Details

analyze786.0ms (11.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
28.1%	71.8%	0.1%	7
32.8%	67.1%	0.1%	8
38.2%	61.7%	0.1%	9
41%	58.9%	0.1%	10
43.9%	56%	0.1%	11
45.4%	54.5%	0.1%	12
46.9%	53%	0.1%	13
47.7%	52.2%	0.1%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample3.8s (55.2%)

Results

2.1s	4002×	body	8192	exit
756.0ms	6778×	body	128	valid
441.0ms	4009×	body	128	invalid
201.0ms	697×	body	512	valid
153.0ms	753×	body	256	valid
10.0ms	28×	body	1024	valid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

568×	`neg-mul-1_binary64`
503×	`fma-def_binary64`
491×	`fma-neg_binary64`
484×	`div-sub_binary64`
416×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	22	23
2	58	23
3	152	21
4	338	18
5	1090	18
6	2902	18
7	3695	18
8	4706	18
9	4881	18

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.7b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 58 to 32 computations (44.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (exp.f64 wj))
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	4.4b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series47.0ms (0.7%)

Counts

3 → 52

Calls

3 calls:

18.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
15.0ms	(/.f64 x (exp.f64 wj))
14.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

3 → 100

Calls

3 calls:

13.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
12.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
3.0ms	(/.f64 x (exp.f64 wj))

simplify105.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-neg_binary64`
444×	`fma-def_binary64`
331×	`distribute-rgt-in_binary64`
292×	`associate--l+_binary64`
278×	`distribute-lft-in_binary64`

Counts

152 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3154
1	583	3016
2	1604	2995
3	4798	2993
4	5298	2993

prune100.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	152	3	155

Error

0.0b

Counts

155 → 3

Alt Table

Status	Error	Program
	34.2b	(+.f64 wj (/.f64 (-.f64 (.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj))) (.f64 wj wj)) (*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj))))
▶	1.1b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
✓	13.7b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 3268 to 1413 computations (56.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
✓	0.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
✓	0.1b	(*.f64 8/3 (pow.f64 wj 3))
✓	8.7b	(.f64 x (.f64 wj wj))

series59.0ms (0.9%)

Counts

4 → 72

Calls

4 calls:

28.0ms	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
19.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
8.0ms	(.f64 x (.f64 wj wj))
3.0ms	(*.f64 8/3 (pow.f64 wj 3))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-r_binary64`

Counts

4 → 96

Calls

4 calls:

7.0ms	(*.f64 8/3 (pow.f64 wj 3))
4.0ms	(.f64 x (.f64 wj wj))
4.0ms	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
0.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))

simplify117.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-def_binary64`
521×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
479×	`fma-neg_binary64`
401×	`cancel-sign-sub-inv_binary64`

Counts

168 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	3853
1	409	3376
2	1438	3085
3	4985	3004
4	5189	3004

prune188.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	172	4	176

Error

0.0b

Counts

176 → 4

Alt Table

Status	Error	Program
▶	34.2b	(+.f64 wj (/.f64 (-.f64 (.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj))) (.f64 wj wj)) (*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj))))
✓	1.1b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
	52.9b	(fma.f64 wj wj (.f64 (.f64 wj wj) (-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj))))
✓	13.7b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 6274 to 3425 computations (45.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj)))
✓	0.0b	(*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj))
✓	4.4b	(+.f64 wj (/.f64 (-.f64 (.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj))) (.f64 wj wj)) (*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj))))
✓	21.9b	(/.f64 (-.f64 (.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj))) (.f64 wj wj)) (*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj)))

series200.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

74.0ms	(+.f64 wj (/.f64 (-.f64 (.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj))) (.f64 wj wj)) (*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj))))
61.0ms	(*.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj)))
53.0ms	(/.f64 (-.f64 (.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj))) (.f64 wj wj)) (*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj)))
12.0ms	(*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj))

rewrite63.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
23×	`add-cbrt-cube_binary64`

Counts

4 → 155

Calls

4 calls:

