Details

Time bar (total: 9.6s)

analyze1.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%0%50%2

sample29.0ms (0.3%)

Algorithm
1×intervals
Results
10.0ms68×body640valid
6.0ms33×body1280valid
4.0ms118×body80valid
2.0ms22×body320valid
1.0ms15×body160valid

simplify13.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (11.0ms)

IterNodesCost
026511
126511

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 21.8b

Counts
2 → 1

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
3.7b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite53.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 132
Calls

4 calls:

35.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
3.0ms
(sqrt (+ x 1.0))

series30.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

13.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
8.0ms
(/ 1.0 (sqrt x))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))

simplify34.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
050761839

prune329.0ms (3.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New13311144
Fresh000
Picked101
Done000
Total13411145

Merged error: 21.0b

Counts
145 → 11

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ 1.0 x)))
0.3b
(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
0.3b
(/ 1.0 (sqrt x))
3.7b
(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

rewrite374.0ms (3.9%)

Algorithm
1×rewrite-expression-head
Rules
2937×times-frac
2554×*-un-lft-identity
1354×add-sqr-sqrt
778×add-cube-cbrt
708×distribute-lft-out
508×sqrt-prod
368×distribute-lft-out--
211×div-inv
144×difference-of-squares
64×distribute-rgt-out--
45×associate-/l*
37×associate-/r/
27×associate-/r*
10×add-exp-log add-cbrt-cube
6×add-log-exp
4×pow1
3×cbrt-undiv frac-2neg div-exp clear-num associate-/l/
2×flip3-- flip3-+ sqrt-div frac-sub flip-- flip-+
1×sub-neg diff-log div-sub frac-add
Counts
4 → 750
Calls

4 calls:

137.0ms
(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
93.0ms
(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))
6.0ms
(/ 1.0 (sqrt (+ 1.0 x)))
4.0ms
(/ 1.0 (sqrt x))

series45.0ms (0.5%)

Counts
4 → 12
Calls

4 calls:

20.0ms
(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
15.0ms
(/ 1.0 (sqrt x))
6.0ms
(/ 1.0 (sqrt (+ 1.0 x)))
4.0ms
(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

simplify185.0ms (1.9%)

Algorithm
1×egg-herbie
Counts
762 → 762
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
0498323232
1498323232

prune4.9s (51.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New7593762
Fresh9110
Picked101
Done000
Total7694773

Merged error: 3.9b

Counts
773 → 4

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ 1.0 x)))
0.2b
(/ (/ (- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1)) (* (/ x 1.0) (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
0.3b
(/ 1.0 (sqrt x))
3.2b
(- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1))

rewrite92.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
422×times-frac
403×*-un-lft-identity
160×sqrt-prod
158×distribute-lft-out
142×add-sqr-sqrt add-cube-cbrt
50×associate-/r/
40×div-inv
33×add-exp-log add-cbrt-cube
27×associate-/r*
17×cbrt-undiv div-exp
16×associate-*r/ associate-/l*
15×frac-times associate-*l/
6×add-log-exp
4×pow1 prod-exp cbrt-unprod
3×frac-2neg clear-num
2×flip3-+ sqrt-div div-sub flip-+
1×sub-neg flip3-- diff-log frac-add frac-sub flip-- associate-/l/
Counts
4 → 287
Calls

4 calls:

50.0ms
(/ (/ (- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1)) (* (/ x 1.0) (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
9.0ms
(- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1))
8.0ms
(/ 1.0 (sqrt (+ 1.0 x)))
4.0ms
(/ 1.0 (sqrt x))

series50.0ms (0.5%)

Counts
4 → 12
Calls

4 calls:

31.0ms
(/ (/ (- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1)) (* (/ x 1.0) (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
10.0ms
(/ 1.0 (sqrt (+ 1.0 x)))
8.0ms
(/ 1.0 (sqrt x))
1.0ms
(- (* 1.0 (/ (+ 1.0 x) 1.0)) (/ x 1))

simplify63.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
299 → 299
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
050229018

prune1.2s (12.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2972299
Fresh123
Picked101
Done000
Total2994303

Merged error: 3.9b

Counts
303 → 4

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ 1.0 x)))
0.3b
(/ 1.0 (sqrt x))
0.4b
(/ 1.0 (* (/ x 1.0) (/ (+ 1.0 x) 1.0)))
3.8b
(/ (/ 1.0 (* (/ x 1.0) (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))

rewrite84.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
425×times-frac
405×*-un-lft-identity
160×sqrt-prod
158×distribute-lft-out
144×add-sqr-sqrt add-cube-cbrt
53×associate-/r/
51×add-exp-log add-cbrt-cube
41×div-inv
28×associate-/r*
26×cbrt-undiv div-exp
19×associate-/l*
16×frac-times associate-*r/ associate-*l/
8×prod-exp cbrt-unprod
4×pow1 frac-2neg clear-num add-log-exp
2×flip3-+ sqrt-div flip-+
1×frac-add associate-/l/
Counts
4 → 304
Calls

4 calls:

44.0ms
(/ (/ 1.0 (* (/ x 1.0) (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
9.0ms
(/ 1.0 (* (/ x 1.0) (/ (+ 1.0 x) 1.0)))
6.0ms
(/ 1.0 (sqrt (+ 1.0 x)))
4.0ms
(/ 1.0 (sqrt x))

series49.0ms (0.5%)

Counts
4 → 12
Calls

4 calls:

34.0ms
(/ (/ 1.0 (* (/ x 1.0) (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
7.0ms
(/ 1.0 (sqrt x))
6.0ms
(/ 1.0 (sqrt (+ 1.0 x)))
3.0ms
(/ 1.0 (* (/ x 1.0) (/ (+ 1.0 x) 1.0)))

simplify86.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
316 → 316
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
053537345

prune943.0ms (9.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New3079316
Fresh123
Picked011
Done000
Total30812320

Merged error: 0.0b

Counts
320 → 12

regimes71.0ms (0.7%)

Accuracy

Total 0.4b remaining (87.7%)

Threshold costs 0.4b (87.7%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01825
11825

end0.0ms (0%)

sample817.0ms (8.5%)

Algorithm
1×intervals
Results
271.0ms1869×body640valid
209.0ms1126×body1280valid
159.0ms4088×body80valid
64.0ms601×body320valid
22.0ms316×body160valid

Profiling

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