Average Error: 1.9 → 0.3
Time: 6.0s
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 r614223 = x;
        double r614224 = y;
        double r614225 = z;
        double r614226 = r614224 - r614225;
        double r614227 = t;
        double r614228 = r614227 - r614225;
        double r614229 = 1.0;
        double r614230 = r614228 + r614229;
        double r614231 = a;
        double r614232 = r614230 / r614231;
        double r614233 = r614226 / r614232;
        double r614234 = r614223 - r614233;
        return r614234;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r614235 = x;
        double r614236 = y;
        double r614237 = z;
        double r614238 = r614236 - r614237;
        double r614239 = t;
        double r614240 = r614239 - r614237;
        double r614241 = 1.0;
        double r614242 = r614240 + r614241;
        double r614243 = r614238 / r614242;
        double r614244 = a;
        double r614245 = r614243 * r614244;
        double r614246 = r614235 - r614245;
        return r614246;
}

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
Target0.3
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

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/0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020035 +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))))