Average Error: 0.1 → 0.1
Time: 16.2s
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 r203053 = x;
        double r203054 = 0.5;
        double r203055 = r203053 * r203054;
        double r203056 = y;
        double r203057 = 1.0;
        double r203058 = z;
        double r203059 = r203057 - r203058;
        double r203060 = log(r203058);
        double r203061 = r203059 + r203060;
        double r203062 = r203056 * r203061;
        double r203063 = r203055 + r203062;
        return r203063;
}
↓
double f(double x, double y, double z) {
        double r203064 = x;
        double r203065 = 0.5;
        double r203066 = r203064 * r203065;
        double r203067 = y;
        double r203068 = 2.0;
        double r203069 = z;
        double r203070 = cbrt(r203069);
        double r203071 = log(r203070);
        double r203072 = r203068 * r203071;
        double r203073 = 1.0;
        double r203074 = r203072 + r203073;
        double r203075 = r203074 - r203069;
        double r203076 = r203075 + r203071;
        double r203077 = r203067 * r203076;
        double r203078 = r203066 + r203077;
        return r203078;
}

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 2019323 
(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)))))