Details

Time bar (total: 8.7s)

sample573.0ms

Algorithm
intervals
Results
373.0ms4095×body80nan
63.0ms170×body640valid
10.0ms37×body320valid
3.0ms19×body160valid
2.0ms5×body1280valid
2.0ms25×body80valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05119
115619
290719
3500119

prune5.0ms

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: 5.8b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (sqrt (+ x 1.0)) (sqrt x))
2.6b
(- (sqrt (+ t 1.0)) (sqrt t))
3.1b
(- (sqrt (+ z 1.0)) (sqrt z))
3.7b
(- (sqrt (+ y 1.0)) (sqrt y))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
32×*-un-lft-identity sqrt-prod
16×difference-of-squares
12×distribute-lft-out-- add-log-exp
4×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out
Counts
4 → 76
Calls
4 calls:
8.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

series275.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
70.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
66.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
71.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

simplify45.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0472702
11521635
25001620

prune351.0ms

Filtered
88 candidates to 56 candidates (63.6%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New83588
Fresh000
Picked101
Done000
Total84589

Merged error: 0.8b

Counts
89 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.1b
(- (sqrt (+ x 1.0)) (sqrt x))
2.6b
(- (sqrt (+ t 1.0)) (sqrt t))
3.7b
(- (sqrt (+ y 1.0)) (sqrt y))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
86×*-un-lft-identity
44×sqrt-prod
40×add-sqr-sqrt
30×distribute-lft-out
24×times-frac
16×add-cube-cbrt
12×difference-of-squares
10×add-log-exp
9×distribute-lft-out--
6×add-exp-log associate-/r* add-cbrt-cube
4×pow1 associate-/l*
3×sub-neg flip3-- diff-log flip--
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 107
Calls
4 calls:
12.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
8.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

series341.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
65.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
67.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
69.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

simplify65.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06271071
12341979
25001943

prune475.0ms

Filtered
119 candidates to 71 candidates (59.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1145119
Fresh314
Picked101
Done000
Total1186124

Merged error: 0.6b

Counts
124 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.1b
(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
2.1b
(- (sqrt (+ x 1.0)) (sqrt x))
2.6b
(- (sqrt (+ t 1.0)) (sqrt t))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity
52×sqrt-prod
45×distribute-lft-out
43×add-sqr-sqrt
42×times-frac
27×add-cube-cbrt
12×associate-/r*
8×add-exp-log add-cbrt-cube add-log-exp difference-of-squares
7×associate-/l*
6×distribute-lft-out--
4×pow1 associate-/r/
3×flip3-+ flip-+
2×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv associate-/l/
Counts
4 → 129
Calls
4 calls:
15.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
10.0ms
(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
8.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

series428.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
144.0ms
(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
67.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
72.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

simplify71.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
07211296
127311180
250011137

prune564.0ms

Filtered
141 candidates to 83 candidates (58.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1392141
Fresh145
Picked101
Done000
Total1416147

Merged error: 0.5b

Counts
147 → 6

localize45.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (sqrt (+ x 1.0)) (sqrt x))
2.6b
(- (sqrt (+ t 1.0)) (sqrt t))
3.6b
(- (* (sqrt y) (sqrt y)) (* (sqrt (+ y 1.0)) (sqrt y)))
9.2b
(* (/ 1.0 (+ (pow (sqrt (+ y 1.0)) 3) (pow (sqrt y) 3))) (+ (* (sqrt (+ y 1.0)) (sqrt (+ y 1.0))) (- (* (sqrt y) (sqrt y)) (* (sqrt (+ y 1.0)) (sqrt y)))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
130×*-un-lft-identity
64×sqrt-prod
57×associate-*l*
53×distribute-lft-out
52×times-frac
48×sqrt-div
47×add-sqr-sqrt
36×unpow-prod-down cube-prod
34×frac-times
32×frac-add
27×flip3-+ flip-+
26×add-cube-cbrt associate-*r/
19×flip3-- flip--
10×add-log-exp
9×add-exp-log associate-*l/ add-cbrt-cube
8×difference-of-squares
6×pow1 distribute-lft-out--
3×sub-neg diff-log associate-*r* sum-cubes
2×prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv distribute-rgt-in distribute-rgt-out-- distribute-lft-in div-exp pow-prod-down *-commutative div-inv
Counts
4 → 165
Calls
4 calls:
10.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
6.0ms
(- (* (sqrt y) (sqrt y)) (* (sqrt (+ y 1.0)) (sqrt y)))
51.0ms
(* (/ 1.0 (+ (pow (sqrt (+ y 1.0)) 3) (pow (sqrt y) 3))) (+ (* (sqrt (+ y 1.0)) (sqrt (+ y 1.0))) (- (* (sqrt y) (sqrt y)) (* (sqrt (+ y 1.0)) (sqrt y)))))

series498.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
70.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
87.0ms
(- (* (sqrt y) (sqrt y)) (* (sqrt (+ y 1.0)) (sqrt y)))
269.0ms
(* (/ 1.0 (+ (pow (sqrt (+ y 1.0)) 3) (pow (sqrt y) 3))) (+ (* (sqrt (+ y 1.0)) (sqrt (+ y 1.0))) (- (* (sqrt y) (sqrt y)) (* (sqrt (+ y 1.0)) (sqrt y)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
015214094
150013804

prune1.0s

Filtered
177 candidates to 110 candidates (62.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1761177
Fresh145
Picked011
Done000
Total1776183

Merged error: 0.5b

Counts
183 → 6

regimes687.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05039
16039
26039

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.9s20226×body80nan
320.0ms850×body640valid
68.0ms245×body320valid
18.0ms99×body160valid
12.0ms25×body1280valid
9.0ms100×body80valid