Average Error: 2.1 → 2.1
Time: 16.6s
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 r605110 = x;
        double r605111 = y;
        double r605112 = z;
        double r605113 = log(r605112);
        double r605114 = r605111 * r605113;
        double r605115 = t;
        double r605116 = 1.0;
        double r605117 = r605115 - r605116;
        double r605118 = a;
        double r605119 = log(r605118);
        double r605120 = r605117 * r605119;
        double r605121 = r605114 + r605120;
        double r605122 = b;
        double r605123 = r605121 - r605122;
        double r605124 = exp(r605123);
        double r605125 = r605110 * r605124;
        double r605126 = r605125 / r605111;
        return r605126;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r605127 = x;
        double r605128 = y;
        double r605129 = z;
        double r605130 = log(r605129);
        double r605131 = r605128 * r605130;
        double r605132 = t;
        double r605133 = 1.0;
        double r605134 = r605132 - r605133;
        double r605135 = a;
        double r605136 = log(r605135);
        double r605137 = r605134 * r605136;
        double r605138 = r605131 + r605137;
        double r605139 = b;
        double r605140 = r605138 - r605139;
        double r605141 = exp(r605140);
        double r605142 = r605127 * r605141;
        double r605143 = r605142 / r605128;
        return r605143;
}

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

Original2.1
Target11.3
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;t \lt -0.88458485041274715:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.22883740731:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 2.1

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

  2. Final simplification2.1

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

Reproduce

herbie shell --seed 2020043 
(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))