Average Error: 0.1 → 0.1
Time: 22.7s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left(\left(\sqrt[3]{\sqrt[3]{c}} \cdot \sqrt[3]{\sqrt[3]{c}}\right) \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + y \cdot i\]
\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(2 \cdot \log \left(\left(\sqrt[3]{\sqrt[3]{c}} \cdot \sqrt[3]{\sqrt[3]{c}}\right) \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left(\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 r102356 = x;
        double r102357 = y;
        double r102358 = log(r102357);
        double r102359 = r102356 * r102358;
        double r102360 = z;
        double r102361 = r102359 + r102360;
        double r102362 = t;
        double r102363 = r102361 + r102362;
        double r102364 = a;
        double r102365 = r102363 + r102364;
        double r102366 = b;
        double r102367 = 0.5;
        double r102368 = r102366 - r102367;
        double r102369 = c;
        double r102370 = log(r102369);
        double r102371 = r102368 * r102370;
        double r102372 = r102365 + r102371;
        double r102373 = i;
        double r102374 = r102357 * r102373;
        double r102375 = r102372 + r102374;
        return r102375;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r102376 = x;
        double r102377 = y;
        double r102378 = log(r102377);
        double r102379 = r102376 * r102378;
        double r102380 = z;
        double r102381 = r102379 + r102380;
        double r102382 = t;
        double r102383 = r102381 + r102382;
        double r102384 = a;
        double r102385 = r102383 + r102384;
        double r102386 = 2.0;
        double r102387 = c;
        double r102388 = cbrt(r102387);
        double r102389 = cbrt(r102388);
        double r102390 = r102389 * r102389;
        double r102391 = r102390 * r102389;
        double r102392 = log(r102391);
        double r102393 = r102386 * r102392;
        double r102394 = b;
        double r102395 = 0.5;
        double r102396 = r102394 - r102395;
        double r102397 = r102393 * r102396;
        double r102398 = log(r102388);
        double r102399 = r102396 * r102398;
        double r102400 = r102397 + r102399;
        double r102401 = r102385 + r102400;
        double r102402 = i;
        double r102403 = r102377 * r102402;
        double r102404 = r102401 + r102403;
        return r102404;
}

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

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

  8. Applied add-cube-cbrt0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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)))