Details

analyze74.0ms (2.1%)

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 26 to 19 computations (26.9% saved)

sample122.0ms (3.4%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
6.0ms	258×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 43 to 32 computations (25.6% saved)

simplify157.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

1247×	`unsub-neg_binary64`
616×	`neg-sub0_binary64`
571×	`neg-mul-1_binary64`
560×	`fma-neg_binary64`
452×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	20	19
2	46	17
3	116	17
4	358	17
5	1331	17
6	3463	17
7	3625	17
8	4293	17
9	4678	17
10	4650	17
11	4895	17
12	4905	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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
	0.4b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 85 to 61 computations (28.2% 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 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)

series26.0ms (0.7%)

Counts

3 → 56

Calls

3 calls:

14.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite34.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
26×	`distribute-lft-in_binary64`

Counts

3 → 137

Calls

3 calls:

14.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify115.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

806×	`distribute-rgt-in_binary64`
733×	`distribute-lft-in_binary64`
365×	`fma-neg_binary64`
242×	`associate-l_binary64`
194×	`associate-r_binary64`

Counts

193 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	3683
1	464	3476
2	1999	3134
3	4909	3134
4	5060	3134

prune203.0ms (5.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	216	3	219
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	218	3	221

Error

Counts

221 → 3

Alt Table

Status	Error	Program
	3.3b	(/.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (.f64 1 1) (.f64 m m))) (+.f64 1 m))
	0.4b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))
▶	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 5355 to 3234 computations (39.6% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
✓	0.0b	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1))
✓	8.2b	(/.f64 (pow.f64 m 3) v)
✓	12.1b	(/.f64 (*.f64 m m) v)

series61.0ms (1.7%)

Counts

4 → 72

Calls

4 calls:

19.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
18.0ms	(/.f64 (pow.f64 m 3) v)
13.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1))
10.0ms	(/.f64 (*.f64 m m) v)

rewrite65.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
49×	`add-cube-cbrt_binary64`
39×	`times-frac_binary64`
24×	`prod-diff_binary64`

Counts

4 → 172

Calls

4 calls:

36.0ms	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))
7.0ms	(-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1))
4.0ms	(/.f64 (pow.f64 m 3) v)
3.0ms	(/.f64 (*.f64 m m) v)

simplify128.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

611×	`associate-/l/_binary64`
458×	`fma-neg_binary64`
451×	`unswap-sqr_binary64`
187×	`cancel-sign-sub-inv_binary64`
136×	`associate-/l*_binary64`

Counts

244 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	4559
1	487	4206
2	2089	3968
3	4854	3968
4	5037	3968

prune213.0ms (6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	229	3	232

Error

Counts

232 → 3

Alt Table

Status	Error	Program
	3.3b	(/.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (.f64 1 1) (.f64 m m))) (+.f64 1 m))
▶	0.4b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 7629 to 3415 computations (55.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))
✓	0.5b	(.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v))

series23.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))
10.0ms	(.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v))

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
26×	`add-exp-log_binary64`
25×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64`

Counts

2 → 101

Calls

2 calls:

16.0ms	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))
8.0ms	(.f64 (.f64 m (-.f64 1 m)) (/.f64 1 v))

simplify77.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

850×	`distribute-rgt-in_binary64`
806×	`distribute-lft-in_binary64`
279×	`associate-l_binary64`
201×	`fma-neg_binary64`
189×	`associate-r_binary64`

Counts

149 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	3188
1	467	2879
2	1855	2803
3	5321	2803

prune245.0ms (6.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	240	3	243

Error

Counts

243 → 3

Alt Table

Status	Error	Program
▶	3.3b	(/.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (.f64 1 1) (.f64 m m))) (+.f64 1 m))
✓	0.4b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 6230 to 4015 computations (35.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 m (-.f64 1 m))
	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.0b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (.f64 1 1) (.f64 m m)))
✓	3.0b	(/.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (.f64 1 1) (.f64 m m))) (+.f64 1 m))

series149.0ms (4.2%)

Counts

2 → 48

Calls

2 calls:

132.0ms	(/.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (.f64 1 1) (.f64 m m))) (+.f64 1 m))
17.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (.f64 1 1) (.f64 m m)))

rewrite37.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
12×	`flip--_binary64`
12×	`flip3--_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`

Counts

2 → 74

Calls

2 calls:

17.0ms	(/.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (.f64 1 1) (.f64 m m))) (+.f64 1 m))
13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (.f64 1 1) (.f64 m m)))

simplify109.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

790×	`fma-def_binary64`
316×	`associate-/r*_binary64`
292×	`associate-/l/_binary64`
264×	`associate-/r/_binary64`
200×	`fma-neg_binary64`

Counts

122 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	192	4141
1	545	3805
2	2148	3422
3	4607	3413
4	4939	3413

prune277.0ms (7.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	279	0	279
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	279	3	282

Error

Counts

282 → 3

Alt Table

Status	Error	Program
✓	3.3b	(/.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (.f64 1 1) (.f64 m m))) (+.f64 1 m))
✓	0.4b	(.f64 (-.f64 (.f64 (*.f64 m (-.f64 1 m)) (/.f64 1 v)) 1) (-.f64 1 m))
✓	0.0b	(+.f64 (-.f64 (+.f64 m (/.f64 m v)) (fma.f64 2 (/.f64 (*.f64 m m) v) 1)) (/.f64 (pow.f64 m 3) v))

Compiler

Compiled 8556 to 5383 computations (37.1% saved)

regimes502.0ms (14.1%)

Accuracy

Total 0.0b remaining (66.4%)

Threshold costs 0.0b (66.4%)

Counts

166 → 1

Compiler

Compiled 8782 to 6251 computations (28.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-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	14	29
1	21	29
2	25	29
3	27	29
4	28	29
5	27	29

end1.0ms (0%)

Compiler: Compiled 22 to 13 computations (40.9% saved)

sample871.0ms (24.5%)

Algorithm

1×

intervals

Results

357.0ms	8000×	body	128	valid
179.0ms	8067×	pre	128	true
3.0ms	67×	body	128	invalid

Compiler

Compiled 112 to 78 computations (30.4% saved)

Details

analyze74.0ms (2.1%)

sample122.0ms (3.4%)

simplify157.0ms (4.4%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series26.0ms (0.7%)

rewrite34.0ms (1%)

simplify115.0ms (3.2%)

prune203.0ms (5.7%)

localize13.0ms (0.4%)

series61.0ms (1.7%)

rewrite65.0ms (1.8%)

simplify128.0ms (3.6%)

prune213.0ms (6%)

localize8.0ms (0.2%)

series23.0ms (0.7%)

rewrite31.0ms (0.9%)

simplify77.0ms (2.2%)

prune245.0ms (6.9%)

localize12.0ms (0.3%)

series149.0ms (4.2%)

rewrite37.0ms (1%)

simplify109.0ms (3.1%)

prune277.0ms (7.8%)

regimes502.0ms (14.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample871.0ms (24.5%)

Profiling