Average Error: 37.8 → 37.8
Time: 45.7s
Precision: 64
Internal Precision: 2368
\[\frac{y \cdot \left({e}^{\left(\left(a + b\right) \cdot y\right)} - 1\right)}{\left({e}^{\left(a \cdot y\right)} - 1\right) \cdot \left({e}^{\left(b \cdot y\right)} - 1\right)}\]
\[\frac{y \cdot \left({e}^{\left(y \cdot \left(b + a\right)\right)} - 1\right)}{\left({e}^{\left(b \cdot y\right)} - 1\right) \cdot \left(\left(\sqrt{{e}^{\left(y \cdot a\right)}} + 1\right) \cdot \left(\left(\sqrt{\sqrt{{e}^{\left(y \cdot a\right)}}} - 1\right) \cdot \left(1 + \sqrt{\sqrt{{e}^{\left(y \cdot a\right)}}}\right)\right)\right)}\]

Error

Bits error versus y

Bits error versus e

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 37.8

    \[\frac{y \cdot \left({e}^{\left(\left(a + b\right) \cdot y\right)} - 1\right)}{\left({e}^{\left(a \cdot y\right)} - 1\right) \cdot \left({e}^{\left(b \cdot y\right)} - 1\right)}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt37.8

    \[\leadsto \frac{y \cdot \left({e}^{\left(\left(a + b\right) \cdot y\right)} - 1\right)}{\left(\color{blue}{\sqrt{{e}^{\left(a \cdot y\right)}} \cdot \sqrt{{e}^{\left(a \cdot y\right)}}} - 1\right) \cdot \left({e}^{\left(b \cdot y\right)} - 1\right)}\]
  4. Applied difference-of-sqr-137.8

    \[\leadsto \frac{y \cdot \left({e}^{\left(\left(a + b\right) \cdot y\right)} - 1\right)}{\color{blue}{\left(\left(\sqrt{{e}^{\left(a \cdot y\right)}} + 1\right) \cdot \left(\sqrt{{e}^{\left(a \cdot y\right)}} - 1\right)\right)} \cdot \left({e}^{\left(b \cdot y\right)} - 1\right)}\]
  5. Using strategy rm
  6. Applied add-sqr-sqrt37.8

    \[\leadsto \frac{y \cdot \left({e}^{\left(\left(a + b\right) \cdot y\right)} - 1\right)}{\left(\left(\sqrt{{e}^{\left(a \cdot y\right)}} + 1\right) \cdot \left(\color{blue}{\sqrt{\sqrt{{e}^{\left(a \cdot y\right)}}} \cdot \sqrt{\sqrt{{e}^{\left(a \cdot y\right)}}}} - 1\right)\right) \cdot \left({e}^{\left(b \cdot y\right)} - 1\right)}\]
  7. Applied difference-of-sqr-137.8

    \[\leadsto \frac{y \cdot \left({e}^{\left(\left(a + b\right) \cdot y\right)} - 1\right)}{\left(\left(\sqrt{{e}^{\left(a \cdot y\right)}} + 1\right) \cdot \color{blue}{\left(\left(\sqrt{\sqrt{{e}^{\left(a \cdot y\right)}}} + 1\right) \cdot \left(\sqrt{\sqrt{{e}^{\left(a \cdot y\right)}}} - 1\right)\right)}\right) \cdot \left({e}^{\left(b \cdot y\right)} - 1\right)}\]
  8. Final simplification37.8

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

Runtime

Time bar (total: 45.7s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (y e a b)
  :name "(y*(e^((a+b)*y)-1))/((e^(a*y)-1)(e^(b*y)-1))"
  (/ (* y (- (pow e (* (+ a b) y)) 1)) (* (- (pow e (* a y)) 1) (- (pow e (* b y)) 1))))