Details

analyze873.0ms (13.3%)

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 (57.7%)

Results

2.0s	3868×	body	8192	exit
750.0ms	6706×	body	128	valid
521.0ms	4044×	body	128	invalid
222.0ms	768×	body	512	valid
153.0ms	762×	body	256	valid
7.0ms	20×	body	1024	valid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify78.0ms (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

3 alts after pruning (3 fresh and 0 done)

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

Error

12.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.0b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
▶	12.8b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 94 to 48 computations (48.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	0.0b	(/.f64 x (exp.f64 wj))
✓	3.8b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series48.0ms (0.7%)

Counts

3 → 52

Calls

3 calls:

17.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
16.0ms	(/.f64 x (exp.f64 wj))
15.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))

rewrite35.0ms (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:

15.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
11.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
3.0ms	(/.f64 x (exp.f64 wj))

simplify105.0ms (1.6%)

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 → 152

Iterations

Useful iterations: 3 (0.0ms)

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

prune104.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	152	2	154

Error

0.0b

Counts

154 → 2

Alt Table

Status	Error	Program
▶	2.5b	(-.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)))
	12.7b	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))

Status

Error

Program

▶

2.5b

(-.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)))

12.7b

(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))

Compiler

Compiled 3161 to 1373 computations (56.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 wj (*.f64 8/3 (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)))
✓	0.2b	(*.f64 8/3 (pow.f64 wj 3))
✓	8.7b	(.f64 x (.f64 wj wj))

series43.0ms (0.7%)

Counts

4 → 60

Calls

4 calls:

27.0ms	(-.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)))
10.0ms	(.f64 x (.f64 wj wj))
3.0ms	(fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3)))
3.0ms	(*.f64 8/3 (pow.f64 wj 3))

rewrite57.0ms (0.9%)

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:

5.0ms	(*.f64 8/3 (pow.f64 wj 3))
5.0ms	(.f64 x (.f64 wj wj))
3.0ms	(-.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 2 wj (*.f64 8/3 (pow.f64 wj 3)))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
541×	`distribute-rgt-in_binary64`
527×	`distribute-lft-in_binary64`
401×	`cancel-sign-sub-inv_binary64`
178×	`fma-neg_binary64`

Counts

156 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	3470
1	415	3028
2	1455	2737
3	4974	2737

prune181.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	168	3	171

Error

0.0b

Counts

171 → 3

Alt Table

Status	Error	Program
	33.6b	(exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (-.f64 (.f64 wj 5/2) 2))) (.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
✓	2.5b	(-.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)))
▶	12.7b	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))

Compiler

Compiled 6143 to 3378 computations (45% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1))
✓	0.0b	(*.f64 x (exp.f64 (neg.f64 wj)))
✓	3.8b	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))

series30.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

13.0ms	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))
11.0ms	(/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1))
6.0ms	(*.f64 x (exp.f64 (neg.f64 wj)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 79

Calls

3 calls:

14.0ms	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))
11.0ms	(/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1))
5.0ms	(*.f64 x (exp.f64 (neg.f64 wj)))

simplify99.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-def_binary64`
466×	`fma-neg_binary64`
325×	`distribute-rgt-in_binary64`
276×	`distribute-lft-in_binary64`
238×	`associate-/l*_binary64`

Counts

151 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	210	2935
1	529	2507
2	1729	2474
3	4474	2472
4	5221	2472

prune83.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

0.0b

Counts

172 → 3

Alt Table

Status	Error	Program
▶	33.6b	(exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (-.f64 (.f64 wj 5/2) 2))) (.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
✓	2.5b	(-.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)))
✓	12.7b	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))

Compiler

Compiled 3631 to 1600 computations (55.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 wj x) (-.f64 (*.f64 wj 5/2) 2))
✓	0.2b	(fma.f64 x 8/3 1)
✓	2.9b	(exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (-.f64 (.f64 wj 5/2) 2))) (.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
✓	4.5b	(*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))

series46.0ms (0.7%)

Counts

4 → 84

Calls

4 calls:

24.0ms	(exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (-.f64 (.f64 wj 5/2) 2))) (.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
12.0ms	(*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))
9.0ms	(.f64 (.f64 wj x) (-.f64 (*.f64 wj 5/2) 2))
2.0ms	(fma.f64 x 8/3 1)

