Error

Target

Derivation

1. Split input into 2 regimes

2. if (+ (/ 1 b) (/ 1 a)) < -7.904813181761047e-110 or 1.8312438674022283e-191 < (+ (/ 1 b) (/ 1 a))

   1. Initial program 60.3

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

   2. Taylor expanded around 0 1.7

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

   if -7.904813181761047e-110 < (+ (/ 1 b) (/ 1 a)) < 1.8312438674022283e-191

   1. Initial program 29.4

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

4. Applied simplify3.2

   \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{1}{a} + \frac{1}{b} \le -7.904813181761047 \cdot 10^{-110} \lor \neg \left(\frac{1}{a} + \frac{1}{b} \le 1.8312438674022283 \cdot 10^{-191}\right):\\ \;\;\;\;\frac{1}{a} + \frac{1}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{\varepsilon \cdot b} - 1\right) \cdot \left(e^{\varepsilon \cdot a} - 1\right)}\\ \end{array}}\]

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed '#(1072107073 2127697367 3936270018 2300570620 2134894798 4023771849)' 
(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))))