Details

analyze1.1s (4.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
12.5%	78%	9.5%	6
20.3%	68.7%	11%	7
21.1%	62.4%	16.5%	8
25.4%	57%	17.7%	9
26%	52.1%	22%	10
28.3%	49%	22.7%	11
28.6%	47.2%	24.2%	12
29.8%	45.6%	24.7%	13
29.9%	43.9%	26.2%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample15.7s (69%)

Results

11.4s	4885×	body	8192	exit
1.9s	3379×	body	1024	invalid
1.2s	8256×	body	128	valid
759.0ms	1696×	body	512	invalid
196.0ms	854×	body	256	invalid
84.0ms	629×	body	128	invalid
6.0ms	2×	body	8192	invalid
3.0ms	2×	body	4096	invalid
3.0ms	4×	body	2048	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify86.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

656×	`unswap-sqr_binary64`
607×	`times-frac_binary64`
540×	`sqr-pow_binary64`
391×	`pow-sqr_binary64`
205×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	37	11
3	79	11
4	200	11
5	635	11
6	2301	11
7	2298	11
8	2410	11
9	2637	11
10	3067	11
11	3698	11
12	4907	11
13	4890	11

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))
▶	0.3b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))

Compiler

Compiled 55 to 32 computations (41.8% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))
✓	0.3b	(pow.f64 l (exp.f64 w))

series290.0ms (1.3%)

Counts

2 → 44

Calls

2 calls:

146.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))
144.0ms	(pow.f64 l (exp.f64 w))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`unpow-prod-down_binary64`
7×	`add-cube-cbrt_binary64`

Counts

2 → 48

Calls

2 calls:

6.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 l (exp.f64 w)))
2.0ms	(pow.f64 l (exp.f64 w))

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
739×	`fma-neg_binary64`
459×	`associate-+l+_binary64`
213×	`associate--l+_binary64`
162×	`cancel-sign-sub-inv_binary64`

Counts

92 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	1391
1	348	1242
2	1307	1192
3	4511	1192
4	5132	1192

prune57.0ms (0.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Error

0.0b

Counts

87 → 4

Alt Table

Status	Error	Program
	2.3b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 l (exp.f64 w)) (exp.f64 w))))
	4.4b	(*.f64 (exp.f64 (neg.f64 w)) (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))))
▶	0.3b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
	1.1b	(.f64 (exp.f64 (neg.f64 w)) (fma.f64 (log.f64 l) (.f64 l w) l))

Compiler

Compiled 1563 to 514 computations (67.1% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
✓	0.0b	(sqrt.f64 (exp.f64 w))
✓	0.2b	(pow.f64 l (sqrt.f64 (exp.f64 w)))
✓	0.2b	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))

series1.7s (7.4%)

Counts

4 → 68

Calls

4 calls:

773.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
758.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
144.0ms	(pow.f64 l (sqrt.f64 (exp.f64 w)))
3.0ms	(sqrt.f64 (exp.f64 w))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`unpow-prod-down_binary64`
26×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`pow-unpow_binary64`

Counts

4 → 105

Calls

4 calls:

8.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
3.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w)))
2.0ms	(pow.f64 l (sqrt.f64 (exp.f64 w)))
1.0ms	(sqrt.f64 (exp.f64 w))

simplify97.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-neg_binary64`
220×	`associate-r_binary64`
213×	`associate--l+_binary64`
204×	`unswap-sqr_binary64`
181×	`times-frac_binary64`

Counts

173 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	2917
1	535	2425
2	1911	2364
3	4284	2364
4	4978	2364

prune128.0ms (0.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	192	3	195
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	194	5	199

Error

0.0b

Counts

199 → 5

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (pow.f64 (exp.f64 1) (/.f64 w 2))))
	0.3b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w))))))
	0.7b	(*.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (exp.f64 w)) (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
	4.4b	(*.f64 (exp.f64 (neg.f64 w)) (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))))
	1.1b	(.f64 (exp.f64 (neg.f64 w)) (fma.f64 (log.f64 l) (.f64 l w) l))

Compiler

Compiled 4247 to 1202 computations (71.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (pow.f64 (exp.f64 1) (/.f64 w 2))))
	0.0b	(sqrt.f64 (exp.f64 w))
	0.2b	(pow.f64 l (sqrt.f64 (exp.f64 w)))
✓	0.2b	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (pow.f64 (exp.f64 1) (/.f64 w 2)))

series1.8s (8.1%)

Counts

2 → 48

Calls

2 calls:

