Average Error: 7.4 → 7.4
Time: 2.3s
Precision: binary64
\[\frac{x + y}{1 - \frac{y}{z}}\]
↓
\[\frac{x + y}{1 - \frac{y}{z}}\]
\frac{x + y}{1 - \frac{y}{z}}
↓
\frac{x + y}{1 - \frac{y}{z}}
(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))
↓
(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ 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 - (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
Target3.8
Herbie7.4
\[\begin{array}{l} \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \end{array}\]

Derivation

  1. Initial program 7.4

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

  2. Final simplification7.4

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

Reproduce

herbie shell --seed 2020220 
(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) (- 1.0 (/ y z))) (* (/ (+ y x) (- y)) z)))

  (/ (+ x y) (- 1.0 (/ y z))))