Details

analyze111.0ms (1.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15
0	1	1
1	1	1

Search

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

Compiler

Compiled 13 to 13 computations (0% saved)

sample52.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms	70×	body	2048	valid
9.0ms	34×	body	1024	valid
7.0ms	125×	body	128	valid
3.0ms	18×	body	512	valid
1.0ms	9×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

17.6b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
2.9b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite174.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

17.6b

Rules

28×	`*-un-lft-identity_binary64_1442`
24×	`add-sqr-sqrt_binary64_1464`
15×	`add-cube-cbrt_binary64_1477`
12×	`sqrt-prod_binary64_1458`
9×	`times-frac_binary64_1448`
8×	`add-log-exp_binary64_1481`
7×	`cancel-sign-sub-inv_binary64_1408`
6×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
5×	`pow1_binary64_1503`
4×	`difference-of-squares_binary64_1411` `distribute-lft-out_binary64_1393`
3×	`distribute-lft-out--_binary64_1394` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
2×	`flip3-+_binary64_1445` `sqrt-div_binary64_1459` `flip-+_binary64_1416`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 80

Calls

4 calls:

10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
8.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 1520 to 1379 computations (9.3% saved)

series209.0ms (2.4%)

Error

17.6b

Counts

4 → 12

Calls

4 calls:

70.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
59.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
45.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
26.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 414 to 403 computations (2.7% saved)

simplify126.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4823	1444
1	4823	1444

prune129.0ms (1.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	2	93

Error

17.1b

Counts

93 → 2

Compiler

Compiled 1445 to 1311 computations (9.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
2.4b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite232.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

16.8b

Rules

34×	`add-sqr-sqrt_binary64_1464`
32×	`*-un-lft-identity_binary64_1442`
28×	`add-cube-cbrt_binary64_1477` `times-frac_binary64_1448`
13×	`cancel-sign-sub-inv_binary64_1408`
8×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
6×	`add-log-exp_binary64_1481` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
5×	`pow1_binary64_1503`
4×	`sqrt-prod_binary64_1458`
3×	`div-inv_binary64_1439`
2×	`difference-of-squares_binary64_1411` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `sqrt-div_binary64_1459`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417` `distribute-lft-out--_binary64_1394` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `distribute-lft-out_binary64_1393` `rem-sqrt-square_binary64_1455`

Counts

4 → 97

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
8.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
4.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 2547 to 2279 computations (10.5% saved)

series236.0ms (2.7%)

Error

17.1b

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
54.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
43.0ms	(/.f64 1/2 (hypot.f64 1 x))
40.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 684 to 637 computations (6.9% saved)

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5281	1419

prune191.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Error

16.8b

Counts

111 → 4

Compiler

Compiled 2596 to 2325 computations (10.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
0.1b	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
0.5b	(*.f64 (+.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
2.4b	(-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))

rewrite758.0ms (8.7%)

Algorithm

1×	rewrite-expression-head

Error

16.7b

Rules

85×	`sqrt-prod_binary64_1458`
80×	`add-sqr-sqrt_binary64_1464`
56×	`*-un-lft-identity_binary64_1442`
51×	`times-frac_binary64_1448`
48×	`cancel-sign-sub-inv_binary64_1408`
44×	`add-cube-cbrt_binary64_1477`
17×	`distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391`
12×	`difference-of-squares_binary64_1411`
11×	`associate-r_binary64_1382`
8×	`pow1_binary64_1503`
6×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
5×	`div-inv_binary64_1439` `associate-l_binary64_1383`
4×	`flip3--_binary64_1446` `flip--_binary64_1417` `distribute-lft-out--_binary64_1394` `frac-times_binary64_1452` `rem-sqrt-square_binary64_1455`
3×	`sub-neg_binary64_1435` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`associate-l/_binary64_1385` `associate-r/_binary64_1384` `distribute-lft-out_binary64_1393` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `sqrt-div_binary64_1459`
1×	`diff-log_binary64_1534` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`

Counts

4 → 155

Calls

4 calls:

35.0ms	(*.f64 (+.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
16.0ms	(-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))

Compiler

Compiled 6813 to 6162 computations (9.6% saved)

series530.0ms (6.1%)

Error

16.8b

Counts

4 → 12

Calls

4 calls:

