Average Error: 3.7 → 0.9
Time: 8.9s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\frac{\sqrt[3]{t}}{3}}{\sqrt[3]{y}}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\frac{\sqrt[3]{t}}{3}}{\sqrt[3]{y}}
(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))
↓
(FPCore (x y z t)
 :precision binary64
 (+
  (- x (/ y (* z 3.0)))
  (*
   (/ (/ (* (cbrt t) (cbrt t)) z) (* (cbrt y) (cbrt y)))
   (/ (/ (cbrt t) 3.0) (cbrt y)))))
double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}
↓
double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((((cbrt(t) * cbrt(t)) / z) / (cbrt(y) * cbrt(y))) * ((cbrt(t) / 3.0) / cbrt(y)));
}

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

Original3.7
Target1.7
Herbie0.9
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.7

    \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
  2. Using strategy rm

  3. Applied associate-/r*_binary64_177541.7

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt_binary64_178452.0

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\]

  6. Applied add-cube-cbrt_binary64_178452.0

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}{z \cdot 3}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}\]

  7. Applied times-frac_binary64_178162.0

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z} \cdot \frac{\sqrt[3]{t}}{3}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}\]

  8. Applied times-frac_binary64_178160.9

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\frac{\sqrt[3]{t}}{3}}{\sqrt[3]{y}}}\]

  9. Final simplification0.9

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{z}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\frac{\sqrt[3]{t}}{3}}{\sqrt[3]{y}}\]

Reproduce

herbie shell --seed 2021019 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))