Details

analyze61.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample1.2s (33.3%)

Results

882.0ms	8256×	body	128	valid
5.0ms	46×	body	128	invalid

Compiler

Compiled 61 to 43 computations (29.5% saved)

simplify117.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def_binary64`
913×	`fma-neg_binary64`
520×	`distribute-rgt-in_binary64`
481×	`div-sub_binary64`
441×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	78	14
4	233	14
5	529	14
6	976	14
7	1686	14
8	1746	14
9	1952	14
10	2334	14
11	2818	14
12	3104	14
13	4560	14
14	4195	14
15	4799	14

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
▶	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series27.0ms (0.8%)

Counts

3 → 56

Calls

3 calls:

13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
4.0ms	(*.f64 m (-.f64 1 m))

rewrite95.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

103× egg-rr

Counts

3 → 103

Calls

2 calls:

93.0ms	((.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m) (/.f64 (.f64 m (-.f64 1 m)) v) (.f64 m (-.f64 1 m)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	201	33
2	2716	31
3	4997	31
4	5369	31
0	0	0
1	0	0

simplify59.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

577×	`unsub-neg_binary64`
458×	`fma-def_binary64`
426×	`associate-/l*_binary64`
379×	`fma-neg_binary64`
318×	`div-sub_binary64`

Counts

159 → 126

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	638
1	66	584
2	135	584
3	341	584
4	1077	584
5	3918	584
6	4987	584

prune113.0ms (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	120	6	126
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	122	6	128

Error

0.0b

Counts

128 → 6

Alt Table

Status	Error	Program
▶	0.2b	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 1) m)
	0.4b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
	11.0b	(.f64 (-.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 m (-.f64 1 m))) 2) v) 1) m)
	6.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	12.4b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 2) -1) m) (fma.f64 (/.f64 m v) (-.f64 1 m) 1))
	21.1b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) -1) m) (+.f64 (pow.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 2) (fma.f64 (/.f64 m v) (-.f64 1 m) 1)))

Compiler

Compiled 2097 to 1318 computations (37.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 m v) (-.f64 1 m))
✓	0.2b	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 1) m)

series24.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 1) m)
11.0ms	(*.f64 (/.f64 m v) (-.f64 1 m))

rewrite90.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

103× egg-rr

Counts

2 → 103

Calls

2 calls:

88.0ms	((.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1 m)) 1) m) (*.f64 (/.f64 m v) (-.f64 1 m)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	201	24
2	2656	24
3	4888	24
4	5177	24
0	0	0
1	0	0

simplify63.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

676×	`unsub-neg_binary64`
511×	`fma-neg_binary64`
503×	`fma-def_binary64`
346×	`cancel-sign-sub-inv_binary64`
308×	`div-sub_binary64`

Counts

151 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	602
1	74	548
2	147	548
3	368	518
4	1318	518
5	3996	518
6	5066	518

prune109.0ms (3.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	122	5	127

Error

0.0b

Counts

127 → 5

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (-.f64 (fma.f64 (/.f64 (sqrt.f64 m) 1) (/.f64 (sqrt.f64 m) v) (.f64 (neg.f64 m) (/.f64 m v))) 1) m)
	0.4b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
	6.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	12.4b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 2) -1) m) (fma.f64 (/.f64 m v) (-.f64 1 m) 1))
	21.1b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) -1) m) (+.f64 (pow.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 2) (fma.f64 (/.f64 m v) (-.f64 1 m) 1)))

Compiler

Compiled 2141 to 1096 computations (48.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (fma.f64 (/.f64 (sqrt.f64 m) 1) (/.f64 (sqrt.f64 m) v) (.f64 (neg.f64 m) (/.f64 m v))) 1) m)
✓	0.2b	(/.f64 (sqrt.f64 m) v)
✓	0.2b	(*.f64 (neg.f64 m) (/.f64 m v))
✓	0.3b	(fma.f64 (/.f64 (sqrt.f64 m) 1) (/.f64 (sqrt.f64 m) v) (*.f64 (neg.f64 m) (/.f64 m v)))

series80.0ms (2.2%)

Counts

4 → 65

Calls

4 calls:

30.0ms	(.f64 (-.f64 (fma.f64 (/.f64 (sqrt.f64 m) 1) (/.f64 (sqrt.f64 m) v) (.f64 (neg.f64 m) (/.f64 m v))) 1) m)
27.0ms	(fma.f64 (/.f64 (sqrt.f64 m) 1) (/.f64 (sqrt.f64 m) v) (*.f64 (neg.f64 m) (/.f64 m v)))
12.0ms	(*.f64 (neg.f64 m) (/.f64 m v))
10.0ms	(/.f64 (sqrt.f64 m) v)

rewrite159.0ms (4.5%)

Algorithm

2×	batch-egg-rewrite

Rules

123× egg-rr

Counts

4 → 123

Calls

2 calls:

