Details

analyze89.0ms (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)

sample147.0ms (3.4%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 43 to 32 computations (25.6% saved)

simplify122.0ms (2.9%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

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

series36.0ms (0.9%)

Counts

4 → 80

Calls

4 calls:

14.0ms	(.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))

rewrite91.0ms (2.1%)

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:

57.0ms	(.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))

simplify140.0ms (3.3%)

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 → 294

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	4962
1	502	4321
2	2059	4004
3	4566	3999
4	5030	3999

prune300.0ms (7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	291	3	294
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	292	4	296

Error

Counts

296 → 4

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	27.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) (-.f64 1 m)) v)
▶	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
	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))))

Compiler

Compiled 7185 to 4590 computations (36.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series43.0ms (1%)

Counts

4 → 84

Calls

4 calls:

14.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
10.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
10.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
9.0ms	(/.f64 v (-.f64 1 m))

rewrite149.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

684×	`times-frac_binary64`
597×	`add-sqr-sqrt_binary64`
563×	`*-un-lft-identity_binary64`
394×	`add-cube-cbrt_binary64`
249×	`prod-diff_binary64`

Counts

4 → 563

Calls

4 calls:

28.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
28.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
7.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
4.0ms	(/.f64 v (-.f64 1 m))

simplify456.0ms (10.7%)

Algorithm

1×	egg-herbie

Rules

425×	`fma-neg_binary64`
233×	`associate-/l*_binary64`
232×	`*-commutative_binary64`
213×	`associate-l_binary64`
213×	`associate-*l/_binary64`

Counts

647 → 768

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	422	14395
1	945	13545
2	3863	13035
3	4614	13035
4	4996	13035
5	4935	13035

prune765.0ms (17.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	768	0	768
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	768	4	772

Error

Counts

772 → 4

Alt Table

Status	Error	Program
	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	27.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) (-.f64 1 m)) v)
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
▶	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))))

Compiler

Compiled 23018 to 15390 computations (33.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))))
✓	0.0b	(+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m))
✓	8.0b	(/.f64 (pow.f64 m 3) v)
✓	12.9b	(/.f64 (pow.f64 m 2) v)

series57.0ms (1.3%)

Counts

4 → 18

Calls

4 calls:

17.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
14.0ms	(+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m))
14.0ms	(/.f64 (pow.f64 m 3) v)
11.0ms	(/.f64 (pow.f64 m 2) v)

rewrite67.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64`
96×	`times-frac_binary64`
80×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
40×	`fma-def_binary64`

Counts

4 → 232

Calls

4 calls:

23.0ms	(-.f64 (+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m)) (+.f64 1 (*.f64 2 (/.f64 (pow.f64 m 2) v))))
18.0ms	(+.f64 (/.f64 (pow.f64 m 3) v) (+.f64 (/.f64 m v) m))
4.0ms	(/.f64 (pow.f64 m 3) v)
3.0ms	(/.f64 (pow.f64 m 2) v)

simplify160.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-neg_binary64`
446×	`unswap-sqr_binary64`
229×	`distribute-rgt-in_binary64`
220×	`associate-l_binary64`
219×	`associate-r_binary64`

Counts

250 → 295

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	325	6358
1	813	4815
2	3493	4538
3	4468	4536
4	4986	4536

prune288.0ms (6.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	295	0	295
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	295	4	299

Error

Counts

299 → 4

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	27.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) (-.f64 1 m)) v)
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
✓	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))))

Compiler

Compiled 10368 to 5632 computations (45.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series26.0ms (0.6%)

Counts

3 → 64

Calls

3 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)
6.0ms	(/.f64 (-.f64 1 m) v)

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

3 → 81

Calls

3 calls:

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

simplify85.0ms (2%)

Algorithm

1×	egg-herbie

Rules

426×	`fma-neg_binary64`
388×	`associate-l_binary64`
380×	`div-sub_binary64`
323×	`associate-r_binary64`
319×	`distribute-rgt-in_binary64`

Counts

145 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2355
1	323	2151
2	936	2109
3	3601	2109
4	5118	2109

prune98.0ms (2.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	131	4	135

Error

Counts

135 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	27.7b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) (-.f64 1 m)) v)
✓	0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
✓	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))))

Compiler

Compiled 2406 to 1591 computations (33.9% saved)

regimes195.0ms (4.6%)

Accuracy

Total 0.1b remaining (85.3%)

Threshold costs 0.1b (85.3%)

Counts

73 → 1

Compiler

Compiled 3657 to 2574 computations (29.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	17	19
2	21	19
3	23	19
4	24	19
5	22	19

end0.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

sample904.0ms (21.2%)

Algorithm

1×

intervals

Results

389.0ms	8000×	body	128	valid
178.0ms	8052×	pre	128	true
2.0ms	52×	body	128	invalid

Compiler

Compiled 108 to 78 computations (27.8% saved)

Details

analyze89.0ms (2.1%)

sample147.0ms (3.4%)

simplify122.0ms (2.9%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series36.0ms (0.9%)

rewrite91.0ms (2.1%)

simplify140.0ms (3.3%)

prune300.0ms (7%)

localize7.0ms (0.2%)

series43.0ms (1%)

rewrite149.0ms (3.5%)

simplify456.0ms (10.7%)

prune765.0ms (17.9%)

localize12.0ms (0.3%)

series57.0ms (1.3%)

rewrite67.0ms (1.6%)

simplify160.0ms (3.7%)

prune288.0ms (6.8%)

localize6.0ms (0.1%)

series26.0ms (0.6%)

rewrite15.0ms (0.4%)

simplify85.0ms (2%)

prune98.0ms (2.3%)

regimes195.0ms (4.6%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample904.0ms (21.2%)

Profiling