Details

analyze263.0ms (8.1%)

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 23 to 18 computations (21.7% saved)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
6.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify262.0ms (8.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5013	19

prune4.0ms (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)

localize8.0ms (0.3%)

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))

rewrite50.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
12×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-l_binary64`
9×	`add-cube-cbrt_binary64`
8×	`flip3--_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` `distribute-lft-in_binary64` `distribute-rgt-in_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 → 83

Calls

3 calls:

19.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
8.0ms	(*.f64 m (-.f64 1 m))

series174.0ms (5.3%)

Counts

3 → 9

Calls

3 calls:

66.0ms	(*.f64 m (-.f64 1 m))
58.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
50.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify58.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4959	1544
1	4959	1544

prune125.0ms (3.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 0b

Counts

93 → 6

Compiler

Compiled 1908 to 1330 computations (30.3% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 m (+.f64 m -1))
0.0b	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
0.1b	(/.f64 (*.f64 m (-.f64 1 m)) v)
0.2b	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))

rewrite64.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64` `add-log-exp_binary64`
8×	`cbrt-undiv_binary64` `div-exp_binary64`
7×	`distribute-lft-out_binary64`
6×	`pow1_binary64` `associate-*r/_binary64` `sum-log_binary64`
5×	`flip3-+_binary64` `associate-r_binary64` `flip-+_binary64`
4×	`associate-/l/_binary64` `cbrt-unprod_binary64` `frac-add_binary64` `prod-exp_binary64` `div-inv_binary64`
3×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64`
2×	`diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `associate-+l-_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `difference-of-sqr--1_binary64` `+-commutative_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

4 → 120

Calls

4 calls:

24.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
10.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
7.0ms	(*.f64 m (+.f64 m -1))

series217.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(*.f64 m (+.f64 m -1))
57.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
51.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
49.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify72.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4958	2717
1	4958	2717

prune159.0ms (4.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	132	6	138

Merged error: 0b

Counts

138 → 6

Compiler

Compiled 3740 to 2125 computations (43.2% saved)

localize11.0ms (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)))

rewrite76.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`frac-times_binary64`
30×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`flip3--_binary64` `flip--_binary64`
20×	`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` `associate-l_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` `sqrt-prod_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×	`difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 134

Calls

4 calls:

27.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
18.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
8.0ms	(*.f64 m (-.f64 1 m))

series254.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
72.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
56.0ms	(*.f64 m (-.f64 1 m))
46.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify81.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5543	3809

prune212.0ms (6.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	146	6	152

Merged error: 0b

Counts

152 → 6

Compiler

Compiled 4221 to 2767 computations (34.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 1 m) v)
0.1b	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) (-.f64 1 m))
0.3b	(*.f64 m (/.f64 (-.f64 1 m) v))

rewrite45.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
28×	`associate-r_binary64`
27×	`add-cube-cbrt_binary64`
16×	`difference-of-squares_binary64`
12×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`distribute-lft-out--_binary64`
7×	`pow1_binary64` `flip3--_binary64` `flip--_binary64`
6×	`associate-l_binary64` `associate-/l*_binary64`
4×	`frac-times_binary64`
3×	`associate-/r_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

3 → 114

Calls

3 calls:

16.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) (-.f64 1 m))
12.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
7.0ms	(/.f64 (-.f64 1 m) v)

series143.0ms (4.4%)

Counts

3 → 9

Calls

3 calls:

51.0ms	(*.f64 m (/.f64 (-.f64 1 m) v))
46.0ms	(/.f64 (-.f64 1 m) v)
45.0ms	(.f64 (-.f64 (.f64 m (/.f64 (-.f64 1 m) v)) 1) (-.f64 1 m))

simplify41.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4985	2081
1	4985	2081

prune120.0ms (3.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	123	6	129

Merged error: 0b

Counts

129 → 6

Compiler

Compiled 2501 to 1667 computations (33.3% saved)

regimes34.0ms (1%)

Compiler: Compiled 230 to 190 computations (17.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	31
1	31	31

end0.0ms (0%)

sample738.0ms (22.7%)

Algorithm

1×

intervals

Results

279.0ms	8000×	body	128	valid
158.0ms	8051×	pre	128	true
2.0ms	51×	body	128	invalid

Compiler

Compiled 157 to 126 computations (19.7% saved)

Details

analyze263.0ms (8.1%)

sample24.0ms (0.7%)

simplify262.0ms (8.1%)

prune4.0ms (0.1%)

localize8.0ms (0.3%)

rewrite50.0ms (1.5%)

series174.0ms (5.3%)

simplify58.0ms (1.8%)

prune125.0ms (3.8%)

localize13.0ms (0.4%)

rewrite64.0ms (2%)

series217.0ms (6.7%)

simplify72.0ms (2.2%)

prune159.0ms (4.9%)

localize11.0ms (0.3%)

rewrite76.0ms (2.3%)

series254.0ms (7.8%)

simplify81.0ms (2.5%)

prune212.0ms (6.5%)

localize7.0ms (0.2%)

rewrite45.0ms (1.4%)

series143.0ms (4.4%)

simplify41.0ms (1.3%)

prune120.0ms (3.7%)

regimes34.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample738.0ms (22.7%)

Profiling