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)

sample257.0ms (10%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify230.0ms (9%)

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

prune4.0ms (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 83 to 64 computations (22.9% saved)

localize7.0ms (0.3%)

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)))

series22.0ms (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)))
5.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
2.0ms	(fma.f64 6 x -6)

rewrite5.0ms (0.2%)

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

simplify93.0ms (3.6%)

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

prune58.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	60	6	66

Error

Counts

66 → 6

Alt Table

Status	Error	Program
	1.0b	(cbrt.f64 (.f64 (.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	30.7b	(exp.f64 (log.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	30.7b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (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)))
▶	0.1b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
	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)))))

Compiler

Compiled 1477 to 1068 computations (27.7% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series27.0ms (1.1%)

Counts

3 → 17

Calls

3 calls:

20.0ms	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
6.0ms	(fma.f64 4 (sqrt.f64 x) x)
2.0ms	(fma.f64 -6 x 6)

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

3 → 59

Calls

3 calls:

4.0ms	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
0.0ms	(fma.f64 4 (sqrt.f64 x) x)
0.0ms	(fma.f64 -6 x 6)

simplify91.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

506×	`times-frac_binary64`
445×	`distribute-rgt-in_binary64`
428×	`distribute-lft-in_binary64`
337×	`associate-/l*_binary64`
242×	`fma-def_binary64`

Counts

76 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	1396
1	166	1291
2	388	1291
3	1085	1289
4	4582	1289
5	4984	1289
6	4940	1289

prune63.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	71	4	75

Error

Counts

75 → 4

Alt Table

Status	Error	Program
	19.8b	(.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 -1 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 3))) (+.f64 (.f64 -1 -1) (+.f64 (.f64 (fma.f64 4 (sqrt.f64 x) x) (fma.f64 4 (sqrt.f64 x) x)) (.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))))
▶	0.3b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	30.7b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	0.4b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)))))

Compiler

Compiled 1588 to 1131 computations (28.8% saved)

localize9.0ms (0.4%)

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))

series25.0ms (1%)

Counts

2 → 6

Calls

2 calls:

15.0ms	(/.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))

rewrite14.0ms (0.6%)

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))

simplify170.0ms (6.7%)

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

prune153.0ms (6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	170	4	174

Error

Counts

174 → 4

Alt Table

Status	Error	Program
	19.8b	(.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 -1 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 3))) (+.f64 (.f64 -1 -1) (+.f64 (.f64 (fma.f64 4 (sqrt.f64 x) x) (fma.f64 4 (sqrt.f64 x) x)) (.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))))
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	30.7b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
▶	0.4b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)))))

Compiler

Compiled 4455 to 3335 computations (25.1% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (fma.f64 4 (sqrt.f64 x) x))
	0.1b	(fma.f64 -6 x 6)
✓	0.1b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)))))
✓	0.5b	(*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)))

series43.0ms (1.7%)

Counts

3 → 5

Calls

3 calls:

17.0ms

(sqrt.f64 (fma.f64 4 (sqrt.f64 x) x))

17.0ms

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

9.0ms

(*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)))

rewrite15.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`

Counts

3 → 103

Calls

3 calls:

5.0ms

(*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)))

3.0ms

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

1.0ms

(sqrt.f64 (fma.f64 4 (sqrt.f64 x) x))

simplify96.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

538×	`fma-def_binary64`
526×	`fma-neg_binary64`
340×	`associate-/l*_binary64`
266×	`associate-l_binary64`
263×	`cancel-sign-sub-inv_binary64`

Counts

108 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	1916
1	211	1748
2	571	1708
3	1887	1681
4	4517	1681
5	5037	1681

prune163.0ms (6.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	173	4	177

Error

Counts

177 → 4

Alt Table

Status	Error	Program
	19.8b	(.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 -1 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 3))) (+.f64 (.f64 -1 -1) (+.f64 (.f64 (fma.f64 4 (sqrt.f64 x) x) (fma.f64 4 (sqrt.f64 x) x)) (.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))))
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)) (fma.f64 6 x -6)))
	30.7b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
✓	0.4b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (*.f64 (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) x)))))

Compiler

Compiled 4788 to 3285 computations (31.4% saved)

regimes300.0ms (11.7%)

Accuracy

Total 0.1b remaining (60.3%)

Threshold costs 0.1b (60.3%)

Counts

142 → 1

Compiler

Compiled 6473 to 5048 computations (22% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	17
1	21	17
2	24	17
3	26	17
4	27	17
5	24	17

end1.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

sample678.0ms (26.5%)

Algorithm

1×

intervals

Results

423.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 120 to 90 computations (25% saved)

Details

analyze3.0ms (0.1%)

sample257.0ms (10%)

simplify230.0ms (9%)

prune4.0ms (0.1%)

localize7.0ms (0.3%)

series22.0ms (0.8%)

rewrite5.0ms (0.2%)

simplify93.0ms (3.6%)

prune58.0ms (2.3%)

localize10.0ms (0.4%)

series27.0ms (1.1%)

rewrite8.0ms (0.3%)

simplify91.0ms (3.5%)

prune63.0ms (2.5%)

localize9.0ms (0.4%)

series25.0ms (1%)

rewrite14.0ms (0.6%)

simplify170.0ms (6.7%)

prune153.0ms (6%)

localize9.0ms (0.4%)

series43.0ms (1.7%)

rewrite15.0ms (0.6%)

simplify96.0ms (3.8%)

prune163.0ms (6.4%)

regimes300.0ms (11.7%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample678.0ms (26.5%)

Profiling