Details

analyze6.0ms (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)

sample41.0ms (0.9%)

Algorithm

1×

intervals

Results

7.0ms	65×	body	512	valid
5.0ms	144×	body	128	valid
2.0ms	17×	body	1024	valid
2.0ms	30×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify12.0ms (0.3%)

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 (0.1%)

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

14.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.4b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 47 to 39 computations (17% saved)

localize6.0ms (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))
✓	2.9b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

series10.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(/.f64 1 (+.f64 x 1))
4.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
2.0ms	(/.f64 1 (-.f64 x 1))

rewrite161.0ms (3.6%)

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:

33.0ms	(-.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))

simplify605.0ms (13.7%)

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

prune555.0ms (12.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	529	2	531
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	529	3	532

Error

0.7b

Counts

532 → 3

Alt Table

Status	Error	Program
▶	14.1b	(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
	33.1b	(-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 2 (pow.f64 x 4)))
✓	14.4b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 23079 to 19160 computations (17% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
✓	2.7b	(-.f64 x (+.f64 2 x))

series4.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
1.0ms	(-.f64 x (+.f64 2 x))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
12×	`prod-diff_binary64`

Counts

2 → 81

Calls

2 calls:

9.0ms	(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
5.0ms	(-.f64 x (+.f64 2 x))

simplify729.0ms (16.5%)

Algorithm

1×	egg-herbie

Rules

512×	`fma-def_binary64`
468×	`associate-r_binary64`
325×	`distribute-rgt-in_binary64`
280×	`distribute-lft-in_binary64`
260×	`div-sub_binary64`

Counts

105 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	1716
1	371	1547
2	1143	1129
3	4408	1129
4	4877	1129

prune91.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	126	4	130

Error

0.6b

Counts

130 → 4

Alt Table

Status	Error	Program
	33.0b	(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
▶	0.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (/.f64 -2 (cbrt.f64 (fma.f64 x x -1))))
	1.8b	(.f64 (.f64 (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1)))) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))))
	10.3b	(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))

Compiler

Compiled 2471 to 1705 computations (31% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 -2 (cbrt.f64 (fma.f64 x x -1)))
✓	0.2b	(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))
✓	0.8b	(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))
✓	15.9b	(cbrt.f64 (fma.f64 x x -1))

series37.0ms (0.8%)

Counts

4 → 48

Calls

4 calls:

16.0ms	(/.f64 -2 (cbrt.f64 (fma.f64 x x -1)))
7.0ms	(cbrt.f64 (fma.f64 x x -1))
6.0ms	(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))
6.0ms	(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
31×	`cbrt-prod_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`

Counts

4 → 133

Calls

4 calls:

6.0ms	(/.f64 -2 (cbrt.f64 (fma.f64 x x -1)))
5.0ms	(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))
5.0ms	(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))
1.0ms	(cbrt.f64 (fma.f64 x x -1))

simplify131.0ms (3%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-def_binary64`
499×	`associate-l_binary64`
417×	`fma-neg_binary64`
242×	`times-frac_binary64`
231×	`cancel-sign-sub-inv_binary64`

Counts

181 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	251	3566
1	581	3284
2	1639	3053
3	4512	3042
4	4995	3042
5	4902	3042

prune291.0ms (6.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	290	2	292
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	292	4	296

Error

0.6b

Counts

296 → 4

Alt Table

Status	Error	Program
	33.0b	(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
▶	0.9b	(.f64 (.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x -1))) (/.f64 1 (cbrt.f64 (fma.f64 x x -1)))) (/.f64 -2 (cbrt.f64 (fma.f64 x x -1))))
	1.1b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x -1))) 6)) (/.f64 -2 (cbrt.f64 (fma.f64 x x -1))))
	10.3b	(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))

Compiler

Compiled 8360 to 6366 computations (23.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 -2 (cbrt.f64 (fma.f64 x x -1)))
✓	0.1b	(/.f64 1 (cbrt.f64 (fma.f64 x x -1)))
✓	0.2b	(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x -1))) (/.f64 1 (cbrt.f64 (fma.f64 x x -1))))
	15.9b	(cbrt.f64 (fma.f64 x x -1))

series14.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(/.f64 1 (cbrt.f64 (fma.f64 x x -1)))
7.0ms	(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x -1))) (/.f64 1 (cbrt.f64 (fma.f64 x x -1))))

rewrite39.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`add-sqr-sqrt_binary64`
130×	`times-frac_binary64`
91×	`*-un-lft-identity_binary64`
69×	`add-cube-cbrt_binary64`
68×	`cbrt-prod_binary64`

Counts

2 → 189

Calls

2 calls:

14.0ms	(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x -1))) (/.f64 1 (cbrt.f64 (fma.f64 x x -1))))
3.0ms	(/.f64 1 (cbrt.f64 (fma.f64 x x -1)))

simplify196.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

465×	`associate-/l/_binary64`
386×	`times-frac_binary64`
356×	`associate-l_binary64`
321×	`unswap-sqr_binary64`
306×	`fma-def_binary64`

Counts

213 → 269

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	176	5398
1	400	4750
2	937	4408
3	2489	4262
4	4715	4121
5	4963	4121
6	4894	4121

prune508.0ms (11.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	497	0	497
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	497	4	501

Error

0.6b

Counts

501 → 4

Alt Table

Status	Error	Program
	33.0b	(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
✓	0.9b	(.f64 (.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x -1))) (/.f64 1 (cbrt.f64 (fma.f64 x x -1)))) (/.f64 -2 (cbrt.f64 (fma.f64 x x -1))))
	1.1b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x x -1))) 6)) (/.f64 -2 (cbrt.f64 (fma.f64 x x -1))))
	10.3b	(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))

Compiler

Compiled 16103 to 12479 computations (22.5% saved)

regimes156.0ms (3.5%)

Accuracy

Total 0.0b remaining (5.9%)

Threshold costs 0.0b (5.9%)

Counts

87 → 1

Compiler

Compiled 3182 to 2442 computations (23.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	6	8

end0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

sample764.0ms (17.3%)

Algorithm

1×

intervals

Results

225.0ms	1996×	body	512	valid
173.0ms	4581×	body	128	valid
73.0ms	1026×	body	256	valid
57.0ms	397×	body	1024	valid

Compiler

Compiled 88 to 68 computations (22.7% 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

analyze6.0ms (0.1%)

sample41.0ms (0.9%)

simplify12.0ms (0.3%)

prune2.0ms (0.1%)

localize6.0ms (0.1%)

series10.0ms (0.2%)

rewrite161.0ms (3.6%)

simplify605.0ms (13.7%)

prune555.0ms (12.5%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite19.0ms (0.4%)

simplify729.0ms (16.5%)

prune91.0ms (2%)

localize8.0ms (0.2%)

series37.0ms (0.8%)

rewrite22.0ms (0.5%)

simplify131.0ms (3%)

prune291.0ms (6.6%)

localize10.0ms (0.2%)

series14.0ms (0.3%)

rewrite39.0ms (0.9%)

simplify196.0ms (4.4%)

prune508.0ms (11.5%)

regimes156.0ms (3.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample764.0ms (17.3%)

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