Average Error: 2.2 → 0.2
Time: 19.4s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[\frac{a}{\frac{\left(t - z\right) + 1}{z - y}} + x\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
\frac{a}{\frac{\left(t - z\right) + 1}{z - y}} + x
double f(double x, double y, double z, double t, double a) {
        double r404310 = x;
        double r404311 = y;
        double r404312 = z;
        double r404313 = r404311 - r404312;
        double r404314 = t;
        double r404315 = r404314 - r404312;
        double r404316 = 1.0;
        double r404317 = r404315 + r404316;
        double r404318 = a;
        double r404319 = r404317 / r404318;
        double r404320 = r404313 / r404319;
        double r404321 = r404310 - r404320;
        return r404321;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r404322 = a;
        double r404323 = t;
        double r404324 = z;
        double r404325 = r404323 - r404324;
        double r404326 = 1.0;
        double r404327 = r404325 + r404326;
        double r404328 = y;
        double r404329 = r404324 - r404328;
        double r404330 = r404327 / r404329;
        double r404331 = r404322 / r404330;
        double r404332 = x;
        double r404333 = r404331 + r404332;
        return r404333;
}

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

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

Derivation

  1. Initial program 2.2

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

  2. Simplified0.2

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

  4. Applied clear-num0.2

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

  6. Applied fma-udef0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 +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))))