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)

sample1.1s (36.7%)

Results

887.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify232.0ms (7.5%)

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

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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
▶	0.4b	(/.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 (0.2%)

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)
✓	0.4b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))

series19.0ms (0.6%)

Counts

3 → 18

Calls

3 calls:

14.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))
4.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))
1.0ms	(fma.f64 6 x -6)

rewrite4.0ms (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 6 x -6)
0.0ms	(fma.f64 4 (sqrt.f64 x) (+.f64 x 1))

simplify96.0ms (3.1%)

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

prune54.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	57	7	64
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	59	7	66

Error

Counts

66 → 7

Alt Table

Status	Error	Program
	1.8b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (*.f64 (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))) (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
▶	0.4b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
	30.8b	(exp.f64 (log.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	32.1b	6
	0.4b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))
	31.3b	(*.f64 (/.f64 (sqrt.f64 (fma.f64 6 x -6)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))) (/.f64 (sqrt.f64 (fma.f64 6 x -6)) (sqrt.f64 (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	1.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 6 x -6)) (cbrt.f64 (fma.f64 6 x -6))) (/.f64 (cbrt.f64 (fma.f64 6 x -6)) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1))))

Compiler

Compiled 1489 to 1084 computations (27.2% saved)

localize12.0ms (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)
✓	0.4b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))

series23.0ms (0.7%)

Counts

3 → 17

Calls

3 calls:

16.0ms	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
5.0ms	(fma.f64 4 (sqrt.f64 x) x)
1.0ms	(fma.f64 -6 x 6)

rewrite12.0ms (0.4%)

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:

6.0ms	(fma.f64 4 (sqrt.f64 x) x)
3.0ms	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
0.0ms	(fma.f64 -6 x 6)

simplify95.0ms (3%)

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

prune61.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	70	6	76

Error

Counts

76 → 6

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
▶	14.9b	(.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 1 (.f64 (fma.f64 4 (sqrt.f64 x) x) (fma.f64 4 (sqrt.f64 x) x)))) (+.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
	30.8b	(exp.f64 (log.f64 (/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (+.f64 x 1)))))
	20.7b	(.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)))))
	31.2b	(*.f64 (sqrt.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))) (sqrt.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))))
	32.1b	6

Compiler

Compiled 1643 to 1169 computations (28.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (/.f64 (fma.f64 -6 x 6) (-.f64 1 (.f64 (fma.f64 4 (sqrt.f64 x) x) (fma.f64 4 (sqrt.f64 x) x)))) (+.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
	0.1b	(fma.f64 -6 x 6)
✓	0.3b	(*.f64 (fma.f64 4 (sqrt.f64 x) x) (fma.f64 4 (sqrt.f64 x) x))
✓	14.3b	(/.f64 (fma.f64 -6 x 6) (-.f64 1 (*.f64 (fma.f64 4 (sqrt.f64 x) x) (fma.f64 4 (sqrt.f64 x) x))))

series53.0ms (1.7%)

Counts

3 → 9

Calls

3 calls:

24.0ms

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

18.0ms

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

10.0ms

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

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64`
24×	`associate-l_binary64`

Counts

3 → 117

Calls

3 calls:

8.0ms

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

3.0ms

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

3.0ms

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

simplify131.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary64`
393×	`associate-*l/_binary64`
382×	`times-frac_binary64`
371×	`associate-/l*_binary64`
214×	`fma-neg_binary64`

Counts

126 → 201

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	4328
1	513	3855
2	1885	3465
3	4944	3459
4	5069	3459

prune229.0ms (7.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	213	2	215
Fresh	3	1	4
Picked	1	0	1
Done	1	0	1
Total	218	3	221

Error

Counts

221 → 3

Alt Table

Status	Error	Program
	32.1b	6
	14.9b	(.f64 (.f64 (fma.f64 -6 x 6) (/.f64 1 (-.f64 1 (*.f64 (fma.f64 4 (sqrt.f64 x) x) (fma.f64 4 (sqrt.f64 x) x))))) (+.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
▶	0.5b	(.f64 (.f64 (/.f64 1 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))) (/.f64 (fma.f64 x -6 6) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x)))) (+.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))

