Average Error: 10.6 → 1.2
Time: 8.8s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{1}{\frac{\frac{z - a}{z - t}}{y}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{1}{\frac{\frac{z - a}{z - t}}{y}}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- z a))))
↓
(FPCore (x y z t a)
 :precision binary64
 (+ x (/ 1.0 (/ (/ (- z a) (- z t)) y))))
double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (z - a));
}
↓
double code(double x, double y, double z, double t, double a) {
	return x + (1.0 / (((z - a) / (z - t)) / y));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.6
Target1.1
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied associate-/l*_binary64_25641.1

    \[\leadsto x + \color{blue}{\frac{y}{\frac{z - a}{z - t}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity_binary64_25001.1

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

  6. Applied associate-/l*_binary64_25641.2

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

  7. Final simplification1.2

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

Reproduce

herbie shell --seed 2020231 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (/ (* y (- z t)) (- z a))))