Details

analyze62.0ms (1.6%)

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)

sample141.0ms (3.6%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 43 to 32 computations (25.6% saved)

simplify122.0ms (3.1%)

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

prune4.0ms (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
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 85 to 61 computations (28.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series34.0ms (0.9%)

Counts

4 → 80

Calls

4 calls:

13.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
11.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite94.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
57×	`prod-diff_binary64`
54×	`add-cube-cbrt_binary64`
26×	`distribute-lft-in_binary64`

Counts

4 → 188

Calls

4 calls:

61.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
7.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify135.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

359×	`associate-/l/_binary64`
345×	`associate-/r*_binary64`
257×	`associate-/r/_binary64`
250×	`associate-l_binary64`
225×	`exp-prod_binary64`

Counts

268 → 295

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	4650
1	502	4087
2	2059	4004
3	4566	3999
4	5030	3999

prune297.0ms (7.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	293	2	295
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	294	3	297

Error

0.0b

Counts

297 → 3

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
	30.6b	(.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))) (sqrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 7204 to 4577 computations (36.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (/.f64 (pow.f64 m 2) v))
✓	0.0b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
✓	7.1b	(/.f64 (pow.f64 m 3) v)
✓	12.5b	(/.f64 (pow.f64 m 2) v)

series56.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
13.0ms	(/.f64 (pow.f64 m 3) v)
13.0ms	(*.f64 2 (/.f64 (pow.f64 m 2) v))
12.0ms	(/.f64 (pow.f64 m 2) v)

rewrite67.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`*-un-lft-identity_binary64`
88×	`times-frac_binary64`
86×	`add-sqr-sqrt_binary64`
72×	`add-cube-cbrt_binary64`
34×	`unpow-prod-down_binary64`

Counts

4 → 227

Calls

4 calls:

22.0ms	(*.f64 2 (/.f64 (pow.f64 m 2) v))
21.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
5.0ms	(/.f64 (pow.f64 m 2) v)
4.0ms	(/.f64 (pow.f64 m 3) v)

simplify165.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

671×	`fma-neg_binary64`
436×	`unswap-sqr_binary64`
248×	`associate-r_binary64`
236×	`associate-l_binary64`
221×	`distribute-rgt-in_binary64`

Counts

239 → 320

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	366	6616
1	903	4942
2	3718	4665
3	4653	4663
4	4907	4663

prune359.0ms (9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	319	1	320
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	319	4	323

Error

Counts

323 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
	30.6b	(.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))) (sqrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))))
▶	0.1b	(-.f64 (+.f64 (.f64 (pow.f64 m 3/2) (/.f64 (pow.f64 m 3/2) v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 11045 to 6050 computations (45.2% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 (pow.f64 m 3/2) (/.f64 (pow.f64 m 3/2) v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))
✓	0.2b	(*.f64 (pow.f64 m 3/2) (/.f64 (pow.f64 m 3/2) v))
	12.5b	(/.f64 (pow.f64 m 2) v)
✓	15.9b	(/.f64 (pow.f64 m 3/2) v)

series60.0ms (1.5%)

Counts

3 → 52

Calls

3 calls:

22.0ms

(-.f64 (+.f64 (*.f64 (pow.f64 m 3/2) (/.f64 (pow.f64 m 3/2) v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))

21.0ms

(/.f64 (pow.f64 m 3/2) v)

16.0ms

(*.f64 (pow.f64 m 3/2) (/.f64 (pow.f64 m 3/2) v))

rewrite45.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
34×	`add-exp-log_binary64`

Counts

3 → 161

Calls

3 calls:

17.0ms

(-.f64 (+.f64 (*.f64 (pow.f64 m 3/2) (/.f64 (pow.f64 m 3/2) v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))

9.0ms

(*.f64 (pow.f64 m 3/2) (/.f64 (pow.f64 m 3/2) v))

3.0ms

(/.f64 (pow.f64 m 3/2) v)

simplify217.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

858×	`times-frac_binary64`
301×	`associate-l_binary64`
265×	`fma-neg_binary64`
261×	`associate-r_binary64`
224×	`distribute-rgt-in_binary64`

Counts

213 → 236

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	5289
1	871	4838
2	3617	4696
3	5198	4696

prune369.0ms (9.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	311	0	311
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	311	4	315

Error

Counts

315 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
	30.6b	(.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))) (sqrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))))
✓	0.1b	(-.f64 (+.f64 (.f64 (pow.f64 m 3/2) (/.f64 (pow.f64 m 3/2) v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))
▶	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 12154 to 7121 computations (41.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series20.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
8.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
6×	`associate-l_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 37

Calls

2 calls:

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

simplify57.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

589×	`associate-+l+_binary64`
277×	`associate-*l/_binary64`
237×	`distribute-rgt-in_binary64`
226×	`associate-*r/_binary64`
226×	`distribute-lft-in_binary64`

Counts

85 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	1617
1	188	1453
2	578	1407
3	1862	1343
4	5062	1343

prune72.0ms (1.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	79	4	83

Error

Counts

83 → 4

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
	30.6b	(.f64 (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))) (sqrt.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))))
✓	0.1b	(-.f64 (+.f64 (.f64 (pow.f64 m 3/2) (/.f64 (pow.f64 m 3/2) v)) (+.f64 (/.f64 m v) m)) (+.f64 1 (.f64 2 (/.f64 (pow.f64 m 2) v))))
✓	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

Compiler

Compiled 1449 to 966 computations (33.3% saved)

regimes660.0ms (16.6%)

Accuracy

Total 0.1b remaining (89.3%)

Threshold costs 0.1b (89.3%)

Counts

204 → 1

Compiler

Compiled 12648 to 8922 computations (29.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`*-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	17	34
1	26	34
2	34	34
3	46	34
4	53	34
5	58	34
6	61	34
7	62	34
8	59	34

end1.0ms (0%)

Compiler: Compiled 25 to 18 computations (28% saved)

sample878.0ms (22.1%)

Algorithm

1×

intervals

Results

348.0ms	8000×	body	128	valid
166.0ms	8060×	pre	128	true
3.0ms	60×	body	128	invalid

Compiler

Compiled 148 to 107 computations (27.7% saved)

Details

analyze62.0ms (1.6%)

sample141.0ms (3.6%)

simplify122.0ms (3.1%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series34.0ms (0.9%)

rewrite94.0ms (2.4%)

simplify135.0ms (3.4%)

prune297.0ms (7.5%)

localize12.0ms (0.3%)

series56.0ms (1.4%)

rewrite67.0ms (1.7%)

simplify165.0ms (4.2%)

prune359.0ms (9%)

localize17.0ms (0.4%)

series60.0ms (1.5%)

rewrite45.0ms (1.1%)

simplify217.0ms (5.5%)

prune369.0ms (9.3%)

localize6.0ms (0.2%)

series20.0ms (0.5%)

rewrite7.0ms (0.2%)

simplify57.0ms (1.4%)

prune72.0ms (1.8%)

regimes660.0ms (16.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample878.0ms (22.1%)

Profiling