Average Error: 10.6 → 1.2
Time: 21.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a}{z - t} - \frac{t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r394408 = x;
        double r394409 = y;
        double r394410 = z;
        double r394411 = t;
        double r394412 = r394410 - r394411;
        double r394413 = r394409 * r394412;
        double r394414 = a;
        double r394415 = r394414 - r394411;
        double r394416 = r394413 / r394415;
        double r394417 = r394408 + r394416;
        return r394417;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r394418 = x;
        double r394419 = y;
        double r394420 = a;
        double r394421 = z;
        double r394422 = t;
        double r394423 = r394421 - r394422;
        double r394424 = r394420 / r394423;
        double r394425 = r394422 / r394423;
        double r394426 = r394424 - r394425;
        double r394427 = r394419 / r394426;
        double r394428 = r394418 + r394427;
        return r394428;
}

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

Original10.6
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied associate-/l*1.2

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

  5. Applied div-sub1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019199 
(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))))