Average Error: 2.1 → 0.2
Time: 4.6s
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 r2075637 = x;
        double r2075638 = y;
        double r2075639 = z;
        double r2075640 = r2075638 - r2075639;
        double r2075641 = t;
        double r2075642 = r2075641 - r2075639;
        double r2075643 = 1.0;
        double r2075644 = r2075642 + r2075643;
        double r2075645 = a;
        double r2075646 = r2075644 / r2075645;
        double r2075647 = r2075640 / r2075646;
        double r2075648 = r2075637 - r2075647;
        return r2075648;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2075649 = x;
        double r2075650 = y;
        double r2075651 = z;
        double r2075652 = r2075650 - r2075651;
        double r2075653 = t;
        double r2075654 = r2075653 - r2075651;
        double r2075655 = 1.0;
        double r2075656 = r2075654 + r2075655;
        double r2075657 = r2075652 / r2075656;
        double r2075658 = a;
        double r2075659 = r2075657 * r2075658;
        double r2075660 = r2075649 - r2075659;
        return r2075660;
}

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

Derivation

  1. Initial program 2.1

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

  3. Applied associate-/r/0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020018 +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))))