Average Error: 1.9 → 1.2
Time: 21.6s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\left(\log \left(\frac{1}{a}\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + b\right)}}}{y}\]
\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(\log \left(\frac{1}{a}\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t} + b\right)}}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r475273 = x;
        double r475274 = y;
        double r475275 = z;
        double r475276 = log(r475275);
        double r475277 = r475274 * r475276;
        double r475278 = t;
        double r475279 = 1.0;
        double r475280 = r475278 - r475279;
        double r475281 = a;
        double r475282 = log(r475281);
        double r475283 = r475280 * r475282;
        double r475284 = r475277 + r475283;
        double r475285 = b;
        double r475286 = r475284 - r475285;
        double r475287 = exp(r475286);
        double r475288 = r475273 * r475287;
        double r475289 = r475288 / r475274;
        return r475289;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r475290 = x;
        double r475291 = 1.0;
        double r475292 = a;
        double r475293 = r475291 / r475292;
        double r475294 = 1.0;
        double r475295 = pow(r475293, r475294);
        double r475296 = y;
        double r475297 = z;
        double r475298 = r475291 / r475297;
        double r475299 = log(r475298);
        double r475300 = r475296 * r475299;
        double r475301 = log(r475293);
        double r475302 = t;
        double r475303 = cbrt(r475302);
        double r475304 = r475303 * r475303;
        double r475305 = r475301 * r475304;
        double r475306 = r475305 * r475303;
        double r475307 = b;
        double r475308 = r475306 + r475307;
        double r475309 = r475300 + r475308;
        double r475310 = exp(r475309);
        double r475311 = r475295 / r475310;
        double r475312 = r475290 * r475311;
        double r475313 = r475312 / r475296;
        return r475313;
}

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
Target11.4
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;t \lt -0.88458485041274715:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.22883740731:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 1.9

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

  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

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

  6. Applied associate-*r*1.2

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

  7. Final simplification1.2

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

Reproduce

herbie shell --seed 2020021 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))