Average Error: 3.6 → 2.5
Time: 2.9m
Precision: 64
Internal Precision: 128
\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
↓
\[\begin{array}{l} \mathbf{if}\;\beta \le 1.9464430483839193 \cdot 10^{+161}:\\ \;\;\;\;\frac{1}{\frac{\left(\alpha + \beta\right) + 2}{\alpha \cdot \beta + \left(\left(\beta + 1.0\right) + \alpha\right)}} \cdot \frac{\frac{1}{\left(\alpha + 2\right) + \left(\beta + 1.0\right)}}{\left(\alpha + \beta\right) + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\left(\alpha + 2\right) + \left(\beta + 1.0\right)}}{\left(\alpha + \beta\right) + 2} \cdot \frac{1}{2.0 - 1.0 \cdot \left(\alpha + \beta\right)}\\ \end{array}\]

Error

Bits error versus alpha

Bits error versus beta

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if beta < 1.9464430483839193e+161

    1. Initial program 1.2

      \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity1.2

      \[\leadsto \frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\color{blue}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0\right)}}\]

    4. Applied div-inv1.2

      \[\leadsto \frac{\color{blue}{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1} \cdot \frac{1}{\left(\alpha + \beta\right) + 2 \cdot 1}}}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0\right)}\]

    5. Applied times-frac1.5

      \[\leadsto \color{blue}{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{1} \cdot \frac{\frac{1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}}\]

    6. Simplified1.5

      \[\leadsto \color{blue}{\frac{\alpha \cdot \beta + \left(\alpha + \left(\beta + 1.0\right)\right)}{2 + \left(\beta + \alpha\right)}} \cdot \frac{\frac{1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]

    7. Simplified1.5

      \[\leadsto \frac{\alpha \cdot \beta + \left(\alpha + \left(\beta + 1.0\right)\right)}{2 + \left(\beta + \alpha\right)} \cdot \color{blue}{\frac{\frac{1}{\left(\alpha + 2\right) + \left(1.0 + \beta\right)}}{\left(\alpha + \beta\right) + 2}}\]
    8. Using strategy rm

    9. Applied clear-num1.5

      \[\leadsto \color{blue}{\frac{1}{\frac{2 + \left(\beta + \alpha\right)}{\alpha \cdot \beta + \left(\alpha + \left(\beta + 1.0\right)\right)}}} \cdot \frac{\frac{1}{\left(\alpha + 2\right) + \left(1.0 + \beta\right)}}{\left(\alpha + \beta\right) + 2}\]

    if 1.9464430483839193e+161 < beta

    1. Initial program 15.8

      \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity15.8

      \[\leadsto \frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\color{blue}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0\right)}}\]

    4. Applied div-inv15.8

      \[\leadsto \frac{\color{blue}{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1} \cdot \frac{1}{\left(\alpha + \beta\right) + 2 \cdot 1}}}{1 \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0\right)}\]

    5. Applied times-frac17.1

      \[\leadsto \color{blue}{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{1} \cdot \frac{\frac{1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}}\]

    6. Simplified17.1

      \[\leadsto \color{blue}{\frac{\alpha \cdot \beta + \left(\alpha + \left(\beta + 1.0\right)\right)}{2 + \left(\beta + \alpha\right)}} \cdot \frac{\frac{1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]

    7. Simplified17.1

      \[\leadsto \frac{\alpha \cdot \beta + \left(\alpha + \left(\beta + 1.0\right)\right)}{2 + \left(\beta + \alpha\right)} \cdot \color{blue}{\frac{\frac{1}{\left(\alpha + 2\right) + \left(1.0 + \beta\right)}}{\left(\alpha + \beta\right) + 2}}\]
    8. Using strategy rm

    9. Applied clear-num17.1

      \[\leadsto \color{blue}{\frac{1}{\frac{2 + \left(\beta + \alpha\right)}{\alpha \cdot \beta + \left(\alpha + \left(\beta + 1.0\right)\right)}}} \cdot \frac{\frac{1}{\left(\alpha + 2\right) + \left(1.0 + \beta\right)}}{\left(\alpha + \beta\right) + 2}\]

