Average Error: 2.0 → 1.4
Time: 33.0s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{{\left(\frac{1}{{a}^{1}}\right)}^{1}}{\frac{y}{e^{\left(y \cdot \log z - \left(-\log a\right) \cdot t\right) - b}}} \cdot x\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{{\left(\frac{1}{{a}^{1}}\right)}^{1}}{\frac{y}{e^{\left(y \cdot \log z - \left(-\log a\right) \cdot t\right) - b}}} \cdot x
double f(double x, double y, double z, double t, double a, double b) {
        double r64990 = x;
        double r64991 = y;
        double r64992 = z;
        double r64993 = log(r64992);
        double r64994 = r64991 * r64993;
        double r64995 = t;
        double r64996 = 1.0;
        double r64997 = r64995 - r64996;
        double r64998 = a;
        double r64999 = log(r64998);
        double r65000 = r64997 * r64999;
        double r65001 = r64994 + r65000;
        double r65002 = b;
        double r65003 = r65001 - r65002;
        double r65004 = exp(r65003);
        double r65005 = r64990 * r65004;
        double r65006 = r65005 / r64991;
        return r65006;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r65007 = 1.0;
        double r65008 = a;
        double r65009 = 1.0;
        double r65010 = pow(r65008, r65009);
        double r65011 = r65007 / r65010;
        double r65012 = pow(r65011, r65009);
        double r65013 = y;
        double r65014 = z;
        double r65015 = log(r65014);
        double r65016 = r65013 * r65015;
        double r65017 = log(r65008);
        double r65018 = -r65017;
        double r65019 = t;
        double r65020 = r65018 * r65019;
        double r65021 = r65016 - r65020;
        double r65022 = b;
        double r65023 = r65021 - r65022;
        double r65024 = exp(r65023);
        double r65025 = r65013 / r65024;
        double r65026 = r65012 / r65025;
        double r65027 = x;
        double r65028 = r65026 * r65027;
        return r65028;
}

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

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 associate-/l*2.0

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

  4. Simplified18.1

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

  6. Applied pow-sub18.1

    \[\leadsto \frac{x}{\frac{y \cdot e^{b}}{\color{blue}{\frac{{a}^{t}}{{a}^{1}}} \cdot {z}^{y}}}\]

  7. Applied associate-*l/18.1

    \[\leadsto \frac{x}{\frac{y \cdot e^{b}}{\color{blue}{\frac{{a}^{t} \cdot {z}^{y}}{{a}^{1}}}}}\]

  8. Applied associate-/r/18.1

    \[\leadsto \frac{x}{\color{blue}{\frac{y \cdot e^{b}}{{a}^{t} \cdot {z}^{y}} \cdot {a}^{1}}}\]
  9. Using strategy rm

  10. Applied div-inv18.2

    \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{y \cdot e^{b}}{{a}^{t} \cdot {z}^{y}} \cdot {a}^{1}}}\]

  11. Simplified18.2

    \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{t} \cdot {z}^{y}}{y \cdot e^{b}}}{{a}^{1}}}\]

  12. Taylor expanded around inf 18.2

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

  13. Simplified1.4

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

  14. Final simplification1.4

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

Reproduce

herbie shell --seed 2019323 
(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))