Details

analyze509.0ms (17.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample58.0ms (1.9%)

Algorithm

1×

intervals

Results

21.0ms	132×	body	2048	nan
14.0ms	256×	body	128	valid
7.0ms	57×	body	1024	nan
3.0ms	32×	body	512	nan
1.0ms	17×	body	256	nan
0.0ms	10×	body	128	nan
0.0ms	1×	body	4096	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify153.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	4922	14
1	4922	14

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

29.6b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
27.5b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`sqrt-prod_binary64_1458` `*-un-lft-identity_binary64_1442`
5×	`add-sqr-sqrt_binary64_1464`
4×	`add-log-exp_binary64_1481`
3×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
2×	`add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `add-exp-log_binary64_1480` `difference-of-squares_binary64_1411`
1×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `sum-log_binary64_1533` `flip3--_binary64_1446` `+-commutative_binary64_1372` `difference-of-sqr-1_binary64_1412` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/2_binary64_1522`

Counts

2 → 30

Calls

2 calls:

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

series50.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

28.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
21.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify54.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4912	536
1	4912	536

prune34.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	2	37

Error

Counts

37 → 2

Compiler

Compiled 529 to 350 computations (33.8% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (-.f64 x 1))
0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite26.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1464`
22×	`sqrt-prod_binary64_1458`
16×	`*-un-lft-identity_binary64_1442`
14×	`sqrt-div_binary64_1459`
10×	`associate-r_binary64_1382`
8×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
7×	`associate-l_binary64_1383`
5×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
4×	`flip3--_binary64_1446` `flip--_binary64_1417` `frac-times_binary64_1452` `flip3-+_binary64_1445` `flip-+_binary64_1416` `difference-of-squares_binary64_1411` `unswap-sqr_binary64_1410`
3×	`sqrt-pow1_binary64_1460` `pow-prod-down_binary64_1513` `pow1/2_binary64_1522`
2×	`associate-r/_binary64_1384` `difference-of-sqr-1_binary64_1412` `distribute-lft-out--_binary64_1394` `associate-l/_binary64_1385`
1×	`rem-sqrt-square_binary64_1455` `cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `+-commutative_binary64_1372` `*-commutative_binary64_1373` `sqrt-unprod_binary64_1462` `distribute-lft-out_binary64_1393` `prod-exp_binary64_1491`

Counts

3 → 73

Calls

3 calls:

14.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
4.0ms	(sqrt.f64 (-.f64 x 1))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

series84.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

35.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
34.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
16.0ms	(sqrt.f64 (-.f64 x 1))

simplify76.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4920	1517
1	4920	1517

prune86.0ms (2.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	82	2	84

Error

Counts

84 → 2

Compiler

Compiled 1569 to 1178 computations (24.9% saved)

regimes28.0ms (1%)

Accuracy

Total 0.0b remaining (1.1%)

Threshold costs 0.0b (1.1%)

Compiler

Compiled 99 to 79 computations (20.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	19
1	23	19

end0.0ms (0%)

sample1.8s (59.8%)

Algorithm

1×

intervals

Results

661.0ms	4121×	body	2048	nan
358.0ms	8000×	body	128	valid
250.0ms	1964×	body	1024	nan
97.0ms	1044×	body	512	nan
33.0ms	515×	body	256	nan
19.0ms	501×	body	128	nan
1.0ms	6×	body	4096	nan

Compiler

Compiled 43 to 36 computations (16.3% saved)

Details

analyze509.0ms (17.1%)

sample58.0ms (1.9%)

simplify153.0ms (5.1%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite14.0ms (0.5%)

series50.0ms (1.7%)

simplify54.0ms (1.8%)

prune34.0ms (1.2%)

localize9.0ms (0.3%)

rewrite26.0ms (0.9%)

series84.0ms (2.8%)

simplify76.0ms (2.5%)

prune86.0ms (2.9%)

regimes28.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.8s (59.8%)

Profiling