Error

Target

Derivation

1. Split input into 2 regimes

2. if (+ (/ 1 b) (/ 1 a)) < -4.549790872176706e-158 or 2.201452965804001e-159 < (+ (/ 1 b) (/ 1 a))

   1. Initial program 60.0

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

   2. Taylor expanded around 0 2.0

      \[\leadsto \color{blue}{\frac{1}{b} + \frac{1}{a}}\]

   if -4.549790872176706e-158 < (+ (/ 1 b) (/ 1 a)) < 2.201452965804001e-159

   1. Initial program 23.4

      \[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
   2. Using strategy rm

   3. Applied add-log-exp23.6

      \[\leadsto \frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \color{blue}{\log \left(e^{e^{b \cdot \varepsilon} - 1}\right)}}\]
3. Recombined 2 regimes into one program.

4. Applied simplify2.9

   \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{1}{a} + \frac{1}{b} \le -4.549790872176706 \cdot 10^{-158} \lor \neg \left(\frac{1}{a} + \frac{1}{b} \le 2.201452965804001 \cdot 10^{-159}\right):\\ \;\;\;\;\frac{1}{a} + \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\log \left(e^{e^{\varepsilon \cdot b} - 1}\right) \cdot \left(e^{\varepsilon \cdot a} - 1\right)}\\ \end{array}}\]

Runtime

Time bar (total: 46.4s)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' 
(FPCore (a b eps)
  :name "expq3 (problem 3.4.2)"
  :pre (and (< -1 eps) (< eps 1))

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

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