Average Error: 1.9 → 0.2
Time: 5.2s
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 r502322 = x;
        double r502323 = y;
        double r502324 = z;
        double r502325 = r502323 - r502324;
        double r502326 = t;
        double r502327 = r502326 - r502324;
        double r502328 = 1.0;
        double r502329 = r502327 + r502328;
        double r502330 = a;
        double r502331 = r502329 / r502330;
        double r502332 = r502325 / r502331;
        double r502333 = r502322 - r502332;
        return r502333;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r502334 = x;
        double r502335 = y;
        double r502336 = z;
        double r502337 = r502335 - r502336;
        double r502338 = t;
        double r502339 = r502338 - r502336;
        double r502340 = 1.0;
        double r502341 = r502339 + r502340;
        double r502342 = r502337 / r502341;
        double r502343 = a;
        double r502344 = r502342 * r502343;
        double r502345 = r502334 - r502344;
        return r502345;
}

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

Original1.9
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.9

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  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 2020062 +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))))