Average Error: 10.9 → 2.9
Time: 3.3s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{\frac{y}{z - a}}{\frac{1}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{\frac{y}{z - a}}{\frac{1}{z - t}}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / ((double) (z - a))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (y / ((double) (z - a)))) / ((double) (1.0 / ((double) (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

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Target

Original10.9
Target1.3
Herbie2.9
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied associate-/l*1.3

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

  5. Applied div-inv1.4

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

  6. Applied associate-/r*2.9

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

  7. Final simplification2.9

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

Reproduce

herbie shell --seed 2020150 
(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))))