Details

analyze255.0ms (7.2%)

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

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	259×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify267.0ms (7.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

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: 0.0b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite56.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 82

Calls

3 calls:

19.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
18.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
11.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series138.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

62.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
46.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
30.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify41.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5055	1861

prune184.0ms (5.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	86	6	92

Merged error: 0b

Counts

92 → 6

Compiler

Compiled 3321 to 2415 computations (27.3% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite126.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 226

Calls

4 calls:

45.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
34.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)
11.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
6.0ms	(/.f64 v (-.f64 1 m))

series186.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(/.f64 v (-.f64 1 m))
49.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) (-.f64 1 m))
46.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
29.0ms	(-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1)

simplify94.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4954	5059
1	4954	5059

prune271.0ms (7.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	238	6	244

Merged error: 0b

Counts

244 → 6

Compiler

Compiled 5334 to 3313 computations (37.9% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite63.0ms (1.8%)

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:

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 m -1)) (/.f64 v m))
9.0ms	(+.f64 m (/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m)))
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series192.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(+.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 m (/.f64 (.f64 m (+.f64 m -1)) (/.f64 v m))))
50.0ms	(/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m))
50.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
38.0ms	(+.f64 m (/.f64 (*.f64 m (+.f64 m -1)) (/.f64 v m)))

simplify56.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5018	2918

prune141.0ms (4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	125	6	131

Merged error: 0b

Counts

131 → 6

Compiler

Compiled 3576 to 2004 computations (44% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

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 (*.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)))

rewrite83.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 139

Calls

4 calls:

28.0ms	(.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)))
11.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
8.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series237.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
78.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
44.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
27.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify87.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5020	4520

prune226.0ms (6.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	151	6	157

Merged error: 0b

Counts

157 → 6

Compiler

Compiled 4547 to 2920 computations (35.8% saved)

regimes47.0ms (1.3%)

Compiler: Compiled 360 to 294 computations (18.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	19
1	31	19

end0.0ms (0%)

sample732.0ms (20.6%)

Algorithm

1×

intervals

Results

275.0ms	8000×	body	128	valid
163.0ms	8064×	pre	128	true
2.0ms	64×	body	128	invalid

Compiler

Compiled 146 to 119 computations (18.5% saved)

Details

analyze255.0ms (7.2%)

sample24.0ms (0.7%)

simplify267.0ms (7.5%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite56.0ms (1.6%)

series138.0ms (3.9%)

simplify41.0ms (1.2%)

prune184.0ms (5.2%)

localize7.0ms (0.2%)

rewrite126.0ms (3.5%)

series186.0ms (5.2%)

simplify94.0ms (2.6%)

prune271.0ms (7.6%)

localize16.0ms (0.4%)

rewrite63.0ms (1.8%)

series192.0ms (5.4%)

simplify56.0ms (1.6%)

prune141.0ms (4%)

localize12.0ms (0.3%)

rewrite83.0ms (2.3%)

series237.0ms (6.7%)

simplify87.0ms (2.4%)

prune226.0ms (6.4%)

regimes47.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample732.0ms (20.6%)

Profiling