Average Error: 0.1 → 0.1
Time: 14.0s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70254 = x;
        double r70255 = y;
        double r70256 = log(r70255);
        double r70257 = r70254 * r70256;
        double r70258 = z;
        double r70259 = r70257 + r70258;
        double r70260 = t;
        double r70261 = r70259 + r70260;
        double r70262 = a;
        double r70263 = r70261 + r70262;
        double r70264 = b;
        double r70265 = 0.5;
        double r70266 = r70264 - r70265;
        double r70267 = c;
        double r70268 = log(r70267);
        double r70269 = r70266 * r70268;
        double r70270 = r70263 + r70269;
        double r70271 = i;
        double r70272 = r70255 * r70271;
        double r70273 = r70270 + r70272;
        return r70273;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70274 = x;
        double r70275 = 2.0;
        double r70276 = y;
        double r70277 = cbrt(r70276);
        double r70278 = log(r70277);
        double r70279 = r70275 * r70278;
        double r70280 = r70274 * r70279;
        double r70281 = r70274 * r70278;
        double r70282 = r70280 + r70281;
        double r70283 = z;
        double r70284 = r70282 + r70283;
        double r70285 = t;
        double r70286 = r70284 + r70285;
        double r70287 = a;
        double r70288 = r70286 + r70287;
        double r70289 = b;
        double r70290 = 0.5;
        double r70291 = r70289 - r70290;
        double r70292 = c;
        double r70293 = log(r70292);
        double r70294 = r70291 * r70293;
        double r70295 = r70288 + r70294;
        double r70296 = i;
        double r70297 = r70276 * r70296;
        double r70298 = r70295 + r70297;
        return r70298;
}

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 add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

    \[\leadsto \left(\left(\left(\left(\left(\color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  7. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))