    10. Taylor expanded around 0 7.6

      \[\leadsto \frac{1}{\color{blue}{2.0 - \left(1.0 \cdot \beta + 1.0 \cdot \alpha\right)}} \cdot \frac{\frac{1}{\left(\alpha + 2\right) + \left(1.0 + \beta\right)}}{\left(\alpha + \beta\right) + 2}\]

    11. Simplified7.6

      \[\leadsto \frac{1}{\color{blue}{2.0 - \left(\beta + \alpha\right) \cdot 1.0}} \cdot \frac{\frac{1}{\left(\alpha + 2\right) + \left(1.0 + \beta\right)}}{\left(\alpha + \beta\right) + 2}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\beta \le 1.9464430483839193 \cdot 10^{+161}:\\ \;\;\;\;\frac{1}{\frac{\left(\alpha + \beta\right) + 2}{\alpha \cdot \beta + \left(\left(\beta + 1.0\right) + \alpha\right)}} \cdot \frac{\frac{1}{\left(\alpha + 2\right) + \left(\beta + 1.0\right)}}{\left(\alpha + \beta\right) + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\left(\alpha + 2\right) + \left(\beta + 1.0\right)}}{\left(\alpha + \beta\right) + 2} \cdot \frac{1}{2.0 - 1.0 \cdot \left(\alpha + \beta\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019016 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/3"
  :pre (and (> alpha -1) (> beta -1))
  (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))

Details

Time bar (total: 2.9m)Debug log

sample72.0ms

Algorithm
intervals
Results
256×(pre true 80)
256×(body real 80)

simplify456.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
456.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.3b

localize32.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
0.0b
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
0.0b
(+ (+ alpha beta) (* beta alpha))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
450×times-frac
212×add-cube-cbrt
212×*-un-lft-identity
212×add-sqr-sqrt
54×associate-/l*
36×associate-/r/
21×flip-+
21×flip3-+
18×div-inv
15×add-exp-log
15×add-cbrt-cube
7×div-exp
7×cbrt-undiv
6×add-log-exp
6×associate-/r*
4×pow1
3×associate-/l/
2×frac-2neg
2×clear-num
2×associate-+l+
2×+-commutative
1×sum-log
Counts
4 → 280
Calls
4 calls:
Slowest
109.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
42.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
22.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)
6.0ms
(+ (+ alpha beta) (* beta alpha))

series187.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
65.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
10.0ms
(+ (+ alpha beta) (* beta alpha))
8.0ms
(+ (+ (+ alpha beta) (* 2 1)) 1.0)

simplify1.2m

Counts
411 → 292
Calls
411 calls:
Slowest
1.0s
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) 1)
776.0ms
(+ (pow (+ (+ alpha beta) (* beta alpha)) 3) (pow 1.0 3))
736.0ms
(/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
697.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
678.0ms
(/ (/ (/ 1 (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

prune4.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (+ (* alpha beta) (+ alpha (+ beta 1.0))) (+ 2 (+ beta alpha)))
0.3b
(* (/ (+ (* alpha beta) (+ alpha (+ beta 1.0))) (+ 2 (+ beta alpha))) (/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2)))
0.1b
(/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2))
0.0b
(/ 1 (+ (+ alpha 2) (+ 1.0 beta)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
56×associate-/r/
51×*-un-lft-identity
49×add-cube-cbrt
49×add-sqr-sqrt
45×flip-+
45×flip3-+
36×associate-*r*
32×frac-add
30×add-exp-log
20×add-cbrt-cube
15×associate-*l*
13×associate-/l*
12×div-inv
10×div-exp
10×associate-/r*
7×pow1
6×prod-exp
6×cbrt-undiv
4×add-log-exp
4×cbrt-unprod
4×rec-exp
3×associate-/l/
3×frac-2neg
3×clear-num
1×inv-pow
1×distribute-lft-out
1×pow-flip
1×*-commutative
1×associate-*r/
1×associate-*l/
1×pow-prod-down
1×frac-times
Counts
4 → 186
Calls
4 calls:
Slowest
18.0ms
(/ (+ (* alpha beta) (+ alpha (+ beta 1.0))) (+ 2 (+ beta alpha)))
15.0ms
(* (/ (+ (* alpha beta) (+ alpha (+ beta 1.0))) (+ 2 (+ beta alpha))) (/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2)))
7.0ms
(/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2))
3.0ms
(/ 1 (+ (+ alpha 2) (+ 1.0 beta)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(* (/ (+ (* alpha beta) (+ alpha (+ beta 1.0))) (+ 2 (+ beta alpha))) (/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2)))
65.0ms
(/ (+ (* alpha beta) (+ alpha (+ beta 1.0))) (+ 2 (+ beta alpha)))
55.0ms
(/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2))
32.0ms
(/ 1 (+ (+ alpha 2) (+ 1.0 beta)))

