Average Error: 5.7 → 4.0
Time: 23.7s
Precision: 64
\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le 2.176139995006076 \cdot 10^{+35}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + \left(\left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right)\right) - x\right) + 0.91893853320467\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z \cdot z}{x} \cdot \left(y + 0.0007936500793651\right) - \frac{z}{x} \cdot 0.0027777777777778\right) + \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + 0.91893853320467\right)\\ \end{array}\]
\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}
↓
\begin{array}{l}
\mathbf{if}\;x \le 2.176139995006076 \cdot 10^{+35}:\\
\;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + \left(\left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right)\right) - x\right) + 0.91893853320467\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{z \cdot z}{x} \cdot \left(y + 0.0007936500793651\right) - \frac{z}{x} \cdot 0.0027777777777778\right) + \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + 0.91893853320467\right)\\

\end{array}
double f(double x, double y, double z) {
        double r21089302 = x;
        double r21089303 = 0.5;
        double r21089304 = r21089302 - r21089303;
        double r21089305 = log(r21089302);
        double r21089306 = r21089304 * r21089305;
        double r21089307 = r21089306 - r21089302;
        double r21089308 = 0.91893853320467;
        double r21089309 = r21089307 + r21089308;
        double r21089310 = y;
        double r21089311 = 0.0007936500793651;
        double r21089312 = r21089310 + r21089311;
        double r21089313 = z;
        double r21089314 = r21089312 * r21089313;
        double r21089315 = 0.0027777777777778;
        double r21089316 = r21089314 - r21089315;
        double r21089317 = r21089316 * r21089313;
        double r21089318 = 0.083333333333333;
        double r21089319 = r21089317 + r21089318;
        double r21089320 = r21089319 / r21089302;
        double r21089321 = r21089309 + r21089320;
        return r21089321;
}
↓
double f(double x, double y, double z) {
        double r21089322 = x;
        double r21089323 = 2.176139995006076e+35;
        bool r21089324 = r21089322 <= r21089323;
        double r21089325 = 0.083333333333333;
        double r21089326 = z;
        double r21089327 = y;
        double r21089328 = 0.0007936500793651;
        double r21089329 = r21089327 + r21089328;
        double r21089330 = r21089326 * r21089329;
        double r21089331 = 0.0027777777777778;
        double r21089332 = r21089330 - r21089331;
        double r21089333 = r21089326 * r21089332;
        double r21089334 = r21089325 + r21089333;
        double r21089335 = r21089334 / r21089322;
        double r21089336 = 0.5;
        double r21089337 = r21089322 - r21089336;
        double r21089338 = cbrt(r21089322);
        double r21089339 = r21089338 * r21089338;
        double r21089340 = log(r21089339);
        double r21089341 = r21089337 * r21089340;
        double r21089342 = log(r21089338);
        double r21089343 = r21089342 * r21089337;
        double r21089344 = r21089341 + r21089343;
        double r21089345 = r21089344 - r21089322;
        double r21089346 = 0.91893853320467;
        double r21089347 = r21089345 + r21089346;
        double r21089348 = r21089335 + r21089347;
        double r21089349 = r21089326 * r21089326;
        double r21089350 = r21089349 / r21089322;
        double r21089351 = r21089350 * r21089329;
        double r21089352 = r21089326 / r21089322;
        double r21089353 = r21089352 * r21089331;
        double r21089354 = r21089351 - r21089353;
        double r21089355 = r21089343 - r21089322;
        double r21089356 = r21089341 + r21089355;
        double r21089357 = r21089356 + r21089346;
        double r21089358 = r21089354 + r21089357;
        double r21089359 = r21089324 ? r21089348 : r21089358;
        return r21089359;
}

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

Original5.7
Target1.1
Herbie4.0
\[\left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.91893853320467 - x\right)\right) + \frac{0.083333333333333}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)\]

Derivation

  1. Split input into 2 regimes

  2. if x < 2.176139995006076e+35

    1. Initial program 0.2

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt0.2

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

    4. Applied log-prod0.2

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right)} - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

    5. Applied distribute-rgt-in0.2

      \[\leadsto \left(\left(\color{blue}{\left(\log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(x - 0.5\right) + \log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right)\right)} - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

    if 2.176139995006076e+35 < x

    1. Initial program 10.5

      \[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt10.5

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

    4. Applied log-prod10.6

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right)\right)} - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

    5. Applied distribute-lft-in10.5

      \[\leadsto \left(\left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x}\right)\right)} - x\right) + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

    6. Applied associate--l+10.5

      \[\leadsto \left(\color{blue}{\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x}\right) - x\right)\right)} + 0.91893853320467\right) + \frac{\left(\left(y + 0.0007936500793651\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.083333333333333}{x}\]

    7. Taylor expanded around inf 10.6

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x}\right) - x\right)\right) + 0.91893853320467\right) + \color{blue}{\left(\left(0.0007936500793651 \cdot \frac{{z}^{2}}{x} + \frac{{z}^{2} \cdot y}{x}\right) - 0.0027777777777778 \cdot \frac{z}{x}\right)}\]

    8. Simplified7.3

      \[\leadsto \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x}\right) - x\right)\right) + 0.91893853320467\right) + \color{blue}{\left(\frac{z \cdot z}{x} \cdot \left(0.0007936500793651 + y\right) - 0.0027777777777778 \cdot \frac{z}{x}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le 2.176139995006076 \cdot 10^{+35}:\\ \;\;\;\;\frac{0.083333333333333 + z \cdot \left(z \cdot \left(y + 0.0007936500793651\right) - 0.0027777777777778\right)}{x} + \left(\left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right)\right) - x\right) + 0.91893853320467\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z \cdot z}{x} \cdot \left(y + 0.0007936500793651\right) - \frac{z}{x} \cdot 0.0027777777777778\right) + \left(\left(\left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + \left(\log \left(\sqrt[3]{x}\right) \cdot \left(x - 0.5\right) - x\right)\right) + 0.91893853320467\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, B"

  :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)))