Average Error: 3.5 → 1.6
Time: 6.3s
Precision: binary64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{\frac{3}{\frac{1}{y}}}\]
\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{t}{z}}{\frac{3}{\frac{1}{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))) (/ (/ t z) (/ 3.0 (/ 1.0 y)))))
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x - (y / ((double) (z * 3.0))))) + (t / ((double) (((double) (z * 3.0)) * y)))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x - (y / ((double) (z * 3.0))))) + ((t / z) / (3.0 / (1.0 / 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

Original3.5
Target1.6
Herbie1.6
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Initial program 3.5

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

  3. Applied add-cube-cbrt_binary643.8

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

  4. Applied associate-/l*_binary643.8

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

  5. Simplified2.9

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

  7. Applied div-inv_binary642.9

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

  8. Applied times-frac_binary642.2

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

  9. Applied associate-/r*_binary641.8

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

  10. Simplified1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{t}{z}}}{\frac{3}{\frac{1}{y}}}\]

  11. Final simplification1.6

    \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z}}{\frac{3}{\frac{1}{y}}}\]

Reproduce

herbie shell --seed 2020210 
(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))))