Details

analyze63.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.8%	87.2%	0
0%	12.8%	87.2%	1
0%	12.8%	87.2%	2
6.4%	6.4%	87.2%	3
6.4%	4.8%	88.8%	4
7.2%	3.2%	89.6%	5
7.2%	2.4%	90.4%	6
7.6%	1.6%	90.8%	7
7.6%	1.2%	91.2%	8
7.8%	0.8%	91.4%	9
7.8%	0.6%	91.5%	10
7.9%	0.4%	91.7%	11
8%	0.3%	91.7%	12
8.1%	0.2%	91.7%	13
8.1%	0.2%	91.8%	14

Compiler

Compiled 25 to 17 computations (32% saved)

sample2.4s (43.3%)

Results

931.0ms	5273×	body	128	valid
639.0ms	1134×	body	1024	valid
482.0ms	1107×	body	512	valid
214.0ms	699×	body	256	valid
40.0ms	43×	body	2048	valid
14.0ms	91×	body	128	invalid

Compiler

Compiled 60 to 40 computations (33.3% saved)

simplify24.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

107×	`fma-def_binary64`
72×	`fma-neg_binary64`
27×	`cancel-sign-sub-inv_binary64`
24×	`distribute-rgt-in_binary64`
24×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	50	12
5	95	12
6	144	12
7	182	12
8	214	12
9	234	12
10	242	12
11	246	12
12	227	12

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

22.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	22.7b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	0.0b	(-.f64 (*.f64 x x) eps)
✓	2.6b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

series65.0ms (1.2%)

Counts

3 → 56

Calls

3 calls:

35.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
23.0ms	(sqrt.f64 (-.f64 (*.f64 x x) eps))
7.0ms	(-.f64 (*.f64 x x) eps)

rewrite96.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

871×	`log1p-expm1-u_binary64`
871×	`expm1-log1p-u_binary64`
104×	`egg-rr`
82×	`add-sqr-sqrt_binary64`
78×	`add-log-exp_binary64`

Counts

3 → 104

Calls

3 calls:

92.0ms	(sqrt.f64 (-.f64 (*.f64 x x) eps))
92.0ms	(-.f64 (*.f64 x x) eps)
92.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
1	161	28
2	2130	28
3	5196	28
0	0	0
1	0	0

simplify92.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

615×	`cancel-sign-sub-inv_binary64`
586×	`associate-*l/_binary64`
324×	`fma-neg_binary64`
227×	`associate-/r/_binary64`
219×	`associate-/l/_binary64`

Counts

160 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	858
1	207	844
2	582	834
3	2203	816
4	4997	816

prune133.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	148	6	154

Error

0.0b

Counts

154 → 6

Alt Table

Status	Error	Program
	46.1b	(fma.f64 1/16 (/.f64 (pow.f64 eps 3) (pow.f64 x 5)) (.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x))))))
	38.9b	(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))
	40.5b	(+.f64 (.f64 1/8 (/.f64 (pow.f64 eps 2) (pow.f64 x 3))) (.f64 1/2 (/.f64 eps x)))
	37.1b	(*.f64 1/2 (/.f64 eps x))
✓	22.7b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	23.0b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))

Compiler

Compiled 2560 to 1035 computations (59.6% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.2b	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps)))
✓	0.2b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))
✓	2.5b	(-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))

series285.0ms (5.1%)

Counts

4 → 72

Calls

4 calls:

130.0ms	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))
121.0ms	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps)))
29.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
4.0ms	(-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))

rewrite177.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

732×	`fma-def_binary64`
342×	`egg-rr`
336×	`fma-neg_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`

Counts

4 → 341

Calls

4 calls:

164.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
164.0ms	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps)))
164.0ms	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))
164.0ms	(-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	82
1	259	40
2	3353	40
3	4904	40
0	0	0
1	0	0

simplify109.0ms (2%)

Algorithm

1×	egg-herbie

Rules

558×	`fma-neg_binary64`
486×	`times-frac_binary64`
320×	`associate-/l*_binary64`
303×	`associate-/r*_binary64`
294×	`unswap-sqr_binary64`

Counts

413 → 391

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	1173
1	283	1132
2	878	1118
3	3908	1086
4	5073	1086

prune303.0ms (5.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	388	3	391
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	392	5	397

Error

Counts

397 → 5

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps))
	38.9b	(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))
✓	22.7b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	1.6b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (.f64 (cbrt.f64 eps) (pow.f64 (cbrt.f64 eps) 2))))
	39.0b	(/.f64 1 (fma.f64 2 (/.f64 x eps) (fma.f64 (/.f64 eps (pow.f64 x 3)) -1/8 (/.f64 -1/2 x))))

Compiler

Compiled 10361 to 2717 computations (73.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 x x) eps)
	0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.2b	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps)
✓	0.3b	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps))

series152.0ms (2.7%)

Counts

2 → 32

Calls

2 calls:

