Average Error: 1.9 → 1.9
Time: 32.2s
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 r319647 = x;
        double r319648 = y;
        double r319649 = z;
        double r319650 = log(r319649);
        double r319651 = r319648 * r319650;
        double r319652 = t;
        double r319653 = 1.0;
        double r319654 = r319652 - r319653;
        double r319655 = a;
        double r319656 = log(r319655);
        double r319657 = r319654 * r319656;
        double r319658 = r319651 + r319657;
        double r319659 = b;
        double r319660 = r319658 - r319659;
        double r319661 = exp(r319660);
        double r319662 = r319647 * r319661;
        double r319663 = r319662 / r319648;
        return r319663;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r319664 = x;
        double r319665 = y;
        double r319666 = z;
        double r319667 = log(r319666);
        double r319668 = r319665 * r319667;
        double r319669 = t;
        double r319670 = 1.0;
        double r319671 = r319669 - r319670;
        double r319672 = a;
        double r319673 = log(r319672);
        double r319674 = r319671 * r319673;
        double r319675 = r319668 + r319674;
        double r319676 = b;
        double r319677 = r319675 - r319676;
        double r319678 = exp(r319677);
        double r319679 = r319664 * r319678;
        double r319680 = r319679 / r319665;
        return r319680;
}

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
Target11.3
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 2019326 
(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))