Details

analyze1.2s (29.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.7s (40.3%)

Results

1.2s	8256×	body	128	valid
369.0ms	2642×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify68.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
719×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`
163×	`distribute-rgt-in_binary64`
116×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	31	11
3	62	11
4	130	11
5	231	11
6	390	11
7	639	11
8	955	11
9	1272	11
10	1381	11
11	1449	11
12	1474	11
13	1471	11
14	1471	11
15	1398	11

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
▶	4.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z t))
✓	5.1b	(/.f64 (*.f64 y (-.f64 z t)) a)

series25.0ms (0.6%)

Counts

2 → 84

Calls

2 calls:

18.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
7.0ms	(*.f64 y (-.f64 z t))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 75

Calls

2 calls:

6.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
5.0ms	(*.f64 y (-.f64 z t))

simplify90.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-/l*_binary64`
508×	`times-frac_binary64`
338×	`fma-def_binary64`
275×	`distribute-rgt-in_binary64`
261×	`distribute-lft-in_binary64`

Counts

159 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	1706
1	335	1575
2	1241	1521
3	4826	1521
4	4942	1521

prune82.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	109	6	115

Error

Counts

115 → 6

Alt Table

Status	Error	Program
	5.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	5.0b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 y (-.f64 z t)) a)) (cbrt.f64 (/.f64 (.f64 y (-.f64 z t)) a))) (cbrt.f64 (/.f64 (*.f64 y (-.f64 z t)) a))))
	4.6b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	4.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
▶	4.5b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	31.6b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 a)) (/.f64 (-.f64 z t) (sqrt.f64 a))))

Compiler

Compiled 2118 to 670 computations (68.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 z t))
✓	6.1b	(/.f64 y (/.f64 a (-.f64 z t)))

series34.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

18.0ms	(/.f64 y (/.f64 a (-.f64 z t)))
16.0ms	(/.f64 a (-.f64 z t))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
102×	`*-un-lft-identity_binary64`
102×	`add-sqr-sqrt_binary64`
70×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

2 → 143

Calls

2 calls:

8.0ms	(/.f64 y (/.f64 a (-.f64 z t)))
3.0ms	(/.f64 a (-.f64 z t))

simplify170.0ms (4%)

Algorithm

1×	egg-herbie

Rules

556×	`associate-/l*_binary64`
552×	`associate-/r/_binary64`
505×	`times-frac_binary64`
323×	`fma-def_binary64`
250×	`distribute-rgt-in_binary64`

Counts

215 → 214

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	266	4051
1	597	3937
2	2072	3812
3	4851	3812
4	4978	3812

prune125.0ms (2.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	215	5	220

Error

Counts

220 → 5

Alt Table

Status	Error	Program
	4.6b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	4.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	5.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
✓	4.5b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
▶	1.7b	(+.f64 x (*.f64 (/.f64 y a) (-.f64 z t)))

Compiler

Compiled 4185 to 1097 computations (73.8% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	8.0b	(*.f64 (/.f64 y a) (-.f64 z t))

series18.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

18.0ms

(*.f64 (/.f64 y a) (-.f64 z t))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`associate-l_binary64`

Counts

1 → 66

Calls

1 calls:

10.0ms

(*.f64 (/.f64 y a) (-.f64 z t))

simplify84.0ms (2%)

Algorithm

1×	egg-herbie

Rules

476×	`div-sub_binary64`
413×	`fma-def_binary64`
316×	`fma-neg_binary64`
307×	`associate-*l/_binary64`
296×	`*-commutative_binary64`

Counts

114 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	1596
1	368	1494
2	1165	1440
3	3542	1332
4	4457	1332
5	5104	1332

prune60.0ms (1.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	99	5	104

Error

Counts

104 → 5

Alt Table

Status	Error	Program
▶	4.6b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	4.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	5.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
✓	4.5b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
✓	1.7b	(+.f64 x (*.f64 (/.f64 y a) (-.f64 z t)))

Compiler

Compiled 2009 to 562 computations (72% saved)

localize13.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 z t))
✓	5.1b	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))

series19.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

19.0ms

(*.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`add-cbrt-cube_binary64`
12×	`prod-exp_binary64`
9×	`times-frac_binary64`

Counts

1 → 44

Calls

1 calls:

11.0ms

(*.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a))

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

809×	`times-frac_binary64`
669×	`fma-def_binary64`
382×	`distribute-rgt-in_binary64`
380×	`distribute-lft-in_binary64`
243×	`*-commutative_binary64`

Counts

92 → 73

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	102	1120
1	265	1012
2	901	1012
3	2987	1012
4	4986	1012

prune88.0ms (2.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	140	5	145

Error

Counts

145 → 5

Alt Table

Status	Error	Program
✓	4.6b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	4.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	5.3b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
✓	4.5b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
✓	1.7b	(+.f64 x (*.f64 (/.f64 y a) (-.f64 z t)))

Compiler

Compiled 2712 to 1044 computations (61.5% saved)

regimes207.0ms (4.9%)

Accuracy

Total 2.8b remaining (99.5%)

Threshold costs 0b (0%)

Counts

21 → 1

Compiler

Compiled 3539 to 2119 computations (40.1% saved)

simplify3.0ms (0.1%)

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	13	25
1	17	25
2	22	25
3	24	25
4	25	25
5	25	25

end65.0ms (1.5%)

Compiler: Compiled 113 to 70 computations (38.1% saved)

Details

analyze1.2s (29.2%)

sample1.7s (40.3%)

simplify68.0ms (1.6%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series25.0ms (0.6%)

rewrite16.0ms (0.4%)

simplify90.0ms (2.1%)

prune82.0ms (1.9%)

localize6.0ms (0.1%)

series34.0ms (0.8%)

rewrite24.0ms (0.6%)

simplify170.0ms (4%)

prune125.0ms (2.9%)

localize7.0ms (0.2%)

series18.0ms (0.4%)

rewrite15.0ms (0.3%)

simplify84.0ms (2%)

prune60.0ms (1.4%)

localize13.0ms (0.3%)

series19.0ms (0.4%)

rewrite14.0ms (0.3%)

simplify57.0ms (1.3%)

prune88.0ms (2.1%)

regimes207.0ms (4.9%)

simplify3.0ms (0.1%)

end65.0ms (1.5%)

Profiling