Details

analyze80.0ms (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)

sample96.0ms (1.3%)

Algorithm

1×

intervals

Results

65.0ms	122×	body	2048	valid
14.0ms	57×	body	1024	valid
7.0ms	46×	body	512	valid
2.0ms	19×	body	256	valid
1.0ms	12×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify63.0ms (0.8%)

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

32.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	32.5b	(+.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)
✓	5.2b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite15.0ms (0.2%)

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:

8.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

series6.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

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

simplify91.0ms (1.2%)

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 → 148

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

prune136.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	145	4	149

Error

0.0b

Counts

149 → 4

Alt Table

Status	Error	Program
✓	32.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	1.0b	(+.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))))
	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	32.7b	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)) (fma.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2) (+.f64 (expm1.f64 (*.f64 x -2)) (/.f64 2 (exp.f64 x)))))

Compiler

Compiled 2149 to 1234 computations (42.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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))

rewrite25.0ms (0.3%)

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 → 97

Calls

4 calls:

8.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2)))
5.0ms	(*.f64 1/360 (pow.f64 x 6))
4.0ms	(*.f64 1/12 (pow.f64 x 4))
4.0ms	(*.f64 1/20160 (pow.f64 x 8))

series69.0ms (0.9%)

Counts

4 → 6

Calls

4 calls:

19.0ms	(*.f64 1/360 (pow.f64 x 6))
19.0ms	(*.f64 1/20160 (pow.f64 x 8))
17.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2)))
13.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify124.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

341×	`*-commutative_binary64`
298×	`unswap-sqr_binary64`
291×	`fma-def_binary64`
264×	`fma-neg_binary64`
234×	`distribute-rgt-in_binary64`

Counts

103 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	1333
1	361	1268
2	990	1186
3	2364	1184
4	4620	1184
5	4987	1184
6	4902	1184

prune158.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	168	4	172

Error

0.0b

Counts

172 → 4

Alt Table

Status	Error	Program
✓	32.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	1.0b	(+.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))))
▶	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	32.7b	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)) (fma.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2) (+.f64 (expm1.f64 (*.f64 x -2)) (/.f64 2 (exp.f64 x)))))

Compiler

Compiled 3759 to 3024 computations (19.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

2.0ms

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

series15.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

15.0ms

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

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

540×	`distribute-rgt-in_binary64`
530×	`distribute-lft-in_binary64`
522×	`unswap-sqr_binary64`
436×	`distribute-rgt-out_binary64`
363×	`*-commutative_binary64`

Counts

22 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	277
1	30	254
2	68	254
3	195	254
4	915	254
5	3165	254
6	4937	254
7	4897	254

prune42.0ms (0.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	76	4	80

Error

0.0b

Counts

80 → 4

Alt Table

Status	Error	Program
✓	32.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	1.0b	(+.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))))
✓	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
▶	32.7b	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)) (fma.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2) (+.f64 (expm1.f64 (*.f64 x -2)) (/.f64 2 (exp.f64 x)))))

Compiler

Compiled 751 to 523 computations (30.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (exp.f64 x) 2)
✓	0.1b	(pow.f64 (exp.f64 x) -3)
✓	0.3b	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)) (fma.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2) (+.f64 (expm1.f64 (*.f64 x -2)) (/.f64 2 (exp.f64 x)))))
✓	5.0b	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
16×	`fma-def_binary64`
12×	`times-frac_binary64`

Counts

3 → 87

Calls

3 calls:

15.0ms

(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))

12.0ms

(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)) (fma.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2) (+.f64 (expm1.f64 (*.f64 x -2)) (/.f64 2 (exp.f64 x)))))

2.0ms

(pow.f64 (exp.f64 x) -3)

series238.0ms (3.2%)

Counts

3 → 36

Calls

3 calls:

166.0ms

(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)) (fma.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2) (+.f64 (expm1.f64 (*.f64 x -2)) (/.f64 2 (exp.f64 x)))))

49.0ms

(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))

22.0ms

(pow.f64 (exp.f64 x) -3)

simplify161.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

505×	`fma-def_binary64`
463×	`associate-l_binary64`
457×	`fma-neg_binary64`
443×	`associate-r_binary64`
305×	`distribute-rgt-in_binary64`

Counts

123 → 204

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	4192
1	445	3905
2	1248	3865
3	4707	3844
4	4971	3844

prune447.0ms (6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	261	2	263
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	262	5	267

Error

Counts

267 → 5

Alt Table

Status	Error	Program
	32.7b	(/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))) (cbrt.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)))) (cbrt.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)))) (fma.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2) (+.f64 (expm1.f64 (*.f64 x -2)) (/.f64 2 (exp.f64 x)))))
✓	32.5b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	1.0b	(+.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))))
✓	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	32.7b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) -3) (pow.f64 (-.f64 (exp.f64 x) 2) 3)) (fma.f64 (-.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) 2) (+.f64 (expm1.f64 (*.f64 x -2)) (/.f64 2 (exp.f64 x)))))

Compiler

Compiled 7954 to 5239 computations (34.1% saved)

regimes107.0ms (1.4%)

Accuracy

Total 0.6b remaining (98.5%)

Threshold costs 0.6b (98.5%)

Compiler

Compiled 976 to 732 computations (25% saved)

simplify6.0ms (0.1%)

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

end1.0ms (0%)

Compiler: Compiled 21 to 17 computations (19% saved)

sample5.4s (72.4%)

Algorithm

1×

intervals

Results

3.7s	4209×	body	2048	valid
823.0ms	1954×	body	1024	valid
270.0ms	985×	body	512	valid
74.0ms	499×	body	256	valid
29.0ms	353×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 161 to 118 computations (26.7% saved)

Details

analyze80.0ms (1.1%)

sample96.0ms (1.3%)

simplify63.0ms (0.8%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite15.0ms (0.2%)

series6.0ms (0.1%)

simplify91.0ms (1.2%)

prune136.0ms (1.8%)

localize12.0ms (0.2%)

rewrite25.0ms (0.3%)

series69.0ms (0.9%)

simplify124.0ms (1.7%)

prune158.0ms (2.1%)

localize5.0ms (0.1%)

rewrite3.0ms (0%)

series15.0ms (0.2%)

simplify85.0ms (1.2%)

prune42.0ms (0.6%)

localize13.0ms (0.2%)

rewrite35.0ms (0.5%)

series238.0ms (3.2%)

simplify161.0ms (2.2%)

prune447.0ms (6%)

regimes107.0ms (1.4%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample5.4s (72.4%)

Profiling