Average Error: 5.8 → 5.8
Time: 8.5s
Precision: 64
\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]
↓
\[\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \left(1 \cdot {x}^{\frac{1}{3}}\right)\right) + \left(\left(\log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467001\right)\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]
\left(\left(\left(x - 0.5\right) \cdot \log 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(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \left(1 \cdot {x}^{\frac{1}{3}}\right)\right) + \left(\left(\log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right) - x\right) + 0.91893853320467001\right)\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}
double f(double x, double y, double z) {
        double r369328 = x;
        double r369329 = 0.5;
        double r369330 = r369328 - r369329;
        double r369331 = log(r369328);
        double r369332 = r369330 * r369331;
        double r369333 = r369332 - r369328;
        double r369334 = 0.91893853320467;
        double r369335 = r369333 + r369334;
        double r369336 = y;
        double r369337 = 0.0007936500793651;
        double r369338 = r369336 + r369337;
        double r369339 = z;
        double r369340 = r369338 * r369339;
        double r369341 = 0.0027777777777778;
        double r369342 = r369340 - r369341;
        double r369343 = r369342 * r369339;
        double r369344 = 0.083333333333333;
        double r369345 = r369343 + r369344;
        double r369346 = r369345 / r369328;
        double r369347 = r369335 + r369346;
        return r369347;
}
↓
double f(double x, double y, double z) {
        double r369348 = x;
        double r369349 = 0.5;
        double r369350 = r369348 - r369349;
        double r369351 = cbrt(r369348);
        double r369352 = 1.0;
        double r369353 = 0.3333333333333333;
        double r369354 = pow(r369348, r369353);
        double r369355 = r369352 * r369354;
        double r369356 = r369351 * r369355;
        double r369357 = log(r369356);
        double r369358 = r369350 * r369357;
        double r369359 = log(r369351);
        double r369360 = r369359 * r369350;
        double r369361 = r369360 - r369348;
        double r369362 = 0.91893853320467;
        double r369363 = r369361 + r369362;
        double r369364 = r369358 + r369363;
        double r369365 = y;
        double r369366 = 0.0007936500793651;
        double r369367 = r369365 + r369366;
        double r369368 = z;
        double r369369 = r369367 * r369368;
        double r369370 = 0.0027777777777778;
        double r369371 = r369369 - r369370;
        double r369372 = r369371 * r369368;
        double r369373 = 0.083333333333333;
        double r369374 = r369372 + r369373;
        double r369375 = r369374 / r369348;
        double r369376 = r369364 + r369375;
        return r369376;
}

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

Original5.8
Target1.2
Herbie5.8
\[\left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.91893853320467001 - x\right)\right) + \frac{0.0833333333333329956}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 7.93650079365100015 \cdot 10^{-4}\right) - 0.0027777777777778\right)\]

Derivation

  1. Initial program 5.8

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

  3. Applied add-cube-cbrt5.8

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

  4. Applied log-prod5.9

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

  5. Applied distribute-lft-in5.9

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

  6. Applied associate--l+5.9

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

  7. Applied associate-+l+5.9

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

  8. Simplified5.9

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

  10. Applied *-un-lft-identity5.9

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

  11. Applied cbrt-prod5.9

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

  12. Simplified5.9

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

  13. Simplified5.8

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

  14. Final simplification5.8

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

Reproduce

herbie shell --seed 2020021 
(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)))