Average Error: 2.0 → 0.3
Time: 12.1s
Precision: binary64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - a \cdot \frac{y - z}{\left(t + 1\right) - z}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - a \cdot \frac{y - z}{\left(t + 1\right) - z}
(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))
↓
(FPCore (x y z t a)
 :precision binary64
 (- x (* a (/ (- y z) (- (+ t 1.0) 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 * ((y - z) / ((t + 1.0) - 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

Original2.0
Target0.3
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.0

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

  2. Taylor expanded around 0 10.5

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

  3. Simplified0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2021044 
(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))))