Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.2s (32.7%)

Results

898.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify232.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

2682×	`fma-neg_binary64`
690×	`times-frac_binary64`
636×	`fma-def_binary64`
533×	`sub-neg_binary64`
432×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	45	17
3	65	17
4	78	17
5	89	17
6	129	17
7	180	17
8	288	17
9	497	17
10	671	17
11	811	17
12	976	17
13	1611	17
14	3407	17
15	3743	17
16	3727	17
17	3787	17
18	3819	17
19	3887	17
20	3898	17
21	4186	17
22	4220	17
23	4236	17
24	4236	17
25	4236	17
26	6212	17

prune3.0ms (0.1%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

Compiler

Compiled 53 to 40 computations (24.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.1b	(fma.f64 6 x -6)
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series27.0ms (0.8%)

Counts

3 → 18

Calls

3 calls:

15.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
10.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
2.0ms	(fma.f64 6 x -6)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
0.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
0.0ms	(fma.f64 6 x -6)

simplify89.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

492×	`div-sub_binary64`
426×	`fma-neg_binary64`
384×	`*-commutative_binary64`
348×	`distribute-rgt-in_binary64`
336×	`distribute-lft-in_binary64`

Counts

67 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	1136
1	110	1034
2	285	1034
3	751	1025
4	2413	1025
5	3154	1025
6	4752	1025
7	4942	1025

prune56.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	4	65

Error

Counts

65 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	23.1b	(cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
▶	0.3b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 1404 to 1010 computations (28.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
✓	0.0b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	0.1b	(fma.f64 6 x -6)
✓	0.2b	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

series28.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

18.0ms	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
10.0ms	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
2.0ms	(/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6))

simplify152.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

710×	`distribute-rgt-in_binary64`
694×	`distribute-lft-in_binary64`
455×	`div-sub_binary64`
283×	`associate-/l*_binary64`
276×	`+-commutative_binary64`

Counts

113 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	3414
1	179	3099
2	493	3072
3	1384	3057
4	3517	3057
5	4145	3057
6	5164	3057

prune167.0ms (4.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	170	4	174

Error

Counts

174 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	23.1b	(cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 4482 to 3357 computations (25.1% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	0.1b	(fma.f64 6 x -6)
	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	1.0b	(cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

series76.0ms (2.1%)

Counts

2 → 6

Calls

2 calls:

39.0ms

(*.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

37.0ms

(cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`cbrt-prod_binary64`
65×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`

Counts

2 → 104

Calls

2 calls:

13.0ms

(*.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

2.0ms

(cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

simplify194.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-def_binary64`
481×	`associate-/r/_binary64`
451×	`unswap-sqr_binary64`
356×	`*-commutative_binary64`
331×	`times-frac_binary64`

Counts

110 → 140

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	4765
1	205	4765
2	538	4367
3	1137	4321
4	2439	3959
5	4263	3959
6	4960	3959
7	4933	3959

prune428.0ms (12%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	354	0	354
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	354	4	358

Error

Counts

358 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
▶	23.1b	(cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 18231 to 13239 computations (27.4% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 6 x -6)
✓	0.1b	(*.f64 (fma.f64 6 x -6) (fma.f64 6 x -6))
✓	1.0b	(cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	21.9b	(/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

series43.0ms (1.2%)

Counts

3 → 18

Calls

3 calls:

25.0ms

(/.f64 (*.f64 (*.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (*.f64 (*.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

15.0ms

(cbrt.f64 (/.f64 (*.f64 (*.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (*.f64 (*.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

2.0ms

(*.f64 (fma.f64 6 x -6) (fma.f64 6 x -6))

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-cbrt-cube_binary64`
41×	`add-exp-log_binary64`
19×	`cbrt-unprod_binary64`
19×	`prod-exp_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

3 → 78

Calls

3 calls:

15.0ms

(/.f64 (*.f64 (*.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (*.f64 (*.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

7.0ms

(cbrt.f64 (/.f64 (*.f64 (*.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (*.f64 (*.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))

3.0ms

(*.f64 (fma.f64 6 x -6) (fma.f64 6 x -6))

simplify95.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
422×	`associate-/r*_binary64`
368×	`associate-*l/_binary64`
325×	`distribute-rgt-in_binary64`
315×	`distribute-lft-in_binary64`

Counts

96 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	4745
1	229	1925
2	944	1676
3	4512	1654
4	5225	1654

prune163.0ms (4.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	164	4	168

Error

Counts

168 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (cbrt.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	23.1b	(cbrt.f64 (/.f64 (.f64 (.f64 (fma.f64 6 x -6) (fma.f64 6 x -6)) (fma.f64 6 x -6)) (.f64 (.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))

Compiler

Compiled 7284 to 5200 computations (28.6% saved)

regimes402.0ms (11.3%)

Accuracy

Total 0.1b remaining (42.6%)

Threshold costs 0.1b (42.6%)

Counts

166 → 1

Compiler

Compiled 9307 to 7228 computations (22.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	14	17
2	13	17

end100.0ms (2.8%)

Compiler: Compiled 136 to 102 computations (25% saved)

Details

analyze3.0ms (0.1%)

sample1.2s (32.7%)

simplify232.0ms (6.5%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series27.0ms (0.8%)

rewrite5.0ms (0.1%)

simplify89.0ms (2.5%)

prune56.0ms (1.6%)

localize8.0ms (0.2%)

series28.0ms (0.8%)

rewrite15.0ms (0.4%)

simplify152.0ms (4.3%)

prune167.0ms (4.7%)

localize11.0ms (0.3%)

series76.0ms (2.1%)

rewrite29.0ms (0.8%)

simplify194.0ms (5.4%)

prune428.0ms (12%)

localize16.0ms (0.5%)

series43.0ms (1.2%)

rewrite40.0ms (1.1%)

simplify95.0ms (2.7%)

prune163.0ms (4.6%)

regimes402.0ms (11.3%)

simplify3.0ms (0.1%)

end100.0ms (2.8%)

Profiling