Average Error: 28.9 → 0.2
Time: 6.6s
Precision: binary64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \frac{\frac{x + z}{y}}{\frac{1}{z - x}}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \frac{\frac{x + z}{y}}{\frac{1}{z - x}}}{2}
double code(double x, double y, double z) {
	return (((double) (((double) (((double) (x * x)) + ((double) (y * y)))) - ((double) (z * z)))) / ((double) (y * 2.0)));
}
↓
double code(double x, double y, double z) {
	return (((double) (y - ((((double) (x + z)) / y) / (1.0 / ((double) (z - x)))))) / 2.0);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original28.9
Target0.2
Herbie0.2
\[y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)\]

Derivation

  1. Initial program 28.9

    \[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]

  2. Simplified0.2

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

  4. Applied clear-num0.2

    \[\leadsto \frac{y - \left(x + z\right) \cdot \color{blue}{\frac{1}{\frac{y}{z - x}}}}{2}\]
  5. Using strategy rm

  6. Applied un-div-inv0.2

    \[\leadsto \frac{y - \color{blue}{\frac{x + z}{\frac{y}{z - x}}}}{2}\]
  7. Using strategy rm

  8. Applied div-inv0.2

    \[\leadsto \frac{y - \frac{x + z}{\color{blue}{y \cdot \frac{1}{z - x}}}}{2}\]

  9. Applied associate-/r*0.2

    \[\leadsto \frac{y - \color{blue}{\frac{\frac{x + z}{y}}{\frac{1}{z - x}}}}{2}\]

  10. Final simplification0.2

    \[\leadsto \frac{y - \frac{\frac{x + z}{y}}{\frac{1}{z - x}}}{2}\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"
  :precision binary64

  :herbie-target
  (- (* y 0.5) (* (* (/ 0.5 y) (+ z x)) (- z x)))

  (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0)))