Average Error: 0.1 → 0.1
Time: 6.4s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(2 \cdot \log \left(\sqrt{z}\right) + \left(1 - z\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + y \cdot \left(2 \cdot \log \left(\sqrt{z}\right) + \left(1 - z\right)\right)
double f(double x, double y, double z) {
        double r1500 = x;
        double r1501 = 0.5;
        double r1502 = r1500 * r1501;
        double r1503 = y;
        double r1504 = 1.0;
        double r1505 = z;
        double r1506 = r1504 - r1505;
        double r1507 = log(r1505);
        double r1508 = r1506 + r1507;
        double r1509 = r1503 * r1508;
        double r1510 = r1502 + r1509;
        return r1510;
}
↓
double f(double x, double y, double z) {
        double r1511 = x;
        double r1512 = 0.5;
        double r1513 = r1511 * r1512;
        double r1514 = y;
        double r1515 = 2.0;
        double r1516 = z;
        double r1517 = sqrt(r1516);
        double r1518 = log(r1517);
        double r1519 = r1515 * r1518;
        double r1520 = 1.0;
        double r1521 = r1520 - r1516;
        double r1522 = r1519 + r1521;
        double r1523 = r1514 * r1522;
        double r1524 = r1513 + r1523;
        return r1524;
}

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. Using strategy rm

  11. Applied distribute-lft-out0.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 
(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)))))