Average Error: 1.5 → 3.0
Time: 6.1s
Precision: binary64
\[x + y \cdot \frac{z - t}{z - a} \]
↓
\[x + \frac{y}{z - a} \cdot \left(z - t\right) \]
x + y \cdot \frac{z - t}{z - a}
↓
x + \frac{y}{z - a} \cdot \left(z - t\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 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 - 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

Original1.5
Target1.3
Herbie3.0
\[x + \frac{y}{\frac{z - a}{z - t}} \]

Derivation

  1. Initial program 1.5

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

  2. Applied clear-num_binary641.5

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

  3. Applied associate-/r/_binary641.5

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

  4. Applied associate-*r*_binary643.0

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

  5. Simplified3.0

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

  6. Final simplification3.0

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

Reproduce

herbie shell --seed 2022125 
(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)))))