Average Error: 1.8 → 0.3
Time: 5.1s
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 r508490 = x;
        double r508491 = y;
        double r508492 = z;
        double r508493 = r508491 - r508492;
        double r508494 = t;
        double r508495 = r508494 - r508492;
        double r508496 = 1.0;
        double r508497 = r508495 + r508496;
        double r508498 = a;
        double r508499 = r508497 / r508498;
        double r508500 = r508493 / r508499;
        double r508501 = r508490 - r508500;
        return r508501;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r508502 = x;
        double r508503 = y;
        double r508504 = z;
        double r508505 = r508503 - r508504;
        double r508506 = t;
        double r508507 = r508506 - r508504;
        double r508508 = 1.0;
        double r508509 = r508507 + r508508;
        double r508510 = r508505 / r508509;
        double r508511 = a;
        double r508512 = r508510 * r508511;
        double r508513 = r508502 - r508512;
        return r508513;
}

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

Original1.8
Target0.3
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.8

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

  3. Applied associate-/r/0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020021 +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))))