Average Error: 10.5 → 1.2
Time: 16.2s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + t \cdot \frac{y - z}{a - z}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + t \cdot \frac{y - z}{a - z}
double f(double x, double y, double z, double t, double a) {
        double r29429722 = x;
        double r29429723 = y;
        double r29429724 = z;
        double r29429725 = r29429723 - r29429724;
        double r29429726 = t;
        double r29429727 = r29429725 * r29429726;
        double r29429728 = a;
        double r29429729 = r29429728 - r29429724;
        double r29429730 = r29429727 / r29429729;
        double r29429731 = r29429722 + r29429730;
        return r29429731;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29429732 = x;
        double r29429733 = t;
        double r29429734 = y;
        double r29429735 = z;
        double r29429736 = r29429734 - r29429735;
        double r29429737 = a;
        double r29429738 = r29429737 - r29429735;
        double r29429739 = r29429736 / r29429738;
        double r29429740 = r29429733 * r29429739;
        double r29429741 = r29429732 + r29429740;
        return r29429741;
}

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
Target0.6
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.5

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

  3. Applied associate-/l*3.0

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

  5. Applied associate-/r/1.2

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

  6. Final simplification1.2

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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