Average Error: 1.3 → 0.3
Time: 42.6s
Precision: 64
\[\frac{1.0}{3.0} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]
↓
\[\left(\frac{1.0}{\sqrt[3]{3.0}} \cdot \cos^{-1} \left(\frac{\frac{x}{27.0 \cdot y} \cdot 3.0}{2.0 \cdot z} \cdot \sqrt{t}\right)\right) \cdot \frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}}\]
\frac{1.0}{3.0} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)
↓
\left(\frac{1.0}{\sqrt[3]{3.0}} \cdot \cos^{-1} \left(\frac{\frac{x}{27.0 \cdot y} \cdot 3.0}{2.0 \cdot z} \cdot \sqrt{t}\right)\right) \cdot \frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}}
double f(double x, double y, double z, double t) {
        double r34229542 = 1.0;
        double r34229543 = 3.0;
        double r34229544 = r34229542 / r34229543;
        double r34229545 = x;
        double r34229546 = y;
        double r34229547 = 27.0;
        double r34229548 = r34229546 * r34229547;
        double r34229549 = r34229545 / r34229548;
        double r34229550 = r34229543 * r34229549;
        double r34229551 = z;
        double r34229552 = 2.0;
        double r34229553 = r34229551 * r34229552;
        double r34229554 = r34229550 / r34229553;
        double r34229555 = t;
        double r34229556 = sqrt(r34229555);
        double r34229557 = r34229554 * r34229556;
        double r34229558 = acos(r34229557);
        double r34229559 = r34229544 * r34229558;
        return r34229559;
}
↓
double f(double x, double y, double z, double t) {
        double r34229560 = 1.0;
        double r34229561 = 3.0;
        double r34229562 = cbrt(r34229561);
        double r34229563 = r34229560 / r34229562;
        double r34229564 = x;
        double r34229565 = 27.0;
        double r34229566 = y;
        double r34229567 = r34229565 * r34229566;
        double r34229568 = r34229564 / r34229567;
        double r34229569 = r34229568 * r34229561;
        double r34229570 = 2.0;
        double r34229571 = z;
        double r34229572 = r34229570 * r34229571;
        double r34229573 = r34229569 / r34229572;
        double r34229574 = t;
        double r34229575 = sqrt(r34229574);
        double r34229576 = r34229573 * r34229575;
        double r34229577 = acos(r34229576);
        double r34229578 = r34229563 * r34229577;
        double r34229579 = 1.0;
        double r34229580 = r34229562 * r34229562;
        double r34229581 = r34229579 / r34229580;
        double r34229582 = r34229578 * r34229581;
        return r34229582;
}

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
\[\frac{\cos^{-1} \left(\frac{\frac{x}{27.0}}{y \cdot z} \cdot \frac{\sqrt{t}}{\frac{2.0}{3.0}}\right)}{3.0}\]

Derivation

  1. Initial program 1.3

    \[\frac{1.0}{3.0} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.3

    \[\leadsto \frac{1.0}{\color{blue}{\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \sqrt[3]{3.0}}} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]

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

    \[\leadsto \frac{\color{blue}{1 \cdot 1.0}}{\left(\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}\right) \cdot \sqrt[3]{3.0}} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]

  5. Applied times-frac0.3

    \[\leadsto \color{blue}{\left(\frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \frac{1.0}{\sqrt[3]{3.0}}\right)} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\]

  6. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}} \cdot \left(\frac{1.0}{\sqrt[3]{3.0}} \cdot \cos^{-1} \left(\frac{3.0 \cdot \frac{x}{y \cdot 27.0}}{z \cdot 2.0} \cdot \sqrt{t}\right)\right)}\]

  7. Final simplification0.3

    \[\leadsto \left(\frac{1.0}{\sqrt[3]{3.0}} \cdot \cos^{-1} \left(\frac{\frac{x}{27.0 \cdot y} \cdot 3.0}{2.0 \cdot z} \cdot \sqrt{t}\right)\right) \cdot \frac{1}{\sqrt[3]{3.0} \cdot \sqrt[3]{3.0}}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(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)))))