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
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)

sample2.9s (75.8%)

Results

1.8s	4068×	body	1024	valid
556.0ms	2052×	body	512	valid
218.0ms	447×	body	2048	valid
169.0ms	985×	body	256	valid
74.0ms	704×	body	128	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify55.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
579×	`fma-def_binary64`
510×	`associate-/l*_binary64`
467×	`div-sub_binary64`
425×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	19	13
2	33	13
3	57	13
4	112	13
5	224	13
6	514	13
7	1303	13
8	3047	12
9	4469	12
10	4859	12

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

57.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	57.6b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Compiler

Compiled 35 to 25 computations (28.6% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.3b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series2.0ms (0.1%)

Counts

1 → 8

Calls

1 calls:

2.0ms

(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite16.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

68×	`add-sqr-sqrt_binary64`
65×	`log1p-expm1-u_binary64`
65×	`expm1-log1p-u_binary64`
64×	`add-log-exp_binary64`
62×	`add-cbrt-cube_binary64`

Counts

1 → 0

Calls

1 calls:

16.0ms

(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	130	6
2	71	6
0	0	0
1	0	0

simplify68.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
676×	`unswap-sqr_binary64`
328×	`associate-l_binary64`
309×	`*-commutative_binary64`
305×	`associate-*l/_binary64`

Counts

8 → 9

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	98
1	64	98
2	145	98
3	321	98
4	579	98
5	1161	98
6	1669	98
7	2683	98
8	4571	98
9	4964	98
10	4734	98

prune10.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	8	1	9
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	8	2	10

Error

0.0b

Counts

10 → 2

Alt Table

Status	Error	Program
▶	0.9b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) 2)
✓	57.6b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Compiler

Compiled 170 to 136 computations (20% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
✓	0.0b	(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))
✓	0.1b	(*.f64 1/3 (pow.f64 x 3))

series13.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

6.0ms	(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))
4.0ms	(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
3.0ms	(*.f64 1/3 (pow.f64 x 3))

rewrite60.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

269×	`expm1-udef_binary64`
269×	`log1p-udef_binary64`
226×	`log-pow_binary64`
215×	`prod-diff_binary64`
158×	`add-sqr-sqrt_binary64`

Counts

3 → 70

Calls

3 calls:

58.0ms	(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
58.0ms	(fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))))
58.0ms	(*.f64 1/3 (pow.f64 x 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	50
1	342	50
2	3393	50
3	4697	50
0	0	0
1	0	0

simplify153.0ms (4%)

Algorithm

1×	egg-herbie

Rules

1116×	`sqr-pow_binary64`
672×	`cube-prod_binary64`
636×	`fabs-mul_binary64`
624×	`unswap-sqr_binary64`
435×	`fma-def_binary64`

Counts

94 → 87

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	357
1	64	357
2	137	357
3	287	357
4	478	357
5	931	357
6	1305	357
7	1831	357
8	1979	357
9	2207	357
10	2483	357
11	2853	357
12	3199	357
13	3718	357
14	3940	357
15	4073	357
16	4271	357
17	4388	357
18	4514	357
19	5224	357

prune71.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	86	3	89

Error

0.0b

Counts

89 → 3

Alt Table

Status	Error	Program
✓	0.9b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) 2)
▶	58.3b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 x 2 (*.f64 1/3 (pow.f64 x 3)))))) 1)) 2)
✓	57.6b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Compiler

Compiled 2178 to 1790 computations (17.8% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/60 (pow.f64 x 5) (-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 x 2 (*.f64 1/3 (pow.f64 x 3)))))) 1))
✓	0.0b	(exp.f64 (log1p.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 x 2 (*.f64 1/3 (pow.f64 x 3))))))
	0.1b	(*.f64 1/3 (pow.f64 x 3))
✓	6.3b	(-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 x 2 (*.f64 1/3 (pow.f64 x 3)))))) 1)

series23.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

11.0ms

(-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 x 2 (*.f64 1/3 (pow.f64 x 3)))))) 1)

6.0ms

(fma.f64 1/60 (pow.f64 x 5) (-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 x 2 (*.f64 1/3 (pow.f64 x 3)))))) 1))

5.0ms

(exp.f64 (log1p.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 x 2 (*.f64 1/3 (pow.f64 x 3))))))

rewrite67.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

371×	`prod-diff_binary64`
310×	`log1p-udef_binary64`
184×	`add-sqr-sqrt_binary64`
182×	`expm1-log1p-u_binary64`
181×	`log1p-expm1-u_binary64`

Counts

3 → 94

Calls

3 calls:

65.0ms

(fma.f64 1/60 (pow.f64 x 5) (-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 x 2 (*.f64 1/3 (pow.f64 x 3)))))) 1))

65.0ms

(exp.f64 (log1p.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 x 2 (*.f64 1/3 (pow.f64 x 3))))))

65.0ms

(-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 x 2 (*.f64 1/3 (pow.f64 x 3)))))) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	65
1	403	64
2	4018	64
3	4966	64
0	0	0
1	0	0

simplify80.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

757×	`associate-/r*_binary64`
623×	`associate-/l*_binary64`
384×	`fma-def_binary64`
242×	`associate-*l/_binary64`
241×	`associate-+l+_binary64`

Counts

130 → 155

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	92	1320
1	258	1008
2	702	958
3	2027	812
4	4846	781
5	4965	781
6	4824	781

prune148.0ms (3.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	169	3	172

Error

0.0b

Counts

172 → 3

Alt Table

Status	Error	Program
✓	0.9b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))) 2)
✓	58.3b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 x 2 (*.f64 1/3 (pow.f64 x 3)))))) 1)) 2)
✓	57.6b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)

Compiler

Compiled 5233 to 4425 computations (15.4% saved)

regimes38.0ms (1%)

Accuracy

Total 0.5b remaining (98.4%)

Threshold costs 0.5b (98.4%)

Counts

12 → 1

Compiler

Compiled 615 to 503 computations (18.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	18	28
2	18	28

end85.0ms (2.2%)

Compiler: Compiled 97 to 79 computations (18.6% saved)

Details

analyze5.0ms (0.1%)

sample2.9s (75.8%)

simplify55.0ms (1.4%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

series2.0ms (0.1%)

rewrite16.0ms (0.4%)

simplify68.0ms (1.8%)

prune10.0ms (0.3%)

localize11.0ms (0.3%)

series13.0ms (0.3%)

rewrite60.0ms (1.6%)

simplify153.0ms (4%)

prune71.0ms (1.8%)

localize14.0ms (0.4%)

series23.0ms (0.6%)

rewrite67.0ms (1.8%)

simplify80.0ms (2.1%)

prune148.0ms (3.9%)

regimes38.0ms (1%)

simplify2.0ms (0.1%)

end85.0ms (2.2%)

Profiling