Average Error: 1.9 → 1.2
Time: 15.2s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\left(\sqrt[3]{\log \left(\frac{1}{a}\right) \cdot t} \cdot \sqrt[3]{\log \left(\frac{1}{a}\right) \cdot t}\right) \cdot \sqrt[3]{\log \left(\frac{1}{a}\right) \cdot t} + b\right)}}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\left(\sqrt[3]{\log \left(\frac{1}{a}\right) \cdot t} \cdot \sqrt[3]{\log \left(\frac{1}{a}\right) \cdot t}\right) \cdot \sqrt[3]{\log \left(\frac{1}{a}\right) \cdot t} + b\right)}}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r73947 = x;
        double r73948 = y;
        double r73949 = z;
        double r73950 = log(r73949);
        double r73951 = r73948 * r73950;
        double r73952 = t;
        double r73953 = 1.0;
        double r73954 = r73952 - r73953;
        double r73955 = a;
        double r73956 = log(r73955);
        double r73957 = r73954 * r73956;
        double r73958 = r73951 + r73957;
        double r73959 = b;
        double r73960 = r73958 - r73959;
        double r73961 = exp(r73960);
        double r73962 = r73947 * r73961;
        double r73963 = r73962 / r73948;
        return r73963;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r73964 = x;
        double r73965 = 1.0;
        double r73966 = a;
        double r73967 = r73965 / r73966;
        double r73968 = 1.0;
        double r73969 = pow(r73967, r73968);
        double r73970 = y;
        double r73971 = z;
        double r73972 = r73965 / r73971;
        double r73973 = log(r73972);
        double r73974 = r73970 * r73973;
        double r73975 = log(r73967);
        double r73976 = t;
        double r73977 = r73975 * r73976;
        double r73978 = cbrt(r73977);
        double r73979 = r73978 * r73978;
        double r73980 = r73979 * r73978;
        double r73981 = b;
        double r73982 = r73980 + r73981;
        double r73983 = r73974 + r73982;
        double r73984 = exp(r73983);
        double r73985 = r73969 / r73984;
        double r73986 = r73964 * r73985;
        double r73987 = r73986 / r73970;
        return r73987;
}

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

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

  2. Taylor expanded around inf 1.9

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

  3. Simplified1.2

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

  5. Applied add-cube-cbrt1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2020021 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))