Average Error: 10.5 → 1.3
Time: 5.1s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + y \cdot \frac{z - t}{a - t}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + y \cdot \frac{z - t}{a - t}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- a t))))
↓
(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- a t)))))
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((double) (y * ((double) (z - t)))) / ((double) (a - t)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (y * (((double) (z - t)) / ((double) (a - 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

Original10.5
Target1.1
Herbie1.3
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program Error: 10.5 bits

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

  2. SimplifiedError: 1.3 bits

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

  3. Final simplificationError: 1.3 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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