Average Error: 10.8 → 1.2
Time: 23.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r22225328 = x;
        double r22225329 = y;
        double r22225330 = z;
        double r22225331 = t;
        double r22225332 = r22225330 - r22225331;
        double r22225333 = r22225329 * r22225332;
        double r22225334 = a;
        double r22225335 = r22225334 - r22225331;
        double r22225336 = r22225333 / r22225335;
        double r22225337 = r22225328 + r22225336;
        return r22225337;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r22225338 = x;
        double r22225339 = y;
        double r22225340 = a;
        double r22225341 = t;
        double r22225342 = r22225340 - r22225341;
        double r22225343 = z;
        double r22225344 = r22225343 - r22225341;
        double r22225345 = r22225342 / r22225344;
        double r22225346 = r22225339 / r22225345;
        double r22225347 = r22225338 + r22225346;
        return r22225347;
}

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

Derivation

  1. Initial program 10.8

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(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))))