Average Error: 10.7 → 1.2
Time: 10.2s
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 r420312 = x;
        double r420313 = y;
        double r420314 = z;
        double r420315 = t;
        double r420316 = r420314 - r420315;
        double r420317 = r420313 * r420316;
        double r420318 = a;
        double r420319 = r420318 - r420315;
        double r420320 = r420317 / r420319;
        double r420321 = r420312 + r420320;
        return r420321;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r420322 = x;
        double r420323 = y;
        double r420324 = a;
        double r420325 = t;
        double r420326 = r420324 - r420325;
        double r420327 = z;
        double r420328 = r420327 - r420325;
        double r420329 = r420326 / r420328;
        double r420330 = r420323 / r420329;
        double r420331 = r420322 + r420330;
        return r420331;
}

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

Original10.7
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.4275099853550002e-37 or 9.032302851762362e-182 < y

    1. Initial program 16.4

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

    3. Applied associate-/l*0.6

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

    if -1.4275099853550002e-37 < y < 9.032302851762362e-182

    1. Initial program 0.2

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

    3. Applied div-inv0.2

      \[\leadsto x + \color{blue}{\left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019294 
(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))))