Average Error: 1.2 → 0.3
Time: 4.7s
Precision: binary64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[1 \cdot \left(\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \frac{\cos^{-1} \left(x \cdot \left(3 \cdot \frac{\sqrt{t}}{y \cdot \left(27 \cdot \left(z \cdot 2\right)\right)}\right)\right)}{\sqrt[3]{3}}\right)\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
1 \cdot \left(\frac{1}{\sqrt[3]{3} \cdot \sqrt[3]{3}} \cdot \frac{\cos^{-1} \left(x \cdot \left(3 \cdot \frac{\sqrt{t}}{y \cdot \left(27 \cdot \left(z \cdot 2\right)\right)}\right)\right)}{\sqrt[3]{3}}\right)
(FPCore (x y z t)
 :precision binary64
 (* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t)))))
↓
(FPCore (x y z t)
 :precision binary64
 (*
  1.0
  (*
   (/ 1.0 (* (cbrt 3.0) (cbrt 3.0)))
   (/ (acos (* x (* 3.0 (/ (sqrt t) (* y (* 27.0 (* z 2.0))))))) (cbrt 3.0)))))
double code(double x, double y, double z, double t) {
	return ((double) ((1.0 / 3.0) * ((double) acos(((double) ((((double) (3.0 * (x / ((double) (y * 27.0))))) / ((double) (z * 2.0))) * ((double) sqrt(t))))))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (1.0 * ((double) ((1.0 / ((double) (((double) cbrt(3.0)) * ((double) cbrt(3.0))))) * (((double) acos(((double) (x * ((double) (3.0 * (((double) sqrt(t)) / ((double) (y * ((double) (27.0 * ((double) (z * 2.0))))))))))))) / ((double) cbrt(3.0)))))));
}

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

Original1.2
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 1.2

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

  2. Simplified1.2

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

  4. Applied add-cube-cbrt1.2

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

  5. Applied *-un-lft-identity1.2

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020198 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, D"
  :precision binary64

  :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)))))