Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2

Average Error: 0.1 → 0.1

Time: 8.3s

Precision: binary64

Math

\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]

↓

\[x - \left(\log y \cdot \left(y + 0.5\right) + \left(z - y\right)\right)\]

FPCore

(FPCore (x y z) :precision binary64 (- (+ (- x (* (+ y 0.5) (log y))) y) z))

↓

(FPCore (x y z) :precision binary64 (- x (+ (* (log y) (+ y 0.5)) (- z y))))

C

double code(double x, double y, double z) {
	return ((x - ((y + 0.5) * log(y))) + y) - z;
}

↓

double code(double x, double y, double z) {
	return x - ((log(y) * (y + 0.5)) + (z - y));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.1
Target	0.1
Herbie	0.1

\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

1. Initial program 0.1

   \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
2. Using strategy rm

3. Applied associate-+l-_binary64_10243 0.1

   \[\leadsto \color{blue}{\left(x - \left(\left(y + 0.5\right) \cdot \log y - y\right)\right)} - z\]

4. Applied associate--l-_binary64_10246 0.1

   \[\leadsto \color{blue}{x - \left(\left(\left(y + 0.5\right) \cdot \log y - y\right) + z\right)}\]

5. Simplified 0.1

   \[\leadsto x - \color{blue}{\left(\log y \cdot \left(y + 0.5\right) + \left(z - y\right)\right)}\]

6. Final simplification 0.1

   \[\leadsto x - \left(\log y \cdot \left(y + 0.5\right) + \left(z - y\right)\right)\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))