Average Error: 1.8 → 1.8
Time: 43.6s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r18302946 = x;
        double r18302947 = y;
        double r18302948 = z;
        double r18302949 = log(r18302948);
        double r18302950 = r18302947 * r18302949;
        double r18302951 = t;
        double r18302952 = 1.0;
        double r18302953 = r18302951 - r18302952;
        double r18302954 = a;
        double r18302955 = log(r18302954);
        double r18302956 = r18302953 * r18302955;
        double r18302957 = r18302950 + r18302956;
        double r18302958 = b;
        double r18302959 = r18302957 - r18302958;
        double r18302960 = exp(r18302959);
        double r18302961 = r18302946 * r18302960;
        double r18302962 = r18302961 / r18302947;
        return r18302962;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r18302963 = x;
        double r18302964 = exp(1.0);
        double r18302965 = a;
        double r18302966 = log(r18302965);
        double r18302967 = t;
        double r18302968 = 1.0;
        double r18302969 = r18302967 - r18302968;
        double r18302970 = r18302966 * r18302969;
        double r18302971 = z;
        double r18302972 = log(r18302971);
        double r18302973 = y;
        double r18302974 = r18302972 * r18302973;
        double r18302975 = r18302970 + r18302974;
        double r18302976 = b;
        double r18302977 = r18302975 - r18302976;
        double r18302978 = pow(r18302964, r18302977);
        double r18302979 = r18302963 * r18302978;
        double r18302980 = r18302979 / r18302973;
        double r18302981 = cbrt(r18302980);
        double r18302982 = exp(r18302977);
        double r18302983 = r18302963 * r18302982;
        double r18302984 = r18302983 / r18302973;
        double r18302985 = cbrt(r18302984);
        double r18302986 = r18302985 * r18302985;
        double r18302987 = r18302981 * r18302986;
        return r18302987;
}

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

Original1.8
Target10.9
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1.0\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1.0\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1.0\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 1.8

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity1.8

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot e^{\color{blue}{1 \cdot \left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}{y}}\]

  6. Applied exp-prod1.8

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot \color{blue}{{\left(e^{1}\right)}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}{y}}\]

  7. Simplified1.8

    \[\leadsto \left(\sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot {\color{blue}{e}}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}{y}}\]

  8. Final simplification1.8

    \[\leadsto \sqrt[3]{\frac{x \cdot {e}^{\left(\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b\right)}}{y}} \cdot \left(\sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}} \cdot \sqrt[3]{\frac{x \cdot e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{y}}\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1) (* 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) (* y (log z))))))

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