Average Error: 1.9 → 1.9
Time: 18.3s
Precision: binary64
\[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\]
↓
\[x \cdot \sqrt[3]{{\left(e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\right)}^{3}}\]
x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}
↓
x \cdot \sqrt[3]{{\left(e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\right)}^{3}}
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (x * ((double) exp(((double) (((double) (y * ((double) (((double) log(z)) - t)))) + ((double) (a * ((double) (((double) log(((double) (1.0 - z)))) - b))))))))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (x * ((double) cbrt(((double) pow(((double) exp(((double) (((double) (y * ((double) (((double) log(z)) - t)))) + ((double) (a * ((double) (((double) log(((double) (1.0 - z)))) - b)))))))), 3.0))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.9

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

  3. Applied add-cbrt-cube1.9

    \[\leadsto x \cdot \color{blue}{\sqrt[3]{\left(e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\right) \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}}}\]

  4. Simplified1.9

    \[\leadsto x \cdot \sqrt[3]{\color{blue}{{\left(e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\right)}^{3}}}\]

  5. Final simplification1.9

    \[\leadsto x \cdot \sqrt[3]{{\left(e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\right)}^{3}}\]

Reproduce

herbie shell --seed 2020148 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))