Average Error: 2.1 → 0.3
Time: 3.5s
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 r652464 = x;
        double r652465 = y;
        double r652466 = z;
        double r652467 = r652465 - r652466;
        double r652468 = t;
        double r652469 = r652468 - r652466;
        double r652470 = 1.0;
        double r652471 = r652469 + r652470;
        double r652472 = a;
        double r652473 = r652471 / r652472;
        double r652474 = r652467 / r652473;
        double r652475 = r652464 - r652474;
        return r652475;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r652476 = x;
        double r652477 = y;
        double r652478 = z;
        double r652479 = r652477 - r652478;
        double r652480 = t;
        double r652481 = r652480 - r652478;
        double r652482 = 1.0;
        double r652483 = r652481 + r652482;
        double r652484 = r652479 / r652483;
        double r652485 = a;
        double r652486 = r652484 * r652485;
        double r652487 = r652476 - r652486;
        return r652487;
}

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
Target0.3
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 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 2020002 +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))))