Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	59×	body	1024	valid
6.0ms	146×	body	128	valid
3.0ms	26×	body	512	valid
2.0ms	25×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify177.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 19.7b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
5.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite75.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

124×	`add-sqr-sqrt_binary64_1477`
118×	`times-frac_binary64_1461`
113×	`*-un-lft-identity_binary64_1455`
72×	`sqrt-prod_binary64_1471`
54×	`add-cube-cbrt_binary64_1490`
27×	`cancel-sign-sub-inv_binary64_1421`
25×	`difference-of-squares_binary64_1424`
13×	`distribute-lft-out--_binary64_1407` `associate-/r*_binary64_1399`
11×	`add-exp-log_binary64_1493`
10×	`distribute-lft-out_binary64_1406`
7×	`pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `div-inv_binary64_1452`
6×	`pow-flip_binary64_1529` `associate-/l*_binary64_1400`
5×	`add-log-exp_binary64_1494`
4×	`associate-/r/_binary64_1401` `sqrt-div_binary64_1472` `div-exp_binary64_1506`
2×	`sqrt-pow1_binary64_1473` `inv-pow_binary64_1540` `flip-+_binary64_1429` `1-exp_binary64_1499` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `pow1/2_binary64_1535` `flip3-+_binary64_1458` `rec-exp_binary64_1505`
1×	`flip--_binary64_1430` `diff-log_binary64_1547` `frac-sub_binary64_1464` `sub-neg_binary64_1448` `flip3--_binary64_1459`

Counts

3 → 173

Calls

3 calls:

40.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))

series156.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

71.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
48.0ms	(/.f64 1 (sqrt.f64 x))
37.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify82.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4920	3438
1	4920	3438

prune560.0ms (11%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	172	10	182
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	173	10	183

Merged error: 18.9b

Counts

183 → 10

Compiler

Compiled 8648 to 6907 computations (20.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
5.3b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite53.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_1477`
38×	`sqrt-prod_binary64_1471`
34×	`*-un-lft-identity_binary64_1455`
12×	`difference-of-squares_binary64_1424`
11×	`add-cube-cbrt_binary64_1490`
10×	`add-cbrt-cube_binary64_1491` `associate-/l*_binary64_1400` `times-frac_binary64_1461` `add-exp-log_binary64_1493`
9×	`distribute-lft-out--_binary64_1407`
7×	`associate-r_binary64_1395` `pow1_binary64_1516`
6×	`cancel-sign-sub-inv_binary64_1421` `associate-l_binary64_1396`
5×	`add-log-exp_binary64_1494`
4×	`distribute-lft-out_binary64_1406` `associate-*r/_binary64_1397` `sqrt-div_binary64_1472` `unswap-sqr_binary64_1423`
3×	`pow-prod-down_binary64_1526`
2×	`prod-exp_binary64_1504` `sqrt-pow1_binary64_1473` `associate-/r/_binary64_1401` `flip-+_binary64_1429` `associate-/l/_binary64_1402` `div-exp_binary64_1506` `flip--_binary64_1430` `cbrt-undiv_binary64_1489` `cbrt-unprod_binary64_1488` `pow1/2_binary64_1535` `flip3-+_binary64_1458` `flip3--_binary64_1459`
1×	`clear-num_binary64_1454` `associate-/r_binary64_1399` `-commutative_binary64_1386` `sqrt-unprod_binary64_1475` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `sub-neg_binary64_1448` `div-inv_binary64_1452` `div-sub_binary64_1460`

Counts

3 → 97

Calls

3 calls:

19.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
13.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
12.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

series301.0ms (5.9%)

Counts

3 → 9

Calls

3 calls:

172.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
72.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
57.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5017	2435

