Details

Time bar (total: 24.8s)

sample729.0ms

Algorithm
intervals
Results
471.0ms3602×body80nan
88.0ms154×body640valid
22.0ms64×body320valid
3.0ms5×body1280valid
3.0ms14×body160valid
2.0ms19×body80valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
024765
151765
2155765
3897765
done5001765

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.3b

localize101.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (sqrt (+ y 1.0)) (sqrt y))
1.9b
(- (sqrt (+ z 1.0)) (sqrt z))
2.6b
(- (sqrt (+ t 1.0)) (sqrt t))
3.0b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite205.0ms

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 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt flip-- distribute-lft-out
Counts
4 → 76
Calls
4 calls:
41.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
61.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
64.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
35.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series368.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
82.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
72.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
111.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.5s

Counts
88 → 88
Iterations

Useful iterations: done (1.4s)

IterNodesCost
021431616
149625556
2182224628
done500024468

prune681.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
1.7b
(- (sqrt (+ y 1.0)) (sqrt y))
2.6b
(- (sqrt (+ t 1.0)) (sqrt t))
3.0b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite233.0ms

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×associate-/r* add-cbrt-cube add-exp-log
4×pow1 associate-/l*
3×sub-neg flip3-- diff-log flip--
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 107
Calls
4 calls:
82.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
65.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
44.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
38.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series484.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
93.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
97.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
89.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.9s

Counts
119 → 119
Iterations

Useful iterations: done (1.9s)

IterNodesCost
027746128
166635985
2278734685
done500434361

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.8b

localize82.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.1b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
1.7b
(- (sqrt (+ y 1.0)) (sqrt y))
2.6b
(- (sqrt (+ t 1.0)) (sqrt t))

rewrite220.0ms

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-cbrt-cube add-exp-log add-log-exp difference-of-squares
7×associate-/l*
6×distribute-lft-out--
4×pow1 associate-/r/
3×flip3-+ flip-+
2×cbrt-undiv clear-num sub-neg frac-2neg flip3-- diff-log div-exp div-inv flip-- associate-/l/
Counts
4 → 129
Calls
4 calls:
63.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
38.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
51.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
60.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

series608.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
216.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
108.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
105.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

simplify2.2s

Counts
141 → 141
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
031655231
176643907
2325342274
done500042274

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.8b

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
1.7b
(- (sqrt (+ y 1.0)) (sqrt y))
2.6b
(- (sqrt (+ t 1.0)) (sqrt t))

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
740×*-un-lft-identity
696×sqrt-prod
594×times-frac
274×distribute-lft-out
266×add-sqr-sqrt
250×add-cube-cbrt
36×associate-/l*
24×sqrt-div associate-/r/
18×associate-/r*
12×flip3-+ flip-+ div-inv
11×add-cbrt-cube add-exp-log
8×add-log-exp difference-of-squares
6×distribute-lft-out--
4×pow1 cbrt-undiv div-exp
2×clear-num sub-neg frac-2neg flip3-- diff-log flip--
1×associate-/l/
Counts
4 → 447
Calls
4 calls:
40.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
120.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
35.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
35.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

series835.0ms

Counts
4 → 12
Calls
4 calls:
435.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
213.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
88.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
99.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

simplify3.5s

Counts
459 → 459
Iterations

Useful iterations: 2 (2.2s)

IterNodesCost
0528296035
11256247349
24922243448
done5000243448

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.8b

regimes1.8s

bsearch0.0ms

simplify28.0ms

Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
0411406
1571365
2611365
done611365

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.5s6236×body80nan
150.0ms293×body640valid
42.0ms107×body320valid
7.0ms10×body1280valid
6.0ms25×body160valid
4.0ms33×body80valid