Details

analyze267.0ms (6.7%)

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)

sample26.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
6.0ms	261×	pre	128	true
0.0ms	5×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify273.0ms (6.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4905	19
1	4905	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)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 64

Calls

2 calls:

22.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series121.0ms (3%)

Counts

2 → 6

Calls

2 calls:

66.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
55.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify38.0ms (1%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5018	1486

prune98.0ms (2.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	5	71

Merged error: 0b

Counts

71 → 5

Compiler

Compiled 1551 to 1051 computations (32.2% saved)

localize7.0ms (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))

rewrite96.0ms (2.4%)

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:

50.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
12.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
7.0ms	(/.f64 v (-.f64 1 m))

series157.0ms (4%)

Counts

3 → 9

Calls

3 calls:

56.0ms	(/.f64 v (-.f64 1 m))
52.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
49.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))

simplify92.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4954	4468
1	4954	4468

prune241.0ms (6.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	211	5	216

Merged error: 0b

Counts

216 → 5

Compiler

Compiled 4763 to 2936 computations (38.4% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite96.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
18×	`add-log-exp_binary64`
16×	`associate-/r*_binary64`
8×	`cbrt-undiv_binary64` `div-exp_binary64`
7×	`distribute-lft-out_binary64` `sum-log_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-/l/_binary64` `pow1_binary64` `associate-*r/_binary64` `frac-add_binary64` `associate-+l+_binary64` `div-inv_binary64`
3×	`flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `cancel-sign-sub-inv_binary64` `prod-exp_binary64` `flip--_binary64`
2×	`diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64`
1×	`sub-neg_binary64` `distribute-rgt-out_binary64` `distribute-rgt1-in_binary64` `associate-+l-_binary64` `associate-+r+_binary64`

Counts

4 → 113

Calls

4 calls:

25.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
11.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
10.0ms	(+.f64 m (/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m)))
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series196.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
53.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
49.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
36.0ms	(+.f64 m (/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m)))

simplify58.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5018	2918

prune143.0ms (3.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	125	5	130

Merged error: 0b

Counts

130 → 5

Compiler

Compiled 3578 to 2006 computations (43.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 1 (sqrt.f64 m))
0.0b	(/.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)))

rewrite82.0ms (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`
18×	`cancel-sign-sub-inv_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `associate-*l/_binary64`
15×	`add-cube-cbrt_binary64`
14×	`associate-r_binary64`
12×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
11×	`pow1_binary64`
10×	`difference-of-squares_binary64`
8×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64`
4×	`pow-prod-down_binary64`
3×	`associate-/r*_binary64` `sub-neg_binary64` `times-frac_binary64`
2×	`associate-/l/_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 144

Calls

4 calls:

29.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
19.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
9.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
5.0ms	(-.f64 1 (sqrt.f64 m))

series237.0ms (6%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
76.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
47.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
29.0ms	(-.f64 1 (sqrt.f64 m))

simplify88.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5084	4440

prune230.0ms (5.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	156	5	161

Merged error: 0b

Counts

161 → 5

Compiler

Compiled 4512 to 2873 computations (36.3% saved)

regimes161.0ms (4.1%)

Compiler: Compiled 1920 to 1503 computations (21.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19

end0.0ms (0%)

sample1.2s (29.6%)

Algorithm

1×

intervals

Results

294.0ms	8000×	body	128	valid
171.0ms	8065×	pre	128	true
2.0ms	65×	body	128	invalid

Compiler

Compiled 666 to 522 computations (21.6% saved)

Details

analyze267.0ms (6.7%)

sample26.0ms (0.7%)

simplify273.0ms (6.9%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite39.0ms (1%)

series121.0ms (3%)

simplify38.0ms (1%)

prune98.0ms (2.5%)

localize7.0ms (0.2%)

rewrite96.0ms (2.4%)

series157.0ms (4%)

simplify92.0ms (2.3%)

prune241.0ms (6.1%)

localize16.0ms (0.4%)

rewrite96.0ms (2.4%)

series196.0ms (4.9%)

simplify58.0ms (1.5%)

prune143.0ms (3.6%)

localize12.0ms (0.3%)

rewrite82.0ms (2.1%)

series237.0ms (6%)

simplify88.0ms (2.2%)

prune230.0ms (5.8%)

regimes161.0ms (4.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (29.6%)

Profiling