Details

analyze191.0ms (2.3%)

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)

sample35.0ms (0.4%)

Algorithm

1×

intervals

Results

17.0ms	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)

simplify140.0ms (1.7%)

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%)

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 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 (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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))

series33.0ms (0.4%)

Counts

3 → 68

Calls

3 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)

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
39×	`prod-diff_binary64`
37×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`

Counts

3 → 137

Calls

3 calls:

12.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
6.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify196.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

351×	`associate-/l/_binary64`
336×	`associate-/r*_binary64`
279×	`associate-+l+_binary64`
244×	`associate-/r/_binary64`
193×	`associate-l_binary64`

Counts

205 → 223

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	4112
1	462	3580
2	1832	3499
3	4716	3499
4	4995	3499
5	4924	3499

prune244.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	219	4	223
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	220	5	225

Error

0.0b

Counts

225 → 5

Alt Table

Status	Error	Program
	0.6b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 (pow.f64 1 3) (pow.f64 m 3))) (*.f64 v (+.f64 1 (fma.f64 m m m)))) 1) (-.f64 1 m))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	27.9b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) (-.f64 1 m)) v)
	0.4b	(.f64 (-.f64 (/.f64 (.f64 (/.f64 m (sqrt.f64 v)) (-.f64 1 m)) (sqrt.f64 v)) 1) (-.f64 1 m))
▶	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 (sqrt.f64 m) (sqrt.f64 m)))) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (.f64 (fma.f64 (neg.f64 (sqrt.f64 m)) (sqrt.f64 m) (.f64 (sqrt.f64 m) (sqrt.f64 m))) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))

Compiler

Compiled 5665 to 3735 computations (34.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.1b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 (sqrt.f64 m) (sqrt.f64 m)))) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
✓	0.6b	(*.f64 (sqrt.f64 m) (sqrt.f64 m))
✓	59.4b	(fma.f64 (neg.f64 (sqrt.f64 m)) (sqrt.f64 m) (*.f64 (sqrt.f64 m) (sqrt.f64 m)))

series152.0ms (1.8%)

Counts

3 → 34

Calls

3 calls:

125.0ms

(fma.f64 (neg.f64 (sqrt.f64 m)) (sqrt.f64 m) (*.f64 (sqrt.f64 m) (sqrt.f64 m)))

23.0ms

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

4.0ms

(*.f64 (sqrt.f64 m) (sqrt.f64 m))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64`
42×	`prod-diff_binary64`
41×	`add-cube-cbrt_binary64`
25×	`distribute-lft-in_binary64`

Counts

3 → 138

Calls

3 calls:

11.0ms

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

5.0ms

(*.f64 (sqrt.f64 m) (sqrt.f64 m))

0.0ms

(fma.f64 (neg.f64 (sqrt.f64 m)) (sqrt.f64 m) (*.f64 (sqrt.f64 m) (sqrt.f64 m)))

simplify117.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-neg_binary64`
346×	`distribute-rgt-in_binary64`
320×	`distribute-lft-in_binary64`
283×	`fma-def_binary64`
262×	`associate-/l*_binary64`

Counts

172 → 187

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	168	2626
1	318	2346
2	981	2247
3	3493	2235
4	4564	2235
5	4911	2235

prune527.0ms (6.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	334	3	337
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	337	5	342

Error

Counts

342 → 5

Alt Table

Status	Error	Program
	0.1b	(+.f64 (+.f64 (/.f64 (.f64 (-.f64 m (.f64 m m)) (-.f64 1 m)) v) (+.f64 m -1)) (.f64 (fma.f64 (neg.f64 (sqrt.f64 m)) (sqrt.f64 m) (.f64 (sqrt.f64 m) (sqrt.f64 m))) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)))
	0.2b	(*.f64 (-.f64 1 m) (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	0.2b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 (sqrt.f64 m) (sqrt.f64 m)))) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (.f64 (fma.f64 (neg.f64 (sqrt.f64 m)) (sqrt.f64 m) (.f64 (.f64 (cbrt.f64 (sqrt.f64 m)) (cbrt.f64 (sqrt.f64 m))) (.f64 (cbrt.f64 (sqrt.f64 m)) (sqrt.f64 m)))) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))
▶	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 (sqrt.f64 m) (sqrt.f64 m)))) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (.f64 (+.f64 (neg.f64 m) (.f64 (sqrt.f64 m) (sqrt.f64 m))) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 (sqrt.f64 m) (sqrt.f64 m)))) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (.f64 (fma.f64 (neg.f64 (sqrt.f64 m)) (sqrt.f64 m) (.f64 (sqrt.f64 m) (sqrt.f64 m))) (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)))

