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
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample43.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	144×	body	128	valid
7.0ms	64×	body	512	valid
3.0ms	36×	body	256	valid
2.0ms	12×	body	1024	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
13×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16

prune2.0ms (0%)

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

13.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.9b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 47 to 39 computations (17% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	2.2b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

series9.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
3.0ms	(/.f64 1 (-.f64 x 1))
3.0ms	(/.f64 1 (+.f64 x 1))

rewrite165.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

870×	`*-un-lft-identity_binary64`
804×	`times-frac_binary64`
733×	`add-sqr-sqrt_binary64`
486×	`prod-diff_binary64`
465×	`add-cube-cbrt_binary64`

Counts

3 → 661

Calls

3 calls:

35.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify792.0ms (10.9%)

Algorithm

1×	egg-herbie

Rules

947×	`fma-neg_binary64`
335×	`times-frac_binary64`
236×	`distribute-rgt-in_binary64`
231×	`div-sub_binary64`
202×	`associate-/l*_binary64`

Counts

697 → 531

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	27782
1	632	18403
2	1772	13759
3	3945	12706
4	4972	12706
5	4989	12706
6	4909	12706

prune1.2s (16.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	529	2	531
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	530	2	532

Error

0.6b

Counts

532 → 2

Alt Table

Status	Error	Program
▶	13.9b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 1)))) (/.f64 1 (-.f64 x 1)))
	31.9b	(-.f64 (/.f64 -2 (pow.f64 x 4)) (+.f64 (/.f64 2 (pow.f64 x 6)) (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 (pow.f64 x 8)))))

Compiler

Compiled 23097 to 19180 computations (17% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(log1p.f64 (/.f64 1 (+.f64 x 1)))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 1))))
✓	2.2b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 1)))) (/.f64 1 (-.f64 x 1)))

series17.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 1)))) (/.f64 1 (-.f64 x 1)))
5.0ms	(log1p.f64 (/.f64 1 (+.f64 x 1)))
5.0ms	(expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 1))))

rewrite63.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`add-sqr-sqrt_binary64`
115×	`*-un-lft-identity_binary64`
86×	`times-frac_binary64`
81×	`prod-diff_binary64`
75×	`add-cube-cbrt_binary64`

Counts

3 → 152

Calls

3 calls:

26.0ms	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 1)))) (/.f64 1 (-.f64 x 1)))
1.0ms	(log1p.f64 (/.f64 1 (+.f64 x 1)))
1.0ms	(expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 1))))

simplify317.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-def_binary64`
419×	`associate-r_binary64`
252×	`exp-prod_binary64`
191×	`cancel-sign-sub-inv_binary64`
186×	`div-sub_binary64`

Counts

188 → 190

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	223	6028
1	547	3619
2	1472	2877
3	4282	2877
4	4822	2876
5	4851	2876

prune390.0ms (5.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	243	2	245

Error

0.6b

Counts

245 → 2

Alt Table

Status	Error	Program
✓	13.9b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 1)))) (/.f64 1 (-.f64 x 1)))
▶	31.9b	(-.f64 (/.f64 -2 (pow.f64 x 4)) (+.f64 (/.f64 2 (pow.f64 x 6)) (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 (pow.f64 x 8)))))

Compiler

Compiled 7708 to 6469 computations (16.1% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 2 (pow.f64 x 8))
✓	0.2b	(/.f64 2 (pow.f64 x 6))
✓	0.4b	(/.f64 -2 (pow.f64 x 4))
✓	0.7b	(/.f64 2 (*.f64 x x))

series24.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 -2 (pow.f64 x 4))
6.0ms	(/.f64 2 (pow.f64 x 8))
6.0ms	(/.f64 2 (pow.f64 x 6))
5.0ms	(/.f64 2 (*.f64 x x))

rewrite44.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
36×	`unpow-prod-down_binary64`

Counts

4 → 164

Calls

4 calls:

7.0ms	(/.f64 -2 (pow.f64 x 4))
7.0ms	(/.f64 2 (pow.f64 x 6))
6.0ms	(/.f64 2 (pow.f64 x 8))
6.0ms	(/.f64 2 (*.f64 x x))

simplify225.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

794×	`times-frac_binary64`
462×	`associate-l_binary64`
461×	`associate-/l*_binary64`
352×	`fma-def_binary64`
349×	`associate-/l/_binary64`

Counts

176 → 210

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	254	2522
1	422	2204
2	1130	2087
3	4449	2087
4	4998	2087
5	5154	2087

prune418.0ms (5.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	207	5	212

Error

0.0b

Counts

212 → 5

Alt Table

Status	Error	Program
	32.0b	(-.f64 (/.f64 -2 (pow.f64 x 4)) (+.f64 (/.f64 2 (pow.f64 x 6)) (+.f64 (.f64 (sqrt.f64 (/.f64 2 (.f64 x x))) (sqrt.f64 (/.f64 2 (*.f64 x x)))) (/.f64 2 (pow.f64 x 8)))))
✓	31.9b	(-.f64 (/.f64 -2 (pow.f64 x 4)) (+.f64 (/.f64 2 (pow.f64 x 6)) (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 (pow.f64 x 8)))))
✓	13.9b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 1)))) (/.f64 1 (-.f64 x 1)))
▶	31.3b	(-.f64 (/.f64 -2 (pow.f64 x 4)) (+.f64 (/.f64 2 (pow.f64 x 6)) (+.f64 (/.f64 (/.f64 2 x) x) (/.f64 2 (pow.f64 x 8)))))
	32.1b	(-.f64 (/.f64 -2 (pow.f64 x 4)) (+.f64 (/.f64 2 (pow.f64 x 6)) (+.f64 (/.f64 (sqrt.f64 2) (/.f64 (*.f64 x x) (sqrt.f64 2))) (/.f64 2 (pow.f64 x 8)))))

