Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 20 to 16 computations (20% saved)

sample25.0ms (0.6%)

Algorithm

1×

intervals

Results

6.0ms	186×	body	128	valid
5.0ms	39×	body	1024	valid
4.0ms	256×	pre	128	true
1.0ms	16×	body	512	valid
1.0ms	6×	body	2048	valid
1.0ms	9×	body	256	valid

Compiler

Compiled 33 to 29 computations (12.1% saved)

simplify360.0ms (8.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (258.0ms)

Iter	Nodes	Cost
0	5018	19

prune2.0ms (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

Error

16.9b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
0.9b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite36.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64_1442`
26×	`add-sqr-sqrt_binary64_1464`
25×	`times-frac_binary64_1448`
19×	`distribute-lft-out_binary64_1393`
14×	`add-cube-cbrt_binary64_1477`
6×	`difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
5×	`associate-/r_binary64_1386` `associate-/l_binary64_1387`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
2×	`associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1_binary64_1503` `div-sub_binary64_1447`
1×	`cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `flip3--_binary64_1446` `+-commutative_binary64_1372` `flip--_binary64_1417` `frac-2neg_binary64_1453` `associate-+l-_binary64_1377` `div-exp_binary64_1493`

Counts

2 → 65

Calls

2 calls:

19.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

series76.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

47.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)
29.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

simplify72.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6172	1488

prune85.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	8	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	8	72

Error

16.2b

Counts

72 → 8

Compiler

Compiled 1648 to 919 computations (44.2% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`*-un-lft-identity_binary64_1442`
35×	`add-sqr-sqrt_binary64_1464`
33×	`times-frac_binary64_1448`
24×	`distribute-lft-out_binary64_1393` `add-cube-cbrt_binary64_1477`
10×	`associate-/r*_binary64_1386`
7×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
6×	`associate-/l*_binary64_1387`
5×	`add-log-exp_binary64_1481`
4×	`associate-/r/_binary64_1388` `difference-of-squares_binary64_1411`
3×	`cancel-sign-sub-inv_binary64_1408` `pow1_binary64_1503`
2×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `clear-num_binary64_1441` `difference-of-sqr-1_binary64_1412` `frac-2neg_binary64_1453` `flip3-+_binary64_1445` `flip-+_binary64_1416` `div-exp_binary64_1493`
1×	`sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `distribute-lft-out--_binary64_1394`

Counts

3 → 95

Calls

3 calls:

15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
7.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
7.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

series107.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

51.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
29.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
27.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5478	1708

prune141.0ms (3.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	104	8	112

Error

3.3b

Counts

112 → 8

Compiler

Compiled 2846 to 1694 computations (40.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (+.f64 alpha beta) 2) beta)
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.1b	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
0.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite65.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

185×	`*-un-lft-identity_binary64_1442`
150×	`times-frac_binary64_1448`
92×	`add-sqr-sqrt_binary64_1464`
81×	`add-cube-cbrt_binary64_1477`
60×	`distribute-lft-out_binary64_1393`
27×	`associate-/r*_binary64_1386`
19×	`add-exp-log_binary64_1480`
13×	`add-cbrt-cube_binary64_1478`
11×	`associate-/l*_binary64_1387`
9×	`div-exp_binary64_1493`
7×	`div-inv_binary64_1439`
6×	`add-log-exp_binary64_1481`
5×	`cbrt-undiv_binary64_1476` `pow1_binary64_1503`
4×	`difference-of-squares_binary64_1411`
3×	`cancel-sign-sub-inv_binary64_1408` `associate-/r/_binary64_1388` `clear-num_binary64_1441` `frac-2neg_binary64_1453`
2×	`associate-/l/_binary64_1389` `1-exp_binary64_1486` `difference-of-sqr-1_binary64_1412` `rec-exp_binary64_1492` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`inv-pow_binary64_1527` `sub-neg_binary64_1435` `flip3--_binary64_1446` `pow-flip_binary64_1516` `flip--_binary64_1417` `diff-log_binary64_1534` `distribute-lft-out--_binary64_1394`

Counts

4 → 195

Calls

4 calls:

14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
11.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
8.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) beta)
7.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))

series132.0ms (3%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
38.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
30.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
17.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) beta)

simplify120.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4925	3828
1	4925	3828

prune278.0ms (6.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	208	7	215

Error

3.3b

Counts

215 → 7

Compiler

Compiled 5963 to 3644 computations (38.9% saved)

localize23.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.9b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite41.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64_1442`
19×	`add-sqr-sqrt_binary64_1464`
15×	`cbrt-prod_binary64_1473`
9×	`distribute-lft-out_binary64_1393`
8×	`add-cube-cbrt_binary64_1477`
6×	`cbrt-div_binary64_1474` `add-log-exp_binary64_1481`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503` `difference-of-squares_binary64_1411`
3×	`cancel-sign-sub-inv_binary64_1408` `times-frac_binary64_1448` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/3_binary64_1524`
2×	`difference-of-sqr-1_binary64_1412`
1×	`sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `distribute-lft-out--_binary64_1394`

Counts

4 → 66

Calls

4 calls:

15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))

series247.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
65.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
64.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
47.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify85.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4896	1409
1	4896	1409

prune145.0ms (3.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	77	8	85

Error

3.3b

Counts

85 → 8

Compiler

Compiled 3759 to 2047 computations (45.5% saved)

regimes538.0ms (12.1%)

Accuracy

Total 0.2b remaining (5.7%)

Threshold costs 0.2b (5.7%)

Compiler

Compiled 6790 to 4842 computations (28.7% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	202	119
1	202	119

end0.0ms (0%)

sample1.7s (39.1%)

Algorithm

1×

intervals

Results

191.0ms	5868×	body	128	valid
143.0ms	8000×	pre	128	true
131.0ms	1073×	body	1024	valid
57.0ms	635×	body	512	valid
22.0ms	328×	body	256	valid
17.0ms	96×	body	2048	valid

Compiler

Compiled 1442 to 1024 computations (29% saved)

Details

analyze3.0ms (0.1%)

sample25.0ms (0.6%)

simplify360.0ms (8.1%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite36.0ms (0.8%)

series76.0ms (1.7%)

simplify72.0ms (1.6%)

prune85.0ms (1.9%)

localize12.0ms (0.3%)

rewrite38.0ms (0.9%)

series107.0ms (2.4%)

simplify56.0ms (1.3%)

prune141.0ms (3.2%)

localize12.0ms (0.3%)

rewrite65.0ms (1.4%)

series132.0ms (3%)

simplify120.0ms (2.7%)

prune278.0ms (6.2%)

localize23.0ms (0.5%)

rewrite41.0ms (0.9%)

series247.0ms (5.5%)

simplify85.0ms (1.9%)

prune145.0ms (3.3%)

regimes538.0ms (12.1%)

bsearch3.0ms (0.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.7s (39.1%)

Profiling