Details

analyze344.0ms (8%)

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)

sample26.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
6.0ms	259×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify115.0ms (2.7%)

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

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
✓	0.0b	(*.f64 m (-.f64 1 m))
✓	0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series37.0ms (0.9%)

Counts

4 → 80

Calls

4 calls:

14.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
10.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite39.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
40×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
19×	`add-exp-log_binary64`

Counts

4 → 153

Calls

4 calls:

9.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
7.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
7.0ms	(*.f64 m (-.f64 1 m))
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify107.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
482×	`distribute-rgt-in_binary64`
447×	`distribute-lft-in_binary64`
328×	`fma-neg_binary64`
240×	`associate-l_binary64`

Counts

233 → 245

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	3371
1	413	2852
2	1688	2595
3	4507	2594
4	4922	2594

prune228.0ms (5.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	239	6	245
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	241	6	247

Error

Counts

247 → 6

Alt Table

Status	Error	Program
	21.7b	(.f64 (cbrt.f64 (.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) m)
	0.6b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
	13.0b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
▶	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	8.1b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	10.3b	(.f64 (.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (-.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1)) m)

Compiler

Compiled 5101 to 3108 computations (39.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 m (-.f64 1 m))
✓	0.1b	(/.f64 v (*.f64 m (-.f64 1 m)))
✓	0.1b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
✓	0.2b	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))

series55.0ms (1.3%)

Counts

3 → 68

Calls

3 calls:

31.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))
13.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
11.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))

rewrite36.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
31×	`add-exp-log_binary64`
25×	`add-cube-cbrt_binary64`

Counts

3 → 124

Calls

3 calls:

16.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
7.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))
5.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))

simplify104.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
359×	`distribute-rgt-in_binary64`
334×	`fma-neg_binary64`
327×	`distribute-lft-in_binary64`
273×	`associate-/r/_binary64`

Counts

192 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	3188
1	412	2804
2	1397	2683
3	4268	2683
4	5165	2683

prune272.0ms (6.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	270	6	276

Error

Counts

276 → 6

Alt Table

Status	Error	Program
	21.7b	(.f64 (cbrt.f64 (.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) m)
▶	0.6b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
	13.0b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	8.1b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	10.3b	(.f64 (.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (-.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1)) m)

Compiler

Compiled 5841 to 3755 computations (35.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 m) v)
✓	0.1b	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
✓	0.3b	(*.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m))
✓	0.5b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))

series54.0ms (1.3%)

Counts

4 → 72

Calls

4 calls:

22.0ms	(*.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m))
18.0ms	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
8.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
7.0ms	(/.f64 (-.f64 1 m) v)

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
13×	`add-cbrt-cube_binary64`

Counts

4 → 101

Calls

4 calls:

5.0ms	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
5.0ms	(/.f64 (-.f64 1 m) v)
4.0ms	(*.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m))
0.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

simplify115.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-neg_binary64`
339×	`div-sub_binary64`
261×	`exp-prod_binary64`
251×	`times-frac_binary64`
238×	`*-commutative_binary64`

Counts

173 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	167	2812
1	379	2480
2	1039	2349
3	3116	2347
4	4544	2347
5	5036	2347

prune119.0ms (2.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	168	6	174

Error

Counts

174 → 6

Alt Table

Status	Error	Program
	21.7b	(.f64 (cbrt.f64 (.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))) m)
✓	0.6b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
	13.0b	(/.f64 (.f64 m (fma.f64 (/.f64 (-.f64 m (.f64 m m)) v) (/.f64 (-.f64 m (.f64 m m)) v) -1)) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
▶	8.1b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
	10.3b	(.f64 (.f64 (+.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1) (-.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) 1)) m)

Compiler

Compiled 3513 to 1876 computations (46.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (pow.f64 m 3) v) m)
✓	0.0b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	7.2b	(/.f64 (pow.f64 m 3) v)
✓	12.0b	(/.f64 (pow.f64 m 2) v)

series51.0ms (1.2%)

Counts

4 → 15

Calls

4 calls:

15.0ms	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
14.0ms	(/.f64 (pow.f64 m 3) v)
12.0ms	(/.f64 (pow.f64 m 2) v)
11.0ms	(+.f64 (/.f64 (pow.f64 m 3) v) m)

rewrite82.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

237×	`*-un-lft-identity_binary64`
220×	`times-frac_binary64`
184×	`add-sqr-sqrt_binary64`
172×	`add-cube-cbrt_binary64`
112×	`prod-diff_binary64`

Counts

4 → 340

Calls

4 calls:

23.0ms	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))
14.0ms	(+.f64 (/.f64 (pow.f64 m 3) v) m)
4.0ms	(/.f64 (pow.f64 m 2) v)
4.0ms	(/.f64 (pow.f64 m 3) v)

simplify211.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

766×	`fma-neg_binary64`
335×	`cancel-sign-sub-inv_binary64`
295×	`distribute-rgt-in_binary64`
200×	`distribute-rgt-neg-in_binary64`
196×	`exp-prod_binary64`

Counts

355 → 398

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	10503
1	538	6998
2	2117	5442
3	4041	5442
4	4838	5442

prune437.0ms (10.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	396	2	398
Fresh	3	0	3
Picked	0	1	1
Done	0	2	2
Total	399	5	404

Error

Counts

404 → 5

Alt Table

Status	Error	Program
	0.1b	(-.f64 (/.f64 m (/.f64 v m)) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.6b	(.f64 (.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1) (sqrt.f64 m)) (sqrt.f64 m))
	0.3b	(-.f64 (*.f64 (/.f64 m (sqrt.f64 v)) (/.f64 m (sqrt.f64 v))) (+.f64 (/.f64 (pow.f64 m 3) v) m))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
✓	8.1b	(-.f64 (/.f64 (pow.f64 m 2) v) (+.f64 (/.f64 (pow.f64 m 3) v) m))

Compiler

Compiled 12540 to 7585 computations (39.5% saved)

regimes972.0ms (22.5%)

Accuracy

Total 0.1b remaining (83.9%)

Threshold costs 0.1b (83.9%)

Counts

289 → 1

Compiler

Compiled 17259 to 11779 computations (31.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	18	19
2	26	19
3	37	19
4	44	19
5	48	19
6	49	19
7	48	19

end1.0ms (0%)

Compiler: Compiled 15 to 9 computations (40% saved)

sample856.0ms (19.8%)

Algorithm

1×

intervals

Results

321.0ms	8000×	body	128	valid
182.0ms	8059×	pre	128	true
2.0ms	59×	body	128	invalid

Compiler

Compiled 121 to 78 computations (35.5% saved)

Details

analyze344.0ms (8%)

sample26.0ms (0.6%)

simplify115.0ms (2.7%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series37.0ms (0.9%)

rewrite39.0ms (0.9%)

simplify107.0ms (2.5%)

prune228.0ms (5.3%)

localize7.0ms (0.2%)

series55.0ms (1.3%)

rewrite36.0ms (0.8%)

simplify104.0ms (2.4%)

prune272.0ms (6.3%)

localize8.0ms (0.2%)

series54.0ms (1.3%)

rewrite21.0ms (0.5%)

simplify115.0ms (2.7%)

prune119.0ms (2.8%)

localize8.0ms (0.2%)

series51.0ms (1.2%)

rewrite82.0ms (1.9%)

simplify211.0ms (4.9%)

prune437.0ms (10.1%)

regimes972.0ms (22.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample856.0ms (19.8%)

Profiling