156.0ms

((fma.f64 (/.f64 (sqrt.f64 m) 1) (/.f64 (sqrt.f64 m) v) (*.f64 (neg.f64 m) (/.f64 m v))) (*.f64 (neg.f64 m) (/.f64 m v)) (/.f64 (sqrt.f64 m) v) (*.f64 (-.f64 (fma.f64 (/.f64 (sqrt.f64 m) 1) (/.f64 (sqrt.f64 m) v) (*.f64 (neg.f64 m) (/.f64 m v))) 1) m))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	61
1	266	45
2	3066	45
3	4990	45
4	4503	39
5	4993	39
6	4926	39
0	0	0
1	0	0

simplify61.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

602×	`unsub-neg_binary64`
498×	`fma-def_binary64`
479×	`associate-/l*_binary64`
408×	`fma-neg_binary64`
364×	`div-sub_binary64`

Counts

188 → 137

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	673
1	69	610
2	136	610
3	347	610
4	1141	610
5	3919	610
6	5140	610

prune114.0ms (3.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	137	5	142

Error

0.0b

Counts

142 → 5

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (-.f64 (fma.f64 (/.f64 (sqrt.f64 m) 1) (/.f64 (sqrt.f64 m) v) (.f64 (neg.f64 m) (/.f64 m v))) 1) m)
▶	0.4b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
	6.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	12.4b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 2) -1) m) (fma.f64 (/.f64 m v) (-.f64 1 m) 1))
	21.1b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) -1) m) (+.f64 (pow.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 2) (fma.f64 (/.f64 m v) (-.f64 1 m) 1)))

Compiler

Compiled 3102 to 1175 computations (62.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.2b	(/.f64 m (sqrt.f64 v))
✓	0.3b	(/.f64 (-.f64 1 m) (sqrt.f64 v))
✓	0.3b	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))

series111.0ms (3.1%)

Counts

4 → 64

Calls

4 calls:

41.0ms	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
23.0ms	(/.f64 m (sqrt.f64 v))
23.0ms	(*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v)))
23.0ms	(/.f64 (-.f64 1 m) (sqrt.f64 v))

rewrite85.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

194× egg-rr

Counts

4 → 194

Calls

2 calls:

81.0ms

((*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) (/.f64 (-.f64 1 m) (sqrt.f64 v)) (/.f64 m (sqrt.f64 v)) (*.f64 (-.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	249	41
2	3392	41
3	4965	41
0	0	0
1	0	0

simplify87.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

527×	`div-sub_binary64`
504×	`fma-def_binary64`
350×	`associate-/l*_binary64`
331×	`fma-neg_binary64`
315×	`unswap-sqr_binary64`

Counts

258 → 218

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	791
1	79	746
2	142	701
3	350	677
4	1100	677
5	3424	677
6	4759	677
7	5184	677

prune208.0ms (5.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	217	6	223

Error

0.0b

Counts

223 → 6

Alt Table

Status	Error	Program
	26.6b	(.f64 (/.f64 m v) (-.f64 m (.f64 m m)))
✓	0.4b	(.f64 (-.f64 (.f64 (/.f64 m (sqrt.f64 v)) (/.f64 (-.f64 1 m) (sqrt.f64 v))) 1) m)
✓	0.3b	(.f64 (-.f64 (fma.f64 (/.f64 (sqrt.f64 m) 1) (/.f64 (sqrt.f64 m) v) (.f64 (neg.f64 m) (/.f64 m v))) 1) m)
	6.2b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	12.4b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 2) -1) m) (fma.f64 (/.f64 m v) (-.f64 1 m) 1))
	21.1b	(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 3) -1) m) (+.f64 (pow.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 2) (fma.f64 (/.f64 m v) (-.f64 1 m) 1)))

Compiler

Compiled 5364 to 2727 computations (49.2% saved)

regimes579.0ms (16.3%)

Accuracy

Total 0.1b remaining (83.5%)

Threshold costs 0.1b (83.5%)

Counts

204 → 1

Compiler

Compiled 10511 to 6812 computations (35.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`unsub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	20	16
2	23	16
3	24	16
4	23	16

end90.0ms (2.5%)

Compiler: Compiled 148 to 97 computations (34.5% saved)

Details

analyze61.0ms (1.7%)

sample1.2s (33.3%)

simplify117.0ms (3.3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series27.0ms (0.8%)

rewrite95.0ms (2.7%)

simplify59.0ms (1.7%)

prune113.0ms (3.2%)

localize6.0ms (0.2%)

series24.0ms (0.7%)

rewrite90.0ms (2.5%)

simplify63.0ms (1.8%)

prune109.0ms (3.1%)

localize11.0ms (0.3%)

series80.0ms (2.2%)

rewrite159.0ms (4.5%)

simplify61.0ms (1.7%)

prune114.0ms (3.2%)

localize8.0ms (0.2%)

series111.0ms (3.1%)

rewrite85.0ms (2.4%)

simplify87.0ms (2.4%)

prune208.0ms (5.9%)

regimes579.0ms (16.3%)

simplify3.0ms (0.1%)

end90.0ms (2.5%)

Profiling