Average Error: 2.1 → 0.2
Time: 2.6s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{y - z}{-\left(\left(t - z\right) + 1\right)} \cdot \left(-a\right)\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{y - z}{-\left(\left(t - z\right) + 1\right)} \cdot \left(-a\right)
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 - (((y - z) / -((t - z) + 1.0)) * -a));
}

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 frac-2neg2.1

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

  4. Applied associate-/r/0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020071 +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))))