Details

analyze101.0ms (1.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17
0	1	1
1	1	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)

sample27.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	81×	body	1024	valid
5.0ms	123×	body	128	valid
4.0ms	36×	body	512	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify10.0ms (0.2%)

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: 22.1b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite72.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64_1464`
118×	`times-frac_binary64_1448`
117×	`*-un-lft-identity_binary64_1442`
76×	`sqrt-prod_binary64_1458`
56×	`add-cube-cbrt_binary64_1477`
27×	`cancel-sign-sub-inv_binary64_1408`
25×	`difference-of-squares_binary64_1411`
13×	`associate-/r*_binary64_1386` `distribute-lft-out--_binary64_1394`
12×	`add-exp-log_binary64_1480`
11×	`distribute-lft-out_binary64_1393`
9×	`pow1_binary64_1503`
8×	`add-cbrt-cube_binary64_1478`
7×	`div-inv_binary64_1439`
6×	`associate-/l*_binary64_1387` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `pow-flip_binary64_1516`
4×	`associate-/r/_binary64_1388` `div-exp_binary64_1493`
3×	`sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522`
2×	`inv-pow_binary64_1527` `cbrt-undiv_binary64_1476` `clear-num_binary64_1441` `1-exp_binary64_1486` `rec-exp_binary64_1492` `frac-2neg_binary64_1453`
1×	`rem-sqrt-square_binary64_1455` `sub-neg_binary64_1435` `flip3--_binary64_1446` `frac-sub_binary64_1451` `flip--_binary64_1417` `diff-log_binary64_1534`

Counts

4 → 189

Calls

4 calls:

41.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series94.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
29.0ms	(/.f64 1 (sqrt.f64 x))
17.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify108.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4945	3696
1	4945	3696

prune253.0ms (4.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	190	11	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	191	11	202

Merged error: 21.6b

Counts

202 → 11

Compiler

Compiled 3813 to 2802 computations (26.5% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
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)))
2.9b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite49.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_1464`
42×	`sqrt-prod_binary64_1458`
38×	`*-un-lft-identity_binary64_1442`
13×	`add-cube-cbrt_binary64_1477`
12×	`difference-of-squares_binary64_1411`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
10×	`times-frac_binary64_1448` `associate-/l*_binary64_1387`
9×	`pow1_binary64_1503` `distribute-lft-out--_binary64_1394`
7×	`associate-r_binary64_1382`
6×	`cancel-sign-sub-inv_binary64_1408` `associate-l_binary64_1383` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481`
5×	`distribute-lft-out_binary64_1393`
4×	`associate-*r/_binary64_1384` `unswap-sqr_binary64_1410`
3×	`sqrt-pow1_binary64_1460` `pow-prod-down_binary64_1513` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `prod-exp_binary64_1491` `div-exp_binary64_1493`
1×	`associate-/r_binary64_1386` `rem-sqrt-square_binary64_1455` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `-commutative_binary64_1373` `sqrt-unprod_binary64_1462` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `div-sub_binary64_1447`

Counts

4 → 113

Calls

4 calls:

19.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

series165.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
36.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
25.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
14.0ms	(sqrt.f64 (+.f64 1 x))

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4956	2693
1	4956	2693

prune156.0ms (3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	132	4	136

Merged error: 0.2b

Counts

136 → 4

Compiler

Compiled 2900 to 1878 computations (35.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite67.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_1442`
78×	`times-frac_binary64_1448`
55×	`sqrt-prod_binary64_1458`
47×	`add-sqr-sqrt_binary64_1464`
45×	`distribute-lft-out_binary64_1393`
39×	`add-cube-cbrt_binary64_1477`
32×	`add-exp-log_binary64_1480`
27×	`associate-/l*_binary64_1387`
20×	`add-cbrt-cube_binary64_1478`
14×	`div-exp_binary64_1493`
9×	`pow1_binary64_1503`
8×	`associate-/r/_binary64_1388`
7×	`associate-r_binary64_1382` `cbrt-undiv_binary64_1476` `associate-/r*_binary64_1386`
6×	`associate-l_binary64_1383` `add-log-exp_binary64_1481` `flip3-+_binary64_1445` `flip-+_binary64_1416`
5×	`prod-exp_binary64_1491`
4×	`associate-*r/_binary64_1384` `div-inv_binary64_1439` `sqrt-div_binary64_1459` `unswap-sqr_binary64_1410`
3×	`cbrt-unprod_binary64_1475` `1-exp_binary64_1486` `pow-prod-down_binary64_1513` `rec-exp_binary64_1492`
2×	`sqrt-pow1_binary64_1460` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `pow1/2_binary64_1522`
1×	`inv-pow_binary64_1527` `sum-log_binary64_1533` `associate-/l/_binary64_1389` `+-commutative_binary64_1372` `*-commutative_binary64_1373` `sqrt-unprod_binary64_1462` `pow-flip_binary64_1516`

