Details

analyze18.0ms (0.4%)

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%	1.6%	48.5%	9
50.4%	1.2%	48.5%	10
50.4%	1.2%	48.5%	11
50.4%	1.1%	48.6%	12
50.4%	1%	48.6%	13
50.5%	0.9%	48.6%	14

Compiler

Compiled 15 to 8 computations (46.7% saved)

sample2.9s (67.6%)

Results

1.8s	4038×	body	1024	valid
542.0ms	1972×	body	512	valid
206.0ms	406×	body	2048	valid
188.0ms	979×	body	256	valid
88.0ms	861×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 44 to 23 computations (47.7% saved)

simplify69.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary64`
658×	`unswap-sqr_binary64`
478×	`fma-neg_binary64`
464×	`times-frac_binary64`
388×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	20	22
2	34	22
3	58	22
4	125	22
5	288	22
6	624	22
7	1577	22
8	3798	22
9	4553	22
10	5023	22

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

57.6b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 42 to 21 computations (50% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	1.5b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	4.8b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

series18.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

14.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite73.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite
3×	egg-rewrite

Rules

97×	`add-sqr-sqrt_binary64`
92×	`log1p-expm1-u_binary64`
92×	`expm1-log1p-u_binary64`
91×	`add-log-exp_binary64`
89×	`add-cbrt-cube_binary64`

Counts

3 → 0

Calls

3 calls:

73.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
73.0ms	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
73.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	186	18
2	26	18
0	6	6
1	130	6
2	71	6
0	8	3
1	186	3
2	26	3
0	6	6
1	129	6
2	19	6
0	0	0
1	0	0

simplify72.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-def_binary64`
752×	`fma-neg_binary64`
514×	`cancel-sign-sub-inv_binary64`
508×	`unswap-sqr_binary64`
480×	`associate-l_binary64`

Counts

24 → 27

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	321
1	137	317
2	336	311
3	910	309
4	2632	309
5	4822	309
6	4911	309
7	4936	309

prune20.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	24	3	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	4	28

Error

1.3b

Counts

28 → 4

Alt Table

Status	Error	Program
▶	2.4b	(/.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))))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	57.6b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
	2.6b	(fma.f64 (pow.f64 x 3) -1/3 x)
	2.7b	x

Compiler

Compiled 486 to 267 computations (45.1% saved)

localize16.0ms (0.4%)

Local error

Found 4 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	(/.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))))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	0.0b	(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
✓	0.1b	(*.f64 1/3 (pow.f64 x 3))

series18.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

8.0ms	(/.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))))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
4.0ms	(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
3.0ms	(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
3.0ms	(*.f64 1/3 (pow.f64 x 3))

rewrite211.0ms (4.9%)

Algorithm

2×	batch-egg-rewrite
4×	egg-rewrite

Rules

1218×	`log1p-expm1-u_binary64`
1218×	`expm1-log1p-u_binary64`
1204×	`log1p-udef_binary64`
981×	`log-prod_binary64`
441×	`pow2_binary64`

Counts

4 → 76

Calls

4 calls:

209.0ms	(fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (*.f64 1/3 (pow.f64 x 3))))
209.0ms	(/.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))))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
209.0ms	(fma.f64 2 x (*.f64 1/3 (pow.f64 x 3)))
209.0ms	(*.f64 1/3 (pow.f64 x 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	28
1	456	28
2	73	28
0	6	7
1	125	7
2	1261	7
3	4816	7
4	6163	7
0	8	11
1	166	11
2	1650	11
3	5001	11
0	21	33
1	456	33
2	73	33
0	12	18
1	254	18
2	2520	18
3	4842	18
0	0	0
1	0	0

simplify60.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

651×	`associate-/r/_binary64`
590×	`associate-/l/_binary64`
488×	`fma-neg_binary64`
446×	`fma-def_binary64`
406×	`distribute-rgt-neg-in_binary64`

Counts

112 → 103

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	62	708
1	137	708
2	299	704
3	685	702
4	1704	678
5	2988	678
6	5130	678

prune86.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	103	4	107

Error

1.3b

Counts

107 → 4

Alt Table

Status	Error	Program
	2.7b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (-.f64 (exp.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3)))) 1)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	2.6b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	57.6b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
	2.7b	x