simplify27.4s

Counts
193 → 198
Calls
193 calls:
Slowest
615.0ms
(+ (pow (* alpha beta) 3) (pow (+ alpha (+ beta 1.0)) 3))
600.0ms
(/ (* (* (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (/ 1 (+ (+ alpha 2) (+ 1.0 beta)))) (/ 1 (+ (+ alpha 2) (+ 1.0 beta)))) (* (* (+ (+ alpha beta) 2) (+ (+ alpha beta) 2)) (+ (+ alpha beta) 2)))
546.0ms
(/ (/ 1 (- (* (+ alpha 2) (+ alpha 2)) (* (+ 1.0 beta) (+ 1.0 beta)))) (* (cbrt (+ (+ alpha beta) 2)) (cbrt (+ (+ alpha beta) 2))))
525.0ms
(* (/ (* (* (+ (* alpha beta) (+ alpha (+ beta 1.0))) (+ (* alpha beta) (+ alpha (+ beta 1.0)))) (+ (* alpha beta) (+ alpha (+ beta 1.0)))) (* (* (+ 2 (+ beta alpha)) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))) (* (* (/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2)) (/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2))) (/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2))))
512.0ms
(/ 1 (+ (* (+ (pow alpha 3) (pow 2 3)) (- 1.0 beta)) (* (+ (* alpha alpha) (- (* 2 2) (* alpha 2))) (- (* 1.0 1.0) (* beta beta)))))

prune3.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0))))
0.3b
(* (/ 1 (/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0))))) (/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2)))
0.1b
(/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2))
0.1b
(/ 1 (/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0)))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
52×associate-/r/
49×add-cube-cbrt
49×*-un-lft-identity
49×add-sqr-sqrt
40×flip-+
40×add-exp-log
40×flip3-+
36×associate-*r*
28×frac-add
21×associate-/r*
13×associate-/l*
13×div-inv
13×div-exp
13×add-cbrt-cube
12×rec-exp
9×prod-exp
7×pow1
5×associate-*l*
4×add-log-exp
3×associate-/l/
3×frac-2neg
3×clear-num
3×cbrt-undiv
2×cbrt-unprod
1×inv-pow
1×pow-flip
1×*-commutative
1×associate-*r/
1×associate-*l/
1×pow-prod-down
1×frac-times
Counts
4 → 184
Calls
4 calls:
Slowest
13.0ms
(/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2))
12.0ms
(* (/ 1 (/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0))))) (/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2)))
8.0ms
(/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0))))
5.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0)))))

series272.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(* (/ 1 (/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0))))) (/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2)))
72.0ms
(/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0))))
42.0ms
(/ 1 (/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0)))))
41.0ms
(/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2))

