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
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)

sample4.7s (86.8%)

Results

3.3s	4268×	body	2048	valid
868.0ms	2042×	body	1024	valid
300.0ms	1074×	body	512	valid
135.0ms	516×	body	256	valid
35.0ms	356×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 20 to 16 computations (20% saved)

preprocess35.0ms (0.7%)

Algorithm

2×	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
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify23.0ms (0.4%)

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

prune4.0ms (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

31.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	31.3b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	31.3b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

Compiler

Compiled 53 to 38 computations (28.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 (neg.f64 x)) -2)
✓	5.4b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))	x	0
1.0ms	(+.f64 (exp.f64 (neg.f64 x)) -2)	x	0
1.0ms	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))	x	inf
1.0ms	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))	x	-inf
0.0ms	(+.f64 (exp.f64 (neg.f64 x)) -2)	x	inf

rewrite42.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

799×	`expm1-log1p-u_binary64`
636×	`prod-diff_binary64`
91×	`add-sqr-sqrt_binary64`
88×	`log1p-expm1-u_binary64`
87×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	179	15
2	2582	15

Stop Event

1×	node limit

Counts

2 → 69

simplify34.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

749×	`unswap-sqr_binary64`
623×	`fma-neg_binary64`
554×	`associate-l_binary64`
507×	`fma-def_binary64`
411×	`associate-r_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	268
1	120	260
2	265	260
3	832	260
4	3789	259

Stop Event

1×	node limit

Counts

93 → 90

prune60.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	89	3	92

Error

Counts

92 → 3

Alt Table

Status	Error	Program
▶	0.6b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
	0.7b	(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
✓	31.3b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

Compiler

Compiled 1295 to 822 computations (36.5% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.1%)

Counts

2 → 12

Calls

6 calls:

1.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))	x	-inf
1.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))	x	inf
1.0ms	(*.f64 1/20160 (pow.f64 x 8))	x	0
1.0ms	(*.f64 1/20160 (pow.f64 x 8))	x	-inf
1.0ms	(*.f64 1/20160 (pow.f64 x 8))	x	inf

rewrite50.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

314×	`prod-diff_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
201×	`log-pow_binary64`
142×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	319	32
2	3288	32

Stop Event

1×	node limit

Counts

2 → 40

simplify49.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

508×	`distribute-rgt-out_binary64`
413×	`unswap-sqr_binary64`
378×	`distribute-lft-out_binary64`
312×	`associate-l_binary64`
310×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	192
1	61	192
2	136	192
3	384	192
4	1666	192
5	4013	192
6	4358	192
7	4854	192

Stop Event

1×	node limit

Counts

52 → 53

prune52.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	53	3	56

Error

Counts

56 → 3

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
▶	0.7b	(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
✓	31.3b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

Compiler

Compiled 1173 to 857 computations (26.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series11.0ms (0.2%)

Counts

3 → 24

Calls

9 calls:

1.0ms	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))	x	-inf
1.0ms	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))	x	inf
1.0ms	(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))	x	-inf
1.0ms	(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))	x	inf
1.0ms	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4)))	x	0

rewrite50.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

869×	`log1p-expm1-u_binary64`
869×	`expm1-log1p-u_binary64`
204×	`prod-diff_binary64`
105×	`add-sqr-sqrt_binary64`
102×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	234	39
2	2480	39

Stop Event

1×	node limit

Counts

3 → 60

simplify90.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1194×	`fma-def_binary64`
374×	`sqr-pow_binary64`
359×	`*-commutative_binary64`
294×	`distribute-lft-out_binary64`
285×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	312
1	38	312
2	76	312
3	192	312
4	787	312
5	2277	312
6	3387	312
7	3622	312
8	3822	312
9	4073	312
10	4388	312
11	4825	312

Stop Event

1×	node limit

Counts

84 → 69

prune59.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	69	3	72

Error

Counts

72 → 3

Alt Table

Status	Error	Program
✓	0.6b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	0.7b	(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
✓	31.3b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

Compiler

Compiled 1225 to 913 computations (25.5% saved)

regimes26.0ms (0.5%)

Accuracy

Total 0.5b remaining (97.3%)

Threshold costs 0.5b (97.3%)

Counts

15 → 1

Compiler

Compiled 304 to 228 computations (25% saved)

simplify2.0ms (0%)

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

end82.0ms (1.5%)

Stop Event

1×

done

Compiler

Compiled 80 to 59 computations (26.3% saved)

Details

analyze6.0ms (0.1%)

sample4.7s (86.8%)

preprocess35.0ms (0.7%)

simplify23.0ms (0.4%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite42.0ms (0.8%)

simplify34.0ms (0.6%)

prune60.0ms (1.1%)

localize12.0ms (0.2%)

series7.0ms (0.1%)

rewrite50.0ms (0.9%)

simplify49.0ms (0.9%)

prune52.0ms (1%)

localize8.0ms (0.1%)

series11.0ms (0.2%)

rewrite50.0ms (0.9%)

simplify90.0ms (1.7%)

prune59.0ms (1.1%)

regimes26.0ms (0.5%)

simplify2.0ms (0%)

end82.0ms (1.5%)

Profiling