107.0ms	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps))
44.0ms	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps)

rewrite118.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

461×	`fma-def_binary64`
263×	`fma-neg_binary64`
194×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`
176×	`log-pow_binary64`

Counts

2 → 74

Calls

2 calls:

115.0ms	(/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps)
115.0ms	(/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	226	30
2	2966	28
3	4972	28
0	0	0
1	0	0

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

499×	`fma-neg_binary64`
430×	`times-frac_binary64`
346×	`distribute-neg-frac_binary64`
286×	`associate-/l*_binary64`
279×	`unswap-sqr_binary64`

Counts

106 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	799
1	261	766
2	804	758
3	3512	724
4	5000	724

prune197.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	219	4	223

Error

Counts

223 → 4

Alt Table

Status	Error	Program
	38.9b	(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))
✓	22.7b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	39.0b	(/.f64 1 (fma.f64 2 (/.f64 x eps) (fma.f64 (/.f64 eps (pow.f64 x 3)) -1/8 (/.f64 -1/2 x))))
▶	0.4b	(/.f64 1 (/.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps))

Compiler

Compiled 4101 to 1686 computations (58.9% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 x x) eps)
✓	0.1b	(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	0.2b	(/.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps)
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps))

series210.0ms (3.8%)

Counts

3 → 21

Calls

3 calls:

126.0ms

(/.f64 1 (/.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps))

51.0ms

(/.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps)

32.0ms

(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps)))

rewrite146.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

645×	`prod-diff_binary64`
473×	`fma-udef_binary64`
289×	`fma-def_binary64`
248×	`fma-neg_binary64`
194×	`expm1-udef_binary64`

Counts

3 → 94

Calls

3 calls:

142.0ms

(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps)))

142.0ms

(/.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps)

142.0ms

(/.f64 1 (/.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	45
1	234	42
2	2802	39
3	4750	39
4	4775	39
5	4961	39
0	0	0
1	0	0

simplify108.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

751×	`times-frac_binary64`
649×	`fma-def_binary64`
602×	`associate-/l*_binary64`
502×	`fma-neg_binary64`
411×	`cancel-sign-sub-inv_binary64`

Counts

115 → 129

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	60	316
1	171	308
2	446	306
3	1398	298
4	4562	291
5	4967	291
6	4974	291

prune146.0ms (2.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	177	4	181

Error

Counts

181 → 4

Alt Table

Status	Error	Program
	38.9b	(.f64 (/.f64 eps x) (-.f64 1/2 (.f64 -1/8 (/.f64 eps (*.f64 x x)))))
✓	22.7b	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
	39.0b	(/.f64 1 (fma.f64 2 (/.f64 x eps) (fma.f64 (/.f64 eps (pow.f64 x 3)) -1/8 (/.f64 -1/2 x))))
✓	0.4b	(/.f64 1 (/.f64 (fma.f64 (sqrt.f64 x) (sqrt.f64 x) (sqrt.f64 (-.f64 (*.f64 x x) eps))) eps))

Compiler

Compiled 3104 to 1221 computations (60.7% saved)

regimes438.0ms (7.9%)

Accuracy

Total 0.4b remaining (96.1%)

Threshold costs 0.4b (96.1%)

Counts

95 → 1

Compiler

Compiled 4376 to 2942 computations (32.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	17	18
2	21	18
3	23	18
4	24	18
5	23	18

end127.0ms (2.3%)

Compiler: Compiled 89 to 58 computations (34.8% saved)

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	50	12
5	95	12
6	144	12
7	182	12
8	214	12
9	234	12
10	242	12
11	246	12
12	227	12

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	50	12
5	95	12
6	144	12
7	182	12
8	214	12
9	234	12
10	242	12
11	246	12
12	227	12

Details

analyze63.0ms (1.1%)

sample2.4s (43.3%)

simplify24.0ms (0.4%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series65.0ms (1.2%)

rewrite96.0ms (1.7%)

simplify92.0ms (1.7%)

prune133.0ms (2.4%)

localize19.0ms (0.3%)

series285.0ms (5.1%)

rewrite177.0ms (3.2%)

simplify109.0ms (2%)

prune303.0ms (5.5%)

localize16.0ms (0.3%)

series152.0ms (2.7%)

rewrite118.0ms (2.1%)

simplify88.0ms (1.6%)

prune197.0ms (3.6%)

localize15.0ms (0.3%)

series210.0ms (3.8%)

rewrite146.0ms (2.6%)

simplify108.0ms (1.9%)

prune146.0ms (2.6%)

regimes438.0ms (7.9%)

simplify3.0ms (0.1%)

end127.0ms (2.3%)

Profiling

Iter	Nodes	Cost
0	7	12
1	12	12
2	20	12
3	34	12
4	50	12
5	95	12
6	144	12
7	182	12
8	214	12
9	234	12
10	242	12
11	246	12
12	227	12