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-l_binary64`

Counts

4 → 100

Calls

4 calls:

7.0ms	(.f64 (.f64 wj x) (-.f64 (*.f64 wj 5/2) 2))
6.0ms	(exp.f64 (log.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (-.f64 (.f64 wj 5/2) 2))) (.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
4.0ms	(*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))
0.0ms	(fma.f64 x 8/3 1)

simplify110.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-neg_binary64`
638×	`cancel-sign-sub-inv_binary64`
481×	`exp-prod_binary64`
344×	`associate-l_binary64`
278×	`associate-r_binary64`

Counts

184 → 185

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	3578
1	526	2953
2	2227	2933
3	4087	2907
4	5060	2907

prune142.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	185	3	188

Error

0.0b

Counts

188 → 3

Alt Table

Status	Error	Program
✓	2.5b	(-.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)))
✓	12.7b	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))
	45.6b	(/.f64 (exp.f64 (log.f64 (-.f64 (.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (-.f64 (.f64 wj 5/2) 2))) (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (-.f64 (.f64 wj 5/2) 2)))) (.f64 (.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)) (.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))) (exp.f64 (log.f64 (+.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (-.f64 (.f64 wj 5/2) 2))) (.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1))))))

Compiler

Compiled 6038 to 3842 computations (36.4% saved)

regimes428.0ms (6.5%)

Accuracy

Total 0.3b remaining (79.4%)

Threshold costs 0.3b (79.4%)

Counts

101 → 2

Compiler

Compiled 5799 to 3861 computations (33.4% saved)

bsearch3.0ms (0%)

Compiler: Compiled 18 to 8 computations (55.6% saved)

simplify19.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

73×	`distribute-rgt-neg-in_binary64`
61×	`cancel-sign-sub-inv_binary64`
47×	`distribute-lft-neg-in_binary64`
46×	`neg-sub0_binary64`
46×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	83
1	63	83
2	83	83
3	100	83
4	125	83
5	143	83
6	164	83
7	197	83
8	236	83
9	286	83
10	330	83
11	365	83
12	395	83
13	411	83
14	418	83
15	423	83
16	425	83
17	417	83

end110.0ms (1.7%)

Compiler: Compiled 233 to 144 computations (38.2% saved)

Iter	Nodes	Cost
0	35	83
1	63	83
2	83	83
3	100	83
4	125	83
5	143	83
6	164	83
7	197	83
8	236	83
9	286	83
10	330	83
11	365	83
12	395	83
13	411	83
14	418	83
15	423	83
16	425	83
17	417	83

Iter	Nodes	Cost
0	35	83
1	63	83
2	83	83
3	100	83
4	125	83
5	143	83
6	164	83
7	197	83
8	236	83
9	286	83
10	330	83
11	365	83
12	395	83
13	411	83
14	418	83
15	423	83
16	425	83
17	417	83

Details

analyze873.0ms (13.3%)

sample3.8s (57.7%)

simplify78.0ms (1.2%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series48.0ms (0.7%)

rewrite35.0ms (0.5%)

simplify105.0ms (1.6%)

prune104.0ms (1.6%)

localize13.0ms (0.2%)

series43.0ms (0.7%)

rewrite57.0ms (0.9%)

simplify81.0ms (1.2%)

prune181.0ms (2.8%)

localize8.0ms (0.1%)

series30.0ms (0.5%)

rewrite33.0ms (0.5%)

simplify99.0ms (1.5%)

prune83.0ms (1.3%)

localize16.0ms (0.2%)

series46.0ms (0.7%)

rewrite23.0ms (0.3%)

simplify110.0ms (1.7%)

prune142.0ms (2.2%)

regimes428.0ms (6.5%)

bsearch3.0ms (0%)

simplify19.0ms (0.3%)

end110.0ms (1.7%)

Profiling

Iter	Nodes	Cost
0	35	83
1	63	83
2	83	83
3	100	83
4	125	83
5	143	83
6	164	83
7	197	83
8	236	83
9	286	83
10	330	83
11	365	83
12	395	83
13	411	83
14	418	83
15	423	83
16	425	83
17	417	83