Details

analyze432.0ms (5.7%)

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 23 to 18 computations (21.7% saved)

sample48.0ms (0.6%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
11.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify357.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	4924	19
1	4924	19

prune7.0ms (0.1%)

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

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

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) (-.f64 1 m))

rewrite80.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 95

Calls

3 calls:

35.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
14.0ms	(*.f64 m (-.f64 1 m))
14.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series176.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

60.0ms	(*.f64 m (-.f64 1 m))
59.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
56.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))

simplify127.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5029	1776

prune254.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Merged error: 0.0b

Counts

105 → 7

Compiler

Compiled 2168 to 1478 computations (31.8% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite145.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

171×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
139×	`*-un-lft-identity_binary64`
83×	`add-cube-cbrt_binary64`
40×	`difference-of-squares_binary64`
30×	`associate-/r*_binary64`
18×	`distribute-lft-out--_binary64`
13×	`associate-l_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
6×	`associate-r_binary64` `cancel-sign-sub-inv_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-exp_binary64` `frac-times_binary64`
3×	`add-log-exp_binary64` `difference-of-sqr-1_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` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

3 → 202

Calls

3 calls:

77.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
21.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
10.0ms	(/.f64 v (-.f64 1 m))

series138.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

51.0ms	(/.f64 v (-.f64 1 m))
48.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
38.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))

simplify194.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4973	4468
1	4973	4468

prune419.0ms (5.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	211	7	218

Merged error: 0.0b

Counts

218 → 7

Compiler

Compiled 4819 to 2979 computations (38.2% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite155.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

47.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
35.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
16.0ms	(*.f64 m (-.f64 1 m))
16.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series253.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
65.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
61.0ms	(*.f64 m (-.f64 1 m))
47.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify176.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5030	4454

prune410.0ms (5.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	164	7	171

Merged error: 0b

Counts

171 → 7

Compiler

Compiled 4818 to 3039 computations (36.9% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.1b	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)))
0.1b	(.f64 (+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))

rewrite164.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
25×	`flip3--_binary64` `flip--_binary64`
24×	`-un-lft-identity_binary64` `associate-l/_binary64`
16×	`frac-add_binary64` `add-cube-cbrt_binary64`
15×	`associate-r_binary64` `cancel-sign-sub-inv_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
12×	`frac-times_binary64`
10×	`associate-l_binary64`
9×	`add-log-exp_binary64`
8×	`pow1_binary64`
7×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
6×	`difference-of-squares_binary64`
4×	`flip3-+_binary64` `associate-*r/_binary64` `associate-+l+_binary64` `flip-+_binary64`
3×	`associate-/r*_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `difference-of-sqr-1_binary64` `associate-+l-_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64`

Counts

4 → 130

Calls

4 calls:

46.0ms	(.f64 (+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
30.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)))
27.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
20.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series400.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(.f64 (+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
120.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)))
76.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m))
34.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify213.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4979	5300
1	4979	5300

prune461.0ms (6.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	142	7	149

Merged error: 0b

Counts

149 → 7

Compiler

Compiled 5496 to 3566 computations (35.1% saved)

regimes357.0ms (4.7%)

Compiler: Compiled 2448 to 1938 computations (20.8% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	47	19
1	47	19

end0.0ms (0%)

sample2.5s (33.2%)

Algorithm

1×

intervals

Results

534.0ms	8000×	body	128	valid
309.0ms	8058×	pre	128	true
4.0ms	58×	body	128	invalid

Compiler

Compiled 842 to 666 computations (20.9% saved)

Details

analyze432.0ms (5.7%)

sample48.0ms (0.6%)

simplify357.0ms (4.7%)

prune7.0ms (0.1%)

localize16.0ms (0.2%)

rewrite80.0ms (1.1%)

series176.0ms (2.3%)

simplify127.0ms (1.7%)

prune254.0ms (3.4%)

localize15.0ms (0.2%)

rewrite145.0ms (1.9%)

series138.0ms (1.8%)

simplify194.0ms (2.6%)

prune419.0ms (5.5%)

localize25.0ms (0.3%)

rewrite155.0ms (2.1%)

series253.0ms (3.3%)

simplify176.0ms (2.3%)

prune410.0ms (5.4%)

localize25.0ms (0.3%)

rewrite164.0ms (2.2%)

series400.0ms (5.3%)

simplify213.0ms (2.8%)

prune461.0ms (6.1%)

regimes357.0ms (4.7%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.5s (33.2%)

Profiling