Average Error: 1.3 → 0.3
Time: 22.7s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\frac{1 \cdot \cos^{-1} \left(\log \left(e^{\frac{\frac{x}{y \cdot 27} \cdot 3}{2 \cdot z} \cdot \sqrt{t}}\right)\right)}{\sqrt[3]{3}} \cdot \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\frac{1 \cdot \cos^{-1} \left(\log \left(e^{\frac{\frac{x}{y \cdot 27} \cdot 3}{2 \cdot z} \cdot \sqrt{t}}\right)\right)}{\sqrt[3]{3}} \cdot \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}
double f(double x, double y, double z, double t) {
        double r36698406 = 1.0;
        double r36698407 = 3.0;
        double r36698408 = r36698406 / r36698407;
        double r36698409 = x;
        double r36698410 = y;
        double r36698411 = 27.0;
        double r36698412 = r36698410 * r36698411;
        double r36698413 = r36698409 / r36698412;
        double r36698414 = r36698407 * r36698413;
        double r36698415 = z;
        double r36698416 = 2.0;
        double r36698417 = r36698415 * r36698416;
        double r36698418 = r36698414 / r36698417;
        double r36698419 = t;
        double r36698420 = sqrt(r36698419);
        double r36698421 = r36698418 * r36698420;
        double r36698422 = acos(r36698421);
        double r36698423 = r36698408 * r36698422;
        return r36698423;
}
↓
double f(double x, double y, double z, double t) {
        double r36698424 = 1.0;
        double r36698425 = x;
        double r36698426 = y;
        double r36698427 = 27.0;
        double r36698428 = r36698426 * r36698427;
        double r36698429 = r36698425 / r36698428;
        double r36698430 = 3.0;
        double r36698431 = r36698429 * r36698430;
        double r36698432 = 2.0;
        double r36698433 = z;
        double r36698434 = r36698432 * r36698433;
        double r36698435 = r36698431 / r36698434;
        double r36698436 = t;
        double r36698437 = sqrt(r36698436);
        double r36698438 = r36698435 * r36698437;
        double r36698439 = exp(r36698438);
        double r36698440 = log(r36698439);
        double r36698441 = acos(r36698440);
        double r36698442 = r36698424 * r36698441;
        double r36698443 = cbrt(r36698430);
        double r36698444 = r36698442 / r36698443;
        double r36698445 = 1.0;
        double r36698446 = r36698443 * r36698443;
        double r36698447 = r36698445 / r36698446;
        double r36698448 = r36698444 * r36698447;
        return r36698448;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.3
Target1.2
Herbie0.3
\[\frac{\cos^{-1} \left(\frac{\frac{x}{27}}{y \cdot z} \cdot \frac{\sqrt{t}}{\frac{2}{3}}\right)}{3}\]

Derivation

  1. Initial program 1.3

    \[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.3

    \[\leadsto \frac{1}{\color{blue}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]

  4. Applied *-un-lft-identity1.3

    \[\leadsto \frac{\color{blue}{1 \cdot 1}}{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]

  5. Applied times-frac0.3

    \[\leadsto \color{blue}{\left(\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \frac{1}{\sqrt[3]{3}}\right)} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]

  6. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)}\]
  7. Using strategy rm

  8. Applied associate-*l/0.3

    \[\leadsto \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \color{blue}{\frac{1 \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)}{\sqrt[3]{3}}}\]
  9. Using strategy rm

  10. Applied add-log-exp0.3

    \[\leadsto \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \frac{1 \cdot \cos^{-1} \color{blue}{\left(\log \left(e^{\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}}\right)\right)}}{\sqrt[3]{3}}\]

  11. Final simplification0.3

    \[\leadsto \frac{1 \cdot \cos^{-1} \left(\log \left(e^{\frac{\frac{x}{y \cdot 27} \cdot 3}{2 \cdot z} \cdot \sqrt{t}}\right)\right)}{\sqrt[3]{3}} \cdot \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, D"

  :herbie-target
  (/ (acos (* (/ (/ x 27.0) (* y z)) (/ (sqrt t) (/ 2.0 3.0)))) 3.0)

  (* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t)))))