Average Error: 2.0 → 0.3
Time: 19.7s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[\mathsf{fma}\left(a, \frac{z - y}{\left(t - z\right) + 1}, x\right)\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
\mathsf{fma}\left(a, \frac{z - y}{\left(t - z\right) + 1}, x\right)
double f(double x, double y, double z, double t, double a) {
        double r397234 = x;
        double r397235 = y;
        double r397236 = z;
        double r397237 = r397235 - r397236;
        double r397238 = t;
        double r397239 = r397238 - r397236;
        double r397240 = 1.0;
        double r397241 = r397239 + r397240;
        double r397242 = a;
        double r397243 = r397241 / r397242;
        double r397244 = r397237 / r397243;
        double r397245 = r397234 - r397244;
        return r397245;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r397246 = a;
        double r397247 = z;
        double r397248 = y;
        double r397249 = r397247 - r397248;
        double r397250 = t;
        double r397251 = r397250 - r397247;
        double r397252 = 1.0;
        double r397253 = r397251 + r397252;
        double r397254 = r397249 / r397253;
        double r397255 = x;
        double r397256 = fma(r397246, r397254, r397255);
        return r397256;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original2.0
Target0.3
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.0

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

  2. Simplified0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 +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))))