Details

analyze145.0ms (1.5%)

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)

sample212.0ms (2.1%)

Algorithm

1×

intervals

Results

148.0ms	132×	body	2048	valid
39.0ms	68×	body	1024	valid
9.0ms	34×	body	512	valid
2.0ms	12×	body	256	valid
1.0ms	10×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify91.0ms (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

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

29.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.7b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	3.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series8.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

5.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
3.0ms	(-.f64 (exp.f64 x) 2)

rewrite33.0ms (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:

17.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
7.0ms	(-.f64 (exp.f64 x) 2)

simplify125.0ms (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

prune153.0ms (1.5%)

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
▶	0.3b	(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)))))
	0.5b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
	0.7b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	29.6b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
	29.6b	(/.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 2166 to 1243 computations (42.6% saved)

localize25.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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	(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))

series23.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

9.0ms

(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

8.0ms

(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))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`add-exp-log_binary64`
7×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

3 → 47

Calls

3 calls:

7.0ms

(*.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))))

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
562×	`associate-+l+_binary64`
546×	`associate-+r+_binary64`
247×	`associate-l_binary64`
214×	`associate-r_binary64`

Counts

71 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1228
1	162	1128
2	390	1110
3	1598	1110
4	5154	1110

prune181.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	77	5	82

Error

0.0b

Counts

82 → 5

Alt Table

Status	Error	Program
▶	0.3b	(expm1.f64 (log1p.f64 (fma.f64 1/20160 (pow.f64 x 8) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))
	0.5b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
	0.3b	(fma.f64 1/12 (pow.f64 x 4) (.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
	29.6b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
	29.6b	(/.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 1998 to 1499 computations (25% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))
✓	0.0b	(expm1.f64 (log1p.f64 (fma.f64 1/20160 (pow.f64 x 8) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))
✓	0.0b	(log1p.f64 (fma.f64 1/20160 (pow.f64 x 8) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))))
✓	0.1b	(*.f64 1/12 (pow.f64 x 4))

series30.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

9.0ms	(log1p.f64 (fma.f64 1/20160 (pow.f64 x 8) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))))
8.0ms	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))
8.0ms	(expm1.f64 (log1p.f64 (fma.f64 1/20160 (pow.f64 x 8) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))
6.0ms	(*.f64 1/12 (pow.f64 x 4))

rewrite24.0ms (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 → 59

Calls

4 calls:

18.0ms	(*.f64 1/12 (pow.f64 x 4))
1.0ms	(log1p.f64 (fma.f64 1/20160 (pow.f64 x 8) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))))
1.0ms	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))
1.0ms	(expm1.f64 (log1p.f64 (fma.f64 1/20160 (pow.f64 x 8) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))

simplify178.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

320×	`cancel-sign-sub-inv_binary64`
262×	`exp-prod_binary64`
236×	`associate-l_binary64`
235×	`fma-def_binary64`
223×	`fma-neg_binary64`

Counts

95 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	1900
1	298	1733
2	702	1699
3	2321	1693
4	4579	1693
5	5000	1693
6	4916	1693

prune342.0ms (3.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	136	5	141

Error

0.0b

Counts

141 → 5

Alt Table

Status	Error	Program
	29.9b	(expm1.f64 (log1p.f64 (fma.f64 1/20160 (pow.f64 x 8) (log.f64 (exp.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))))
✓	0.3b	(expm1.f64 (log1p.f64 (fma.f64 1/20160 (pow.f64 x 8) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))
	0.5b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
▶	0.3b	(fma.f64 1/12 (pow.f64 x 4) (.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
	29.6b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))

Compiler

Compiled 3473 to 2672 computations (23.1% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (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))
✓	28.8b	(sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

series29.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

19.0ms

(sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

9.0ms

(*.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

11.0ms

(*.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))))

2.0ms

(sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

simplify180.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

362×	`associate-+l+_binary64`
330×	`associate-+r+_binary64`
299×	`associate-l_binary64`
289×	`fma-neg_binary64`
266×	`associate-/r*_binary64`

Counts

92 → 109

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	2352
1	225	2065
2	616	1957
3	2161	1899
4	4688	1857
5	4974	1857
6	4901	1857

prune862.0ms (8.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	250	5	255

Error

0.0b

Counts

255 → 5

Alt Table

Status	Error	Program
	29.9b	(expm1.f64 (log1p.f64 (fma.f64 1/20160 (pow.f64 x 8) (log.f64 (exp.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))))
✓	0.3b	(expm1.f64 (log1p.f64 (fma.f64 1/20160 (pow.f64 x 8) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))
	0.5b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
✓	0.3b	(fma.f64 1/12 (pow.f64 x 4) (.f64 (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (.f64 1/20160 (pow.f64 x 8))))) (sqrt.f64 (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))))
	29.6b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))

Compiler

Compiled 9772 to 7360 computations (24.7% saved)

regimes152.0ms (1.5%)

Accuracy

Total 0.6b remaining (98.3%)

Threshold costs 0.6b (98.3%)

Counts

41 → 1

Compiler

Compiled 1312 to 982 computations (25.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	18	29
2	18	29

end1.0ms (0%)

Compiler: Compiled 21 to 16 computations (23.8% saved)

sample6.9s (69.7%)

Algorithm

1×

intervals

Results

4.6s	4126×	body	2048	valid
1.2s	1999×	body	1024	valid
336.0ms	962×	body	512	valid
101.0ms	560×	body	256	valid
29.0ms	353×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 134 to 102 computations (23.9% saved)

Details

analyze145.0ms (1.5%)

sample212.0ms (2.1%)

simplify91.0ms (0.9%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series8.0ms (0.1%)

rewrite33.0ms (0.3%)

simplify125.0ms (1.3%)

prune153.0ms (1.5%)

localize25.0ms (0.3%)

series23.0ms (0.2%)

rewrite14.0ms (0.1%)

simplify85.0ms (0.9%)

prune181.0ms (1.8%)

localize30.0ms (0.3%)

series30.0ms (0.3%)

rewrite24.0ms (0.2%)

simplify178.0ms (1.8%)

prune342.0ms (3.5%)

localize28.0ms (0.3%)

series29.0ms (0.3%)

rewrite25.0ms (0.3%)

simplify180.0ms (1.8%)

prune862.0ms (8.7%)

regimes152.0ms (1.5%)

simplify4.0ms (0%)

end1.0ms (0%)

sample6.9s (69.7%)

Profiling