Compiler

Compiled 6513 to 4937 computations (24.2% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 2 (pow.f64 x 8))
✓	0.1b	(/.f64 (/.f64 2 x) x)
	0.2b	(/.f64 2 (pow.f64 x 6))
	0.4b	(/.f64 -2 (pow.f64 x 4))

series7.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

7.0ms

(/.f64 (/.f64 2 x) x)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

1 → 72

Calls

1 calls:

9.0ms

(/.f64 (/.f64 2 x) x)

simplify189.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

508×	`associate-/r/_binary64`
476×	`*-commutative_binary64`
393×	`associate-*r/_binary64`
346×	`distribute-rgt-in_binary64`
345×	`fma-neg_binary64`

Counts

84 → 113

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	141	1388
1	293	1287
2	541	1206
3	1200	1182
4	2176	1177
5	3375	1127
6	4799	1097
7	4968	1097
8	4852	1097

prune661.0ms (9.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	291	3	294
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	292	7	299

Error

Counts

299 → 7

Alt Table

Status	Error	Program
	48.9b	(-.f64 (/.f64 -2 (pow.f64 x 4)) (+.f64 (/.f64 2 (pow.f64 x 6)) (+.f64 (/.f64 (sqrt.f64 (/.f64 2 x)) (/.f64 x (sqrt.f64 (/.f64 2 x)))) (/.f64 2 (pow.f64 x 8)))))
	32.1b	(-.f64 (/.f64 -2 (pow.f64 x 4)) (+.f64 (/.f64 2 (pow.f64 x 6)) (+.f64 (/.f64 (sqrt.f64 2) (/.f64 (*.f64 x x) (sqrt.f64 2))) (/.f64 2 (pow.f64 x 8)))))
	31.6b	(-.f64 (/.f64 -2 (pow.f64 x 4)) (+.f64 (/.f64 2 (pow.f64 x 6)) (+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 2 x)) (cbrt.f64 (/.f64 2 x))) (/.f64 (cbrt.f64 (/.f64 2 x)) x)) (/.f64 2 (pow.f64 x 8)))))
✓	13.9b	(-.f64 (expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 1)))) (/.f64 1 (-.f64 x 1)))
	31.7b	(-.f64 (/.f64 -2 (pow.f64 x 4)) (+.f64 (/.f64 2 (pow.f64 x 6)) (+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 2 x)) (cbrt.f64 (/.f64 2 x))) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (cbrt.f64 (/.f64 2 x)) (cbrt.f64 x))) (/.f64 2 (pow.f64 x 8)))))
✓	31.3b	(-.f64 (/.f64 -2 (pow.f64 x 4)) (+.f64 (/.f64 2 (pow.f64 x 6)) (+.f64 (/.f64 (/.f64 2 x) x) (/.f64 2 (pow.f64 x 8)))))
✓	31.9b	(-.f64 (/.f64 -2 (pow.f64 x 4)) (+.f64 (/.f64 2 (pow.f64 x 6)) (+.f64 (/.f64 2 (*.f64 x x)) (/.f64 2 (pow.f64 x 8)))))

Compiler

Compiled 9250 to 7136 computations (22.9% saved)

regimes837.0ms (11.5%)

Accuracy

Total 0.2b remaining (92.5%)

Threshold costs 0.2b (92.5%)

Counts

158 → 3

Compiler

Compiled 7322 to 6074 computations (17% saved)

bsearch60.0ms (0.8%)

Steps

Iters	Range		Point
7	1.7857404628156563	181.55572041425228	55.498538329832456
9	-946.9103058624548	-0.006027104407589454	-0.9981121859939434

Compiler

Compiled 2 to 1 computations (50% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
15×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`
10×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	87
1	54	87
2	75	87
3	97	87
4	113	87
5	123	87
6	128	87
7	129	87
8	126	87

end3.0ms (0%)

Compiler: Compiled 59 to 46 computations (22% saved)

sample1.7s (23.3%)

Algorithm

1×

intervals

Results

432.0ms	2017×	body	512	valid
347.0ms	4584×	body	128	valid
147.0ms	988×	body	256	valid
125.0ms	411×	body	1024	valid

Compiler

Compiled 269 to 215 computations (20.1% saved)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16

Details

analyze5.0ms (0.1%)

sample43.0ms (0.6%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series9.0ms (0.1%)

rewrite165.0ms (2.3%)

simplify792.0ms (10.9%)

prune1.2s (16.4%)

localize19.0ms (0.3%)

series17.0ms (0.2%)

rewrite63.0ms (0.9%)

simplify317.0ms (4.3%)

prune390.0ms (5.3%)

localize26.0ms (0.4%)

series24.0ms (0.3%)

rewrite44.0ms (0.6%)

simplify225.0ms (3.1%)

prune418.0ms (5.7%)

localize27.0ms (0.4%)

series7.0ms (0.1%)

rewrite21.0ms (0.3%)

simplify189.0ms (2.6%)

prune661.0ms (9.1%)

regimes837.0ms (11.5%)

bsearch60.0ms (0.8%)

simplify11.0ms (0.2%)

end3.0ms (0%)

sample1.7s (23.3%)

Profiling

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16