Details

Time bar (total: 4.4s)

sample22.0ms

Algorithm
intervals
Results
7.0ms52×body1280valid
4.0ms133×body80valid
3.0ms35×body640valid
2.0ms23×body320valid
1.0ms13×body160valid

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0126
1166
2196
3216
4276
5396
6586
7796
81076
91606
102776
113036
123036

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.7b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
4.1b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
52×times-frac
45×add-sqr-sqrt
23×add-cube-cbrt
18×distribute-lft-out distribute-lft-out--
9×associate-/r* difference-of-squares
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
4×associate-/r/
3×pow1
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 104
Calls
3 calls:
5.0ms
(/ x (+ x 1.0))
8.0ms
(/ (+ x 1.0) (- x 1.0))
32.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series198.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ x (+ x 1.0))
39.0ms
(/ (+ x 1.0) (- x 1.0))
126.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify41.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0392760
11379726
25001716

prune200.0ms

Filtered
113 candidates to 76 candidates (67.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1058113
Fresh000
Picked101
Done000
Total1068114

Merged error: 0.0b

Counts
114 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b
(/ (+ x 1.0) (- x 1.0))
4.0b
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
4.1b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
178×*-un-lft-identity
80×times-frac
64×add-sqr-sqrt
44×distribute-lft-out--
32×exp-prod
30×distribute-lft-out
18×add-cube-cbrt
17×log-pow difference-of-squares
9×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 log-prod associate-/r*
4×exp-sum associate-/l*
3×sub-neg
2×flip3-- exp-diff diff-log associate-/r/ flip-- rem-exp-log associate-/l/
1×cbrt-undiv log-div frac-2neg flip3-+ div-exp rem-log-exp clear-num frac-sub flip-+ div-inv
Counts
4 → 130
Calls
4 calls:
34.0ms
(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
8.0ms
(/ (+ x 1.0) (- x 1.0))
33.0ms
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
29.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
37.0ms
(/ (+ x 1.0) (- x 1.0))
127.0ms
(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
126.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
04041009
11249941
25001931

prune210.0ms

Filtered
142 candidates to 85 candidates (59.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1402142
Fresh257
Picked101
Done000
Total1437150

Merged error: 0.0b

Counts
150 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (/ x (+ x 1.0)))
0.0b
(/ (+ x 1.0) (- x 1.0))
0.0b
(* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0)))))
4.0b
(log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
149×*-un-lft-identity
64×times-frac
58×exp-prod
37×add-sqr-sqrt
25×add-cube-cbrt distribute-lft-out
20×pow-prod-up
18×distribute-rgt-neg-in
13×distribute-lft-out--
12×log-pow
9×pow1
8×add-cbrt-cube
7×add-exp-log
5×associate-/r* add-log-exp difference-of-squares
4×exp-neg associate-*r/ associate-/r/ associate-/l*
3×log-div associate-*r* associate-*l*
2×neg-sub0 flip3-+ exp-diff rem-log-exp pow-prod-down prod-exp un-div-inv flip-+ div-inv associate-/l/
1×cbrt-undiv log-prod flip3-- frac-2neg div-exp clear-num *-commutative flip-- cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 127
Calls
4 calls:
6.0ms
(exp (/ x (+ x 1.0)))
8.0ms
(/ (+ x 1.0) (- x 1.0))
67.0ms
(* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0)))))
68.0ms
(log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))

series516.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(exp (/ x (+ x 1.0)))
40.0ms
(/ (+ x 1.0) (- x 1.0))
180.0ms
(* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0)))))
246.0ms
(log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))

simplify50.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0443925
11531833
25002805

prune232.0ms

Filtered
139 candidates to 86 candidates (61.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1381139
Fresh156
Picked011
Done000
Total1397146

Merged error: 0.0b

Counts
146 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cbrt (log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))) (cbrt (log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))))
4.0b
(log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))
4.0b
(log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))
4.0b
(log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))

rewrite383.0ms

Algorithm
rewrite-expression-head
Rules
976×*-un-lft-identity
372×exp-prod
336×times-frac
208×log-pow
192×cbrt-prod
188×pow-prod-up
177×distribute-rgt-neg-in
168×distribute-lft-out
84×distribute-lft-out--
82×swap-sqr
44×pow1
20×add-sqr-sqrt
18×associate-*r* associate-*l*
13×pow-prod-down
12×add-cube-cbrt
9×add-exp-log log-div
6×exp-neg pow1/3 associate-*r/ rem-log-exp
4×prod-exp add-cbrt-cube add-log-exp unswap-sqr
3×neg-sub0 log-prod exp-diff un-div-inv
2×pow-sqr
1×pow2 pow-plus *-commutative cbrt-unprod
Counts
4 → 215
Calls
4 calls:
143.0ms
(* (cbrt (log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))) (cbrt (log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))))
67.0ms
(log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))
68.0ms
(log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))
68.0ms
(log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
611.0ms
(* (cbrt (log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))) (cbrt (log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))))
252.0ms
(log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))
253.0ms
(log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))
247.0ms
(log (* (exp (/ x (+ x 1.0))) (exp (neg (/ (+ x 1.0) (- x 1.0))))))

simplify62.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02773403
110303121
250012387

prune251.0ms

Filtered
227 candidates to 70 candidates (30.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2243227
Fresh145
Picked101
Done101
Total2277234

Merged error: 0.0b

Counts
234 → 7

regimes42.0ms

bsearch3.0ms

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