Average Error: 0.1 → 0.1
Time: 6.1s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + \log \left(\sqrt[3]{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + y \cdot \left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + \log \left(\sqrt[3]{z}\right)\right)
double f(double x, double y, double z) {
        double r379263 = x;
        double r379264 = 0.5;
        double r379265 = r379263 * r379264;
        double r379266 = y;
        double r379267 = 1.0;
        double r379268 = z;
        double r379269 = r379267 - r379268;
        double r379270 = log(r379268);
        double r379271 = r379269 + r379270;
        double r379272 = r379266 * r379271;
        double r379273 = r379265 + r379272;
        return r379273;
}
↓
double f(double x, double y, double z) {
        double r379274 = x;
        double r379275 = 0.5;
        double r379276 = r379274 * r379275;
        double r379277 = y;
        double r379278 = 2.0;
        double r379279 = z;
        double r379280 = cbrt(r379279);
        double r379281 = log(r379280);
        double r379282 = r379278 * r379281;
        double r379283 = 1.0;
        double r379284 = r379282 + r379283;
        double r379285 = r379284 - r379279;
        double r379286 = r379285 + r379281;
        double r379287 = r379277 * r379286;
        double r379288 = r379276 + r379287;
        return r379288;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right)\]

Derivation

  1. Initial program 0.1

    \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\right)\]

  4. Applied log-prod0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)}\right)\]

  5. Applied associate-+r+0.1

    \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(\left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right)}\]

  6. Simplified0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\color{blue}{\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right)} + \log \left(\sqrt[3]{z}\right)\right)\]

  7. Final simplification0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + \log \left(\sqrt[3]{z}\right)\right)\]

Reproduce

herbie shell --seed 2020089 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1 z) (log z)))))