Average Error: 1.3 → 1.3
Time: 3.9s
Precision: binary64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{z - a}\right)\]
x + y \cdot \frac{z - t}{z - a}
↓
x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{z - a}\right)
(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 t) (/ 1.0 (- z a))))))
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 - t) * (1.0 / (z - a))));
}

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

Original1.3
Target1.1
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  3. Applied div-inv_binary641.3

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

  4. Final simplification1.3

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

Reproduce

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

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

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