Average Error: 2.0 → 2.0
Time: 30.9s
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 r301556 = x;
        double r301557 = y;
        double r301558 = z;
        double r301559 = log(r301558);
        double r301560 = r301557 * r301559;
        double r301561 = t;
        double r301562 = 1.0;
        double r301563 = r301561 - r301562;
        double r301564 = a;
        double r301565 = log(r301564);
        double r301566 = r301563 * r301565;
        double r301567 = r301560 + r301566;
        double r301568 = b;
        double r301569 = r301567 - r301568;
        double r301570 = exp(r301569);
        double r301571 = r301556 * r301570;
        double r301572 = r301571 / r301557;
        return r301572;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r301573 = x;
        double r301574 = y;
        double r301575 = z;
        double r301576 = log(r301575);
        double r301577 = r301574 * r301576;
        double r301578 = t;
        double r301579 = 1.0;
        double r301580 = r301578 - r301579;
        double r301581 = a;
        double r301582 = log(r301581);
        double r301583 = r301580 * r301582;
        double r301584 = r301577 + r301583;
        double r301585 = b;
        double r301586 = r301584 - r301585;
        double r301587 = exp(r301586);
        double r301588 = r301573 * r301587;
        double r301589 = r301588 / r301574;
        return r301589;
}

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
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471478852839936735108494759:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.228837407310493290424346923828125:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

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. Final simplification2.0

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

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))