Details

analyze66.0ms (3.9%)

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
50%	50%	0.1%	6
56.2%	37.5%	6.3%	7
68.7%	25%	6.3%	8
71.8%	18.7%	9.5%	9
78%	12.5%	9.5%	10
79.6%	9.4%	11%	11
82.7%	6.2%	11%	12
83.6%	4.6%	11.8%	13
85.1%	3.1%	11.8%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample14.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 23 to 23 computations (0% saved)

simplify123.0ms (7.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	564	13
1	564	13

prune3.0ms (0.2%)

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

0.0b

Counts

2 → 2

Compiler

Compiled 29 to 26 computations (10.3% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))
0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 8277062471433911/9007199254740992)

rewrite22.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`associate--l+_binary64_1379`
14×	`cancel-sign-sub-inv_binary64_1408`
10×	`associate-+l+_binary64_1375`
9×	`add-log-exp_binary64_1481`
8×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `*-un-lft-identity_binary64_1442`
6×	`sub-neg_binary64_1435` `add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477`
2×	`add-cbrt-cube_binary64_1478` `sum-log_binary64_1533` `add-exp-log_binary64_1480` `diff-log_binary64_1534` `pow1_binary64_1503`
1×	`flip3--_binary64_1446` `+-commutative_binary64_1372` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-+l-_binary64_1377`

Counts

2 → 44

Calls

2 calls:

11.0ms	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 8277062471433911/9007199254740992)
7.0ms	(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))

series35.0ms (2.1%)

Counts

2 → 6

Calls

2 calls:

18.0ms	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 8277062471433911/9007199254740992)
17.0ms	(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))

simplify77.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4897	663
1	4897	663

prune39.0ms (2.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	50	2	52

Error

0.0b

Counts

52 → 2

Compiler

Compiled 681 to 460 computations (32.5% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 y (+.f64 x -1/2))
0.0b	(+.f64 (-.f64 (*.f64 y (+.f64 x -1/2)) x) 8277062471433911/9007199254740992)
0.0b	(-.f64 (*.f64 y (+.f64 x -1/2)) x)

rewrite25.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_1442`
10×	`add-log-exp_binary64_1481`
9×	`add-sqr-sqrt_binary64_1464`
7×	`add-cube-cbrt_binary64_1477`
6×	`cancel-sign-sub-inv_binary64_1408` `associate-+l+_binary64_1375`
5×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
4×	`associate--l+_binary64_1379` `associate-r_binary64_1382`
3×	`associate-l_binary64_1383` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
2×	`associate-*r/_binary64_1384` `sum-log_binary64_1533` `sub-neg_binary64_1435` `distribute-lft-out_binary64_1393` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`cbrt-unprod_binary64_1475` `flip3--_binary64_1446` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `flip--_binary64_1417` `prod-exp_binary64_1491` `associate-+l-_binary64_1377` `unswap-sqr_binary64_1410`

Counts

3 → 59

Calls

3 calls:

9.0ms	(+.f64 (-.f64 (*.f64 y (+.f64 x -1/2)) x) 8277062471433911/9007199254740992)
6.0ms	(-.f64 (*.f64 y (+.f64 x -1/2)) x)
6.0ms	(*.f64 y (+.f64 x -1/2))

series56.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

20.0ms	(*.f64 y (+.f64 x -1/2))
19.0ms	(+.f64 (-.f64 (*.f64 y (+.f64 x -1/2)) x) 8277062471433911/9007199254740992)
17.0ms	(-.f64 (*.f64 y (+.f64 x -1/2)) x)

simplify70.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5564	791

prune55.0ms (3.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	68	2	70

Error

Counts

70 → 2

Compiler

Compiled 918 to 630 computations (31.4% saved)

