(asin (pow (/ (/ X (sin x)) Y) (- 1)))

Average Error: 4.8 → 4.8

Time: 3.9s

Precision: binary64

Math

\[\sin^{-1} \left({\left(\frac{\frac{X}{\sin x}}{Y}\right)}^{\left(-1\right)}\right)\]

↓

\[\sin^{-1} \left({\left(\frac{\frac{X}{\sin x}}{Y}\right)}^{\left(-1\right)}\right)\]

Error

Bits error versus X

Bits error versus x

Bits error versus Y

Derivation

1. Initial program 4.8

   \[\sin^{-1} \left({\left(\frac{\frac{X}{\sin x}}{Y}\right)}^{\left(-1\right)}\right)\]

2. Final simplification 4.8

   \[\leadsto \sin^{-1} \left({\left(\frac{\frac{X}{\sin x}}{Y}\right)}^{\left(-1\right)}\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (X x Y)
  :name "(asin (pow (/ (/ X (sin x)) Y) (- 1)))"
  :precision binary64
  (asin (pow (/ (/ X (sin x)) Y) (neg 1.0))))