Details

analyze360.0ms (8.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample86.0ms (2.1%)

Algorithm

1×

intervals

Results

33.0ms	79×	body	1024	valid
13.0ms	39×	body	2048	valid
10.0ms	42×	body	512	valid
4.0ms	72×	body	128	valid
3.0ms	23×	body	256	valid
0.0ms	1×	body	4096	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9
3	13	9

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

45.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.7b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	1.2b	(+.f64 x (hypot.f64 1 x))
✓	3.5b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.f64 x (hypot.f64 1 x))
3.0ms	(hypot.f64 1 x)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-exp-log_binary64`

Counts

3 → 44

Calls

3 calls:

4.0ms	(+.f64 x (hypot.f64 1 x))
2.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
0.0ms	(hypot.f64 1 x)

simplify74.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
469×	`cancel-sign-sub-inv_binary64`
426×	`associate-/r*_binary64`
376×	`fma-def_binary64`
361×	`sub-neg_binary64`

Counts

80 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	1089
1	394	1025
2	959	1013
3	2675	1013
4	4999	1013
5	5338	1013

prune68.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	3	114

Error

Counts

114 → 3

Alt Table

Status	Error	Program
✓	45.7b	(log.f64 (+.f64 x (hypot.f64 1 x)))
▶	32.9b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
	45.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))

Compiler

Compiled 1585 to 1194 computations (24.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	20.1b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))

series8.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
3.0ms	(fma.f64 3/40 (pow.f64 x 5) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
0.0ms	(fma.f64 3/40 (pow.f64 x 5) x)

simplify55.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

612×	`associate-l_binary64`
578×	`associate-r_binary64`
480×	`distribute-lft-in_binary64`
480×	`distribute-rgt-in_binary64`
291×	`fma-def_binary64`

Counts

44 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	584
1	65	520
2	153	518
3	599	518
4	3541	518
5	4941	518

prune20.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	31	3	34

Error

Counts

34 → 3

Alt Table

Status	Error	Program
✓	45.7b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	32.9b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
▶	45.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))

Compiler

Compiled 510 to 389 computations (23.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1/16 (pow.f64 x 5))
✓	0.2b	(/.f64 1/8 (pow.f64 x 3))
✓	11.2b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
✓	17.5b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

series17.0ms (0.4%)

Counts

4 → 24

Calls

4 calls:

5.0ms	(/.f64 1/8 (pow.f64 x 3))
4.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
4.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
3.0ms	(/.f64 1/16 (pow.f64 x 5))

rewrite135.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

487×	`*-un-lft-identity_binary64`
369×	`times-frac_binary64`
245×	`add-sqr-sqrt_binary64`
219×	`add-cube-cbrt_binary64`
200×	`prod-diff_binary64`

Counts

4 → 412

Calls

4 calls:

40.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
32.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
4.0ms	(/.f64 1/8 (pow.f64 x 3))
3.0ms	(/.f64 1/16 (pow.f64 x 5))

simplify343.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

424×	`fma-neg_binary64`
326×	`unswap-sqr_binary64`
251×	`distribute-rgt-neg-in_binary64`
209×	`associate-l_binary64`
203×	`associate-r_binary64`

Counts

436 → 443

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	431	17011
1	810	13622
2	2988	10097
3	4811	10097
4	4893	10097

prune417.0ms (10%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	443	0	443
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	443	3	446

Error

Counts

446 → 3

Alt Table

Status	Error	Program
✓	45.7b	(log.f64 (+.f64 x (hypot.f64 1 x)))
✓	32.9b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
✓	45.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))

Compiler

Compiled 17669 to 14411 computations (18.4% saved)

regimes98.0ms (2.3%)

Accuracy

Total 0.1b remaining (73.8%)

Threshold costs 0.1b (73.8%)

Counts

20 → 3

Compiler

Compiled 729 to 586 computations (19.6% saved)

bsearch32.0ms (0.8%)

Steps

Iters	Range		Point
8	0.0018729809278703795	0.48956141343587944	0.007715320219142624
9	-354.9604004087521	-0.0017117114201246108	-1.0690722005650195

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	60
1	36	60
2	44	60
3	58	60
4	63	60
5	65	60
6	62	60

end1.0ms (0%)

Compiler: Compiled 42 to 32 computations (23.8% saved)

sample2.4s (57.8%)

Algorithm

1×

intervals

Results

1.1s	2431×	body	1024	valid
501.0ms	1251×	body	2048	valid
298.0ms	1225×	body	512	valid
140.0ms	2422×	body	128	valid
84.0ms	611×	body	256	valid
40.0ms	60×	body	4096	valid

Compiler

Compiled 90 to 69 computations (23.3% saved)

Details

analyze360.0ms (8.6%)

sample86.0ms (2.1%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify74.0ms (1.8%)

prune68.0ms (1.6%)

localize7.0ms (0.2%)

series8.0ms (0.2%)

rewrite1.0ms (0%)

simplify55.0ms (1.3%)

prune20.0ms (0.5%)

localize10.0ms (0.2%)

series17.0ms (0.4%)

rewrite135.0ms (3.2%)

simplify343.0ms (8.2%)

prune417.0ms (10%)

regimes98.0ms (2.3%)

bsearch32.0ms (0.8%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.4s (57.8%)

Profiling