Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt{z}\right)\right) + y \cdot \log \left(\sqrt{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt{z}\right)\right) + y \cdot \log \left(\sqrt{z}\right)\right)
double f(double x, double y, double z) {
        double r321372 = x;
        double r321373 = 0.5;
        double r321374 = r321372 * r321373;
        double r321375 = y;
        double r321376 = 1.0;
        double r321377 = z;
        double r321378 = r321376 - r321377;
        double r321379 = log(r321377);
        double r321380 = r321378 + r321379;
        double r321381 = r321375 * r321380;
        double r321382 = r321374 + r321381;
        return r321382;
}
↓
double f(double x, double y, double z) {
        double r321383 = x;
        double r321384 = 0.5;
        double r321385 = r321383 * r321384;
        double r321386 = y;
        double r321387 = 1.0;
        double r321388 = z;
        double r321389 = r321387 - r321388;
        double r321390 = sqrt(r321388);
        double r321391 = log(r321390);
        double r321392 = r321389 + r321391;
        double r321393 = r321386 * r321392;
        double r321394 = r321386 * r321391;
        double r321395 = r321393 + r321394;
        double r321396 = r321385 + r321395;
        return r321396;
}

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 distribute-lft-in0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(y \cdot \left(1 - z\right) + y \cdot \log z\right)}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-lft-in0.1

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

  8. Applied associate-+r+0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 
(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)))))