211.0ms	(*.f64 (+.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
113.0ms	(-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
100.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
82.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))

Compiler

Compiled 1215 to 1132 computations (6.8% saved)

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5051	4538

prune598.0ms (6.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	167	4	171

Error

16.7b

Counts

171 → 4

Compiler

Compiled 6521 to 5891 computations (9.7% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(sqrt.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
1.0b	(sqrt.f64 (sqrt.f64 1/2))
1.0b	(sqrt.f64 (sqrt.f64 1/2))
2.5b	(-.f64 (sqrt.f64 (sqrt.f64 1/2)) (sqrt.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite540.0ms (6.2%)

Algorithm

1×	rewrite-expression-head

Error

16.7b

Rules

113×	`sqrt-prod_binary64_1458`
60×	`add-sqr-sqrt_binary64_1464`
31×	`*-un-lft-identity_binary64_1442`
25×	`add-cube-cbrt_binary64_1477`
22×	`times-frac_binary64_1448`
19×	`cancel-sign-sub-inv_binary64_1408`
12×	`difference-of-squares_binary64_1411` `sqrt-pow1_binary64_1460`
10×	`pow1_binary64_1503`
7×	`rem-sqrt-square_binary64_1455`
6×	`add-log-exp_binary64_1481` `pow1/2_binary64_1522`
4×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
3×	`distribute-lft-out--_binary64_1394`
2×	`div-inv_binary64_1439` `sqrt-div_binary64_1459`
1×	`diff-log_binary64_1534` `flip3--_binary64_1446` `sub-neg_binary64_1435` `flip--_binary64_1417`

Counts

4 → 114

Calls

4 calls:

20.0ms	(-.f64 (sqrt.f64 (sqrt.f64 1/2)) (sqrt.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
4.0ms	(sqrt.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
2.0ms	(sqrt.f64 (sqrt.f64 1/2))
2.0ms	(sqrt.f64 (sqrt.f64 1/2))

Compiler

Compiled 6013 to 5498 computations (8.6% saved)

series422.0ms (4.8%)

Error

16.7b

Counts

4 → 6

Calls

4 calls:

252.0ms	(-.f64 (sqrt.f64 (sqrt.f64 1/2)) (sqrt.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
154.0ms	(sqrt.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))
0.0ms	(sqrt.f64 (sqrt.f64 1/2))
0.0ms	(sqrt.f64 (sqrt.f64 1/2))

Compiler

Compiled 864 to 805 computations (6.8% saved)

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4893	2164
1	4893	2164

prune500.0ms (5.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	119	5	124

Error

16.7b

Counts

124 → 5

Compiler

Compiled 6014 to 5496 computations (8.6% saved)

regimes675.0ms (7.8%)

Accuracy

Total 0.3b remaining (1.8%)

Threshold costs 0.3b (1.8%)

Compiler

Compiled 7339 to 6891 computations (6.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	27
1	30	27

end0.0ms (0%)

sample2.9s (33%)

Algorithm

1×

intervals

Results

683.0ms	2130×	body	2048	valid
252.0ms	1029×	body	1024	valid
219.0ms	4092×	body	128	valid
86.0ms	510×	body	512	valid
25.0ms	239×	body	256	valid

Compiler

Compiled 1066 to 1002 computations (6% saved)

Details

analyze111.0ms (1.3%)

sample52.0ms (0.6%)

simplify11.0ms (0.1%)

prune7.0ms (0.1%)

localize7.0ms (0.1%)

rewrite174.0ms (2%)

series209.0ms (2.4%)

simplify126.0ms (1.4%)

prune129.0ms (1.5%)

localize9.0ms (0.1%)

rewrite232.0ms (2.7%)

series236.0ms (2.7%)

simplify93.0ms (1.1%)

prune191.0ms (2.2%)

localize16.0ms (0.2%)

rewrite758.0ms (8.7%)

series530.0ms (6.1%)

simplify91.0ms (1%)

prune598.0ms (6.9%)

localize24.0ms (0.3%)

rewrite540.0ms (6.2%)

series422.0ms (4.8%)

simplify90.0ms (1%)

prune500.0ms (5.7%)

regimes675.0ms (7.8%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.9s (33%)

Profiling