Details

analyze249.0ms (6.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample22.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify231.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

2682×	`fma-neg_binary64`
690×	`times-frac_binary64`
636×	`fma-def_binary64`
533×	`sub-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	45	17
3	65	17
4	78	17
5	89	17
6	129	17
7	180	17
8	288	17
9	497	17
10	671	17
11	811	17
12	976	17
13	1611	17
14	3407	17
15	3743	17
16	3727	17
17	3787	17
18	3819	17
19	3887	17
20	3898	17
21	4186	17
22	4220	17
23	4236	17
24	4236	17
25	4236	17
26	6212	17

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))

Compiler

Compiled 57 to 44 computations (22.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 6 (-.f64 x 1))
✓	0.0b	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))
✓	0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))

series26.0ms (0.7%)

Counts

3 → 18

Calls

3 calls:

19.0ms	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
5.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))
2.0ms	(*.f64 6 (-.f64 x 1))

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 98

Calls

3 calls:

10.0ms	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
6.0ms	(*.f64 6 (-.f64 x 1))
5.0ms	(+.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x)))

simplify74.0ms (2%)

Algorithm

1×	egg-herbie

Rules

431×	`distribute-rgt-in_binary64`
407×	`times-frac_binary64`
393×	`associate-l_binary64`
389×	`fma-def_binary64`
383×	`distribute-lft-in_binary64`

Counts

116 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	1561
1	341	1205
2	1073	1190
3	4684	1190
4	4933	1190

prune160.0ms (4.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	145	4	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	4	150

Error

0.0b

Counts

150 → 4

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 6 (-.f64 x 1)) (fma.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)) (.f64 4 (sqrt.f64 x))))
▶	0.0b	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
	0.4b	(*.f64 (/.f64 6 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))) (/.f64 (-.f64 x 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))))
	18.1b	(.f64 (/.f64 (.f64 6 (-.f64 x 1)) (-.f64 (.f64 (+.f64 x 1) (+.f64 x 1)) (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))))) (-.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))

Compiler

Compiled 3555 to 2663 computations (25.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 1 x))
✓	0.0b	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
✓	0.0b	(/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))

series40.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

18.0ms	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
17.0ms	(/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))
5.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 1 x))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64`
25×	`associate-r_binary64`

Counts

3 → 104

Calls

3 calls:

8.0ms	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
5.0ms	(/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))
2.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 1 x))

simplify83.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
413×	`associate-/r/_binary64`
378×	`associate-+r+_binary64`
357×	`associate-+l+_binary64`
326×	`associate-/r*_binary64`

Counts

113 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	2657
1	255	2462
2	706	2406
3	2159	2396
4	4947	2396

prune177.0ms (4.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	155	5	160

Error

Counts

160 → 5

Alt Table

Status	Error	Program
	0.3b	(.f64 6 (.f64 (+.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 -1 (sqrt.f64 x)) (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))))
	0.4b	(/.f64 (.f64 6 (-.f64 x 1)) (fma.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)) (.f64 4 (sqrt.f64 x))))
✓	0.0b	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
▶	0.1b	(*.f64 (/.f64 (fma.f64 6 (sqrt.f64 x) 6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))) (/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))))
	18.1b	(.f64 (/.f64 (.f64 6 (-.f64 x 1)) (-.f64 (.f64 (+.f64 x 1) (+.f64 x 1)) (.f64 (.f64 4 (sqrt.f64 x)) (.f64 4 (sqrt.f64 x))))) (-.f64 (+.f64 x 1) (*.f64 4 (sqrt.f64 x))))

Compiler

Compiled 3910 to 2782 computations (28.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 (fma.f64 6 (sqrt.f64 x) 6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))) (/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))))
✓	0.0b	(/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
✓	0.1b	(fma.f64 6 (sqrt.f64 x) 6)
✓	0.2b	(/.f64 (fma.f64 6 (sqrt.f64 x) 6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))

series159.0ms (4.3%)

Counts

4 → 4

Calls

4 calls:

55.0ms	(/.f64 (fma.f64 6 (sqrt.f64 x) 6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
49.0ms	(*.f64 (/.f64 (fma.f64 6 (sqrt.f64 x) 6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))) (/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))))
48.0ms	(/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
7.0ms	(fma.f64 6 (sqrt.f64 x) 6)

rewrite92.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

239×	`add-sqr-sqrt_binary64`
180×	`times-frac_binary64`
157×	`*-un-lft-identity_binary64`
148×	`sqrt-prod_binary64`
92×	`add-cube-cbrt_binary64`

