Average Error: 5.8 → 6.0
Time: 15.2s
Precision: 64
\[\left(\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467001\right) + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]
↓
\[\sqrt{\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467001} \cdot \sqrt{\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467001} + \frac{\left(\left(y + 7.93650079365100015 \cdot 10^{-4}\right) \cdot z - 0.0027777777777778\right) \cdot z + 0.0833333333333329956}{x}\]
\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}
↓
\sqrt{\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467001} \cdot \sqrt{\left(\left(x - 0.5\right) \cdot \log x - x\right) + 0.91893853320467001} + \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 r620301 = x;
        double r620302 = 0.5;
        double r620303 = r620301 - r620302;
        double r620304 = log(r620301);
        double r620305 = r620303 * r620304;
        double r620306 = r620305 - r620301;
        double r620307 = 0.91893853320467;
        double r620308 = r620306 + r620307;
        double r620309 = y;
        double r620310 = 0.0007936500793651;
        double r620311 = r620309 + r620310;
        double r620312 = z;
        double r620313 = r620311 * r620312;
        double r620314 = 0.0027777777777778;
        double r620315 = r620313 - r620314;
        double r620316 = r620315 * r620312;
        double r620317 = 0.083333333333333;
        double r620318 = r620316 + r620317;
        double r620319 = r620318 / r620301;
        double r620320 = r620308 + r620319;
        return r620320;
}
↓
double f(double x, double y, double z) {
        double r620321 = x;
        double r620322 = 0.5;
        double r620323 = r620321 - r620322;
        double r620324 = log(r620321);
        double r620325 = r620323 * r620324;
        double r620326 = r620325 - r620321;
        double r620327 = 0.91893853320467;
        double r620328 = r620326 + r620327;
        double r620329 = sqrt(r620328);
        double r620330 = r620329 * r620329;
        double r620331 = y;
        double r620332 = 0.0007936500793651;
        double r620333 = r620331 + r620332;
        double r620334 = z;
        double r620335 = r620333 * r620334;
        double r620336 = 0.0027777777777778;
        double r620337 = r620335 - r620336;
        double r620338 = r620337 * r620334;
        double r620339 = 0.083333333333333;
        double r620340 = r620338 + r620339;
        double r620341 = r620340 / r620321;
        double r620342 = r620330 + r620341;
        return r620342;
}

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
Target1.0
Herbie6.0
\[\left(\left(\left(x - 0.5\right) \cdot \log x + \left(0.91893853320467001 - x\right)\right) + \frac{0.0833333333333329956}{x}\right) + \frac{z}{x} \cdot \left(z \cdot \left(y + 7.93650079365100015 \cdot 10^{-4}\right) - 0.0027777777777778\right)\]

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-sqr-sqrt6.0

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

  4. Final simplification6.0

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

Reproduce

herbie shell --seed 2020046 
(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)))