Average Error: 7.4 → 7.4
Time: 3.9s
Precision: 64
\[\frac{x + y}{1 - \frac{y}{z}}\]
↓
\[\left(x + y\right) \cdot \frac{1}{1 - \frac{y}{z}}\]
\frac{x + y}{1 - \frac{y}{z}}
↓
\left(x + y\right) \cdot \frac{1}{1 - \frac{y}{z}}
double code(double x, double y, double z) {
	return ((x + y) / (1.0 - (y / z)));
}
↓
double code(double x, double y, double z) {
	return ((x + y) * (1.0 / (1.0 - (y / z))));
}

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

Original7.4
Target3.9
Herbie7.4
\[\begin{array}{l} \mathbf{if}\;y \lt -3.74293107626898565 \cdot 10^{171}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \mathbf{elif}\;y \lt 3.55346624560867344 \cdot 10^{168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \end{array}\]

Derivation

  1. Initial program 7.4

    \[\frac{x + y}{1 - \frac{y}{z}}\]
  2. Using strategy rm

  3. Applied div-inv7.4

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

  4. Final simplification7.4

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

Reproduce

herbie shell --seed 2020102 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, A"
  :precision binary64

  :herbie-target
  (if (< y -3.7429310762689856e+171) (* (/ (+ y x) (- y)) z) (if (< y 3.5534662456086734e+168) (/ (+ x y) (- 1 (/ y z))) (* (/ (+ y x) (- y)) z)))

  (/ (+ x y) (- 1 (/ y z))))