Average Error: 1.9 → 1.0
Time: 1.8m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt[3]{{e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}} \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{{e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt[3]{{e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}} \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{{e}^{\left(\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b\right)}}}}
double f(double x, double y, double z, double t, double a, double b) {
        double r11124930 = x;
        double r11124931 = y;
        double r11124932 = z;
        double r11124933 = log(r11124932);
        double r11124934 = r11124931 * r11124933;
        double r11124935 = t;
        double r11124936 = 1.0;
        double r11124937 = r11124935 - r11124936;
        double r11124938 = a;
        double r11124939 = log(r11124938);
        double r11124940 = r11124937 * r11124939;
        double r11124941 = r11124934 + r11124940;
        double r11124942 = b;
        double r11124943 = r11124941 - r11124942;
        double r11124944 = exp(r11124943);
        double r11124945 = r11124930 * r11124944;
        double r11124946 = r11124945 / r11124931;
        return r11124946;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r11124947 = x;
        double r11124948 = cbrt(r11124947);
        double r11124949 = y;
        double r11124950 = cbrt(r11124949);
        double r11124951 = exp(1.0);
        double r11124952 = z;
        double r11124953 = log(r11124952);
        double r11124954 = r11124949 * r11124953;
        double r11124955 = t;
        double r11124956 = 1.0;
        double r11124957 = r11124955 - r11124956;
        double r11124958 = a;
        double r11124959 = log(r11124958);
        double r11124960 = r11124957 * r11124959;
        double r11124961 = r11124954 + r11124960;
        double r11124962 = b;
        double r11124963 = r11124961 - r11124962;
        double r11124964 = pow(r11124951, r11124963);
        double r11124965 = cbrt(r11124964);
        double r11124966 = r11124950 / r11124965;
        double r11124967 = r11124948 / r11124966;
        double r11124968 = r11124948 * r11124948;
        double r11124969 = r11124950 * r11124950;
        double r11124970 = exp(r11124963);
        double r11124971 = cbrt(r11124970);
        double r11124972 = r11124971 * r11124965;
        double r11124973 = r11124969 / r11124972;
        double r11124974 = r11124968 / r11124973;
        double r11124975 = r11124967 * r11124974;
        return r11124975;
}

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

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

  3. Applied associate-/l*1.8

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

  5. Applied add-cube-cbrt1.8

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

  6. Applied add-cube-cbrt1.8

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

  7. Applied times-frac1.8

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

  8. Applied add-cube-cbrt1.8

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

  9. Applied times-frac1.0

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

  11. Applied *-un-lft-identity1.0

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

  12. Applied *-un-lft-identity1.0

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

  13. Applied distribute-lft-out--1.0

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

  14. Applied exp-prod1.0

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

  15. Simplified1.0

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

  17. Applied *-un-lft-identity1.0

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

  18. Applied exp-prod1.0

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

  19. Simplified1.0

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

  20. Final simplification1.0

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

Reproduce

herbie shell --seed 2019112 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))