Average Error: 2.1 → 0.2
Time: 8.7s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{y - z}{\left(t - z\right) + 1} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r3278 = x;
        double r3279 = y;
        double r3280 = z;
        double r3281 = r3279 - r3280;
        double r3282 = t;
        double r3283 = r3282 - r3280;
        double r3284 = 1.0;
        double r3285 = r3283 + r3284;
        double r3286 = a;
        double r3287 = r3285 / r3286;
        double r3288 = r3281 / r3287;
        double r3289 = r3278 - r3288;
        return r3289;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r3290 = x;
        double r3291 = y;
        double r3292 = z;
        double r3293 = r3291 - r3292;
        double r3294 = t;
        double r3295 = r3294 - r3292;
        double r3296 = 1.0;
        double r3297 = r3295 + r3296;
        double r3298 = r3293 / r3297;
        double r3299 = a;
        double r3300 = r3298 * r3299;
        double r3301 = r3290 - r3300;
        return r3301;
}

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

Original2.1
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  2. Using strategy rm

  3. Applied associate-/r/0.2

    \[\leadsto x - \color{blue}{\frac{y - z}{\left(t - z\right) + 1} \cdot a}\]

  4. Final simplification0.2

    \[\leadsto x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1) a))))