Average Error: 6.0 → 6.0
Time: 10.2s
Precision: 64
\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]
↓
\[\left(\left(\log \left({x}^{\frac{1}{3}}\right) \cdot \left(3 \cdot x - 1.5\right) - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]
\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(\left(\log \left({x}^{\frac{1}{3}}\right) \cdot \left(3 \cdot x - 1.5\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}
double f(double x, double y, double z) {
        double r549399 = x;
        double r549400 = 0.5;
        double r549401 = r549399 - r549400;
        double r549402 = log(r549399);
        double r549403 = r549401 * r549402;
        double r549404 = r549403 - r549399;
        double r549405 = 0.91893853320467;
        double r549406 = r549404 + r549405;
        double r549407 = y;
        double r549408 = 0.0007936500793651;
        double r549409 = r549407 + r549408;
        double r549410 = z;
        double r549411 = r549409 * r549410;
        double r549412 = 0.0027777777777778;
        double r549413 = r549411 - r549412;
        double r549414 = r549413 * r549410;
        double r549415 = 0.083333333333333;
        double r549416 = r549414 + r549415;
        double r549417 = r549416 / r549399;
        double r549418 = r549406 + r549417;
        return r549418;
}
↓
double f(double x, double y, double z) {
        double r549419 = x;
        double r549420 = 0.3333333333333333;
        double r549421 = pow(r549419, r549420);
        double r549422 = log(r549421);
        double r549423 = 3.0;
        double r549424 = r549423 * r549419;
        double r549425 = 1.5;
        double r549426 = r549424 - r549425;
        double r549427 = r549422 * r549426;
        double r549428 = r549427 - r549419;
        double r549429 = 0.91893853320467;
        double r549430 = r549428 + r549429;
        double r549431 = y;
        double r549432 = 0.0007936500793651;
        double r549433 = r549431 + r549432;
        double r549434 = z;
        double r549435 = r549433 * r549434;
        double r549436 = 0.0027777777777778;
        double r549437 = r549435 - r549436;
        double r549438 = r549437 * r549434;
        double r549439 = 0.083333333333333;
        double r549440 = r549438 + r549439;
        double r549441 = r549440 / r549419;
        double r549442 = r549430 + r549441;
        return r549442;
}

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

Original6.0
Target1.2
Herbie6.0
\[\left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.9189385332046700050057097541866824030876 - x\right)\right) + \frac{0.08333333333333299564049667651488562114537}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) - 0.002777777777777800001512975569539776188321\right)\]

Derivation

  1. Initial program 6.0

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

  3. Applied add-cube-cbrt6.0

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

  4. Applied log-prod6.0

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

  5. Applied distribute-lft-in6.0

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

  6. Simplified6.0

    \[\leadsto \left(\left(\left(\color{blue}{\left(x - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{x}\right)\right)} + \left(x - 0.5\right) \cdot \log \left(\sqrt[3]{x}\right)\right) - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

  7. Taylor expanded around 0 6.0

    \[\leadsto \left(\left(\color{blue}{\left(3 \cdot \left(x \cdot \log \left({x}^{\frac{1}{3}}\right)\right) - 1.5 \cdot \log \left({x}^{\frac{1}{3}}\right)\right)} - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

  8. Simplified6.0

    \[\leadsto \left(\left(\color{blue}{\log \left({x}^{\frac{1}{3}}\right) \cdot \left(3 \cdot x - 1.5\right)} - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

  9. Final simplification6.0

    \[\leadsto \left(\left(\log \left({x}^{\frac{1}{3}}\right) \cdot \left(3 \cdot x - 1.5\right) - x\right) + 0.9189385332046700050057097541866824030876\right) + \frac{\left(\left(y + 7.936500793651000149400709382518925849581 \cdot 10^{-4}\right) \cdot z - 0.002777777777777800001512975569539776188321\right) \cdot z + 0.08333333333333299564049667651488562114537}{x}\]

Reproduce

herbie shell --seed 2020001 
(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)))