Average Error: 10.5 → 1.5
Time: 5.2s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \left(y \cdot \frac{z}{a - t} - y \cdot \frac{t}{a - t}\right)\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \left(y \cdot \frac{z}{a - t} - y \cdot \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))) (* y (/ 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))) - (y * (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

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

Derivation

  1. Initial program 10.5

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

  3. Applied *-un-lft-identity_binary64_1712810.5

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

  4. Applied times-frac_binary64_171341.5

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

  5. Simplified1.5

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

  7. Applied div-sub_binary64_171331.5

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

  9. Applied sub-neg_binary64_171211.5

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

  10. Applied distribute-rgt-in_binary64_170781.5

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

  11. Simplified1.5

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

  12. Simplified1.5

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

  13. Final simplification1.5

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

Reproduce

herbie shell --seed 2020295 
(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))))