Average Error: 1.9 → 2.0
Time: 31.6s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\left(x \cdot {\left(\sqrt{e}\right)}^{\left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}\right) \cdot {\left(\sqrt{e}\right)}^{\left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\left(x \cdot {\left(\sqrt{e}\right)}^{\left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}\right) \cdot {\left(\sqrt{e}\right)}^{\left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r271183 = x;
        double r271184 = y;
        double r271185 = z;
        double r271186 = log(r271185);
        double r271187 = r271184 * r271186;
        double r271188 = t;
        double r271189 = 1.0;
        double r271190 = r271188 - r271189;
        double r271191 = a;
        double r271192 = log(r271191);
        double r271193 = r271190 * r271192;
        double r271194 = r271187 + r271193;
        double r271195 = b;
        double r271196 = r271194 - r271195;
        double r271197 = exp(r271196);
        double r271198 = r271183 * r271197;
        double r271199 = r271198 / r271184;
        return r271199;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r271200 = x;
        double r271201 = exp(1.0);
        double r271202 = sqrt(r271201);
        double r271203 = y;
        double r271204 = z;
        double r271205 = log(r271204);
        double r271206 = r271203 * r271205;
        double r271207 = t;
        double r271208 = 1.0;
        double r271209 = r271207 - r271208;
        double r271210 = a;
        double r271211 = log(r271210);
        double r271212 = r271209 * r271211;
        double r271213 = r271206 + r271212;
        double r271214 = b;
        double r271215 = r271213 - r271214;
        double r271216 = pow(r271202, r271215);
        double r271217 = r271200 * r271216;
        double r271218 = r271217 * r271216;
        double r271219 = r271218 / r271203;
        return r271219;
}

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
Target10.7
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 1.9

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

  3. Applied *-un-lft-identity1.9

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

  4. Applied exp-prod2.0

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

  5. Simplified2.0

    \[\leadsto \frac{x \cdot {\color{blue}{e}}^{\left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}}{y}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt2.2

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

  8. Applied unpow-prod-down2.0

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

  9. Applied associate-*r*2.0

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

  10. Final simplification2.0

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

Reproduce

herbie shell --seed 2019322 
(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))