Error: 62.0 → 0.0

Time: 19.1s

Precision: 64

Ground Truth: 128

\[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]

⬇

\[\frac{1}{b} + \frac{1}{a}\]

Error

The X axis may use a short exponential scale — Bits error versus `a`

Derivation

Initial program 62.0
\[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
Applied taylor 0.0
\[\leadsto \frac{1}{b} + \frac{1}{a}\]
Taylor expanded around 0 0.0

\[\leadsto \color{blue}{\frac{1}{b} + \frac{1}{a}}\]
Removed slow pow expressions

Runtime

Please report a bug with the following info:

herbie --seed '#(3973348988 1536589159 1701528493 761420261 1442429943 1569062448)'
(FPCore (a b eps)
  :name "NMSE problem 3.4.2"
  
  :target
  (/ (+ a b) (* a b))(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))))