Average Error: 1.3 → 1.5
Time: 4.1s
Precision: binary64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[0.3333333333333333 \cdot \cos^{-1} \left(x \cdot \left(0.05555555555555555 \cdot \left(\frac{\left|\sqrt[3]{t}\right|}{y} \cdot \frac{\sqrt{\sqrt[3]{t}}}{z}\right)\right)\right)\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
0.3333333333333333 \cdot \cos^{-1} \left(x \cdot \left(0.05555555555555555 \cdot \left(\frac{\left|\sqrt[3]{t}\right|}{y} \cdot \frac{\sqrt{\sqrt[3]{t}}}{z}\right)\right)\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
 (*
  0.3333333333333333
  (acos
   (*
    x
    (* 0.05555555555555555 (* (/ (fabs (cbrt t)) y) (/ (sqrt (cbrt t)) z)))))))
double code(double x, double y, double z, double t) {
	return (1.0 / 3.0) * acos(((3.0 * (x / (y * 27.0))) / (z * 2.0)) * sqrt(t));
}
↓
double code(double x, double y, double z, double t) {
	return 0.3333333333333333 * acos(x * (0.05555555555555555 * ((fabs(cbrt(t)) / y) * (sqrt(cbrt(t)) / z))));
}

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
Herbie1.5
\[\frac{\cos^{-1} \left(\frac{\frac{x}{27}}{y \cdot z} \cdot \frac{\sqrt{t}}{\frac{2}{3}}\right)}{3}\]

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. Simplified1.2

    \[\leadsto \color{blue}{0.3333333333333333 \cdot \cos^{-1} \left(x \cdot \left(0.05555555555555555 \cdot \frac{\sqrt{t}}{y \cdot z}\right)\right)}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt_binary641.2

    \[\leadsto 0.3333333333333333 \cdot \cos^{-1} \left(x \cdot \left(0.05555555555555555 \cdot \frac{\sqrt{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}}{y \cdot z}\right)\right)\]

  5. Applied sqrt-prod_binary641.2

    \[\leadsto 0.3333333333333333 \cdot \cos^{-1} \left(x \cdot \left(0.05555555555555555 \cdot \frac{\color{blue}{\sqrt{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \sqrt{\sqrt[3]{t}}}}{y \cdot z}\right)\right)\]

  6. Applied times-frac_binary641.5

    \[\leadsto 0.3333333333333333 \cdot \cos^{-1} \left(x \cdot \left(0.05555555555555555 \cdot \color{blue}{\left(\frac{\sqrt{\sqrt[3]{t} \cdot \sqrt[3]{t}}}{y} \cdot \frac{\sqrt{\sqrt[3]{t}}}{z}\right)}\right)\right)\]

  7. Simplified1.5

    \[\leadsto 0.3333333333333333 \cdot \cos^{-1} \left(x \cdot \left(0.05555555555555555 \cdot \left(\color{blue}{\frac{\left|\sqrt[3]{t}\right|}{y}} \cdot \frac{\sqrt{\sqrt[3]{t}}}{z}\right)\right)\right)\]

  8. Final simplification1.5

    \[\leadsto 0.3333333333333333 \cdot \cos^{-1} \left(x \cdot \left(0.05555555555555555 \cdot \left(\frac{\left|\sqrt[3]{t}\right|}{y} \cdot \frac{\sqrt{\sqrt[3]{t}}}{z}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020224 
(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)))))