Average Error: 0.1 → 0.1
Time: 28.5s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(\left(\left(\left(\left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right) + \left(x \cdot 2\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right) + \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x\right) + z\right) + t\right) + a\right)\right)\]
\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
↓
y \cdot i + \left(\log c \cdot \left(b - 0.5\right) + \left(\left(\left(\left(\left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right) + \left(x \cdot 2\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right) + \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x\right) + z\right) + t\right) + a\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80220 = x;
        double r80221 = y;
        double r80222 = log(r80221);
        double r80223 = r80220 * r80222;
        double r80224 = z;
        double r80225 = r80223 + r80224;
        double r80226 = t;
        double r80227 = r80225 + r80226;
        double r80228 = a;
        double r80229 = r80227 + r80228;
        double r80230 = b;
        double r80231 = 0.5;
        double r80232 = r80230 - r80231;
        double r80233 = c;
        double r80234 = log(r80233);
        double r80235 = r80232 * r80234;
        double r80236 = r80229 + r80235;
        double r80237 = i;
        double r80238 = r80221 * r80237;
        double r80239 = r80236 + r80238;
        return r80239;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80240 = y;
        double r80241 = i;
        double r80242 = r80240 * r80241;
        double r80243 = c;
        double r80244 = log(r80243);
        double r80245 = b;
        double r80246 = 0.5;
        double r80247 = r80245 - r80246;
        double r80248 = r80244 * r80247;
        double r80249 = x;
        double r80250 = cbrt(r80240);
        double r80251 = cbrt(r80250);
        double r80252 = log(r80251);
        double r80253 = r80249 * r80252;
        double r80254 = 2.0;
        double r80255 = r80249 * r80254;
        double r80256 = r80255 * r80252;
        double r80257 = r80253 + r80256;
        double r80258 = log(r80250);
        double r80259 = r80254 * r80258;
        double r80260 = r80259 * r80249;
        double r80261 = r80257 + r80260;
        double r80262 = z;
        double r80263 = r80261 + r80262;
        double r80264 = t;
        double r80265 = r80263 + r80264;
        double r80266 = a;
        double r80267 = r80265 + r80266;
        double r80268 = r80248 + r80267;
        double r80269 = r80242 + r80268;
        return r80269;
}

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. Using strategy rm

  8. Applied add-cube-cbrt0.1

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

  9. Applied log-prod0.1

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

  10. Applied distribute-lft-in0.1

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

  11. Simplified0.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019195 
(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)))