Average Error: 1.9 → 3.1
Time: 47.7s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\frac{\frac{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{\frac{\sqrt[3]{y}}{x}}}{\sqrt[3]{y}}}{\sqrt[3]{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\frac{\frac{e^{\left(\log a \cdot \left(t - 1.0\right) + \log z \cdot y\right) - b}}{\frac{\sqrt[3]{y}}{x}}}{\sqrt[3]{y}}}{\sqrt[3]{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r24814020 = x;
        double r24814021 = y;
        double r24814022 = z;
        double r24814023 = log(r24814022);
        double r24814024 = r24814021 * r24814023;
        double r24814025 = t;
        double r24814026 = 1.0;
        double r24814027 = r24814025 - r24814026;
        double r24814028 = a;
        double r24814029 = log(r24814028);
        double r24814030 = r24814027 * r24814029;
        double r24814031 = r24814024 + r24814030;
        double r24814032 = b;
        double r24814033 = r24814031 - r24814032;
        double r24814034 = exp(r24814033);
        double r24814035 = r24814020 * r24814034;
        double r24814036 = r24814035 / r24814021;
        return r24814036;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r24814037 = a;
        double r24814038 = log(r24814037);
        double r24814039 = t;
        double r24814040 = 1.0;
        double r24814041 = r24814039 - r24814040;
        double r24814042 = r24814038 * r24814041;
        double r24814043 = z;
        double r24814044 = log(r24814043);
        double r24814045 = y;
        double r24814046 = r24814044 * r24814045;
        double r24814047 = r24814042 + r24814046;
        double r24814048 = b;
        double r24814049 = r24814047 - r24814048;
        double r24814050 = exp(r24814049);
        double r24814051 = cbrt(r24814045);
        double r24814052 = x;
        double r24814053 = r24814051 / r24814052;
        double r24814054 = r24814050 / r24814053;
        double r24814055 = r24814054 / r24814051;
        double r24814056 = r24814055 / r24814051;
        return r24814056;
}

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

Original1.9
Target10.9
Herbie3.1
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1.0\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1.0\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1.0\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 1.9

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

  3. Applied add-sqr-sqrt2.0

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

  4. Taylor expanded around inf 2.0

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

  5. Simplified1.9

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

  7. Applied add-cube-cbrt1.9

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

  9. Applied add-cube-cbrt2.0

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

  10. Applied associate-/r*2.0

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

  11. Simplified3.1

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

  12. Final simplification3.1

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

Reproduce

herbie shell --seed 2019162 
(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))