Average Error: 0.1 → 0.1
Time: 32.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(\left(\left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right)\right) + z\right)\right)\right)\right) + y \cdot i\]
\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(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(\left(\left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right)\right) + z\right)\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 r3840284 = x;
        double r3840285 = y;
        double r3840286 = log(r3840285);
        double r3840287 = r3840284 * r3840286;
        double r3840288 = z;
        double r3840289 = r3840287 + r3840288;
        double r3840290 = t;
        double r3840291 = r3840289 + r3840290;
        double r3840292 = a;
        double r3840293 = r3840291 + r3840292;
        double r3840294 = b;
        double r3840295 = 0.5;
        double r3840296 = r3840294 - r3840295;
        double r3840297 = c;
        double r3840298 = log(r3840297);
        double r3840299 = r3840296 * r3840298;
        double r3840300 = r3840293 + r3840299;
        double r3840301 = i;
        double r3840302 = r3840285 * r3840301;
        double r3840303 = r3840300 + r3840302;
        return r3840303;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3840304 = c;
        double r3840305 = log(r3840304);
        double r3840306 = b;
        double r3840307 = 0.5;
        double r3840308 = r3840306 - r3840307;
        double r3840309 = r3840305 * r3840308;
        double r3840310 = a;
        double r3840311 = t;
        double r3840312 = y;
        double r3840313 = cbrt(r3840312);
        double r3840314 = cbrt(r3840313);
        double r3840315 = log(r3840314);
        double r3840316 = x;
        double r3840317 = r3840315 * r3840316;
        double r3840318 = r3840313 * r3840313;
        double r3840319 = cbrt(r3840318);
        double r3840320 = log(r3840319);
        double r3840321 = r3840316 * r3840320;
        double r3840322 = r3840317 + r3840321;
        double r3840323 = log(r3840313);
        double r3840324 = r3840323 * r3840316;
        double r3840325 = r3840324 + r3840324;
        double r3840326 = r3840322 + r3840325;
        double r3840327 = z;
        double r3840328 = r3840326 + r3840327;
        double r3840329 = r3840311 + r3840328;
        double r3840330 = r3840310 + r3840329;
        double r3840331 = r3840309 + r3840330;
        double r3840332 = i;
        double r3840333 = r3840312 * r3840332;
        double r3840334 = r3840331 + r3840333;
        return r3840334;
}

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

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied cbrt-prod0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-rgt-in0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(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)))