Average Error: 0.1 → 0.1
Time: 37.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(x \cdot \log y + z\right) + \left(a + t\right)\right) + \left(\left(\left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right)\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(x \cdot \log y + z\right) + \left(a + t\right)\right) + \left(\left(\left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4205262 = x;
        double r4205263 = y;
        double r4205264 = log(r4205263);
        double r4205265 = r4205262 * r4205264;
        double r4205266 = z;
        double r4205267 = r4205265 + r4205266;
        double r4205268 = t;
        double r4205269 = r4205267 + r4205268;
        double r4205270 = a;
        double r4205271 = r4205269 + r4205270;
        double r4205272 = b;
        double r4205273 = 0.5;
        double r4205274 = r4205272 - r4205273;
        double r4205275 = c;
        double r4205276 = log(r4205275);
        double r4205277 = r4205274 * r4205276;
        double r4205278 = r4205271 + r4205277;
        double r4205279 = i;
        double r4205280 = r4205263 * r4205279;
        double r4205281 = r4205278 + r4205280;
        return r4205281;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4205282 = x;
        double r4205283 = y;
        double r4205284 = log(r4205283);
        double r4205285 = r4205282 * r4205284;
        double r4205286 = z;
        double r4205287 = r4205285 + r4205286;
        double r4205288 = a;
        double r4205289 = t;
        double r4205290 = r4205288 + r4205289;
        double r4205291 = r4205287 + r4205290;
        double r4205292 = b;
        double r4205293 = 0.5;
        double r4205294 = r4205292 - r4205293;
        double r4205295 = c;
        double r4205296 = cbrt(r4205295);
        double r4205297 = log(r4205296);
        double r4205298 = r4205294 * r4205297;
        double r4205299 = r4205298 + r4205298;
        double r4205300 = 0.3333333333333333;
        double r4205301 = pow(r4205295, r4205300);
        double r4205302 = log(r4205301);
        double r4205303 = r4205294 * r4205302;
        double r4205304 = r4205299 + r4205303;
        double r4205305 = r4205291 + r4205304;
        double r4205306 = i;
        double r4205307 = r4205283 * r4205306;
        double r4205308 = r4205305 + r4205307;
        return r4205308;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  2. Using strategy rm

  3. Applied associate-+l+0.1

    \[\leadsto \left(\color{blue}{\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right)} + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + \left(b - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) \cdot \sqrt[3]{c}\right)}\right) + y \cdot i\]

  6. Applied log-prod0.1

    \[\leadsto \left(\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + \left(b - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) + \log \left(\sqrt[3]{c}\right)\right)}\right) + y \cdot i\]

  7. Applied distribute-lft-in0.1

    \[\leadsto \left(\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + \color{blue}{\left(\left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)}\right) + y \cdot i\]

  8. Simplified0.1

    \[\leadsto \left(\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + \left(\color{blue}{\left(\log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right) + \log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right)} + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + y \cdot i\]

  9. Simplified0.1

    \[\leadsto \left(\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + \left(\left(\log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right) + \log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right) + \color{blue}{\log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)}\right)\right) + y \cdot i\]
  10. Using strategy rm

  11. Applied pow1/30.1

    \[\leadsto \left(\left(\left(x \cdot \log y + z\right) + \left(t + a\right)\right) + \left(\left(\log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right) + \log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right) + \log \color{blue}{\left({c}^{\frac{1}{3}}\right)} \cdot \left(b - 0.5\right)\right)\right) + y \cdot i\]

  12. Final simplification0.1

    \[\leadsto \left(\left(\left(x \cdot \log y + z\right) + \left(a + t\right)\right) + \left(\left(\left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right)\right) + y \cdot i\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))