Average Error: 6.1 → 6.2
Time: 7.5s
Precision: 64
\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]
↓
\[\left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\log \left({x}^{\frac{1}{3}}\right) \cdot \left(x - 0.5\right) - x\right)\right) + 0.91893853320467001\right) + \left(\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956\right) \cdot \frac{1}{x}\]
\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}
↓
\left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\log \left({x}^{\frac{1}{3}}\right) \cdot \left(x - 0.5\right) - x\right)\right) + 0.91893853320467001\right) + \left(\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956\right) \cdot \frac{1}{x}
double f(double x, double y, double z) {
        double r410558 = x;
        double r410559 = 0.5;
        double r410560 = r410558 - r410559;
        double r410561 = log(r410558);
        double r410562 = r410560 * r410561;
        double r410563 = r410562 - r410558;
        double r410564 = 0.91893853320467;
        double r410565 = r410563 + r410564;
        double r410566 = y;
        double r410567 = 0.0007936500793651;
        double r410568 = r410566 + r410567;
        double r410569 = z;
        double r410570 = r410568 * r410569;
        double r410571 = 0.0027777777777778;
        double r410572 = r410570 - r410571;
        double r410573 = r410572 * r410569;
        double r410574 = 0.083333333333333;
        double r410575 = r410573 + r410574;
        double r410576 = r410575 / r410558;
        double r410577 = r410565 + r410576;
        return r410577;
}
↓
double f(double x, double y, double z) {
        double r410578 = x;
        double r410579 = 0.5;
        double r410580 = r410578 - r410579;
        double r410581 = cbrt(r410578);
        double r410582 = r410581 * r410581;
        double r410583 = log(r410582);
        double r410584 = r410580 * r410583;
        double r410585 = 0.3333333333333333;
        double r410586 = pow(r410578, r410585);
        double r410587 = log(r410586);
        double r410588 = r410587 * r410580;
        double r410589 = r410588 - r410578;
        double r410590 = r410584 + r410589;
        double r410591 = 0.91893853320467;
        double r410592 = r410590 + r410591;
        double r410593 = y;
        double r410594 = 0.0007936500793651;
        double r410595 = r410593 + r410594;
        double r410596 = z;
        double r410597 = r410595 * r410596;
        double r410598 = 0.0027777777777778;
        double r410599 = r410597 - r410598;
        double r410600 = r410599 * r410596;
        double r410601 = 0.083333333333333;
        double r410602 = r410600 + r410601;
        double r410603 = 1.0;
        double r410604 = r410603 / r410578;
        double r410605 = r410602 * r410604;
        double r410606 = r410592 + r410605;
        return r410606;
}

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

Original6.1
Target1.2
Herbie6.2
\[\left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.91893853320467001 - x\right)\right) + \frac{0.0833333333333329956}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 7.93650079365100015 \cdot 10^{-4}\right) - 0.0027777777777778\right)\]

Derivation

  1. Initial program 6.1

    \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt6.1

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

  4. Applied log-prod6.1

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right)} - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

  5. Applied distribute-lft-in6.1

    \[\leadsto \left(\left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x}\right)\right)} - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

  6. Applied associate--l+6.1

    \[\leadsto \left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x}\right) - x\right)\right)} + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]

  7. Simplified6.1

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \color{blue}{\left(\log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right) - x\right)}\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]
  8. Using strategy rm

  9. Applied pow1/36.1

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\log \color{blue}{\left({x}^{\frac{1}{3}}\right)} \cdot \left(x - 0.5\right) - x\right)\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]
  10. Using strategy rm

  11. Applied div-inv6.2

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\log \left({x}^{\frac{1}{3}}\right) \cdot \left(x - 0.5\right) - x\right)\right) + 0.91893853320467001\right) + \color{blue}{\left(\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956\right) \cdot \frac{1}{x}}\]

  12. Final simplification6.2

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\log \left({x}^{\frac{1}{3}}\right) \cdot \left(x - 0.5\right) - x\right)\right) + 0.91893853320467001\right) + \left(\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956\right) \cdot \frac{1}{x}\]

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (+ (+ (+ (* (- x 0.5) (log x)) (- 0.91893853320467 x)) (/ 0.083333333333333 x)) (* (/ z x) (- (* z (+ y 0.0007936500793651)) 0.0027777777777778)))

  (+ (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467) (/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)))