Details

analyze252.0ms (5.2%)

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)

sample25.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	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)

simplify195.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4924	19
1	4924	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 4 expressions with local error:

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

rewrite52.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

18.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
9.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)
7.0ms	(*.f64 m (-.f64 1 m))
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

series115.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (-.f64 1 m))
33.0ms	(*.f64 m (-.f64 1 m))
26.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
15.0ms	(-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1)

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5061	2142

prune146.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	6	126

Merged error: 0b

Counts

126 → 6

Compiler

Compiled 2533 to 1736 computations (31.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite72.0ms (1.5%)

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:

22.0ms	(.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)
7.0ms	(*.f64 m (-.f64 1 m))

series137.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m)))
40.0ms	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (+.f64 1 (sqrt.f64 m))) (-.f64 1 (sqrt.f64 m)))
31.0ms	(*.f64 m (-.f64 1 m))
22.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)

simplify92.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5030	4454

prune224.0ms (4.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	164	6	170

Merged error: 0b

Counts

170 → 6

Compiler

Compiled 4770 to 3003 computations (37% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite67.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
48×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
34×	`add-exp-log_binary64`
32×	`add-cube-cbrt_binary64`
22×	`add-cbrt-cube_binary64`
17×	`associate-l_binary64`
14×	`associate-*r/_binary64` `div-exp_binary64`
12×	`flip3--_binary64` `associate-r_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
11×	`associate-/r/_binary64`
10×	`associate-/r*_binary64` `difference-of-squares_binary64`
9×	`pow1_binary64`
8×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
7×	`cbrt-undiv_binary64` `div-inv_binary64`
6×	`prod-exp_binary64` `associate-/l*_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `distribute-lft-out--_binary64` `frac-times_binary64`
3×	`1-exp_binary64` `difference-of-sqr-1_binary64` `rec-exp_binary64`
2×	`pow-prod-down_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 166

Calls

4 calls:

29.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) (-.f64 1 m))
9.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))
8.0ms	(*.f64 m (-.f64 1 m))
7.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))

series124.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))
33.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))
28.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) (-.f64 1 m))
25.0ms	(*.f64 m (-.f64 1 m))

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5030	3065

prune193.0ms (4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	179	5	184

Merged error: 0b

Counts

184 → 5

Compiler

Compiled 3741 to 2638 computations (29.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite314.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Rules

993×	`times-frac_binary64`
694×	`add-sqr-sqrt_binary64`
620×	`*-un-lft-identity_binary64`
381×	`add-cube-cbrt_binary64`
162×	`difference-of-squares_binary64`
90×	`associate-/r*_binary64`
71×	`distribute-lft-out--_binary64`
39×	`div-inv_binary64`
32×	`add-exp-log_binary64`
26×	`associate-l_binary64`
20×	`add-cbrt-cube_binary64`
18×	`div-exp_binary64`
16×	`associate-/l*_binary64`
14×	`difference-of-sqr-1_binary64`
12×	`flip3--_binary64` `flip--_binary64`
11×	`associate-/r/_binary64`
9×	`cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
4×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64`
2×	`associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `inv-pow_binary64` `prod-exp_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 575

Calls

4 calls:

101.0ms	(*.f64 (-.f64 (/.f64 1 (/.f64 (/.f64 v m) (-.f64 1 m))) 1) (-.f64 1 m))
92.0ms	(-.f64 (/.f64 1 (/.f64 (/.f64 v m) (-.f64 1 m))) 1)
22.0ms	(/.f64 1 (/.f64 (/.f64 v m) (-.f64 1 m)))
9.0ms	(/.f64 (/.f64 v m) (-.f64 1 m))

series116.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(/.f64 1 (/.f64 (/.f64 v m) (-.f64 1 m)))
28.0ms	(*.f64 (-.f64 (/.f64 1 (/.f64 (/.f64 v m) (-.f64 1 m))) 1) (-.f64 1 m))
28.0ms	(/.f64 (/.f64 v m) (-.f64 1 m))
22.0ms	(-.f64 (/.f64 1 (/.f64 (/.f64 v m) (-.f64 1 m))) 1)

simplify180.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

587 → 587

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5028	14895

prune949.0ms (19.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	587	0	587
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	587	5	592

Merged error: 0b

Counts

592 → 5

Compiler

Compiled 14907 to 8616 computations (42.2% saved)

regimes165.0ms (3.4%)

Compiler: Compiled 2112 to 1668 computations (21% saved)

bsearch0.0ms (0%)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	187	31
1	187	31

end0.0ms (0%)

sample1.2s (25.4%)

Algorithm

1×

intervals

Results

298.0ms	8000×	body	128	valid
171.0ms	8057×	pre	128	true
2.0ms	57×	body	128	invalid

Compiler

Compiled 738 to 582 computations (21.1% saved)

Details

analyze252.0ms (5.2%)

sample25.0ms (0.5%)

simplify195.0ms (4%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite52.0ms (1.1%)

series115.0ms (2.4%)

simplify69.0ms (1.4%)

prune146.0ms (3%)

localize12.0ms (0.2%)

rewrite72.0ms (1.5%)

series137.0ms (2.8%)

simplify92.0ms (1.9%)

prune224.0ms (4.6%)

localize9.0ms (0.2%)

rewrite67.0ms (1.4%)

series124.0ms (2.6%)

simplify77.0ms (1.6%)

prune193.0ms (4%)

localize10.0ms (0.2%)

rewrite314.0ms (6.5%)

series116.0ms (2.4%)

simplify180.0ms (3.7%)

prune949.0ms (19.6%)

regimes165.0ms (3.4%)

bsearch0.0ms (0%)

simplify9.0ms (0.2%)

end0.0ms (0%)

sample1.2s (25.4%)

Profiling