Average Error: 7.5 → 1.5
Time: 9.6s
Precision: binary64
\[\frac{x + y}{1 - \frac{y}{z}}\]
↓
\[\frac{1}{\frac{1}{x + y} - \frac{1}{z} \cdot \frac{y}{x + y}}\]
\frac{x + y}{1 - \frac{y}{z}}
↓
\frac{1}{\frac{1}{x + y} - \frac{1}{z} \cdot \frac{y}{x + y}}
(FPCore (x y z) :precision binary64 (/ (+ x y) (- 1.0 (/ y z))))
↓
(FPCore (x y z)
 :precision binary64
 (/ 1.0 (- (/ 1.0 (+ x y)) (* (/ 1.0 z) (/ y (+ x y))))))
double code(double x, double y, double z) {
	return (x + y) / (1.0 - (y / z));
}
↓
double code(double x, double y, double z) {
	return 1.0 / ((1.0 / (x + y)) - ((1.0 / z) * (y / (x + y))));
}

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

Original7.5
Target4.1
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;y < -3.7429310762689856 \cdot 10^{+171}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \mathbf{elif}\;y < 3.5534662456086734 \cdot 10^{+168}:\\ \;\;\;\;\frac{x + y}{1 - \frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{-y} \cdot z\\ \end{array}\]

Derivation

  1. Initial program 7.5

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

  3. Applied clear-num_binary64_150817.6

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

  4. Simplified7.6

    \[\leadsto \frac{1}{\color{blue}{\frac{1 - \frac{y}{z}}{y + x}}}\]
  5. Using strategy rm

  6. Applied div-sub_binary64_150877.6

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

  7. Simplified7.6

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

  8. Simplified6.7

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

  10. Applied *-un-lft-identity_binary64_150826.7

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

  11. Applied times-frac_binary64_150881.5

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

  12. Final simplification1.5

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

Reproduce

herbie shell --seed 2021076 
(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))))