Details

analyze121.0ms (3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample23.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify168.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4915	43
1	4915	43

prune7.0ms (0.2%)

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

Error

0.2b

Counts

2 → 1

Compiler

Compiled 58 to 38 computations (34.5% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.0b	(.f64 (.f64 a a) (-.f64 1 a))
0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.8b	(.f64 (.f64 b b) (+.f64 3 a))

rewrite40.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464` `pow1_binary64_1503` `*-un-lft-identity_binary64_1442`
14×	`add-cbrt-cube_binary64_1478`
10×	`associate-r_binary64_1382` `add-cube-cbrt_binary64_1477`
6×	`cancel-sign-sub-inv_binary64_1408` `cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `add-log-exp_binary64_1481` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `prod-exp_binary64_1491`
4×	`associate-*r/_binary64_1384`
3×	`pow-unpow_binary64_1519` `unpow-prod-down_binary64_1521`
2×	`sub-neg_binary64_1435` `associate-l_binary64_1383` `*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416` `difference-of-squares_binary64_1411` `associate-+r+_binary64_1374` `unswap-sqr_binary64_1410`
1×	`sum-log_binary64_1533` `pow-exp_binary64_1510` `unpow2_binary64_1507` `flip3--_binary64_1446` `+-commutative_binary64_1372` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `sqr-pow_binary64_1414` `distribute-lft-out--_binary64_1394` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

4 → 87

Calls

4 calls:

9.0ms	(.f64 (.f64 a a) (-.f64 1 a))
9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
9.0ms	(.f64 (.f64 b b) (+.f64 3 a))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series162.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
34.0ms	(.f64 (.f64 a a) (-.f64 1 a))
27.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
23.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify57.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5239	1789

prune152.0ms (3.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	4	100

Error

0.0b

Counts

100 → 4

Compiler

Compiled 3567 to 1824 computations (48.9% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
0.0b	(.f64 (.f64 a a) (-.f64 1 a))
0.8b	(.f64 (.f64 b b) (+.f64 3 a))
3.5b	(.f64 (.f64 b b) (*.f64 a a))

rewrite76.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_1503`
32×	`associate-*r/_binary64_1384`
26×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
20×	`pow-prod-down_binary64_1513` `frac-add_binary64_1450`
14×	`cbrt-unprod_binary64_1475` `flip3-+_binary64_1445` `flip-+_binary64_1416` `prod-exp_binary64_1491`
13×	`add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
11×	`associate-r_binary64_1382`
8×	`add-cube-cbrt_binary64_1477`
6×	`cancel-sign-sub-inv_binary64_1408` `sum-log_binary64_1533` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
5×	`flip3--_binary64_1446` `flip--_binary64_1417`
4×	`pow-plus_binary64_1505` `pow-prod-up_binary64_1512`
3×	`associate-l_binary64_1383` `*-commutative_binary64_1373` `unswap-sqr_binary64_1410`
2×	`pow2_binary64_1523` `sub-neg_binary64_1435` `pow-sqr_binary64_1415` `difference-of-squares_binary64_1411` `associate-+r+_binary64_1374`
1×	`associate-+l+_binary64_1375` `+-commutative_binary64_1372` `distribute-lft-out_binary64_1393` `distribute-lft-out--_binary64_1394`

Counts

4 → 113

Calls

4 calls:

29.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
10.0ms	(.f64 (.f64 b b) (+.f64 3 a))
10.0ms	(.f64 (.f64 a a) (-.f64 1 a))
9.0ms	(.f64 (.f64 b b) (*.f64 a a))

series156.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(+.f64 (+.f64 (.f64 2 (.f64 (.f64 b b) (.f64 a a))) (+.f64 (pow.f64 b 4) (pow.f64 a 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a)))))
30.0ms	(.f64 (.f64 a a) (-.f64 1 a))
24.0ms	(.f64 (.f64 b b) (*.f64 a a))
23.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify99.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4973	4501
1	4973	4501

