Details

analyze30.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample27.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	145×	body	128	valid
5.0ms	53×	body	512	valid
4.0ms	33×	body	1024	valid
2.0ms	25×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

44×	`sub-neg_binary64`
41×	`cancel-sign-sub-inv_binary64`
28×	`unsub-neg_binary64` `distribute-rgt-in_binary64`
25×	`associate--r+_binary64`
21×	`associate--r-_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	59	22
4	101	22
5	165	22
6	198	22
7	217	22
8	216	22
9	192	22

prune3.0ms (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

10.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 48 to 39 computations (18.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
3.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite291.0ms (7.7%)

Algorithm

1×	rewrite-expression-head

Error

10.0b

Rules

112×	`*-un-lft-identity_binary64`
74×	`times-frac_binary64`
72×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`
26×	`cancel-sign-sub-inv_binary64`

Counts

4 → 161

Calls

4 calls:

40.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
22.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
5.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 3272 to 2646 computations (19.1% saved)

series78.0ms (2.1%)

Error

0.4b

Counts

4 → 37

Calls

4 calls:

18.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
12.0ms	(/.f64 1 (-.f64 x 1))
11.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
10.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 1157 to 948 computations (18.1% saved)

simplify133.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

397×	`associate-l_binary64`
368×	`associate-r_binary64`
324×	`distribute-rgt-in_binary64`
289×	`associate-/l*_binary64`
281×	`distribute-lft-in_binary64`

Counts

198 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	3177
1	582	3099
2	1530	3065
3	4583	3063
4	5106	3063

prune79.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	164	3	167

Error

0.4b

Counts

167 → 3

Alt Table

Status	Error	Program
✓	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	32.5b	(+.f64 (+.f64 (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
▶	27.2b	(/.f64 (+.f64 (.f64 (+.f64 x -1) (-.f64 x (.f64 2 (+.f64 x 1)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 1837 to 1443 computations (21.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 (.f64 (+.f64 x -1) (-.f64 x (.f64 2 (+.f64 x 1)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))
0.0b	(+.f64 x (*.f64 x x))
0.0b	(-.f64 x (*.f64 2 (+.f64 x 1)))
18.5b	(+.f64 (.f64 (+.f64 x -1) (-.f64 x (.f64 2 (+.f64 x 1)))) (+.f64 x (*.f64 x x)))

rewrite208.0ms (5.5%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

46×	`add-sqr-sqrt_binary64`
32×	`frac-add_binary64`
31×	`flip3-+_binary64` `flip-+_binary64` `*-un-lft-identity_binary64`
27×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64` `associate-/l/_binary64`

Counts

4 → 131

Calls

4 calls:

19.0ms	(/.f64 (+.f64 (.f64 (+.f64 x -1) (-.f64 x (.f64 2 (+.f64 x 1)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))
11.0ms	(+.f64 (.f64 (+.f64 x -1) (-.f64 x (.f64 2 (+.f64 x 1)))) (+.f64 x (*.f64 x x)))
3.0ms	(-.f64 x (*.f64 2 (+.f64 x 1)))
3.0ms	(+.f64 x (*.f64 x x))

Compiler

Compiled 6582 to 3629 computations (44.9% saved)

series54.0ms (1.4%)

Error

0.4b

Counts

4 → 24

Calls

4 calls:

16.0ms	(/.f64 (+.f64 (.f64 (+.f64 x -1) (-.f64 x (.f64 2 (+.f64 x 1)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))
12.0ms	(+.f64 x (*.f64 x x))
9.0ms	(-.f64 x (*.f64 2 (+.f64 x 1)))
5.0ms	(+.f64 (.f64 (+.f64 x -1) (-.f64 x (.f64 2 (+.f64 x 1)))) (+.f64 x (*.f64 x x)))

Compiler

Compiled 815 to 602 computations (26.1% saved)

simplify156.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

484×	`distribute-rgt-in_binary64`
469×	`distribute-lft-in_binary64`
375×	`associate-l_binary64`
364×	`associate-r_binary64`
274×	`distribute-rgt-neg-out_binary64`

Counts

155 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	6883
1	929	5790
2	3856	5758
3	5034	5758

prune136.0ms (3.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	132	3	135

Error

0.4b

Counts

135 → 3

Alt Table

Status	Error	Program
✓	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	32.5b	(+.f64 (+.f64 (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
✓	27.2b	(/.f64 (+.f64 (.f64 (+.f64 x -1) (-.f64 x (.f64 2 (+.f64 x 1)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 5011 to 2904 computations (42% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 2 (pow.f64 x 9))
0.0b	(/.f64 2 (pow.f64 x 7))
0.3b	(/.f64 2 (pow.f64 x 5))
0.4b	(/.f64 2 (pow.f64 x 3))

rewrite320.0ms (8.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

99×	`times-frac_binary64`
77×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
48×	`unpow-prod-down_binary64`
33×	`associate-/r*_binary64`
24×	`add-exp-log_binary64`

Counts

4 → 200

Calls

4 calls:

7.0ms	(/.f64 2 (pow.f64 x 9))
5.0ms	(/.f64 2 (pow.f64 x 3))
4.0ms	(/.f64 2 (pow.f64 x 5))
4.0ms	(/.f64 2 (pow.f64 x 7))

Compiler

Compiled 5603 to 4624 computations (17.5% saved)

series46.0ms (1.2%)

Error

0.4b

Counts

4 → 12

Calls

4 calls:

11.0ms	(/.f64 2 (pow.f64 x 9))
11.0ms	(/.f64 2 (pow.f64 x 7))
11.0ms	(/.f64 2 (pow.f64 x 5))
10.0ms	(/.f64 2 (pow.f64 x 3))

