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)

sample5.0s (80.6%)

Results

3.5s	4315×	body	2048	valid
947.0ms	2073×	body	1024	valid
378.0ms	1033×	body	512	valid
85.0ms	495×	body	256	valid
37.0ms	340×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Rules

819×	`div-sub_binary64`
801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	35	13
3	57	13
4	112	13
5	223	13
6	481	13
7	890	13
8	1570	13
9	4778	13
10	5815	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.3b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	6.0b	(+.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)

rewrite82.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

815×	`log1p-expm1-u_binary64`
815×	`expm1-log1p-u_binary64`
536×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
87×	`add-log-exp_binary64`

Counts

2 → 78

Calls

2 calls:

81.0ms	(-.f64 (exp.f64 x) 2)
81.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	181	17
2	2012	17
3	5842	17

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

750×	`unswap-sqr_binary64`
683×	`distribute-rgt-out_binary64`
567×	`associate-l_binary64`
524×	`fma-def_binary64`
411×	`associate-r_binary64`

Counts

94 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	198
1	108	196
2	236	196
3	630	191
4	2026	191
5	4956	191
6	4921	191
7	4962	191

prune65.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	92	4	96

Error

0.0b

Counts

96 → 4

Alt Table

Status	Error	Program
✓	30.3b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
	30.5b	(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))
▶	0.4b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
	0.4b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 1537 to 898 computations (41.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

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

rewrite54.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

869×	`log1p-expm1-u_binary64`
869×	`expm1-log1p-u_binary64`
252×	`prod-diff_binary64`
105×	`add-sqr-sqrt_binary64`
102×	`add-log-exp_binary64`

Counts

2 → 37

Calls

2 calls:

53.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
53.0ms	(*.f64 1/360 (pow.f64 x 6))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	234	25
2	2261	25
3	5581	25

simplify133.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1288×	`fma-def_binary64`
750×	`sqr-pow_binary64`
423×	`cube-prod_binary64`
401×	`*-commutative_binary64`
372×	`pow-sqr_binary64`

Counts

49 → 46

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	165
1	38	165
2	73	165
3	176	165
4	541	165
5	1391	165
6	2055	165
7	2166	165
8	2356	165
9	2599	165
10	2895	165
11	2941	165
12	3495	165
13	3896	165
14	4486	165
15	4652	165
16	4839	165
17	4826	165

prune40.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	46	4	50

Error

0.0b

Counts

50 → 4

Alt Table

Status	Error	Program
✓	30.3b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
	30.5b	(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))
✓	0.4b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
▶	0.4b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 878 to 643 computations (26.8% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

4.0ms

(*.f64 1/12 (pow.f64 x 4))

rewrite76.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

850×	`log1p-udef_binary64`
465×	`log1p-expm1-u_binary64`
465×	`expm1-log1p-u_binary64`
292×	`unpow-prod-down_binary64`
232×	`log-prod_binary64`

Counts

1 → 20

Calls

1 calls:

76.0ms

(*.f64 1/12 (pow.f64 x 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	126	7
2	1237	7
3	4905	7
4	6203	7

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune50.0ms (0.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	20	4	24

Error

0.0b

Counts

24 → 4

Alt Table

Status	Error	Program
✓	30.3b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	30.5b	(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))
✓	0.4b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
✓	0.4b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 343 to 243 computations (29.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 x) 2)
✓	0.0b	(pow.f64 (exp.f64 x) 3)
✓	0.3b	(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))
✓	6.7b	(+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8)))

series85.0ms (1.4%)

Counts

4 → 32

Calls

4 calls:

65.0ms	(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))
11.0ms	(+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8)))
6.0ms	(pow.f64 (exp.f64 x) 3)
3.0ms	(pow.f64 (exp.f64 x) 2)

rewrite98.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

702×	`prod-diff_binary64`
192×	`log1p-expm1-u_binary64`
192×	`expm1-log1p-u_binary64`
188×	`add-sqr-sqrt_binary64`
182×	`add-log-exp_binary64`

Counts

4 → 101

Calls

4 calls:

94.0ms	(pow.f64 (exp.f64 x) 2)
94.0ms	(pow.f64 (exp.f64 x) 3)
94.0ms	(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))
94.0ms	(+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	102
1	404	92
2	4776	92
3	6131	92

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

572×	`distribute-lft-out_binary64`
412×	`unswap-sqr_binary64`
368×	`fma-def_binary64`
329×	`*-commutative_binary64`
309×	`associate-/l/_binary64`

Counts

133 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	789
1	200	770
2	510	680
3	1424	677
4	2411	677
5	4856	677
6	4909	677

prune154.0ms (2.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	152	4	156

Error

0.0b

Counts

156 → 4

Alt Table

Status	Error	Program
✓	30.3b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	30.5b	(/.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 3) -8))) (.f64 (exp.f64 x) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 4 (.f64 (exp.f64 x) 2)))))
✓	0.4b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
✓	0.4b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 6367 to 3982 computations (37.5% saved)

regimes29.0ms (0.5%)

Accuracy

Total 0.6b remaining (96.6%)

Threshold costs 0.6b (96.6%)

Counts

15 → 1

Compiler

Compiled 394 to 278 computations (29.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	12	18
2	12	18

end77.0ms (1.2%)

Compiler: Compiled 97 to 67 computations (30.9% saved)

Details

analyze5.0ms (0.1%)

sample5.0s (80.6%)

simplify61.0ms (1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite82.0ms (1.3%)

simplify79.0ms (1.3%)

prune65.0ms (1%)

localize8.0ms (0.1%)

series7.0ms (0.1%)

rewrite54.0ms (0.9%)

simplify133.0ms (2.1%)

prune40.0ms (0.6%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite76.0ms (1.2%)

simplify6.0ms (0.1%)

prune50.0ms (0.8%)

localize13.0ms (0.2%)

series85.0ms (1.4%)

rewrite98.0ms (1.6%)

simplify70.0ms (1.1%)

prune154.0ms (2.5%)

regimes29.0ms (0.5%)

simplify2.0ms (0%)

end77.0ms (1.2%)

Profiling