prune194.0ms (3.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	113	3	116

Merged error: 0.3b

Counts

116 → 3

Compiler

Compiled 3313 to 2294 computations (30.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite75.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_1455`
78×	`times-frac_binary64_1461`
55×	`sqrt-prod_binary64_1471`
47×	`add-sqr-sqrt_binary64_1477`
45×	`distribute-lft-out_binary64_1406`
39×	`add-cube-cbrt_binary64_1490`
32×	`add-exp-log_binary64_1493`
27×	`associate-/l*_binary64_1400`
20×	`add-cbrt-cube_binary64_1491`
14×	`div-exp_binary64_1506`
9×	`pow1_binary64_1516`
8×	`associate-/r/_binary64_1401`
7×	`associate-r_binary64_1395` `associate-/r*_binary64_1399` `cbrt-undiv_binary64_1489`
6×	`flip-+_binary64_1429` `add-log-exp_binary64_1494` `flip3-+_binary64_1458` `associate-l_binary64_1396`
5×	`prod-exp_binary64_1504`
4×	`associate-*r/_binary64_1397` `sqrt-div_binary64_1472` `div-inv_binary64_1452` `unswap-sqr_binary64_1423`
3×	`1-exp_binary64_1499` `cbrt-unprod_binary64_1488` `rec-exp_binary64_1505` `pow-prod-down_binary64_1526`
2×	`sqrt-pow1_binary64_1473` `clear-num_binary64_1454` `frac-2neg_binary64_1466` `pow1/2_binary64_1535`
1×	`inv-pow_binary64_1540` `associate-/l/_binary64_1402` `pow-flip_binary64_1529` `*-commutative_binary64_1386` `sqrt-unprod_binary64_1475` `sum-log_binary64_1546` `+-commutative_binary64_1385`

Counts

4 → 166

Calls

4 calls:

22.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

series326.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
60.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
51.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
44.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify88.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4944	4177
1	4944	4177

prune669.0ms (13.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	170	8	178
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	172	9	181

Merged error: 0b

Counts

181 → 9

Compiler

Compiled 11483 to 8371 computations (27.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite74.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64_1461`
159×	`*-un-lft-identity_binary64_1455`
156×	`add-sqr-sqrt_binary64_1477`
119×	`add-cube-cbrt_binary64_1490`
87×	`sqrt-prod_binary64_1471`
49×	`distribute-lft-out_binary64_1406`
21×	`associate-/l*_binary64_1400`
20×	`associate-/r/_binary64_1401`
19×	`add-exp-log_binary64_1493`
13×	`add-cbrt-cube_binary64_1491`
12×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
11×	`associate-/r*_binary64_1399`
10×	`div-inv_binary64_1452`
9×	`pow1_binary64_1516`
8×	`div-exp_binary64_1506`
7×	`associate-r_binary64_1395`
6×	`add-log-exp_binary64_1494` `associate-l_binary64_1396`
4×	`sqrt-div_binary64_1472` `cbrt-undiv_binary64_1489` `unswap-sqr_binary64_1423`
3×	`pow-prod-down_binary64_1526`
2×	`sqrt-pow1_binary64_1473` `associate-*r/_binary64_1397` `1-exp_binary64_1499` `clear-num_binary64_1454` `frac-2neg_binary64_1466` `pow1/2_binary64_1535` `rec-exp_binary64_1505`
1×	`prod-exp_binary64_1504` `inv-pow_binary64_1540` `associate-/l/_binary64_1402` `pow-flip_binary64_1529` `*-commutative_binary64_1386` `sqrt-unprod_binary64_1475` `cbrt-unprod_binary64_1488` `sum-log_binary64_1546` `+-commutative_binary64_1385`

Counts

4 → 252

Calls

4 calls:

15.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

series336.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

171.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
74.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
49.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
42.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

simplify161.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4947	9756
1	4947	9756

prune588.0ms (11.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	265	8	273

Merged error: 0b

Counts

273 → 8

Compiler

Compiled 9202 to 6699 computations (27.2% saved)

regimes23.0ms (0.5%)

Compiler: Compiled 170 to 134 computations (21.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

end0.0ms (0%)

sample1.0s (19.8%)

Algorithm

1×

intervals

Results

330.0ms	2154×	body	1024	valid
178.0ms	4311×	body	128	valid
122.0ms	1055×	body	512	valid
36.0ms	480×	body	256	valid

Compiler

Compiled 211 to 169 computations (19.9% saved)

Details

analyze2.0ms (0%)

sample25.0ms (0.5%)

simplify177.0ms (3.5%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

rewrite75.0ms (1.5%)

series156.0ms (3.1%)

simplify82.0ms (1.6%)

prune560.0ms (11%)

localize7.0ms (0.1%)

rewrite53.0ms (1.1%)

series301.0ms (5.9%)

simplify70.0ms (1.4%)

prune194.0ms (3.8%)

localize9.0ms (0.2%)

rewrite75.0ms (1.5%)

series326.0ms (6.4%)

simplify88.0ms (1.7%)

prune669.0ms (13.2%)

localize11.0ms (0.2%)

rewrite74.0ms (1.5%)

series336.0ms (6.6%)

simplify161.0ms (3.2%)

prune588.0ms (11.6%)

regimes23.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.0s (19.8%)

Profiling