Details

analyze4.0ms (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
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample4.8s (89.8%)

Results

3.4s	4318×	body	2048	valid
845.0ms	2030×	body	1024	valid
319.0ms	1016×	body	512	valid
94.0ms	540×	body	256	valid
33.0ms	352×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify27.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`
284×	`cancel-sign-sub-inv_binary64`
199×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	36	13
3	60	13
4	122	13
5	272	13
6	697	13
7	1699	13
8	3110	13

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

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

28.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	28.8b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
	28.8b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

Compiler

Compiled 53 to 38 computations (28.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	4.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series4.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

2.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
1.0ms	(-.f64 (exp.f64 x) 2)

rewrite44.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

815×	`expm1-log1p-u_binary64`
536×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
89×	`log1p-expm1-u_binary64`
88×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	181	17
2	2616	17

Stop Event

1×	node limit

Counts

2 → 78

Calls

2 calls:

42.0ms	(-.f64 (exp.f64 x) 2)
42.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

simplify28.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

749×	`unswap-sqr_binary64`
544×	`associate-l_binary64`
523×	`fma-def_binary64`
398×	`associate-r_binary64`
193×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	198
1	115	196
2	250	196
3	744	191
4	3163	191

Stop Event

1×	node limit

Counts

94 → 96

prune70.0ms (1.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	96	2	98

Error

Counts

98 → 2

Alt Table

Status	Error	Program
✓	28.8b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	0.5b	(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))

Compiler

Compiled 1463 to 801 computations (45.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/20160 (pow.f64 x 8))
✓	0.0b	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
✓	0.1b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))

series11.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

4.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
4.0ms	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
3.0ms	(*.f64 1/20160 (pow.f64 x 8))

rewrite70.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

476×	`log-prod_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
184×	`log-pow_binary64`
152×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	299	42
2	3039	42

Stop Event

1×	node limit

Counts

3 → 75

Calls

3 calls:

68.0ms	(*.f64 1/20160 (pow.f64 x 8))
68.0ms	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
68.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))

simplify70.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

924×	`fma-def_binary64`
472×	`unswap-sqr_binary64`
392×	`*-commutative_binary64`
369×	`sqr-pow_binary64`
244×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	336
1	37	336
2	81	336
3	219	336
4	733	336
5	1611	336
6	3015	336
7	3342	336
8	3527	336
9	3732	336
10	4007	336
11	4363	336
12	4772	336

Stop Event

1×	node limit

Counts

99 → 83

prune82.0ms (1.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	83	2	85

Error

Counts

85 → 2

Alt Table

Status	Error	Program
✓	28.8b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	0.5b	(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))

Compiler

Compiled 2017 to 1548 computations (23.3% saved)

regimes33.0ms (0.6%)

Accuracy

Total 0.4b remaining (96.4%)

Threshold costs 0.4b (96.4%)

Counts

20 → 1

Compiler

Compiled 484 to 354 computations (26.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	16	25

Stop Event

1×

saturated

end71.0ms (1.3%)

Compiler: Compiled 66 to 49 computations (25.8% saved)

Details

analyze4.0ms (0.1%)

sample4.8s (89.8%)

simplify27.0ms (0.5%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series4.0ms (0.1%)

rewrite44.0ms (0.8%)

simplify28.0ms (0.5%)

prune70.0ms (1.3%)

localize10.0ms (0.2%)

series11.0ms (0.2%)

rewrite70.0ms (1.3%)

simplify70.0ms (1.3%)

prune82.0ms (1.5%)

regimes33.0ms (0.6%)

simplify3.0ms (0.1%)

end71.0ms (1.3%)

Profiling