Average Error: 2.0 → 0.3
Time: 16.4s
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 r399275 = x;
        double r399276 = y;
        double r399277 = z;
        double r399278 = r399276 - r399277;
        double r399279 = t;
        double r399280 = r399279 - r399277;
        double r399281 = 1.0;
        double r399282 = r399280 + r399281;
        double r399283 = a;
        double r399284 = r399282 / r399283;
        double r399285 = r399278 / r399284;
        double r399286 = r399275 - r399285;
        return r399286;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r399287 = a;
        double r399288 = z;
        double r399289 = y;
        double r399290 = r399288 - r399289;
        double r399291 = t;
        double r399292 = r399291 - r399288;
        double r399293 = 1.0;
        double r399294 = r399292 + r399293;
        double r399295 = r399290 / r399294;
        double r399296 = x;
        double r399297 = fma(r399287, r399295, r399296);
        return r399297;
}

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))))