Average Error: 0.1 → 0.2
Time: 18.1s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(x - \left(\left(\left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y}\right) - y\right) + \left(y + 0.5\right) \cdot \log \left({y}^{\frac{2}{3}}\right)\right)\right) - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(x - \left(\left(\left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y}\right) - y\right) + \left(y + 0.5\right) \cdot \log \left({y}^{\frac{2}{3}}\right)\right)\right) - z
double f(double x, double y, double z) {
        double r14130539 = x;
        double r14130540 = y;
        double r14130541 = 0.5;
        double r14130542 = r14130540 + r14130541;
        double r14130543 = log(r14130540);
        double r14130544 = r14130542 * r14130543;
        double r14130545 = r14130539 - r14130544;
        double r14130546 = r14130545 + r14130540;
        double r14130547 = z;
        double r14130548 = r14130546 - r14130547;
        return r14130548;
}
↓
double f(double x, double y, double z) {
        double r14130549 = x;
        double r14130550 = y;
        double r14130551 = 0.5;
        double r14130552 = r14130550 + r14130551;
        double r14130553 = cbrt(r14130550);
        double r14130554 = log(r14130553);
        double r14130555 = r14130552 * r14130554;
        double r14130556 = r14130555 - r14130550;
        double r14130557 = 0.6666666666666666;
        double r14130558 = pow(r14130550, r14130557);
        double r14130559 = log(r14130558);
        double r14130560 = r14130552 * r14130559;
        double r14130561 = r14130556 + r14130560;
        double r14130562 = r14130549 - r14130561;
        double r14130563 = z;
        double r14130564 = r14130562 - r14130563;
        return r14130564;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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Target

Original0.1
Target0.1
Herbie0.2
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

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

  3. Applied associate-+l-0.1

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

  5. Applied add-cube-cbrt0.1

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

  6. Applied log-prod0.2

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

  7. Applied distribute-lft-in0.2

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

  8. Applied associate--l+0.2

    \[\leadsto \left(x - \color{blue}{\left(\left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(y + 0.5\right) \cdot \log \left(\sqrt[3]{y}\right) - y\right)\right)}\right) - z\]
  9. Using strategy rm

  10. Applied pow1/30.1

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

  11. Applied pow1/30.2

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

  12. Applied pow-prod-up0.2

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"

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

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