5.5e-27) || !(b <= 640.0)) {
		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 <= -5.5e-27) or not (b <= 640.0):
		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 <= -5.5e-27) || !(b <= 640.0))
		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 <= -5.5e-27) || ~((b <= 640.0)))
		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, -5.5e-27], N[Not[LessEqual[b, 640.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * t), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[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 < -5.5000000000000002e-27 or 640 < 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 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 93.9

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

   5. Applied rewrites 93.9%

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

   if -5.5000000000000002e-27 < b < 640

   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

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}{y}} \]
   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 77.7

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

   5. Applied rewrites 77.7%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{-27} \lor \neg \left(b \leq 640\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot t - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - 1 \leq -2 \cdot 10^{+44} \lor \neg \left(t - 1 \leq 40\right):\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (- t 1.0) -2e+44) (not (<= (- t 1.0) 40.0)))
   (/ (* (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 - 1.0) <= -2e+44) || !((t - 1.0) <= 40.0)) {
		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 - 1.0d0) <= (-2d+44)) .or. (.not. ((t - 1.0d0) <= 40.0d0))) 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 - 1.0) <= -2e+44) || !((t - 1.0) <= 40.0)) {
		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 - 1.0) <= -2e+44) or not ((t - 1.0) <= 40.0):
		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 ((Float64(t - 1.0) <= -2e+44) || !(Float64(t - 1.0) <= 40.0))
		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 - 1.0) <= -2e+44) || ~(((t - 1.0) <= 40.0)))
		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[N[(t - 1.0), $MachinePrecision], -2e+44], N[Not[LessEqual[N[(t - 1.0), $MachinePrecision], 40.0]], $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 (-.f64 t #s(literal 1 binary64)) < -2.0000000000000002e44 or 40 < (-.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 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 64.9

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

   5. Applied rewrites 64.9%

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

   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 82.7%

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

   if -2.0000000000000002e44 < (-.f64 t #s(literal 1 binary64)) < 40

   1. Initial program 96.8%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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 70.3

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

   5. Applied rewrites 70.3%

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

   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 75.6%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t - 1 \leq -2 \cdot 10^{+44} \lor \neg \left(t - 1 \leq 40\right):\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{{z}^{y} \cdot x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+22} \lor \neg \left(b \leq 1700\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.5e+22) (not (<= b 1700.0)))
   (* (/ (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 <= -6.5e+22) || !(b <= 1700.0)) {
		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 <= (-6.5d+22)) .or. (.not. (b <= 1700.0d0))) 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 <= -6.5e+22) || !(b <= 1700.0)) {
		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 <= -6.5e+22) or not (b <= 1700.0):
		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 <= -6.5e+22) || !(b <= 1700.0))
		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 <= -6.5e+22) || ~((b <= 1700.0)))
		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, -6.5e+22], N[Not[LessEqual[b, 1700.0]], $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 < -6.49999999999999979e22 or 1700 < 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 b around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   4. 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 84.4

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

   5. Applied rewrites 84.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   6. 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 84.4

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

   7. Applied rewrites 84.4%

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

   if -6.49999999999999979e22 < b < 1700

   1. Initial program 96.9%

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

   3. Taylor expanded in 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 79.7

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

   5. Applied rewrites 79.7%

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

   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 72.4%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+22} \lor \neg \left(b \leq 1700\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2500000 \lor \neg \left(b \leq 680\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2500000.0) (not (<= b 680.0)))
   (* (/ (exp (- b)) y) x)
   (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2500000.0) || !(b <= 680.0)) {
		tmp = (exp(-b) / y) * x;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2500000.0d0)) .or. (.not. (b <= 680.0d0))) then
        tmp = (exp(-b) / y) * x
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2500000.0) || !(b <= 680.0)) {
		tmp = (Math.exp(-b) / y) * x;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2500000.0) or not (b <= 680.0):
		tmp = (math.exp(-b) / y) * x
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2500000.0) || !(b <= 680.0))
		tmp = Float64(Float64(exp(Float64(-b)) / y) * x);
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2500000.0) || ~((b <= 680.0)))
		tmp = (exp(-b) / y) * x;
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2500000.0], N[Not[LessEqual[b, 680.0]], $MachinePrecision]], N[(N[(N[Exp[(-b)], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.5e6 or 680 < 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 b around inf

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   4. 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 84.0

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

   5. Applied rewrites 84.0%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]
   6. 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 84.0

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

   7. Applied rewrites 84.0%

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

   if -2.5e6 < b < 680

   1. Initial program 96.8%

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

   3. Taylor expanded in b around 0

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z + \log a \cdot \left(t - 1\right)}}}{y} \]
   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 80.8

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

   5. Applied rewrites 80.8%

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

   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 68.0%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 34.6%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2500000 \lor \neg \left(b \leq 680\right):\\ \;\;\;\;\frac{e^{-b}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.1% 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 98.3%

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

3. Taylor expanded in 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 67.7

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

5. Applied rewrites 67.7%

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

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 60.5%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 31.3%

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

    1. lift-/.f64 N/A

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

    2. 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 31.6

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

13. Applied rewrites 31.6%

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

14. Final simplification 31.6%

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

Alternative 13: 30.9% 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 98.3%

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

3. Taylor expanded in 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 67.7

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

5. Applied rewrites 67.7%

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

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 60.5%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 31.3%

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

Developer Target 1: 70.8% 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 2024313 
(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))