Details

analyze73.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample180.0ms (2.6%)

Algorithm

1×

intervals

Results

130.0ms	131×	body	2048	valid
27.0ms	58×	body	1024	valid
9.0ms	37×	body	512	valid
2.0ms	17×	body	256	valid
1.0ms	13×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify103.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

819×	`div-sub_binary64`
801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	35	13
3	57	13
4	112	13
5	223	13
6	481	13
7	890	13
8	1570	13
9	4778	13
10	5815	13

prune3.0ms (0%)

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

29.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	4.2b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series7.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

4.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
3.0ms	(-.f64 (exp.f64 x) 2)

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-+l+_binary64`

Counts

2 → 69

Calls

2 calls:

13.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
7.0ms	(-.f64 (exp.f64 x) 2)

simplify123.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
326×	`fma-def_binary64`
296×	`distribute-rgt-in_binary64`
282×	`distribute-lft-in_binary64`
268×	`distribute-rgt-out_binary64`

Counts

85 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1174
1	295	959
2	717	942
3	2801	932
4	4435	932
5	4838	932

prune141.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Error

0.0b

Counts

115 → 5

Alt Table

Status	Error	Program
	1.3b	(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
	29.5b	(+.f64 (log1p.f64 (expm1.f64 (-.f64 (exp.f64 x) 2))) (exp.f64 (neg.f64 x)))
	29.5b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
▶	0.9b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 2132 to 1225 computations (42.5% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))
✓	0.0b	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
✓	0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	0.0b	(*.f64 1/20160 (pow.f64 x 8))

series28.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

8.0ms	(fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))
8.0ms	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
7.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
6.0ms	(*.f64 1/20160 (pow.f64 x 8))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

4 → 57

Calls

4 calls:

7.0ms	(*.f64 1/20160 (pow.f64 x 8))
3.0ms	(fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))
1.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
1.0ms	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

simplify104.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
610×	`associate-+r+_binary64`
610×	`associate-+l+_binary64`
262×	`associate-l_binary64`
230×	`associate-r_binary64`

Counts

93 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	1505
1	172	1382
2	418	1364
3	1707	1364
4	5576	1364

prune177.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	82	7	89

Error

0.0b

Counts

89 → 7

Alt Table

Status	Error	Program
	1.3b	(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
	29.5b	(+.f64 (log1p.f64 (expm1.f64 (-.f64 (exp.f64 x) 2))) (exp.f64 (neg.f64 x)))
	29.5b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
	3.7b	(fma.f64 1/12 (pow.f64 x 4) (exp.f64 (log.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
	20.2b	(cbrt.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) 3))
✓	0.9b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
▶	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 2074 to 1558 computations (24.9% saved)

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/12 (pow.f64 x 4))

series5.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

5.0ms

(*.f64 1/12 (pow.f64 x 4))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
6×	`add-exp-log_binary64`
4×	`unpow-prod-down_binary64`
4×	`*-un-lft-identity_binary64`

Counts

1 → 27

Calls

1 calls:

7.0ms

(*.f64 1/12 (pow.f64 x 4))

simplify110.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-/l*_binary64`
527×	`unswap-sqr_binary64`
465×	`associate-/l/_binary64`
448×	`associate-/r/_binary64`
442×	`fma-def_binary64`

Counts

27 → 34

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	54	293
1	96	281
2	205	263
3	560	263
4	940	257
5	1988	252
6	4944	252
7	4866	252

prune78.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	34	7	41

Error

0.0b

Counts

41 → 7

Alt Table

Status	Error	Program
▶	1.3b	(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
	29.5b	(+.f64 (log1p.f64 (expm1.f64 (-.f64 (exp.f64 x) 2))) (exp.f64 (neg.f64 x)))
	29.5b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
	3.7b	(fma.f64 1/12 (pow.f64 x 4) (exp.f64 (log.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
	20.2b	(cbrt.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) 3))
✓	0.9b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 645 to 464 computations (28.1% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
	0.1b	(*.f64 1/12 (pow.f64 x 4))

series7.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

7.0ms

(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`+-commutative_binary64`
1×	`flip-+_binary64`
1×	`*-un-lft-identity_binary64`
1×	`flip3-+_binary64`

Counts

1 → 14

Calls

1 calls:

8.0ms

(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-neg_binary64`
595×	`cancel-sign-sub-inv_binary64`
488×	`unswap-sqr_binary64`
363×	`*-commutative_binary64`
313×	`distribute-rgt-out_binary64`

Counts

17 → 26

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	269
1	104	230
2	310	222
3	1256	219
4	3165	219
5	5336	219

prune117.0ms (1.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	60	7	67

Error

0.0b

Counts

67 → 7

Alt Table

Status	Error	Program
✓	1.3b	(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
	29.5b	(+.f64 (log1p.f64 (expm1.f64 (-.f64 (exp.f64 x) 2))) (exp.f64 (neg.f64 x)))
	29.5b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
	3.7b	(fma.f64 1/12 (pow.f64 x 4) (exp.f64 (log.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
	20.2b	(cbrt.f64 (pow.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) 3))
✓	0.9b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 1007 to 782 computations (22.3% saved)

regimes99.0ms (1.5%)

Accuracy

Total 0.6b remaining (97.9%)

Threshold costs 0.6b (97.9%)

Counts

28 → 1

Compiler

Compiled 888 to 668 computations (24.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	25	31
2	25	31

end1.0ms (0%)

Compiler: Compiled 22 to 18 computations (18.2% saved)

sample5.3s (77.4%)

Algorithm

1×

intervals

Results

3.7s	4197×	body	2048	valid
858.0ms	2032×	body	1024	valid
220.0ms	952×	body	512	valid
69.0ms	462×	body	256	valid
24.0ms	357×	body	128	valid

Compiler

Compiled 134 to 104 computations (22.4% saved)

Details

analyze73.0ms (1.1%)

sample180.0ms (2.6%)

simplify103.0ms (1.5%)

prune3.0ms (0%)

localize12.0ms (0.2%)

series7.0ms (0.1%)

rewrite26.0ms (0.4%)

simplify123.0ms (1.8%)

prune141.0ms (2.1%)

localize21.0ms (0.3%)

series28.0ms (0.4%)

rewrite15.0ms (0.2%)

simplify104.0ms (1.5%)

prune177.0ms (2.6%)

localize10.0ms (0.1%)

series5.0ms (0.1%)

rewrite10.0ms (0.1%)

simplify110.0ms (1.6%)

prune78.0ms (1.1%)

localize10.0ms (0.2%)

series7.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify74.0ms (1.1%)

prune117.0ms (1.7%)

regimes99.0ms (1.5%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample5.3s (77.4%)

Profiling