Details

analyze57.0ms (2.2%)

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

sample26.0ms (1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
5.0ms	257×	pre	80	true
0.0ms	1×	body	80	invalid

simplify531.0ms (20.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4963	13
1	4963	13

prune7.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.1b

Counts

2 → 1

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 m (-.f64 1.0 m))
0.1b	(/.f64 (*.f64 m (-.f64 1.0 m)) v)
0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1.0 m)) v) 1.0) (-.f64 1.0 m))

rewrite36.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-r_binary64`
9×	`add-cube-cbrt_binary64`
8×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64`
7×	`pow1_binary64`
6×	`associate-*r/_binary64`
4×	`sub-neg_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

3 → 79

Calls

3 calls:

18.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1.0 m)) v) 1.0) (-.f64 1.0 m))
8.0ms	(/.f64 (*.f64 m (-.f64 1.0 m)) v)
7.0ms	(*.f64 m (-.f64 1.0 m))

series46.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

33.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1.0 m)) v) 1.0) (-.f64 1.0 m))
7.0ms	(/.f64 (*.f64 m (-.f64 1.0 m)) v)
6.0ms	(*.f64 m (-.f64 1.0 m))

simplify28.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5256	1059

prune150.0ms (5.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Merged error: 0b

Counts

89 → 7

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 v (-.f64 1.0 m))
0.1b	(/.f64 m (/.f64 v (-.f64 1.0 m)))
0.1b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1.0 m))) 1.0) (-.f64 1.0 m))

rewrite60.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary64`
118×	`add-sqr-sqrt_binary64`
109×	`*-un-lft-identity_binary64`
73×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`
20×	`difference-of-squares_binary64`
18×	`distribute-lft-out--_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
7×	`associate-l_binary64`
6×	`associate-/l*_binary64` `div-inv_binary64`
5×	`pow1_binary64` `associate-r_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`add-log-exp_binary64`
2×	`sub-neg_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

3 → 173

Calls

3 calls:

37.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1.0 m))) 1.0) (-.f64 1.0 m))
9.0ms	(/.f64 m (/.f64 v (-.f64 1.0 m)))
6.0ms	(/.f64 v (-.f64 1.0 m))

series23.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1.0 m))) 1.0) (-.f64 1.0 m))
7.0ms	(/.f64 v (-.f64 1.0 m))
7.0ms	(/.f64 m (/.f64 v (-.f64 1.0 m)))

simplify57.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4981	2579
1	4981	2579

prune237.0ms (9.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	183	6	189

Merged error: 0b

Counts

189 → 6

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (/.f64 m v) (-.f64 1.0 m))
0.1b	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1.0 m)) 1.0) (-.f64 1.0 m))

rewrite29.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
16×	`-un-lft-identity_binary64` `associate-l*_binary64`
12×	`add-cube-cbrt_binary64`
10×	`associate-r_binary64` `times-frac_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`flip3--_binary64` `flip--_binary64`
6×	`pow1_binary64` `frac-times_binary64`
4×	`sub-neg_binary64` `associate-*r/_binary64`
3×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-*l/_binary64`
2×	`pow-prod-down_binary64` `add-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 70

Calls

2 calls:

17.0ms	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1.0 m)) 1.0) (-.f64 1.0 m))
10.0ms	(*.f64 (/.f64 m v) (-.f64 1.0 m))

series15.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

8.0ms	(.f64 (-.f64 (.f64 (/.f64 m v) (-.f64 1.0 m)) 1.0) (-.f64 1.0 m))
7.0ms	(*.f64 (/.f64 m v) (-.f64 1.0 m))

simplify51.0ms (2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4982	1024
1	4982	1024

prune101.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	76	6	82

Merged error: 0b

Counts

82 → 6

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 m (-.f64 1.0 m))
0.1b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1.0 m)) v) 1.0) (+.f64 (sqrt.f64 1.0) (sqrt.f64 m)))
0.1b	(/.f64 (*.f64 m (-.f64 1.0 m)) v)
0.1b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1.0 m)) v) 1.0) (+.f64 (sqrt.f64 1.0) (sqrt.f64 m))) (-.f64 (sqrt.f64 1.0) (sqrt.f64 m)))

rewrite65.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`frac-times_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64` `flip3--_binary64` `flip--_binary64`
19×	`associate-r_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`associate-*l/_binary64`
14×	`associate-*r/_binary64`
13×	`pow1_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
11×	`add-cube-cbrt_binary64`
9×	`associate-l_binary64`
8×	`sqrt-prod_binary64`
6×	`cbrt-unprod_binary64` `prod-exp_binary64` `difference-of-squares_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `distribute-lft-out--_binary64`
3×	`associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64`
1×	`clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 131

Calls

4 calls:

25.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1.0 m)) v) 1.0) (+.f64 (sqrt.f64 1.0) (sqrt.f64 m))) (-.f64 (sqrt.f64 1.0) (sqrt.f64 m)))
18.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1.0 m)) v) 1.0) (+.f64 (sqrt.f64 1.0) (sqrt.f64 m)))
10.0ms	(/.f64 (*.f64 m (-.f64 1.0 m)) v)
7.0ms	(*.f64 m (-.f64 1.0 m))

series52.0ms (2%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1.0 m)) v) 1.0) (+.f64 (sqrt.f64 1.0) (sqrt.f64 m)))
19.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1.0 m)) v) 1.0) (+.f64 (sqrt.f64 1.0) (sqrt.f64 m))) (-.f64 (sqrt.f64 1.0) (sqrt.f64 m)))
7.0ms	(/.f64 (*.f64 m (-.f64 1.0 m)) v)
6.0ms	(*.f64 m (-.f64 1.0 m))

simplify70.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5067	2706

prune230.0ms (9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	143	6	149

Merged error: 0b

Counts

149 → 6

regimes96.0ms (3.7%)

Accuracy

Total 0.1b remaining (75.6%)

Threshold costs 0.1b (75.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	13
1	28	13

end0.0ms (0%)

sample558.0ms (21.8%)

Algorithm

1×

intervals

Results

271.0ms	8000×	body	80	valid
147.0ms	8070×	pre	80	true
2.0ms	70×	body	80	invalid

Details

analyze57.0ms (2.2%)

sample26.0ms (1%)

simplify531.0ms (20.7%)

prune7.0ms (0.3%)

localize9.0ms (0.3%)

rewrite36.0ms (1.4%)

series46.0ms (1.8%)

simplify28.0ms (1.1%)

prune150.0ms (5.8%)

localize7.0ms (0.3%)

rewrite60.0ms (2.3%)

series23.0ms (0.9%)

simplify57.0ms (2.2%)

prune237.0ms (9.2%)

localize7.0ms (0.3%)

rewrite29.0ms (1.1%)

series15.0ms (0.6%)

simplify51.0ms (2%)

prune101.0ms (3.9%)

localize12.0ms (0.5%)

rewrite65.0ms (2.5%)

series52.0ms (2%)

simplify70.0ms (2.7%)

prune230.0ms (9%)

regimes96.0ms (3.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample558.0ms (21.8%)

Profiling