Average Error: 10.8 → 1.5
Time: 5.4s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)
(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 (- a t)) (/ t (- a t))))))
double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (a - t));
}
↓
double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z / (a - t)) - (t / (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

Original10.8
Target1.4
Herbie1.5
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.8

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

  3. Applied *-un-lft-identity_binary6410.8

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

  4. Applied times-frac_binary641.5

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

  5. Simplified1.5

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

  7. Applied div-sub_binary641.5

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

  8. Final simplification1.5

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

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, B"
  :precision binary64

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

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