19.0ms	(/.f64 (-.f64 (.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj))) (.f64 wj wj)) (*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj)))
12.0ms	(+.f64 wj (/.f64 (-.f64 (.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj))) (.f64 wj wj)) (*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj))))
11.0ms	(*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj))
9.0ms	(*.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj)))

simplify206.0ms (3%)

Algorithm

1×	egg-herbie

Rules

466×	`times-frac_binary64`
384×	`associate-/l*_binary64`
320×	`associate-/r*_binary64`
292×	`fma-def_binary64`
203×	`associate-*l/_binary64`

Counts

251 → 327

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	460	8847
1	1504	8037
2	4807	8016
3	4995	8016
4	4990	8016

prune239.0ms (3.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	327	0	327
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	327	4	331

Error

0.0b

Counts

331 → 4

Alt Table

Status	Error	Program
✓	34.2b	(+.f64 wj (/.f64 (-.f64 (.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj))) (.f64 wj wj)) (*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj))))
✓	1.1b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
▶	52.9b	(fma.f64 wj wj (.f64 (.f64 wj wj) (-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj))))
✓	13.7b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 13367 to 4812 computations (64% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj))
✓	0.1b	(*.f64 (fma.f64 x 8/3 1) wj)
✓	0.1b	(fma.f64 x 8/3 1)
✓	8.7b	(.f64 (.f64 wj wj) (-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj)))

series32.0ms (0.5%)

Counts

4 → 84

Calls

4 calls:

16.0ms	(.f64 (.f64 wj wj) (-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj)))
6.0ms	(-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj))
6.0ms	(*.f64 (fma.f64 x 8/3 1) wj)
4.0ms	(fma.f64 x 8/3 1)

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`

Counts

4 → 75

Calls

4 calls:

7.0ms	(.f64 (.f64 wj wj) (-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj)))
3.0ms	(*.f64 (fma.f64 x 8/3 1) wj)
3.0ms	(-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj))
0.0ms	(fma.f64 x 8/3 1)

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

595×	`fma-neg_binary64`
543×	`fma-def_binary64`
541×	`distribute-rgt-in_binary64`
521×	`distribute-lft-in_binary64`
334×	`*-commutative_binary64`

Counts

159 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	2597
1	356	2215
2	1223	2029
3	3631	1989
4	4888	1989
5	4864	1989

prune88.0ms (1.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	143	4	147

Error

0.0b

Counts

147 → 4

Alt Table

Status	Error	Program
✓	34.2b	(+.f64 wj (/.f64 (-.f64 (.f64 (/.f64 x (exp.f64 wj)) (/.f64 x (exp.f64 wj))) (.f64 wj wj)) (*.f64 (+.f64 wj 1) (+.f64 (/.f64 x (exp.f64 wj)) wj))))
✓	1.1b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
✓	52.9b	(fma.f64 wj wj (.f64 (.f64 wj wj) (-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj))))
✓	13.7b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 3347 to 1966 computations (41.3% saved)

regimes307.0ms (4.5%)

Accuracy

Total 1.5b remaining (92.5%)

Threshold costs 0b (0%)

Counts

93 → 1

Compiler

Compiled 5154 to 3225 computations (37.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	20	35
2	25	35
3	27	35
4	28	35
5	28	35

end234.0ms (3.4%)

Compiler: Compiled 142 to 85 computations (40.1% saved)

Details

analyze786.0ms (11.4%)

sample3.8s (55.2%)

simplify81.0ms (1.2%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series47.0ms (0.7%)

rewrite33.0ms (0.5%)

simplify105.0ms (1.5%)

prune100.0ms (1.5%)

localize14.0ms (0.2%)

series59.0ms (0.9%)

rewrite21.0ms (0.3%)

simplify117.0ms (1.7%)

prune188.0ms (2.7%)

localize15.0ms (0.2%)

series200.0ms (2.9%)

rewrite63.0ms (0.9%)

simplify206.0ms (3%)

prune239.0ms (3.5%)

localize11.0ms (0.2%)

series32.0ms (0.5%)

rewrite17.0ms (0.2%)

simplify109.0ms (1.6%)

prune88.0ms (1.3%)

regimes307.0ms (4.5%)

simplify3.0ms (0%)

end234.0ms (3.4%)

Profiling