Average Error: 1.3 → 0.3
Time: 18.9s
Precision: 64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[\left(\frac{1}{\sqrt[3]{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right) \cdot \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\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) \cdot \frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}}
double f(double x, double y, double z, double t) {
        double r609457 = 1.0;
        double r609458 = 3.0;
        double r609459 = r609457 / r609458;
        double r609460 = x;
        double r609461 = y;
        double r609462 = 27.0;
        double r609463 = r609461 * r609462;
        double r609464 = r609460 / r609463;
        double r609465 = r609458 * r609464;
        double r609466 = z;
        double r609467 = 2.0;
        double r609468 = r609466 * r609467;
        double r609469 = r609465 / r609468;
        double r609470 = t;
        double r609471 = sqrt(r609470);
        double r609472 = r609469 * r609471;
        double r609473 = acos(r609472);
        double r609474 = r609459 * r609473;
        return r609474;
}
↓
double f(double x, double y, double z, double t) {
        double r609475 = 1.0;
        double r609476 = 3.0;
        double r609477 = cbrt(r609476);
        double r609478 = r609475 / r609477;
        double r609479 = x;
        double r609480 = y;
        double r609481 = 27.0;
        double r609482 = r609480 * r609481;
        double r609483 = r609479 / r609482;
        double r609484 = r609476 * r609483;
        double r609485 = z;
        double r609486 = 2.0;
        double r609487 = r609485 * r609486;
        double r609488 = r609484 / r609487;
        double r609489 = t;
        double r609490 = sqrt(r609489);
        double r609491 = r609488 * r609490;
        double r609492 = acos(r609491);
        double r609493 = r609478 * r609492;
        double r609494 = 1.0;
        double r609495 = r609477 * r609477;
        double r609496 = r609494 / r609495;
        double r609497 = r609493 * r609496;
        return r609497;
}

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-frac0.4

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

  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. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019195 
(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)))))