Average Error: 6.2 → 6.3
Time: 22.0s
Precision: 64
\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]
↓
\[\left(x - 0.5\right) \cdot \left(\log \left(\sqrt[3]{x} \cdot {\left({\left(\frac{1}{x}\right)}^{\left(\sqrt[3]{\frac{-1}{3}} \cdot \sqrt[3]{\frac{-1}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{-1}{3}}\right)}\right) + \log \left(\sqrt[3]{x}\right)\right) - \left(x - \left(0.9189385332046700050057097541866824030876 + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\right)\right)\]
\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}
↓
\left(x - 0.5\right) \cdot \left(\log \left(\sqrt[3]{x} \cdot {\left({\left(\frac{1}{x}\right)}^{\left(\sqrt[3]{\frac{-1}{3}} \cdot \sqrt[3]{\frac{-1}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{-1}{3}}\right)}\right) + \log \left(\sqrt[3]{x}\right)\right) - \left(x - \left(0.9189385332046700050057097541866824030876 + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\right)\right)
double f(double x, double y, double z) {
        double r418603 = x;
        double r418604 = 0.5;
        double r418605 = r418603 - r418604;
        double r418606 = log(r418603);
        double r418607 = r418605 * r418606;
        double r418608 = r418607 - r418603;
        double r418609 = 0.91893853320467;
        double r418610 = r418608 + r418609;
        double r418611 = y;
        double r418612 = 0.0007936500793651;
        double r418613 = r418611 + r418612;
        double r418614 = z;
        double r418615 = r418613 * r418614;
        double r418616 = 0.0027777777777778;
        double r418617 = r418615 - r418616;
        double r418618 = r418617 * r418614;
        double r418619 = 0.083333333333333;
        double r418620 = r418618 + r418619;
        double r418621 = r418620 / r418603;
        double r418622 = r418610 + r418621;
        return r418622;
}
↓
double f(double x, double y, double z) {
        double r418623 = x;
        double r418624 = 0.5;
        double r418625 = r418623 - r418624;
        double r418626 = cbrt(r418623);
        double r418627 = 1.0;
        double r418628 = r418627 / r418623;
        double r418629 = -0.3333333333333333;
        double r418630 = cbrt(r418629);
        double r418631 = r418630 * r418630;
        double r418632 = pow(r418628, r418631);
        double r418633 = pow(r418632, r418630);
        double r418634 = r418626 * r418633;
        double r418635 = log(r418634);
        double r418636 = log(r418626);
        double r418637 = r418635 + r418636;
        double r418638 = r418625 * r418637;
        double r418639 = 0.91893853320467;
        double r418640 = y;
        double r418641 = 0.0007936500793651;
        double r418642 = r418640 + r418641;
        double r418643 = z;
        double r418644 = r418642 * r418643;
        double r418645 = 0.0027777777777778;
        double r418646 = r418644 - r418645;
        double r418647 = r418646 * r418643;
        double r418648 = 0.083333333333333;
        double r418649 = r418647 + r418648;
        double r418650 = r418649 / r418623;
        double r418651 = r418639 + r418650;
        double r418652 = r418623 - r418651;
        double r418653 = r418638 - r418652;
        return r418653;
}

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

Original6.2
Target1.2
Herbie6.3
\[\left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.9189385332046700050057097541866824030876 - x\right)\right) + \frac{0.08333333333333299564049667651488562114537}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) - 0.002777777777777800001512975569539776188321\right)\]

Derivation

  1. Initial program 6.2

    \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt6.2

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

  4. Applied log-prod6.3

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right)} - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

  5. Applied distribute-lft-in6.3

    \[\leadsto \left(\left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x}\right)\right)} - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

  6. Applied associate--l+6.2

    \[\leadsto \left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x}\right) - x\right)\right)} + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

  7. Simplified6.2

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \color{blue}{\left(\log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right) - x\right)}\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

  8. Taylor expanded around inf 6.2

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \color{blue}{{\left(\frac{1}{x}\right)}^{\frac{-1}{3}}}\right) + \left(\log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]
  9. Using strategy rm

  10. Applied add-cube-cbrt6.3

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot {\left(\frac{1}{x}\right)}^{\color{blue}{\left(\left(\sqrt[3]{\frac{-1}{3}} \cdot \sqrt[3]{\frac{-1}{3}}\right) \cdot \sqrt[3]{\frac{-1}{3}}\right)}}\right) + \left(\log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

  11. Applied pow-unpow6.3

    \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \color{blue}{{\left({\left(\frac{1}{x}\right)}^{\left(\sqrt[3]{\frac{-1}{3}} \cdot \sqrt[3]{\frac{-1}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{-1}{3}}\right)}}\right) + \left(\log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

  12. Final simplification6.3

    \[\leadsto \left(x - 0.5\right) \cdot \left(\log \left(\sqrt[3]{x} \cdot {\left({\left(\frac{1}{x}\right)}^{\left(\sqrt[3]{\frac{-1}{3}} \cdot \sqrt[3]{\frac{-1}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{-1}{3}}\right)}\right) + \log \left(\sqrt[3]{x}\right)\right) - \left(x - \left(0.9189385332046700050057097541866824030876 + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\right)\right)\]

Reproduce

herbie shell --seed 2019297 
(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)) (- 0.91893853320467001 x)) (/ 0.0833333333333329956 x)) (* (/ z x) (- (* z (+ y 7.93650079365100015e-4)) 0.0027777777777778)))

  (+ (+ (- (* (- x 0.5) (log x)) x) 0.91893853320467001) (/ (+ (* (- (* (+ y 7.93650079365100015e-4) z) 0.0027777777777778) z) 0.0833333333333329956) x)))