Compiler

Compiled 8266 to 5506 computations (33.4% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (/.f64 1 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))) (/.f64 (fma.f64 x -6 6) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x)))) (+.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
✓	0.1b	(fma.f64 x -6 6)
✓	0.2b	(*.f64 (/.f64 1 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))) (/.f64 (fma.f64 x -6 6) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x))))
✓	0.4b	(/.f64 (fma.f64 x -6 6) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x)))

series55.0ms (1.8%)

Counts

4 → 22

Calls

4 calls:

24.0ms	(.f64 (.f64 (/.f64 1 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))) (/.f64 (fma.f64 x -6 6) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x)))) (+.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
17.0ms	(*.f64 (/.f64 1 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))) (/.f64 (fma.f64 x -6 6) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x))))
12.0ms	(/.f64 (fma.f64 x -6 6) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x)))
1.0ms	(fma.f64 x -6 6)

rewrite57.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64`
60×	`add-exp-log_binary64`
55×	`times-frac_binary64`
36×	`add-cbrt-cube_binary64`

Counts

4 → 171

Calls

4 calls:

16.0ms	(.f64 (.f64 (/.f64 1 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))) (/.f64 (fma.f64 x -6 6) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x)))) (+.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
14.0ms	(*.f64 (/.f64 1 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))) (/.f64 (fma.f64 x -6 6) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x))))
5.0ms	(/.f64 (fma.f64 x -6 6) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x)))
0.0ms	(fma.f64 x -6 6)

simplify200.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

632×	`fma-def_binary64`
422×	`associate-/r*_binary64`
294×	`associate-/l/_binary64`
248×	`associate-l_binary64`
236×	`associate-r_binary64`

Counts

193 → 242

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	221	6809
1	606	5824
2	2208	5814
3	4572	5808
4	4987	5808
5	4977	5808

prune247.0ms (7.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	242	3	245

Error

Counts

245 → 3

Alt Table

Status	Error	Program
	32.1b	6
	14.9b	(.f64 (.f64 (fma.f64 -6 x 6) (/.f64 1 (-.f64 1 (*.f64 (fma.f64 4 (sqrt.f64 x) x) (fma.f64 4 (sqrt.f64 x) x))))) (+.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))
✓	0.5b	(.f64 (.f64 (/.f64 1 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))) (/.f64 (fma.f64 x -6 6) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x)))) (+.f64 -1 (fma.f64 4 (sqrt.f64 x) x)))

Compiler

Compiled 10595 to 7264 computations (31.4% saved)

regimes242.0ms (7.8%)

Accuracy

Total 0.2b remaining (86.1%)

Threshold costs 0.2b (86.1%)

Counts

106 → 1

Compiler

Compiled 5349 to 3912 computations (26.9% saved)

simplify2.0ms (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	11	17
1	13	17
2	17	17
3	19	17
4	20	17
5	20	17

end80.0ms (2.6%)

Compiler: Compiled 88 to 64 computations (27.3% saved)

Details

analyze3.0ms (0.1%)

sample1.1s (36.7%)

simplify232.0ms (7.5%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series19.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify96.0ms (3.1%)

prune54.0ms (1.7%)

localize12.0ms (0.4%)

series23.0ms (0.7%)

rewrite12.0ms (0.4%)

simplify95.0ms (3%)

prune61.0ms (2%)

localize10.0ms (0.3%)

series53.0ms (1.7%)

rewrite25.0ms (0.8%)

simplify131.0ms (4.2%)

prune229.0ms (7.4%)

localize15.0ms (0.5%)

series55.0ms (1.8%)

rewrite57.0ms (1.8%)

simplify200.0ms (6.4%)

prune247.0ms (7.9%)

regimes242.0ms (7.8%)

simplify2.0ms (0.1%)

end80.0ms (2.6%)

Profiling