Average Error: 2.1 → 0.3
Time: 14.5s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}
double f(double x, double y, double z, double t, double a) {
        double r428004 = x;
        double r428005 = y;
        double r428006 = z;
        double r428007 = r428005 - r428006;
        double r428008 = t;
        double r428009 = r428008 - r428006;
        double r428010 = 1.0;
        double r428011 = r428009 + r428010;
        double r428012 = a;
        double r428013 = r428011 / r428012;
        double r428014 = r428007 / r428013;
        double r428015 = r428004 - r428014;
        return r428015;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r428016 = x;
        double r428017 = y;
        double r428018 = z;
        double r428019 = r428017 - r428018;
        double r428020 = t;
        double r428021 = r428020 - r428018;
        double r428022 = 1.0;
        double r428023 = r428021 + r428022;
        double r428024 = r428019 / r428023;
        double r428025 = 1.0;
        double r428026 = a;
        double r428027 = r428025 / r428026;
        double r428028 = r428024 / r428027;
        double r428029 = r428016 - r428028;
        return r428029;
}

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

Original2.1
Target0.2
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  2. Using strategy rm

  3. Applied div-inv2.1

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

  4. Applied associate-/r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019208 
(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))))