Average Error: 2.0 → 2.0
Time: 12.8s
Precision: binary64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot {e}^{\left(\left(y \cdot \log z + \left(\left(t - 1\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{a}\right)\right) + \left(t - 1\right) \cdot \log \left(\sqrt[3]{a}\right)\right)\right) - b\right)}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot {e}^{\left(\left(y \cdot \log z + \left(\left(t - 1\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{a}\right)\right) + \left(t - 1\right) \cdot \log \left(\sqrt[3]{a}\right)\right)\right) - b\right)}}{y}
double code(double x, double y, double z, double t, double a, double b) {
	return (((double) (x * ((double) exp(((double) (((double) (((double) (y * ((double) log(z)))) + ((double) (((double) (t - 1.0)) * ((double) log(a)))))) - b)))))) / y);
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return (((double) (x * ((double) pow(((double) M_E), ((double) (((double) (((double) (y * ((double) log(z)))) + ((double) (((double) (((double) (t - 1.0)) * ((double) (2.0 * ((double) log(((double) cbrt(a)))))))) + ((double) (((double) (t - 1.0)) * ((double) log(((double) cbrt(a)))))))))) - b)))))) / y);
}

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

Target

Original2.0
Target11.3
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 2.0

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

  3. Applied *-un-lft-identity2.0

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

  4. Applied exp-prod2.0

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

  5. Simplified2.0

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

  7. Applied add-cube-cbrt2.0

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

  8. Applied log-prod2.0

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

  9. Applied distribute-lft-in2.0

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

  10. Simplified2.0

    \[\leadsto \frac{x \cdot {e}^{\left(\left(y \cdot \log z + \left(\color{blue}{\left(t - 1\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{a}\right)\right)} + \left(t - 1\right) \cdot \log \left(\sqrt[3]{a}\right)\right)\right) - b\right)}}{y}\]

  11. Final simplification2.0

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

Reproduce

herbie shell --seed 2020196 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))