Average Error: 0.1 → 0.1
Time: 11.3s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right)\right) + y \cdot i\]
\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)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\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 r67521 = x;
        double r67522 = y;
        double r67523 = log(r67522);
        double r67524 = r67521 * r67523;
        double r67525 = z;
        double r67526 = r67524 + r67525;
        double r67527 = t;
        double r67528 = r67526 + r67527;
        double r67529 = a;
        double r67530 = r67528 + r67529;
        double r67531 = b;
        double r67532 = 0.5;
        double r67533 = r67531 - r67532;
        double r67534 = c;
        double r67535 = log(r67534);
        double r67536 = r67533 * r67535;
        double r67537 = r67530 + r67536;
        double r67538 = i;
        double r67539 = r67522 * r67538;
        double r67540 = r67537 + r67539;
        return r67540;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r67541 = x;
        double r67542 = y;
        double r67543 = log(r67542);
        double r67544 = r67541 * r67543;
        double r67545 = z;
        double r67546 = r67544 + r67545;
        double r67547 = t;
        double r67548 = r67546 + r67547;
        double r67549 = a;
        double r67550 = r67548 + r67549;
        double r67551 = b;
        double r67552 = 0.5;
        double r67553 = r67551 - r67552;
        double r67554 = 2.0;
        double r67555 = c;
        double r67556 = cbrt(r67555);
        double r67557 = log(r67556);
        double r67558 = r67554 * r67557;
        double r67559 = r67553 * r67558;
        double r67560 = 0.3333333333333333;
        double r67561 = pow(r67555, r67560);
        double r67562 = log(r67561);
        double r67563 = r67553 * r67562;
        double r67564 = r67559 + r67563;
        double r67565 = r67550 + r67564;
        double r67566 = i;
        double r67567 = r67542 * r67566;
        double r67568 = r67565 + r67567;
        return r67568;
}

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 pow1/30.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \color{blue}{\left({c}^{\frac{1}{3}}\right)}\right)\right) + y \cdot i\]

  9. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right)\right) + y \cdot i\]

Reproduce

herbie shell --seed 2020025 
(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)))