Average Error: 0.1 → 0.1
Time: 1.2m
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(z + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)\right)\right) + \log \left(\sqrt[3]{y}\right) \cdot x\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i\]
\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(z + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)\right)\right) + \log \left(\sqrt[3]{y}\right) \cdot x\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4202379 = x;
        double r4202380 = y;
        double r4202381 = log(r4202380);
        double r4202382 = r4202379 * r4202381;
        double r4202383 = z;
        double r4202384 = r4202382 + r4202383;
        double r4202385 = t;
        double r4202386 = r4202384 + r4202385;
        double r4202387 = a;
        double r4202388 = r4202386 + r4202387;
        double r4202389 = b;
        double r4202390 = 0.5;
        double r4202391 = r4202389 - r4202390;
        double r4202392 = c;
        double r4202393 = log(r4202392);
        double r4202394 = r4202391 * r4202393;
        double r4202395 = r4202388 + r4202394;
        double r4202396 = i;
        double r4202397 = r4202380 * r4202396;
        double r4202398 = r4202395 + r4202397;
        return r4202398;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4202399 = z;
        double r4202400 = y;
        double r4202401 = cbrt(r4202400);
        double r4202402 = log(r4202401);
        double r4202403 = x;
        double r4202404 = r4202402 * r4202403;
        double r4202405 = cbrt(r4202401);
        double r4202406 = r4202405 * r4202405;
        double r4202407 = r4202405 * r4202406;
        double r4202408 = log(r4202407);
        double r4202409 = r4202403 * r4202408;
        double r4202410 = r4202404 + r4202409;
        double r4202411 = r4202410 + r4202404;
        double r4202412 = r4202399 + r4202411;
        double r4202413 = t;
        double r4202414 = r4202412 + r4202413;
        double r4202415 = a;
        double r4202416 = r4202414 + r4202415;
        double r4202417 = c;
        double r4202418 = log(r4202417);
        double r4202419 = b;
        double r4202420 = 0.5;
        double r4202421 = r4202419 - r4202420;
        double r4202422 = r4202418 * r4202421;
        double r4202423 = r4202416 + r4202422;
        double r4202424 = i;
        double r4202425 = r4202400 * r4202424;
        double r4202426 = r4202423 + r4202425;
        return r4202426;
}

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

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(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)))