Average Error: 0.1 → 0.1
Time: 14.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right) + \log \left(\sqrt[3]{\sqrt[3]{c} \cdot \sqrt[3]{c}}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{c}}\right)\right)\right) + y \cdot i\]
\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(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right) + \log \left(\sqrt[3]{\sqrt[3]{c} \cdot \sqrt[3]{c}}\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{\sqrt[3]{c}}\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 r91281 = x;
        double r91282 = y;
        double r91283 = log(r91282);
        double r91284 = r91281 * r91283;
        double r91285 = z;
        double r91286 = r91284 + r91285;
        double r91287 = t;
        double r91288 = r91286 + r91287;
        double r91289 = a;
        double r91290 = r91288 + r91289;
        double r91291 = b;
        double r91292 = 0.5;
        double r91293 = r91291 - r91292;
        double r91294 = c;
        double r91295 = log(r91294);
        double r91296 = r91293 * r91295;
        double r91297 = r91290 + r91296;
        double r91298 = i;
        double r91299 = r91282 * r91298;
        double r91300 = r91297 + r91299;
        return r91300;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r91301 = x;
        double r91302 = y;
        double r91303 = log(r91302);
        double r91304 = r91301 * r91303;
        double r91305 = z;
        double r91306 = r91304 + r91305;
        double r91307 = t;
        double r91308 = r91306 + r91307;
        double r91309 = a;
        double r91310 = r91308 + r91309;
        double r91311 = b;
        double r91312 = 0.5;
        double r91313 = r91311 - r91312;
        double r91314 = 2.0;
        double r91315 = c;
        double r91316 = cbrt(r91315);
        double r91317 = log(r91316);
        double r91318 = r91314 * r91317;
        double r91319 = r91316 * r91316;
        double r91320 = cbrt(r91319);
        double r91321 = log(r91320);
        double r91322 = r91318 + r91321;
        double r91323 = r91313 * r91322;
        double r91324 = cbrt(r91316);
        double r91325 = log(r91324);
        double r91326 = r91313 * r91325;
        double r91327 = r91323 + r91326;
        double r91328 = r91310 + r91327;
        double r91329 = i;
        double r91330 = r91302 * r91329;
        double r91331 = r91328 + r91330;
        return r91331;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied cbrt-prod0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Applied associate-+r+0.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020035 
(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)))