922.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (pow.f64 (exp.f64 1) (/.f64 w 2))))
918.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (pow.f64 (exp.f64 1) (/.f64 w 2)))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`unpow-prod-down_binary64`
18×	`add-sqr-sqrt_binary64`
11×	`associate-r_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 66

Calls

2 calls:

8.0ms	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (pow.f64 (exp.f64 1) (/.f64 w 2))))
3.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (pow.f64 (exp.f64 1) (/.f64 w 2)))

simplify96.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-def_binary64`
663×	`fma-neg_binary64`
448×	`associate-+l+_binary64`
211×	`associate--l+_binary64`
164×	`associate-r_binary64`

Counts

114 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	3148
1	462	2879
2	1554	2744
3	4499	2744
4	5033	2744

prune159.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	184	5	189

Error

0.0b

Counts

189 → 5

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 (exp.f64 (neg.f64 w)) (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w))))))
	0.7b	(*.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (exp.f64 w)) (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
	4.4b	(*.f64 (exp.f64 (neg.f64 w)) (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))))
	2.3b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (pow.f64 (E.f64) (/.f64 w 2))) (exp.f64 w))))
	1.1b	(.f64 (exp.f64 (neg.f64 w)) (fma.f64 (log.f64 l) (.f64 l w) l))

Compiler

Compiled 4921 to 2418 computations (50.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w))))
	0.2b	(pow.f64 l (sqrt.f64 (exp.f64 w)))
✓	0.2b	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w)))))
✓	0.2b	(log1p.f64 (sqrt.f64 (exp.f64 w)))

series982.0ms (4.3%)

Counts

3 → 48

Calls

3 calls:

769.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w)))))
211.0ms	(log1p.f64 (sqrt.f64 (exp.f64 w)))
3.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w))))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`unpow-prod-down_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 48

Calls

3 calls:

2.0ms	(pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w)))))
0.0ms	(log1p.f64 (sqrt.f64 (exp.f64 w)))
0.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w))))

simplify61.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

733×	`distribute-rgt-out_binary64`
486×	`fma-def_binary64`
457×	`associate-l_binary64`
358×	`associate-r_binary64`
307×	`unswap-sqr_binary64`

Counts

96 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	140	1252
1	313	1131
2	825	1006
3	3005	1002
4	5469	1002

prune92.0ms (0.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	128	5	133

Error

0.0b

Counts

133 → 5

Alt Table

Status	Error	Program
	0.7b	(*.f64 (/.f64 (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))) (exp.f64 w)) (pow.f64 (pow.f64 (sqrt.f64 l) (sqrt.f64 (exp.f64 w))) (sqrt.f64 (exp.f64 w))))
	0.7b	(.f64 (exp.f64 (neg.f64 w)) (pow.f64 (.f64 (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w)))) (sqrt.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))))) (expm1.f64 (log1p.f64 (sqrt.f64 (exp.f64 w))))))
	4.4b	(*.f64 (exp.f64 (neg.f64 w)) (exp.f64 (log.f64 (pow.f64 l (exp.f64 w)))))
	2.3b	(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (pow.f64 l (sqrt.f64 (exp.f64 w))) (pow.f64 (E.f64) (/.f64 w 2))) (exp.f64 w))))
	1.1b	(.f64 (exp.f64 (neg.f64 w)) (fma.f64 (log.f64 l) (.f64 l w) l))

Compiler

Compiled 2880 to 843 computations (70.7% saved)

regimes143.0ms (0.6%)

Accuracy

Total 0.1b remaining (49.4%)

Threshold costs 0.1b (49.4%)

Counts

58 → 1

Compiler

Compiled 2906 to 1828 computations (37.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	18	13
3	19	13
4	18	13

end78.0ms (0.3%)

Compiler: Compiled 114 to 66 computations (42.1% saved)

Details

analyze1.1s (4.8%)

sample15.7s (69%)

simplify86.0ms (0.4%)

prune3.0ms (0%)

localize6.0ms (0%)

series290.0ms (1.3%)

rewrite10.0ms (0%)

simplify68.0ms (0.3%)

prune57.0ms (0.2%)

localize8.0ms (0%)

series1.7s (7.4%)

rewrite18.0ms (0.1%)

simplify97.0ms (0.4%)

prune128.0ms (0.6%)

localize11.0ms (0.1%)

series1.8s (8.1%)

rewrite15.0ms (0.1%)

simplify96.0ms (0.4%)

prune159.0ms (0.7%)

localize12.0ms (0.1%)

series982.0ms (4.3%)

rewrite4.0ms (0%)

simplify61.0ms (0.3%)

prune92.0ms (0.4%)

regimes143.0ms (0.6%)

simplify3.0ms (0%)

end78.0ms (0.3%)

Profiling