(/ (* pi (pow x (- 19))) (* 20 (sin (/ pi x))))

Average Error: 18.1 → 18.1

Time: 4.2s

Precision: binary64

Math

\[\frac{pi \cdot {x}^{\left(-19\right)}}{20 \cdot \sin \left(\frac{pi}{x}\right)}\]

↓

\[\frac{pi \cdot {x}^{\left(-19\right)}}{20 \cdot \sin \left(\frac{pi}{x}\right)}\]

Error

Bits error versus pi

Bits error versus x

Derivation

1. Initial program 18.1

   \[\frac{pi \cdot {x}^{\left(-19\right)}}{20 \cdot \sin \left(\frac{pi}{x}\right)}\]

2. Final simplification 18.1

   \[\leadsto \frac{pi \cdot {x}^{\left(-19\right)}}{20 \cdot \sin \left(\frac{pi}{x}\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (pi x)
  :name "(/ (* pi (pow x (- 19))) (* 20 (sin (/ pi x))))"
  :precision binary64
  (/ (* pi (pow x (neg 19.0))) (* 20.0 (sin (/ pi x)))))