Average Error: 1.9 → 1.9
Time: 1.3m
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 r421510 = x;
        double r421511 = y;
        double r421512 = z;
        double r421513 = log(r421512);
        double r421514 = r421511 * r421513;
        double r421515 = t;
        double r421516 = 1.0;
        double r421517 = r421515 - r421516;
        double r421518 = a;
        double r421519 = log(r421518);
        double r421520 = r421517 * r421519;
        double r421521 = r421514 + r421520;
        double r421522 = b;
        double r421523 = r421521 - r421522;
        double r421524 = exp(r421523);
        double r421525 = r421510 * r421524;
        double r421526 = r421525 / r421511;
        return r421526;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r421527 = x;
        double r421528 = y;
        double r421529 = z;
        double r421530 = log(r421529);
        double r421531 = r421528 * r421530;
        double r421532 = t;
        double r421533 = 1.0;
        double r421534 = r421532 - r421533;
        double r421535 = a;
        double r421536 = log(r421535);
        double r421537 = r421534 * r421536;
        double r421538 = r421531 + r421537;
        double r421539 = b;
        double r421540 = r421538 - r421539;
        double r421541 = exp(r421540);
        double r421542 = r421527 * r421541;
        double r421543 = r421542 / r421528;
        return r421543;
}

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
Target11.1
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;t \lt -0.88458485041274715:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.22883740731:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

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. 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 2019198 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))