Average Error: 11.0 → 1.2
Time: 16.4s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\frac{y}{\frac{a - t}{z - t}} + x\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\frac{y}{\frac{a - t}{z - t}} + x
double f(double x, double y, double z, double t, double a) {
        double r276271 = x;
        double r276272 = y;
        double r276273 = z;
        double r276274 = t;
        double r276275 = r276273 - r276274;
        double r276276 = r276272 * r276275;
        double r276277 = a;
        double r276278 = r276277 - r276274;
        double r276279 = r276276 / r276278;
        double r276280 = r276271 + r276279;
        return r276280;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r276281 = y;
        double r276282 = a;
        double r276283 = t;
        double r276284 = r276282 - r276283;
        double r276285 = z;
        double r276286 = r276285 - r276283;
        double r276287 = r276284 / r276286;
        double r276288 = r276281 / r276287;
        double r276289 = x;
        double r276290 = r276288 + r276289;
        return r276290;
}

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

Original11.0
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 11.0

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

  2. Simplified11.0

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

  4. Applied associate-/l*1.2

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

  5. Final simplification1.2

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"

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

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