Average Error: 1.2 → 0.7
Time: 5.7s
Precision: binary64
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\]
↓
\[1 \cdot \frac{\frac{\cos^{-1} \left(x \cdot \left(\frac{\frac{\sqrt{t}}{y}}{27 \cdot \left(z \cdot 2\right)} \cdot 3\right)\right)}{\sqrt{3}}}{\sqrt{3}}\]
\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
1 \cdot \frac{\frac{\cos^{-1} \left(x \cdot \left(\frac{\frac{\sqrt{t}}{y}}{27 \cdot \left(z \cdot 2\right)} \cdot 3\right)\right)}{\sqrt{3}}}{\sqrt{3}}
(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
  (/
   (/ (acos (* x (* (/ (/ (sqrt t) y) (* 27.0 (* z 2.0))) 3.0))) (sqrt 3.0))
   (sqrt 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) acos(((double) (x * ((double) (((((double) sqrt(t)) / y) / ((double) (27.0 * ((double) (z * 2.0))))) * 3.0)))))) / ((double) sqrt(3.0))) / ((double) sqrt(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
Herbie0.7
\[\frac{\cos^{-1} \left(\frac{\frac{x}{27}}{y \cdot z} \cdot \frac{\sqrt{t}}{\frac{2}{3}}\right)}{3}\]

Derivation

  1. Initial program Error: 1.2 bits

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

  2. SimplifiedError: 1.2 bits

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

  4. Applied add-sqr-sqrtError: 0.3 bits

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

  5. Applied associate-/r*Error: 0.3 bits

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

  6. SimplifiedError: 0.3 bits

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

  8. Applied associate-/r*Error: 0.7 bits

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

  9. Final simplificationError: 0.7 bits

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

Reproduce

herbie shell --seed 2020203 
(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)))))