localize14.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (.f64 y (+.f64 (pow.f64 x 3) -1/8)) (+.f64 (.f64 x x) (-.f64 (.f64 -1/2 -1/2) (.f64 x -1/2)))) x)
0.0b	(+.f64 (.f64 x x) (-.f64 (.f64 -1/2 -1/2) (*.f64 x -1/2)))
4.0b	(*.f64 y (+.f64 (pow.f64 x 3) -1/8))
14.6b	(/.f64 (.f64 y (+.f64 (pow.f64 x 3) -1/8)) (+.f64 (.f64 x x) (-.f64 (.f64 -1/2 -1/2) (.f64 x -1/2))))

rewrite60.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
11×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
9×	`add-cube-cbrt_binary64_1477`
6×	`pow1_binary64_1503`
4×	`associate-r/_binary64_1384` `associate-r*_binary64_1382` `cancel-sign-sub-inv_binary64_1408` `flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`associate-/r_binary64_1386` `times-frac_binary64_1448` `associate-l*_binary64_1383`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `sub-neg_binary64_1435` `diff-log_binary64_1534` `prod-exp_binary64_1491` `associate-+r+_binary64_1374` `div-exp_binary64_1493`
1×	`associate-+r-_binary64_1376` `div-inv_binary64_1439` `clear-num_binary64_1441` `associate-/l_binary64_1387` `flip3--_binary64_1446` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `frac-2neg_binary64_1453` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`

Counts

4 → 79

Calls

4 calls:

22.0ms	(-.f64 (/.f64 (.f64 y (+.f64 (pow.f64 x 3) -1/8)) (+.f64 (.f64 x x) (-.f64 (.f64 -1/2 -1/2) (.f64 x -1/2)))) x)
15.0ms	(/.f64 (.f64 y (+.f64 (pow.f64 x 3) -1/8)) (+.f64 (.f64 x x) (-.f64 (.f64 -1/2 -1/2) (.f64 x -1/2))))
9.0ms	(*.f64 y (+.f64 (pow.f64 x 3) -1/8))
6.0ms	(+.f64 (.f64 x x) (-.f64 (.f64 -1/2 -1/2) (*.f64 x -1/2)))

series272.0ms (15.9%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(/.f64 (.f64 y (+.f64 (pow.f64 x 3) -1/8)) (+.f64 (.f64 x x) (-.f64 (.f64 -1/2 -1/2) (.f64 x -1/2))))
82.0ms	(-.f64 (/.f64 (.f64 y (+.f64 (pow.f64 x 3) -1/8)) (+.f64 (.f64 x x) (-.f64 (.f64 -1/2 -1/2) (.f64 x -1/2)))) x)
60.0ms	(*.f64 y (+.f64 (pow.f64 x 3) -1/8))
10.0ms	(+.f64 (.f64 x x) (-.f64 (.f64 -1/2 -1/2) (*.f64 x -1/2)))

simplify67.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5489	1763

prune116.0ms (6.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

Counts

93 → 2

Compiler

Compiled 2445 to 1787 computations (26.9% saved)

regimes66.0ms (3.9%)

Accuracy

Total 0.0b remaining (90.7%)

Threshold costs 0.0b (90.7%)

Compiler

Compiled 384 to 332 computations (13.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	16
1	58	16

end0.0ms (0%)

sample510.0ms (29.9%)

Algorithm

1×

intervals

Results

243.0ms	7997×	body	128	valid
2.0ms	76×	body	128	invalid
0.0ms	3×	body	1024	valid

Compiler

Compiled 108 to 95 computations (12% saved)

Details

analyze66.0ms (3.9%)

sample14.0ms (0.8%)

simplify123.0ms (7.2%)

prune3.0ms (0.2%)

localize7.0ms (0.4%)

rewrite22.0ms (1.3%)

series35.0ms (2.1%)

simplify77.0ms (4.5%)

prune39.0ms (2.3%)

localize6.0ms (0.3%)

rewrite25.0ms (1.5%)

series56.0ms (3.3%)

simplify70.0ms (4.1%)

prune55.0ms (3.2%)

localize14.0ms (0.8%)

rewrite60.0ms (3.5%)

series272.0ms (15.9%)

simplify67.0ms (3.9%)

prune116.0ms (6.8%)

regimes66.0ms (3.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample510.0ms (29.9%)

Profiling