Details

analyze5.0ms (0.1%)

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)

sample5.2s (84.7%)

Results

3.5s	4314×	body	2048	valid
1.0s	2061×	body	1024	valid
284.0ms	1013×	body	512	valid
181.0ms	496×	body	256	valid
49.0ms	372×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify58.0ms (0.9%)

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

prune2.0ms (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

30.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	5.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series4.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

2.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
1.0ms	(-.f64 (exp.f64 x) 2)

rewrite16.0ms (0.3%)

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:

9.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

simplify77.0ms (1.3%)

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

prune85.0ms (1.4%)

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
	31.0b	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
	30.7b	(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
▶	0.9b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	30.8b	(/.f64 (-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2)) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))

Compiler

Compiled 2184 to 1257 computations (42.4% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
✓	0.0b	(*.f64 1/20160 (pow.f64 x 8))
✓	0.1b	(*.f64 1/360 (pow.f64 x 6))
✓	0.1b	(*.f64 1/12 (pow.f64 x 4))

series19.0ms (0.3%)

Counts

4 → 9

Calls

4 calls:

7.0ms	(*.f64 1/20160 (pow.f64 x 8))
5.0ms	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
3.0ms	(*.f64 1/360 (pow.f64 x 6))
3.0ms	(*.f64 1/12 (pow.f64 x 4))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`
19×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 98

Calls

4 calls:

13.0ms	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
4.0ms	(*.f64 1/20160 (pow.f64 x 8))
4.0ms	(*.f64 1/360 (pow.f64 x 6))
4.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify72.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

502×	`distribute-rgt-in_binary64`
476×	`distribute-lft-in_binary64`
410×	`unswap-sqr_binary64`
373×	`*-commutative_binary64`
369×	`fma-def_binary64`

Counts

107 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	1560
1	384	1472
2	1127	1398
3	3623	1396
4	4926	1396

prune170.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	140	5	145

Error

0.0b

Counts

145 → 5

Alt Table

Status	Error	Program
	31.0b	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
	30.7b	(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
✓	0.9b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
▶	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	30.8b	(/.f64 (-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2)) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))

Compiler

Compiled 3944 to 3166 computations (19.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

prune35.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	34	5	39

Error

0.0b

Counts

39 → 5

Alt Table

Status	Error	Program
	31.0b	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
▶	30.7b	(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
✓	0.9b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
✓	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	30.8b	(/.f64 (-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2)) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))

Compiler

Compiled 611 to 427 computations (30.1% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	3.7b	(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

series4.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

2.0ms	(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`prod-diff_binary64`
13×	`add-cube-cbrt_binary64`
9×	`add-log-exp_binary64`

Counts

2 → 59

Calls

2 calls:

9.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
7.0ms	(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

674×	`fma-neg_binary64`
555×	`associate-+l+_binary64`
523×	`associate-+r+_binary64`
235×	`times-frac_binary64`
214×	`fma-def_binary64`

Counts

75 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	997
1	260	952
2	580	934
3	1760	642
4	4825	642
5	5214	642

prune64.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	97	5	102

Error

0.0b

Counts

102 → 5

Alt Table

Status	Error	Program
	31.0b	(/.f64 (+.f64 2 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -3))) (.f64 (exp.f64 x) (+.f64 2 (exp.f64 x))))
✓	30.7b	(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
✓	0.9b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
✓	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	30.8b	(/.f64 (-.f64 (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2)) (pow.f64 (exp.f64 x) -2)) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))

Compiler

Compiled 1575 to 857 computations (45.6% saved)

regimes66.0ms (1.1%)

Accuracy

Total 0.6b remaining (98.6%)

Threshold costs 0.6b (98.6%)

Counts

35 → 1

Compiler

Compiled 897 to 683 computations (23.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	29
1	22	29
2	22	29

end99.0ms (1.6%)

Compiler: Compiled 126 to 94 computations (25.4% saved)

Details

analyze5.0ms (0.1%)

sample5.2s (84.7%)

simplify58.0ms (0.9%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite16.0ms (0.3%)

simplify77.0ms (1.3%)

prune85.0ms (1.4%)

localize20.0ms (0.3%)

series19.0ms (0.3%)

rewrite29.0ms (0.5%)

simplify72.0ms (1.2%)

prune170.0ms (2.8%)

localize5.0ms (0.1%)

prune35.0ms (0.6%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite19.0ms (0.3%)

simplify69.0ms (1.1%)

prune64.0ms (1.1%)

regimes66.0ms (1.1%)

simplify2.0ms (0%)

end99.0ms (1.6%)

Profiling