Average Error: 0.1 → 0.1
Time: 39.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(z + \left(\log \left(\sqrt[3]{y}\right) \cdot x + x \cdot \left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)\right)\right)\right)\right) + \left(t + a\right)\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i\]
\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(z + \left(\log \left(\sqrt[3]{y}\right) \cdot x + x \cdot \left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)\right)\right)\right)\right) + \left(t + a\right)\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 r4695451 = x;
        double r4695452 = y;
        double r4695453 = log(r4695452);
        double r4695454 = r4695451 * r4695453;
        double r4695455 = z;
        double r4695456 = r4695454 + r4695455;
        double r4695457 = t;
        double r4695458 = r4695456 + r4695457;
        double r4695459 = a;
        double r4695460 = r4695458 + r4695459;
        double r4695461 = b;
        double r4695462 = 0.5;
        double r4695463 = r4695461 - r4695462;
        double r4695464 = c;
        double r4695465 = log(r4695464);
        double r4695466 = r4695463 * r4695465;
        double r4695467 = r4695460 + r4695466;
        double r4695468 = i;
        double r4695469 = r4695452 * r4695468;
        double r4695470 = r4695467 + r4695469;
        return r4695470;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4695471 = z;
        double r4695472 = y;
        double r4695473 = cbrt(r4695472);
        double r4695474 = log(r4695473);
        double r4695475 = x;
        double r4695476 = r4695474 * r4695475;
        double r4695477 = cbrt(r4695473);
        double r4695478 = r4695477 * r4695477;
        double r4695479 = r4695477 * r4695478;
        double r4695480 = log(r4695479);
        double r4695481 = r4695474 + r4695480;
        double r4695482 = r4695475 * r4695481;
        double r4695483 = r4695476 + r4695482;
        double r4695484 = r4695471 + r4695483;
        double r4695485 = t;
        double r4695486 = a;
        double r4695487 = r4695485 + r4695486;
        double r4695488 = r4695484 + r4695487;
        double r4695489 = c;
        double r4695490 = log(r4695489);
        double r4695491 = b;
        double r4695492 = 0.5;
        double r4695493 = r4695491 - r4695492;
        double r4695494 = r4695490 * r4695493;
        double r4695495 = r4695488 + r4695494;
        double r4695496 = i;
        double r4695497 = r4695472 * r4695496;
        double r4695498 = r4695495 + r4695497;
        return r4695498;
}

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 associate-+l+0.1

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

  5. Applied add-cube-cbrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-rgt-in0.1

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

  8. Simplified0.1

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

  10. Applied add-cube-cbrt0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 
(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)))