Compiler

Compiled 600 to 500 computations (16.7% saved)

simplify164.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

564×	`times-frac_binary64`
540×	`associate-l_binary64`
500×	`log-prod_binary64`
390×	`associate-/l/_binary64`
380×	`associate-/l*_binary64`

Counts

212 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	285	3040
1	473	2920
2	1357	2836
3	4170	2780
4	4613	2780
5	4979	2780

prune97.0ms (2.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	107	9	116

Error

Counts

116 → 9

Alt Table

Status	Error	Program
	32.5b	(+.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
	48.3b	(+.f64 (+.f64 (+.f64 (*.f64 (/.f64 (sqrt.f64 2) (pow.f64 x 3/2)) (/.f64 (sqrt.f64 2) (pow.f64 x 3/2))) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
✓	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	32.3b	(+.f64 (+.f64 (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) (pow.f64 (cbrt.f64 x) 3)) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
✓	32.5b	(+.f64 (+.f64 (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
	48.4b	(+.f64 (+.f64 (+.f64 (/.f64 (/.f64 2 (pow.f64 x 3/2)) (sqrt.f64 (pow.f64 x 3))) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
	32.6b	(+.f64 (+.f64 (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3))) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
✓	27.2b	(/.f64 (+.f64 (.f64 (+.f64 x -1) (-.f64 x (.f64 2 (+.f64 x 1)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))
	39.0b	(+.f64 (+.f64 (+.f64 (cbrt.f64 (pow.f64 (/.f64 2 (pow.f64 x 3)) 3)) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))

Compiler

Compiled 1872 to 1551 computations (17.1% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 2 (*.f64 x x))
0.3b	(/.f64 2 (pow.f64 x 5))
0.6b	(cbrt.f64 x)
0.6b	(pow.f64 (cbrt.f64 x) 3)

rewrite172.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

28×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
24×	`times-frac_binary64`
18×	`unpow-prod-down_binary64`
15×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 107

Calls

4 calls:

5.0ms	(/.f64 2 (*.f64 x x))
4.0ms	(/.f64 2 (pow.f64 x 5))
3.0ms	(pow.f64 (cbrt.f64 x) 3)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 3310 to 2396 computations (27.6% saved)

series71.0ms (1.9%)

Error

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow.f64 (cbrt.f64 x) 3)
19.0ms	(cbrt.f64 x)
11.0ms	(/.f64 2 (pow.f64 x 5))
10.0ms	(/.f64 2 (*.f64 x x))

Compiler

Compiled 885 to 707 computations (20.1% saved)

simplify102.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

698×	`times-frac_binary64`
479×	`log-prod_binary64`
370×	`associate-/l*_binary64`
229×	`cancel-sign-sub-inv_binary64`
184×	`*-commutative_binary64`

Counts

119 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	1231
1	303	1097
2	903	1060
3	3140	1056
4	4736	1056
5	4963	1056

prune61.0ms (1.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	2	3	5
Picked	1	0	1
Done	0	3	3
Total	76	7	83

Error

Counts

83 → 7

Alt Table

Status	Error	Program
	32.5b	(+.f64 (+.f64 (+.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (pow.f64 x 3))) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
	48.3b	(+.f64 (+.f64 (+.f64 (*.f64 (/.f64 (sqrt.f64 2) (pow.f64 x 3/2)) (/.f64 (sqrt.f64 2) (pow.f64 x 3/2))) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
	10.5b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
	32.5b	(+.f64 (+.f64 (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
	32.2b	(+.f64 (+.f64 (+.f64 (/.f64 (/.f64 2 (.f64 x x)) (.f64 1 x)) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
	32.6b	(+.f64 (+.f64 (+.f64 (/.f64 (/.f64 2 (*.f64 x x)) (cbrt.f64 (pow.f64 x 3))) (/.f64 2 (pow.f64 x 5))) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9)))
	27.2b	(/.f64 (+.f64 (.f64 (+.f64 x -1) (-.f64 x (.f64 2 (+.f64 x 1)))) (+.f64 x (*.f64 x x))) (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 1290 to 971 computations (24.7% saved)

regimes553.0ms (14.6%)

Accuracy

Total 0.3b remaining (94.3%)

Threshold costs 0.3b (94.3%)

Compiler

Compiled 9044 to 7349 computations (18.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`sub-neg_binary64` `+-commutative_binary64`
1×	`neg-mul-1_binary64` `neg-sub0_binary64` `*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	9	10
2	14	10
3	16	10
4	17	10
5	17	10

end1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample935.0ms (24.7%)

Algorithm

1×

intervals

Results

181.0ms	1282×	body	1024	valid
160.0ms	4520×	body	128	valid
159.0ms	1469×	body	512	valid
57.0ms	729×	body	256	valid

Compiler

Compiled 207 to 166 computations (19.8% saved)

Details

analyze30.0ms (0.8%)

sample27.0ms (0.7%)

simplify14.0ms (0.4%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite291.0ms (7.7%)

series78.0ms (2.1%)

simplify133.0ms (3.5%)

prune79.0ms (2.1%)

localize13.0ms (0.3%)

rewrite208.0ms (5.5%)

series54.0ms (1.4%)

simplify156.0ms (4.1%)

prune136.0ms (3.6%)

localize14.0ms (0.4%)

rewrite320.0ms (8.5%)

series46.0ms (1.2%)

simplify164.0ms (4.3%)

prune97.0ms (2.6%)

localize17.0ms (0.5%)

rewrite172.0ms (4.5%)

series71.0ms (1.9%)

simplify102.0ms (2.7%)

prune61.0ms (1.6%)

regimes553.0ms (14.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample935.0ms (24.7%)

Profiling