Average Error: 0.1 → 0.1
Time: 28.4s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[y \cdot i + \left(\left(x \cdot \left(\log \left(\sqrt[3]{y} \cdot {y}^{\frac{1}{3}}\right) + \log \left(\sqrt[3]{y}\right)\right) + \left(z + t\right)\right) + \left(a + \left(b - 0.5\right) \cdot \log c\right)\right)\]
\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(\left(x \cdot \left(\log \left(\sqrt[3]{y} \cdot {y}^{\frac{1}{3}}\right) + \log \left(\sqrt[3]{y}\right)\right) + \left(z + t\right)\right) + \left(a + \left(b - 0.5\right) \cdot \log c\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69377 = x;
        double r69378 = y;
        double r69379 = log(r69378);
        double r69380 = r69377 * r69379;
        double r69381 = z;
        double r69382 = r69380 + r69381;
        double r69383 = t;
        double r69384 = r69382 + r69383;
        double r69385 = a;
        double r69386 = r69384 + r69385;
        double r69387 = b;
        double r69388 = 0.5;
        double r69389 = r69387 - r69388;
        double r69390 = c;
        double r69391 = log(r69390);
        double r69392 = r69389 * r69391;
        double r69393 = r69386 + r69392;
        double r69394 = i;
        double r69395 = r69378 * r69394;
        double r69396 = r69393 + r69395;
        return r69396;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69397 = y;
        double r69398 = i;
        double r69399 = r69397 * r69398;
        double r69400 = x;
        double r69401 = cbrt(r69397);
        double r69402 = 0.3333333333333333;
        double r69403 = pow(r69397, r69402);
        double r69404 = r69401 * r69403;
        double r69405 = log(r69404);
        double r69406 = log(r69401);
        double r69407 = r69405 + r69406;
        double r69408 = r69400 * r69407;
        double r69409 = z;
        double r69410 = t;
        double r69411 = r69409 + r69410;
        double r69412 = r69408 + r69411;
        double r69413 = a;
        double r69414 = b;
        double r69415 = 0.5;
        double r69416 = r69414 - r69415;
        double r69417 = c;
        double r69418 = log(r69417);
        double r69419 = r69416 * r69418;
        double r69420 = r69413 + r69419;
        double r69421 = r69412 + r69420;
        double r69422 = r69399 + r69421;
        return r69422;
}

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. Using strategy rm

  7. Applied pow1/30.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \log \left(\sqrt[3]{y} \cdot \color{blue}{{y}^{\frac{1}{3}}}\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  8. Final simplification0.1

    \[\leadsto y \cdot i + \left(\left(x \cdot \left(\log \left(\sqrt[3]{y} \cdot {y}^{\frac{1}{3}}\right) + \log \left(\sqrt[3]{y}\right)\right) + \left(z + t\right)\right) + \left(a + \left(b - 0.5\right) \cdot \log c\right)\right)\]

Reproduce

herbie shell --seed 2019291 
(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)))