Average Error: 1.9 → 1.9
Time: 39.5s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r310651 = x;
        double r310652 = y;
        double r310653 = z;
        double r310654 = log(r310653);
        double r310655 = r310652 * r310654;
        double r310656 = t;
        double r310657 = 1.0;
        double r310658 = r310656 - r310657;
        double r310659 = a;
        double r310660 = log(r310659);
        double r310661 = r310658 * r310660;
        double r310662 = r310655 + r310661;
        double r310663 = b;
        double r310664 = r310662 - r310663;
        double r310665 = exp(r310664);
        double r310666 = r310651 * r310665;
        double r310667 = r310666 / r310652;
        return r310667;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r310668 = x;
        double r310669 = y;
        double r310670 = z;
        double r310671 = log(r310670);
        double r310672 = r310669 * r310671;
        double r310673 = t;
        double r310674 = 1.0;
        double r310675 = r310673 - r310674;
        double r310676 = a;
        double r310677 = log(r310676);
        double r310678 = r310675 * r310677;
        double r310679 = r310672 + r310678;
        double r310680 = b;
        double r310681 = r310679 - r310680;
        double r310682 = exp(r310681);
        double r310683 = r310668 * r310682;
        double r310684 = r310683 / r310669;
        return r310684;
}

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
Target11.0
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471478852839936735108494759:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.228837407310493290424346923828125:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 1.9

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

  2. Final simplification1.9

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

Reproduce

herbie shell --seed 2019306 
(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))