Compiler

Compiled 16848 to 8277 computations (50.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
	0.1b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 (sqrt.f64 m) (sqrt.f64 m)))) (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1))
	0.6b	(*.f64 (sqrt.f64 m) (sqrt.f64 m))
✓	25.1b	(+.f64 (neg.f64 m) (*.f64 (sqrt.f64 m) (sqrt.f64 m)))

series3.0ms (0%)

Counts

1 → 9

Calls

1 calls:

3.0ms

(+.f64 (neg.f64 m) (*.f64 (sqrt.f64 m) (sqrt.f64 m)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`fma-def_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`

Counts

1 → 27

Calls

1 calls:

4.0ms

(+.f64 (neg.f64 m) (*.f64 (sqrt.f64 m) (sqrt.f64 m)))

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Rules

681×	`fma-neg_binary64`
418×	`fma-def_binary64`
320×	`times-frac_binary64`
240×	`distribute-rgt-neg-in_binary64`
224×	`cancel-sign-sub-inv_binary64`

Counts

36 → 39

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	105
1	105	60
2	260	57
3	705	57
4	1426	57
5	2565	57
6	3861	57
7	4528	57
8	4589	57

prune632.0ms (7.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	355	1	356
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	357	4	361

Error

Counts

361 → 4

Alt Table

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

Compiler

Compiled 16542 to 8617 computations (47.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 m (/.f64 v (-.f64 1 m)))
✓	0.1b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 (sqrt.f64 m) (sqrt.f64 m)))) (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1))
	0.6b	(*.f64 (sqrt.f64 m) (sqrt.f64 m))
	25.1b	(+.f64 (neg.f64 m) (*.f64 (sqrt.f64 m) (sqrt.f64 m)))

series33.0ms (0.4%)

Counts

2 → 44

Calls

2 calls:

23.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 (sqrt.f64 m) (sqrt.f64 m)))) (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1))
10.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))

rewrite206.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

909×	`times-frac_binary64`
776×	`add-sqr-sqrt_binary64`
758×	`*-un-lft-identity_binary64`
555×	`add-cube-cbrt_binary64`
462×	`prod-diff_binary64`

Counts

2 → 618

Calls

2 calls:

36.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 (sqrt.f64 m) (sqrt.f64 m)))) (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1))
10.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))

simplify584.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

872×	`fma-def_binary64`
300×	`*-commutative_binary64`
259×	`associate-r_binary64`
250×	`associate-l_binary64`
201×	`associate-*l/_binary64`

Counts

662 → 700

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	23786
1	878	20578
2	3747	19950
3	4921	19950
4	4972	19950

prune1.4s (16.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	851	0	851
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	851	4	855

Error

Counts

855 → 4

Alt Table

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

Compiler

Compiled 52382 to 28938 computations (44.8% saved)

regimes1.8s (21.6%)

Accuracy

Total 0.1b remaining (81.1%)

Threshold costs 0.1b (81.1%)

Counts

276 → 1

Compiler

Compiled 27334 to 18733 computations (31.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	59
1	36	57
2	45	57
3	49	57
4	50	57
5	48	57

end1.0ms (0%)

Compiler: Compiled 39 to 24 computations (38.5% saved)

sample1.8s (21.8%)

Algorithm

1×

intervals

Results

738.0ms	8000×	body	128	valid
332.0ms	8063×	pre	128	true
6.0ms	63×	body	128	invalid

Compiler

Compiled 203 to 128 computations (36.9% saved)

Details

analyze191.0ms (2.3%)

sample35.0ms (0.4%)

simplify140.0ms (1.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series33.0ms (0.4%)

rewrite36.0ms (0.4%)

simplify196.0ms (2.4%)

prune244.0ms (3%)

localize17.0ms (0.2%)

series152.0ms (1.8%)

rewrite35.0ms (0.4%)

simplify117.0ms (1.4%)

prune527.0ms (6.4%)

localize16.0ms (0.2%)

series3.0ms (0%)

rewrite5.0ms (0.1%)

simplify82.0ms (1%)

prune632.0ms (7.7%)

localize19.0ms (0.2%)

series33.0ms (0.4%)

rewrite206.0ms (2.5%)

simplify584.0ms (7.1%)

prune1.4s (16.4%)

regimes1.8s (21.6%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.8s (21.8%)

Profiling