Average Error: 2.0 → 23.3
Time: 28.8s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\frac{x}{y}}{\frac{{\left(\frac{1}{a}\right)}^{t}}{{z}^{y}}} \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{b}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\frac{x}{y}}{\frac{{\left(\frac{1}{a}\right)}^{t}}{{z}^{y}}} \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{b}}
double f(double x, double y, double z, double t, double a, double b) {
        double r376940 = x;
        double r376941 = y;
        double r376942 = z;
        double r376943 = log(r376942);
        double r376944 = r376941 * r376943;
        double r376945 = t;
        double r376946 = 1.0;
        double r376947 = r376945 - r376946;
        double r376948 = a;
        double r376949 = log(r376948);
        double r376950 = r376947 * r376949;
        double r376951 = r376944 + r376950;
        double r376952 = b;
        double r376953 = r376951 - r376952;
        double r376954 = exp(r376953);
        double r376955 = r376940 * r376954;
        double r376956 = r376955 / r376941;
        return r376956;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r376957 = x;
        double r376958 = y;
        double r376959 = r376957 / r376958;
        double r376960 = 1.0;
        double r376961 = a;
        double r376962 = r376960 / r376961;
        double r376963 = t;
        double r376964 = pow(r376962, r376963);
        double r376965 = z;
        double r376966 = pow(r376965, r376958);
        double r376967 = r376964 / r376966;
        double r376968 = r376959 / r376967;
        double r376969 = 1.0;
        double r376970 = pow(r376962, r376969);
        double r376971 = b;
        double r376972 = exp(r376971);
        double r376973 = r376970 / r376972;
        double r376974 = r376968 * r376973;
        return r376974;
}

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

Original2.0
Target11.2
Herbie23.3
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471478852839936735108494759:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.228837407310493290424346923828125:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 2.0

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

  2. Taylor expanded around inf 2.0

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

  3. Simplified1.3

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

  4. Final simplification23.3

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

Reproduce

herbie shell --seed 2019303 
(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 -0.88458485041274715) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 852031.22883740731) (/ (* (/ 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))