Details

sample1.2s

Algorithm

intervals

Results

886.0ms	3602×	body	80	nan
63.0ms	154×	body	640	valid
21.0ms	64×	body	320	valid
3.0ms	14×	body	160	valid
3.0ms	5×	body	1280	valid
2.0ms	19×	body	80	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	897
2	155
1	51
0	24

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.3b

localize48.0ms

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))

rewrite149.0ms

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:

35.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
34.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
35.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
42.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series315.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
70.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
78.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
77.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify944.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1822
1	496
0	214

prune823.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize82.0ms

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))

rewrite180.0ms

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:

48.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
44.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
40.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
43.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series471.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
96.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
94.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
101.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.4s

Counts

119 → 119

Iterations

Iter	Nodes
done	5004
2	2787
1	666
0	277

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.8b

localize88.0ms

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))

rewrite241.0ms

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:

66.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
67.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
35.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
64.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series619.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
198.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
105.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
95.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify2.0s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
2	3253
1	766
0	316

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.8b

localize122.0ms

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))

rewrite333.0ms

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:

51.0ms	(/ 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))))
51.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
53.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series827.0ms

Counts

4 → 12

Calls

4 calls:

423.0ms	(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
199.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
91.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
114.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify2.8s

Counts

459 → 459

Iterations

Iter	Nodes
done	5000
2	4922
1	1256
0	528

prune3.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.8b

regimes1.9s

bsearch0.0ms

simplify29.0ms

Iterations

Iter	Nodes
done	70
3	70
2	67
1	60
0	43

end0.0ms

sample2.0s

Algorithm

intervals

Results

984.0ms	6236×	body	80	nan
547.0ms	293×	body	640	valid
73.0ms	107×	body	320	valid
7.0ms	10×	body	1280	valid
6.0ms	25×	body	160	valid
4.0ms	33×	body	80	valid