Counts

4 → 274

Calls

4 calls:

36.0ms	(*.f64 (/.f64 (fma.f64 6 (sqrt.f64 x) 6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))) (/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))))
8.0ms	(/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
3.0ms	(/.f64 (fma.f64 6 (sqrt.f64 x) 6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
0.0ms	(fma.f64 6 (sqrt.f64 x) 6)

simplify274.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-def_binary64`
580×	`times-frac_binary64`
400×	`associate-/l/_binary64`
305×	`distribute-rgt-in_binary64`
299×	`distribute-lft-in_binary64`

Counts

278 → 310

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	198	11492
1	494	10519
2	1582	10437
3	4064	10291
4	5084	10291

prune388.0ms (10.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	308	2	310
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	311	4	315

Error

Counts

315 → 4

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 6 (-.f64 x 1)) (fma.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)) (.f64 4 (sqrt.f64 x))))
✓	0.0b	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
▶	0.1b	(*.f64 (/.f64 (fma.f64 6 (sqrt.f64 x) 6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))) (log1p.f64 (expm1.f64 (/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))))))
	0.3b	(*.f64 (fma.f64 6 (sqrt.f64 x) 6) (/.f64 (+.f64 -1 (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) 4 (+.f64 x 1))))

Compiler

Compiled 13308 to 8905 computations (33.1% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))))
	0.1b	(fma.f64 6 (sqrt.f64 x) 6)
	0.2b	(/.f64 (fma.f64 6 (sqrt.f64 x) 6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
✓	0.5b	(expm1.f64 (/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))))

series114.0ms (3%)

Counts

2 → 2

Calls

2 calls:

65.0ms	(expm1.f64 (/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))))
49.0ms	(log1p.f64 (expm1.f64 (/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))))
0.0ms	(log1p.f64 (expm1.f64 (/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))))

simplify80.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

714×	`distribute-rgt-in_binary64`
655×	`distribute-lft-in_binary64`
626×	`fma-def_binary64`
548×	`fma-neg_binary64`
515×	`div-sub_binary64`

Counts

24 → 41

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	599
1	47	513
2	74	513
3	148	513
4	371	513
5	1075	513
6	3697	513
7	4949	513
8	5255	513

prune156.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	117	4	121

Error

Counts

121 → 4

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 6 (-.f64 x 1)) (fma.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)) (.f64 4 (sqrt.f64 x))))
✓	0.0b	(*.f64 6 (/.f64 (-.f64 x 1) (fma.f64 4 (sqrt.f64 x) (+.f64 1 x))))
✓	0.1b	(*.f64 (/.f64 (fma.f64 6 (sqrt.f64 x) 6) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))) (log1p.f64 (expm1.f64 (/.f64 (-.f64 (sqrt.f64 x) 1) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 1 x)))))))
	0.3b	(*.f64 (fma.f64 6 (sqrt.f64 x) 6) (/.f64 (+.f64 -1 (sqrt.f64 x)) (fma.f64 (sqrt.f64 x) 4 (+.f64 x 1))))

Compiler

Compiled 4768 to 3283 computations (31.1% saved)

regimes318.0ms (8.5%)

Accuracy

Total 0.0b remaining (78.5%)

Threshold costs 0.0b (78.5%)

Counts

152 → 1

Compiler

Compiled 6442 to 4988 computations (22.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	19	23
2	18	23

end1.0ms (0%)

Compiler: Compiled 16 to 13 computations (18.8% saved)

sample993.0ms (26.6%)

Algorithm

1×

intervals

Results

594.0ms	8000×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 117 to 89 computations (23.9% saved)

Details

analyze249.0ms (6.7%)

sample22.0ms (0.6%)

simplify231.0ms (6.2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series26.0ms (0.7%)

rewrite29.0ms (0.8%)

simplify74.0ms (2%)

prune160.0ms (4.3%)

localize7.0ms (0.2%)

series40.0ms (1.1%)

rewrite24.0ms (0.6%)

simplify83.0ms (2.2%)

prune177.0ms (4.7%)

localize11.0ms (0.3%)

series159.0ms (4.3%)

rewrite92.0ms (2.4%)

simplify274.0ms (7.3%)

prune388.0ms (10.4%)

localize15.0ms (0.4%)

series114.0ms (3%)

rewrite2.0ms (0%)

simplify80.0ms (2.1%)

prune156.0ms (4.2%)

regimes318.0ms (8.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample993.0ms (26.6%)

Profiling