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

Percentage Accurate: 98.6% → 98.6%

Time: 3.4s

Alternatives: 9

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: 24.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \leq 2 \cdot 10^{+147}:\\ \;\;\;\;e^{t - 1}\\ \mathbf{else}:\\ \;\;\;\;e^{e^{\log a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
      2e+147)
   (exp (- t 1.0))
   (exp (exp (log a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y) <= 2e+147) {
		tmp = exp((t - 1.0));
	} else {
		tmp = exp(exp(log(a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y) <= 2d+147) then
        tmp = exp((t - 1.0d0))
    else
        tmp = exp(exp(log(a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y) <= 2e+147) {
		tmp = Math.exp((t - 1.0));
	} else {
		tmp = Math.exp(Math.exp(Math.log(a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y) <= 2e+147:
		tmp = math.exp((t - 1.0))
	else:
		tmp = math.exp(math.exp(math.log(a)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y) <= 2e+147)
		tmp = exp(Float64(t - 1.0));
	else
		tmp = exp(exp(log(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y) <= 2e+147)
		tmp = exp((t - 1.0));
	else
		tmp = exp(exp(log(a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[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], 2e+147], N[Exp[N[(t - 1.0), $MachinePrecision]], $MachinePrecision], N[Exp[N[Exp[N[Log[a], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y) < 2e147

   1. Initial program 98.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 59.6%

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

   6. Taylor expanded in y around 0

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \]

   8. Applied rewrites 23.1%

      \[\leadsto e^{t - 1} \]

   if 2e147 < (/.f64 (*.f64 x (exp.f64 (-.f64 (+.f64 (*.f64 y (log.f64 z)) (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))) b))) y)

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 90.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \]

   8. Applied rewrites 90.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 49.0%

       \[\leadsto e^{e^{\log a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 35.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq -2 \cdot 10^{+36}:\\ \;\;\;\;e^{t - 1}\\ \mathbf{else}:\\ \;\;\;\;e^{e^{\log a} - b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (* (- t 1.0) (log a)) -2e+36)
   (exp (- t 1.0))
   (exp (- (exp (log a)) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * log(a)) <= -2e+36) {
		tmp = exp((t - 1.0));
	} else {
		tmp = exp((exp(log(a)) - b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t - 1.0d0) * log(a)) <= (-2d+36)) then
        tmp = exp((t - 1.0d0))
    else
        tmp = exp((exp(log(a)) - b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t - 1.0) * Math.log(a)) <= -2e+36) {
		tmp = Math.exp((t - 1.0));
	} else {
		tmp = Math.exp((Math.exp(Math.log(a)) - b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t - 1.0) * math.log(a)) <= -2e+36:
		tmp = math.exp((t - 1.0))
	else:
		tmp = math.exp((math.exp(math.log(a)) - b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(t - 1.0) * log(a)) <= -2e+36)
		tmp = exp(Float64(t - 1.0));
	else
		tmp = exp(Float64(exp(log(a)) - b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t - 1.0) * log(a)) <= -2e+36)
		tmp = exp((t - 1.0));
	else
		tmp = exp((exp(log(a)) - b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision], -2e+36], N[Exp[N[(t - 1.0), $MachinePrecision]], $MachinePrecision], N[Exp[N[(N[Exp[N[Log[a], $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a)) < -2.00000000000000008e36

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 86.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \]

   8. Applied rewrites 61.1%

      \[\leadsto e^{t - 1} \]

   if -2.00000000000000008e36 < (*.f64 (-.f64 t #s(literal 1 binary64)) (log.f64 a))

   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 y around 0

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

   5. Applied rewrites 59.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \]

   8. Applied rewrites 59.4%

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

   9. Taylor expanded in y around 0

      \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \]

   11. Applied rewrites 36.7%

       \[\leadsto e^{e^{\log a} - b} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 65.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = exp(((((((y * log(z)) + ((t - 1.0d0) * log(a))) - b) - b) - b) - b))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[Exp[N[(N[(N[(N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision] - b), $MachinePrecision] - b), $MachinePrecision] - b), $MachinePrecision]], $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 y around 0

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

5. Applied rewrites 66.4%

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

6. Taylor expanded in y around 0

   \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \]

8. Applied rewrites 66.4%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 66.4%

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

12. Taylor expanded in y around 0

    \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \]

14. Applied rewrites 66.4%

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

Alternative 5: 65.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = exp((((((y * log(z)) + ((t - 1.0d0) * log(a))) - b) - b) - b))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[Exp[N[(N[(N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision] - b), $MachinePrecision] - b), $MachinePrecision]], $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 y around 0

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

5. Applied rewrites 66.4%

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

6. Taylor expanded in y around 0

   \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \]

8. Applied rewrites 66.4%

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

9. Taylor expanded in y around 0

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

11. Applied rewrites 66.4%

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

Alternative 6: 65.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = exp(((((y * log(z)) + ((t - 1.0d0) * log(a))) - b) - b))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[Exp[N[(N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision] - b), $MachinePrecision]], $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 y around 0

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

5. Applied rewrites 66.4%

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

6. Taylor expanded in y around 0

   \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \]

8. Applied rewrites 66.4%

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

Alternative 7: 65.9% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

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 = exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := 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]

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 y around 0

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

5. Applied rewrites 66.4%

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

Alternative 8: 19.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ e^{t - 1} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return exp((t - 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 = exp((t - 1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[Exp[N[(t - 1.0), $MachinePrecision]], $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 y around 0

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

5. Applied rewrites 66.4%

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

6. Taylor expanded in y around 0

   \[\leadsto e^{\log a \cdot \left(t - 1\right) - b} \]

8. Applied rewrites 25.0%

   \[\leadsto e^{t - 1} \]
9. Add Preprocessing

Alternative 9: 2.6% accurate, 84.0× speedup

Math

\[\begin{array}{l} \\ t - 1 \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return t - 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 = t - 1.0d0
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return t - 1.0

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(t - 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 y around 0

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

5. Applied rewrites 3.0%

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

6. Taylor expanded in y around 0

   \[\leadsto \log a \cdot \left(t - 1\right) - \color{blue}{b} \]

8. Applied rewrites 2.7%

   \[\leadsto t - \color{blue}{1} \]
9. 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))