Compiler

Compiled 3081 to 1984 computations (35.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(fma.f64 (pow.f64 x 3) -1/3 x)

rewrite72.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

492×	`log1p-expm1-u_binary64`
492×	`expm1-log1p-u_binary64`
281×	`unpow-prod-down_binary64`
223×	`log-prod_binary64`
208×	`prod-diff_binary64`

Counts

1 → 36

Calls

1 calls:

71.0ms

(fma.f64 (pow.f64 x 3) -1/3 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	126	8
2	1279	8
3	4882	8
4	5006	8
0	0	0
1	0	0

simplify168.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1705×	`fma-def_binary64`
865×	`fma-neg_binary64`
818×	`unswap-sqr_binary64`
615×	`sqr-pow_binary64`
528×	`cube-prod_binary64`

Counts

48 → 41

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	105
1	23	105
2	59	87
3	147	87
4	298	87
5	774	87
6	1120	87
7	1710	87
8	3217	87
9	4164	87
10	4277	87
11	4261	87
12	4044	87
13	3304	87
14	3939	87
15	4360	87
16	4810	87
17	4770	87

prune26.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	41	4	45

Error

1.3b

Counts

45 → 4

Alt Table

Status	Error	Program
▶	2.7b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (-.f64 (exp.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3)))) 1)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	2.6b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	57.6b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
	2.7b	x

Compiler

Compiled 581 to 445 computations (23.4% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (-.f64 (exp.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3)))) 1)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	0.0b	(exp.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3))))
	0.1b	(*.f64 1/3 (pow.f64 x 3))
✓	2.9b	(-.f64 (exp.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3)))) 1)

series62.0ms (1.4%)

Counts

3 → 36

Calls

3 calls:

37.0ms

(-.f64 (exp.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3)))) 1)

15.0ms

(exp.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3))))

9.0ms

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

rewrite72.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

386×	`log1p-udef_binary64`
241×	`add-sqr-sqrt_binary64`
236×	`expm1-log1p-u_binary64`
235×	`log1p-expm1-u_binary64`
230×	`add-log-exp_binary64`

Counts

3 → 72

Calls

3 calls:

70.0ms

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

70.0ms

(exp.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3))))

70.0ms

(-.f64 (exp.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3)))) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	51
1	515	50
2	4409	50
3	4788	50
0	0	0
1	0	0

simplify71.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

764×	`fma-neg_binary64`
613×	`fma-def_binary64`
244×	`associate-/r*_binary64`
235×	`associate-+l+_binary64`
230×	`unswap-sqr_binary64`

Counts

108 → 101

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	83	675
1	198	643
2	496	635
3	1350	617
4	3651	613
5	4914	613
6	4625	613

prune115.0ms (2.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	118	4	122

Error

1.3b

Counts

122 → 4

Alt Table

Status	Error	Program
✓	2.7b	(/.f64 (fma.f64 1/60 (pow.f64 x 5) (fma.f64 1/2520 (pow.f64 x 7) (fma.f64 2 x (-.f64 (exp.f64 (log1p.f64 (*.f64 1/3 (pow.f64 x 3)))) 1)))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	2.6b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	57.6b	(/.f64 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
	2.7b	x

Compiler

Compiled 3845 to 2667 computations (30.6% saved)

regimes31.0ms (0.7%)

Accuracy

Total 0.7b remaining (37.1%)

Threshold costs 0.7b (37.1%)

Counts

14 → 1

Compiler

Compiled 576 to 434 computations (24.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	37
1	27	37
2	29	37
3	30	37
4	30	37

end76.0ms (1.8%)

Compiler: Compiled 105 to 77 computations (26.7% saved)

Details

analyze18.0ms (0.4%)

sample2.9s (67.6%)

simplify69.0ms (1.6%)

prune2.0ms (0%)

localize7.0ms (0.2%)

series18.0ms (0.4%)

rewrite73.0ms (1.7%)

simplify72.0ms (1.7%)

prune20.0ms (0.5%)

localize16.0ms (0.4%)

series18.0ms (0.4%)

rewrite211.0ms (4.9%)

simplify60.0ms (1.4%)

prune86.0ms (2%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite72.0ms (1.7%)

simplify168.0ms (3.9%)

prune26.0ms (0.6%)

localize18.0ms (0.4%)

series62.0ms (1.4%)

rewrite72.0ms (1.7%)

simplify71.0ms (1.7%)

prune115.0ms (2.7%)

regimes31.0ms (0.7%)

simplify2.0ms (0.1%)

end76.0ms (1.8%)

Profiling