Counts

4 → 166

Calls

4 calls:

20.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series157.0ms (3%)

Counts

4 → 12

Calls

4 calls:

79.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
28.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
27.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
23.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4952	4177
1	4952	4177

prune259.0ms (4.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	172	6	178
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	175	7	182

Merged error: 0b

Counts

182 → 7

Compiler

Compiled 4372 to 2990 computations (31.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
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)))

rewrite65.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64_1448`
162×	`*-un-lft-identity_binary64_1442`
157×	`add-sqr-sqrt_binary64_1464`
120×	`add-cube-cbrt_binary64_1477`
91×	`sqrt-prod_binary64_1458`
49×	`distribute-lft-out_binary64_1393`
21×	`associate-/l*_binary64_1387`
20×	`associate-/r/_binary64_1388`
19×	`add-exp-log_binary64_1480`
13×	`add-cbrt-cube_binary64_1478`
12×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
11×	`associate-/r*_binary64_1386`
10×	`div-inv_binary64_1439` `pow1_binary64_1503`
8×	`div-exp_binary64_1493`
7×	`associate-r_binary64_1382`
6×	`associate-l_binary64_1383` `sqrt-div_binary64_1459`
4×	`cbrt-undiv_binary64_1476` `add-log-exp_binary64_1481` `unswap-sqr_binary64_1410`
3×	`sqrt-pow1_binary64_1460` `pow-prod-down_binary64_1513` `pow1/2_binary64_1522`
2×	`associate-*r/_binary64_1384` `clear-num_binary64_1441` `1-exp_binary64_1486` `rec-exp_binary64_1492` `frac-2neg_binary64_1453`
1×	`inv-pow_binary64_1527` `rem-sqrt-square_binary64_1455` `cbrt-unprod_binary64_1475` `associate-/l/_binary64_1389` `*-commutative_binary64_1373` `sqrt-unprod_binary64_1462` `pow-flip_binary64_1516` `prod-exp_binary64_1491`

Counts

4 → 256

Calls

4 calls:

13.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
9.0ms	(*.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	(sqrt.f64 (+.f64 1 x))

series153.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
40.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
24.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
14.0ms	(sqrt.f64 (+.f64 1 x))

simplify150.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5007	9677

prune478.0ms (9.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	267	1	268
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	269	6	275

Merged error: 0b

Counts

275 → 6

Compiler

Compiled 7634 to 5449 computations (28.6% saved)

regimes290.0ms (5.5%)

Compiler: Compiled 3660 to 2900 computations (20.8% 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%)

sample2.4s (45.6%)

Algorithm

1×

intervals

Results

340.0ms	2353×	body	1024	valid
162.0ms	4214×	body	128	valid
100.0ms	939×	body	512	valid
34.0ms	494×	body	256	valid

Compiler

Compiled 1861 to 1476 computations (20.7% saved)

Details

analyze101.0ms (1.9%)

sample27.0ms (0.5%)

simplify10.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

rewrite72.0ms (1.4%)

series94.0ms (1.8%)

simplify108.0ms (2.1%)

prune253.0ms (4.8%)

localize7.0ms (0.1%)

rewrite49.0ms (0.9%)

series165.0ms (3.1%)

simplify75.0ms (1.4%)

prune156.0ms (3%)

localize8.0ms (0.2%)

rewrite67.0ms (1.3%)

series157.0ms (3%)

simplify84.0ms (1.6%)

prune259.0ms (4.9%)

localize11.0ms (0.2%)

rewrite65.0ms (1.2%)

series153.0ms (2.9%)

simplify150.0ms (2.9%)

prune478.0ms (9.1%)

regimes290.0ms (5.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.4s (45.6%)

Profiling