Average Error: 1.9 → 1.9
Time: 30.6s
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 r416033 = x;
        double r416034 = y;
        double r416035 = z;
        double r416036 = log(r416035);
        double r416037 = r416034 * r416036;
        double r416038 = t;
        double r416039 = 1.0;
        double r416040 = r416038 - r416039;
        double r416041 = a;
        double r416042 = log(r416041);
        double r416043 = r416040 * r416042;
        double r416044 = r416037 + r416043;
        double r416045 = b;
        double r416046 = r416044 - r416045;
        double r416047 = exp(r416046);
        double r416048 = r416033 * r416047;
        double r416049 = r416048 / r416034;
        return r416049;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r416050 = x;
        double r416051 = y;
        double r416052 = z;
        double r416053 = log(r416052);
        double r416054 = r416051 * r416053;
        double r416055 = t;
        double r416056 = 1.0;
        double r416057 = r416055 - r416056;
        double r416058 = a;
        double r416059 = log(r416058);
        double r416060 = r416057 * r416059;
        double r416061 = r416054 + r416060;
        double r416062 = b;
        double r416063 = r416061 - r416062;
        double r416064 = exp(r416063);
        double r416065 = r416050 * r416064;
        double r416066 = r416065 / r416051;
        return r416066;
}

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))