Average Error: 1.9 → 0.3
Time: 5.1s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x + \frac{-a}{\frac{\left(t - z\right) + 1}{y - z}}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x + \frac{-a}{\frac{\left(t - z\right) + 1}{y - z}}
double code(double x, double y, double z, double t, double a) {
	return (x - ((y - z) / (((t - z) + 1.0) / a)));
}
↓
double code(double x, double y, double z, double t, double a) {
	return (x + (-a / (((t - z) + 1.0) / (y - z))));
}

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

Original1.9
Target0.2
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.9

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  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 clear-num0.3

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

  7. Applied sub-neg0.3

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020058 
(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))))