Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Average Error: 2.1 → 0.7

Time: 4.8s

Precision: 64

Math

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

↓

\[x - \left(\frac{y - z}{\left(t - z\right) + 1} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}\]

C

double code(double x, double y, double z, double t, double a) {
	return ((double) (x - ((double) (((double) (y - z)) / ((double) (((double) (((double) (t - z)) + 1.0)) / a))))));
}

↓

double code(double x, double y, double z, double t, double a) {
	return ((double) (x - ((double) (((double) (((double) (((double) (y - z)) / ((double) (((double) (t - z)) + 1.0)))) * ((double) (((double) cbrt(a)) * ((double) cbrt(a)))))) * ((double) cbrt(a))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	2.1
Target	0.2
Herbie	0.7

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

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. Using strategy rm

5. Applied add-cube-cbrt 0.7

   \[\leadsto x - \frac{y - z}{\left(t - z\right) + 1} \cdot \color{blue}{\left(\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}\right)}\]

6. Applied associate-*r* 0.7

   \[\leadsto x - \color{blue}{\left(\frac{y - z}{\left(t - z\right) + 1} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}}\]

7. Final simplification 0.7

   \[\leadsto x - \left(\frac{y - z}{\left(t - z\right) + 1} \cdot \left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right)\right) \cdot \sqrt[3]{a}\]

Reproduce

herbie shell --seed 2020126 
(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) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))