Average Error: 1.3 → 0.3
Time: 31.8s
Precision: binary64
Cost: 26496
\[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]
↓
\[\frac{\frac{-\cos^{-1} \left(\frac{\frac{x \cdot 0.05555555555555555}{y} \cdot \sqrt{t}}{z}\right)}{\sqrt[3]{-3}}}{\sqrt[3]{9}} \]
(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
 (/
  (/ (- (acos (/ (* (/ (* x 0.05555555555555555) y) (sqrt t)) z))) (cbrt -3.0))
  (cbrt 9.0)))
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 (-acos(((((x * 0.05555555555555555) / y) * sqrt(t)) / z)) / cbrt(-3.0)) / cbrt(9.0);
}

public static double code(double x, double y, double z, double t) {
	return (1.0 / 3.0) * Math.acos((((3.0 * (x / (y * 27.0))) / (z * 2.0)) * Math.sqrt(t)));
}
↓
public static double code(double x, double y, double z, double t) {
	return (-Math.acos(((((x * 0.05555555555555555) / y) * Math.sqrt(t)) / z)) / Math.cbrt(-3.0)) / Math.cbrt(9.0);
}

function code(x, y, z, t)
	return Float64(Float64(1.0 / 3.0) * acos(Float64(Float64(Float64(3.0 * Float64(x / Float64(y * 27.0))) / Float64(z * 2.0)) * sqrt(t))))
end
↓
function code(x, y, z, t)
	return Float64(Float64(Float64(-acos(Float64(Float64(Float64(Float64(x * 0.05555555555555555) / y) * sqrt(t)) / z))) / cbrt(-3.0)) / cbrt(9.0))
end

code[x_, y_, z_, t_] := N[(N[(1.0 / 3.0), $MachinePrecision] * N[ArcCos[N[(N[(N[(3.0 * N[(x / N[(y * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * 2.0), $MachinePrecision]), $MachinePrecision] * N[Sqrt[t], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_, z_, t_] := N[(N[((-N[ArcCos[N[(N[(N[(N[(x * 0.05555555555555555), $MachinePrecision] / y), $MachinePrecision] * N[Sqrt[t], $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]], $MachinePrecision]) / N[Power[-3.0, 1/3], $MachinePrecision]), $MachinePrecision] / N[Power[9.0, 1/3], $MachinePrecision]), $MachinePrecision]

\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)
↓
\frac{\frac{-\cos^{-1} \left(\frac{\frac{x \cdot 0.05555555555555555}{y} \cdot \sqrt{t}}{z}\right)}{\sqrt[3]{-3}}}{\sqrt[3]{9}}

Error

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. Simplified1.3

    \[\leadsto \color{blue}{0.3333333333333333 \cdot \cos^{-1} \left(\frac{\frac{x}{y \cdot 27}}{\frac{z}{1.5}} \cdot \sqrt{t}\right)} \]
    Proof

  3. Applied egg-rr1.2

    \[\leadsto \color{blue}{\frac{\cos^{-1} \left(\frac{1.5 \cdot x}{\left(y \cdot 27\right) \cdot z} \cdot \sqrt{t}\right)}{3}} \]

  4. Simplified1.3

    \[\leadsto \color{blue}{\frac{\cos^{-1} \left(\frac{\frac{x}{y \cdot 27}}{z} \cdot \left(1.5 \cdot \sqrt{t}\right)\right)}{3}} \]
    Proof

  5. Applied egg-rr0.2

    \[\leadsto \color{blue}{\frac{\frac{-\cos^{-1} \left(\frac{x \cdot 1.5}{z \cdot \left(y \cdot 27\right)} \cdot \sqrt{t}\right)}{\sqrt[3]{-3}}}{\sqrt[3]{9}}} \]

  6. Applied egg-rr0.3

    \[\leadsto \frac{\frac{-\cos^{-1} \color{blue}{\left(\frac{\frac{x \cdot 0.05555555555555555}{y} \cdot \sqrt{t}}{z}\right)}}{\sqrt[3]{-3}}}{\sqrt[3]{9}} \]

Alternatives

Alternative 1
Error0.3
Cost26432
\[\frac{\sqrt[3]{0.1111111111111111} \cdot \cos^{-1} \left(\frac{0.05555555555555555}{y} \cdot \left(\frac{x}{z} \cdot \sqrt{t}\right)\right)}{\sqrt[3]{3}} \]
Alternative 2
Error1.3
Cost13504
\[0.3333333333333333 \cdot \cos^{-1} \left(\frac{\frac{\frac{x}{y} \cdot \sqrt{t}}{z}}{18}\right) \]
Alternative 3
Error1.3
Cost13504
\[\frac{\cos^{-1} \left(\left(\frac{\frac{x}{y}}{z} \cdot \sqrt{t}\right) \cdot 0.05555555555555555\right)}{3} \]

Error

Reproduce

herbie shell --seed 2023010 
(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)))))