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

⬇

\[\begin{array}{l} \mathbf{if}\;b \cdot \varepsilon \le -3.3769268280788495 \cdot 10^{+66}:\\ \;\;\;\;\frac{1}{b} + \frac{1}{a}\\ \mathbf{if}\;b \cdot \varepsilon \le -2.0841593466205432 \cdot 10^{+48}:\\ \;\;\;\;\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{b} + \frac{1}{a}\\ \end{array}\]

Original	61.8
Comparison	14.5
Herbie	0.5

Derivation

Split input into 2 regimes.
if (* b eps) < -3.3769268280788495e+66 or -2.0841593466205432e+48 < (* b eps)
1. Initial program 62.0
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
2. Applied taylor 0.0
  \[\leadsto \frac{1}{b} + \frac{1}{a}\]
3. Taylor expanded around 0 0.0
  
  \[\leadsto \color{blue}{\frac{1}{b} + \frac{1}{a}}\]
if -3.3769268280788495e+66 < (* b eps) < -2.0841593466205432e+48
1. Initial program 45.5
  \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
Recombined 2 regimes into one program.
Removed slow pow expressions

Runtime

Please include this information when filing a bug report:

herbie shell --seed '#(1068028399 4028058041 2917032441 2563479541 765645300 1132738916)'
(FPCore (a b eps)
  :name "expq3 (problem 3.4.2)"
  :pre (and (< -1 eps) (< eps 1))

  :target
  (/ (+ a b) (* a b))

  (/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))))

Error

Target

Derivation

`if (* b eps) < -3.3769268280788495e+66 or -2.0841593466205432e+48 < (* b eps)`

`if -3.3769268280788495e+66 < (* b eps) < -2.0841593466205432e+48`

Runtime