Average Error: 1.9 → 1.9
Time: 7.6m
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 r1136199 = x;
        double r1136200 = y;
        double r1136201 = z;
        double r1136202 = log(r1136201);
        double r1136203 = r1136200 * r1136202;
        double r1136204 = t;
        double r1136205 = 1.0;
        double r1136206 = r1136204 - r1136205;
        double r1136207 = a;
        double r1136208 = log(r1136207);
        double r1136209 = r1136206 * r1136208;
        double r1136210 = r1136203 + r1136209;
        double r1136211 = b;
        double r1136212 = r1136210 - r1136211;
        double r1136213 = exp(r1136212);
        double r1136214 = r1136199 * r1136213;
        double r1136215 = r1136214 / r1136200;
        return r1136215;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1136216 = x;
        double r1136217 = y;
        double r1136218 = z;
        double r1136219 = log(r1136218);
        double r1136220 = r1136217 * r1136219;
        double r1136221 = t;
        double r1136222 = 1.0;
        double r1136223 = r1136221 - r1136222;
        double r1136224 = a;
        double r1136225 = log(r1136224);
        double r1136226 = r1136223 * r1136225;
        double r1136227 = r1136220 + r1136226;
        double r1136228 = b;
        double r1136229 = r1136227 - r1136228;
        double r1136230 = exp(r1136229);
        double r1136231 = r1136216 * r1136230;
        double r1136232 = r1136231 / r1136217;
        return r1136232;
}

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
Target11.0
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 2019306 +o rules:numerics
(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))