Average Error: 0.1 → 0.1
Time: 39.6s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{\sqrt{y}} \cdot \sqrt[3]{\sqrt{y}}\right)\right) + \log \left(\left(\sqrt[3]{{y}^{\frac{1}{3}}} \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right) \cdot x\right) + z\right)\right)\right)\right)\]
\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
↓
i \cdot y + \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(\left(x \cdot \left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{\sqrt{y}} \cdot \sqrt[3]{\sqrt{y}}\right)\right) + \log \left(\left(\sqrt[3]{{y}^{\frac{1}{3}}} \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right) \cdot x\right) + z\right)\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3571467 = x;
        double r3571468 = y;
        double r3571469 = log(r3571468);
        double r3571470 = r3571467 * r3571469;
        double r3571471 = z;
        double r3571472 = r3571470 + r3571471;
        double r3571473 = t;
        double r3571474 = r3571472 + r3571473;
        double r3571475 = a;
        double r3571476 = r3571474 + r3571475;
        double r3571477 = b;
        double r3571478 = 0.5;
        double r3571479 = r3571477 - r3571478;
        double r3571480 = c;
        double r3571481 = log(r3571480);
        double r3571482 = r3571479 * r3571481;
        double r3571483 = r3571476 + r3571482;
        double r3571484 = i;
        double r3571485 = r3571468 * r3571484;
        double r3571486 = r3571483 + r3571485;
        return r3571486;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3571487 = i;
        double r3571488 = y;
        double r3571489 = r3571487 * r3571488;
        double r3571490 = c;
        double r3571491 = log(r3571490);
        double r3571492 = b;
        double r3571493 = 0.5;
        double r3571494 = r3571492 - r3571493;
        double r3571495 = r3571491 * r3571494;
        double r3571496 = a;
        double r3571497 = t;
        double r3571498 = x;
        double r3571499 = cbrt(r3571488);
        double r3571500 = log(r3571499);
        double r3571501 = sqrt(r3571488);
        double r3571502 = cbrt(r3571501);
        double r3571503 = r3571502 * r3571502;
        double r3571504 = log(r3571503);
        double r3571505 = r3571500 + r3571504;
        double r3571506 = r3571498 * r3571505;
        double r3571507 = 0.3333333333333333;
        double r3571508 = pow(r3571488, r3571507);
        double r3571509 = cbrt(r3571508);
        double r3571510 = r3571509 * r3571509;
        double r3571511 = r3571510 * r3571509;
        double r3571512 = log(r3571511);
        double r3571513 = r3571512 * r3571498;
        double r3571514 = r3571506 + r3571513;
        double r3571515 = z;
        double r3571516 = r3571514 + r3571515;
        double r3571517 = r3571497 + r3571516;
        double r3571518 = r3571496 + r3571517;
        double r3571519 = r3571495 + r3571518;
        double r3571520 = r3571489 + r3571519;
        return r3571520;
}

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-rgt-in0.1

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

  6. Simplified0.1

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

  8. Applied add-sqr-sqrt0.1

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

  9. Applied cbrt-prod0.1

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

  11. Applied pow1/30.1

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

  13. Applied add-cube-cbrt0.1

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

  14. Final simplification0.1

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

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)))