prune399.0ms (9.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	125	4	129

Error

Counts

129 → 4

Compiler

Compiled 6531 to 3795 computations (41.9% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.8b	(.f64 (.f64 b b) (+.f64 3 a))
16.2b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
16.2b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
16.2b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64_1473`
13×	`*-un-lft-identity_binary64_1442`
12×	`add-sqr-sqrt_binary64_1464`
11×	`add-cube-cbrt_binary64_1477`
9×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503` `unpow-prod-down_binary64_1521`
4×	`associate-r_binary64_1382` `add-log-exp_binary64_1481`
3×	`cbrt-unprod_binary64_1475` `unpow2_binary64_1507` `pow-prod-down_binary64_1513` `sqr-pow_binary64_1414` `pow1/3_binary64_1524` `prod-exp_binary64_1491`
2×	`associate-*r/_binary64_1384`
1×	`associate-l_binary64_1383` `*-commutative_binary64_1373` `distribute-lft-out_binary64_1393` `distribute-lft-in_binary64_1391` `flip3-+_binary64_1445` `distribute-rgt-in_binary64_1392` `flip-+_binary64_1416` `unswap-sqr_binary64_1410`

Counts

4 → 72

Calls

4 calls:

8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))

series269.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
81.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
80.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 2))
24.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify95.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4892	1428
1	4892	1428

prune164.0ms (4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	84	4	88

Error

Counts

88 → 4

Compiler

Compiled 4937 to 2213 computations (55.2% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 a a) (-.f64 1 a))
0.2b	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)
0.8b	(.f64 (.f64 b b) (+.f64 3 a))
29.3b	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6))

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
15×	`add-exp-log_binary64_1480` `pow1_binary64_1503`
14×	`add-cbrt-cube_binary64_1478`
12×	`add-cube-cbrt_binary64_1477`
10×	`associate-r_binary64_1382`
7×	`cbrt-prod_binary64_1473`
6×	`cancel-sign-sub-inv_binary64_1408` `cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `unpow-prod-down_binary64_1521`
5×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
4×	`associate-*r/_binary64_1384` `add-log-exp_binary64_1481`
3×	`pow-unpow_binary64_1519`
2×	`sub-neg_binary64_1435` `associate-l_binary64_1383` `*-commutative_binary64_1373` `sqr-pow_binary64_1414` `difference-of-squares_binary64_1411` `unswap-sqr_binary64_1410`
1×	`pow-exp_binary64_1510` `flip3--_binary64_1446` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/3_binary64_1524` `distribute-lft-out--_binary64_1394` `pow-to-exp_binary64_1511` `pow-pow_binary64_1514`

Counts

4 → 88

Calls

4 calls:

9.0ms	(.f64 (.f64 a a) (-.f64 1 a))
9.0ms	(.f64 (.f64 b b) (+.f64 3 a))
5.0ms	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)
5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6))

series258.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6)
31.0ms	(.f64 (.f64 a a) (-.f64 1 a))
29.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 b b) (.f64 a a)) 6))
22.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5130	1402

prune136.0ms (3.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	100	4	104

Error

Counts

104 → 4

Compiler

Compiled 3427 to 1791 computations (47.7% saved)

regimes266.0ms (6.5%)

Accuracy

Total 0.0b remaining (78.2%)

Threshold costs 0.0b (78.2%)

Compiler

Compiled 4844 to 3103 computations (35.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	55
1	55	55

end0.0ms (0%)

sample1.2s (30%)

Algorithm

1×

intervals

Results

482.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 941 to 607 computations (35.5% saved)

Details

analyze121.0ms (3%)

sample23.0ms (0.6%)

simplify168.0ms (4.1%)

prune7.0ms (0.2%)

localize15.0ms (0.4%)

rewrite40.0ms (1%)

series162.0ms (3.9%)

simplify57.0ms (1.4%)

prune152.0ms (3.7%)

localize20.0ms (0.5%)

rewrite76.0ms (1.9%)

series156.0ms (3.8%)

simplify99.0ms (2.4%)

prune399.0ms (9.7%)

localize20.0ms (0.5%)

rewrite33.0ms (0.8%)

series269.0ms (6.6%)

simplify95.0ms (2.3%)

prune164.0ms (4%)

localize18.0ms (0.4%)

rewrite36.0ms (0.9%)

series258.0ms (6.3%)

simplify76.0ms (1.9%)

prune136.0ms (3.3%)

regimes266.0ms (6.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (30%)

Profiling