Average Error: 10.7 → 1.2
Time: 5.0s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z}{z - t} - \frac{a}{z - t}}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- z a))))
↓
(FPCore (x y z t a)
 :precision binary64
 (+ x (/ y (- (/ z (- z t)) (/ a (- z t))))))
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 + (y / ((z / (z - t)) - (a / (z - t))));
}

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

Original10.7
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*_binary641.2

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

  5. Applied div-sub_binary641.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2020253 
(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))))