Average Error: 10.4 → 1.2
Time: 15.2s
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 r31129502 = x;
        double r31129503 = y;
        double r31129504 = z;
        double r31129505 = r31129503 - r31129504;
        double r31129506 = t;
        double r31129507 = r31129505 * r31129506;
        double r31129508 = a;
        double r31129509 = r31129508 - r31129504;
        double r31129510 = r31129507 / r31129509;
        double r31129511 = r31129502 + r31129510;
        return r31129511;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r31129512 = x;
        double r31129513 = t;
        double r31129514 = y;
        double r31129515 = z;
        double r31129516 = r31129514 - r31129515;
        double r31129517 = a;
        double r31129518 = r31129517 - r31129515;
        double r31129519 = r31129516 / r31129518;
        double r31129520 = r31129513 * r31129519;
        double r31129521 = r31129512 + r31129520;
        return r31129521;
}

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

Original10.4
Target0.5
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.4

    \[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
  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 2019179 
(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))))