simplify26.7s

Counts
189 → 196
Calls
189 calls:
Slowest
869.0ms
(/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2))
551.0ms
(/ (/ 1 (- (* (+ alpha 2) (+ alpha 2)) (* (+ 1.0 beta) (+ 1.0 beta)))) (* (cbrt (+ (+ alpha beta) 2)) (cbrt (+ (+ alpha beta) 2))))
523.0ms
(/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2))
523.0ms
(+ (- (log (/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0)))))) (log (/ (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (+ (+ alpha beta) 2))))
519.0ms
(* (* (* (/ 1 (/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0))))) (/ 1 (/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0)))))) (/ 1 (/ (+ 2 (+ beta alpha)) (+ (* alpha beta) (+ alpha (+ beta 1.0)))))) (/ (* (* (/ 1 (+ (+ alpha 2) (+ 1.0 beta))) (/ 1 (+ (+ alpha 2) (+ 1.0 beta)))) (/ 1 (+ (+ alpha 2) (+ 1.0 beta)))) (* (* (+ (+ alpha beta) 2) (+ (+ alpha beta) 2)) (+ (+ alpha beta) 2))))

prune3.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize78.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ (+ 2 beta) alpha))
2.2b
(/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))
0.9b
(/ (sqrt (/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))) (* (sqrt (+ 2 (+ beta alpha))) (+ (+ beta alpha) (+ 1.0 2))))
0.5b
(* (sqrt (+ 2 (+ beta alpha))) (+ (+ beta alpha) (+ 1.0 2)))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
50×flip-+
50×flip3-+
41×*-un-lft-identity
39×add-cube-cbrt
39×add-sqr-sqrt
33×sqrt-prod
29×sqrt-div
28×associate-/r/
24×associate-/l*
24×frac-add
24×frac-times
15×add-exp-log
15×add-cbrt-cube
12×associate-*r/
7×associate-/r*
6×associate-*l*
6×pow1
5×associate-/l/
5×div-inv
4×add-log-exp
4×associate-*l/
4×associate-*r*
4×div-exp
4×cbrt-undiv
3×frac-2neg
3×clear-num
2×cbrt-unprod
2×prod-exp
1×distribute-lft-out
1×*-commutative
1×pow-prod-down
1×distribute-lft-in
1×distribute-rgt-in
Counts
4 → 177
Calls
4 calls:
Slowest
45.0ms
(/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ (+ 2 beta) alpha))
37.0ms
(/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))
35.0ms
(/ (sqrt (/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))) (* (sqrt (+ 2 (+ beta alpha))) (+ (+ beta alpha) (+ 1.0 2))))
9.0ms
(* (sqrt (+ 2 (+ beta alpha))) (+ (+ beta alpha) (+ 1.0 2)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
90.0ms
(/ (sqrt (/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))) (* (sqrt (+ 2 (+ beta alpha))) (+ (+ beta alpha) (+ 1.0 2))))
55.0ms
(/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))
54.0ms
(/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ (+ 2 beta) alpha))
50.0ms
(* (sqrt (+ 2 (+ beta alpha))) (+ (+ beta alpha) (+ 1.0 2)))

simplify25.0s

Counts
195 → 189
Calls
195 calls:
Slowest
1.0s
(- (* (+ (+ beta 1.0) (* alpha beta)) (+ (+ beta 1.0) (* alpha beta))) (* alpha alpha))
753.0ms
(+ (pow (+ (+ beta 1.0) (* alpha beta)) 3) (pow alpha 3))
736.0ms
(- (* (+ (+ beta 1.0) (* alpha beta)) (+ (+ beta 1.0) (* alpha beta))) (* alpha alpha))
584.0ms
(+ (pow (+ (+ beta 1.0) (* alpha beta)) 3) (pow alpha 3))
507.0ms
(/ (* (* (sqrt (/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha)))) (sqrt (/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha))))) (sqrt (/ (+ (+ (+ beta 1.0) (* alpha beta)) alpha) (+ 2 (+ beta alpha))))) (* (* (* (sqrt (+ 2 (+ beta alpha))) (sqrt (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (* (* (+ (+ beta alpha) (+ 1.0 2)) (+ (+ beta alpha) (+ 1.0 2))) (+ (+ beta alpha) (+ 1.0 2)))))

prune3.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes181.0ms

Accuracy

54.5% (1.3b remaining)

Error of 2.5b against oracle of 1.2b and baseline of 4.1b

bsearch138.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
8000×(pre true 80)
8000×(body real 80)