Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

sample26.0ms (1%)

Algorithm

1×

intervals

Results

8.0ms	56×	body	640	valid
5.0ms	128×	body	80	valid
3.0ms	19×	body	1280	valid
3.0ms	29×	body	320	valid
2.0ms	24×	body	160	valid

simplify67.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	880	15
1	880	15

prune4.0ms (0.2%)

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: 9.8b

Counts

2 → 1

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1.0 (+.f64 x 1.0))
0.0b	(-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x))
0.0b	(/.f64 1.0 (-.f64 x 1.0))
2.1b	(+.f64 (-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x)) (/.f64 1.0 (-.f64 x 1.0)))

rewrite66.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`*-un-lft-identity_binary64`
47×	`times-frac_binary64`
43×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
14×	`distribute-lft-out--_binary64`
13×	`distribute-lft-out_binary64`
11×	`add-log-exp_binary64`
9×	`associate-/r*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
6×	`associate-/l*_binary64`
4×	`pow1_binary64` `associate-/r/_binary64`
3×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64`

Counts

4 → 112

Calls

4 calls:

34.0ms	(+.f64 (-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x)) (/.f64 1.0 (-.f64 x 1.0)))
17.0ms	(-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x))
6.0ms	(/.f64 1.0 (-.f64 x 1.0))
5.0ms	(/.f64 1.0 (+.f64 x 1.0))

series24.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(+.f64 (-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x)) (/.f64 1.0 (-.f64 x 1.0)))
4.0ms	(-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x))
3.0ms	(/.f64 1.0 (+.f64 x 1.0))
3.0ms	(/.f64 1.0 (-.f64 x 1.0))

simplify52.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4954	1594
1	4954	1594

prune197.0ms (7.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	3	125

Merged error: 0.2b

Counts

125 → 3

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x))
0.2b	(/.f64 1.0 (-.f64 (.f64 x x) (.f64 1.0 1.0)))
6.7b	(+.f64 (-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x)) (.f64 (/.f64 1.0 (-.f64 (.f64 x x) (*.f64 1.0 1.0))) (+.f64 x 1.0)))
16.1b	(.f64 (/.f64 1.0 (-.f64 (.f64 x x) (*.f64 1.0 1.0))) (+.f64 x 1.0))

rewrite65.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
33×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
18×	`associate-l_binary64`
15×	`frac-add_binary64`
11×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`flip3--_binary64` `associate-*r/_binary64` `flip--_binary64` `frac-times_binary64`
6×	`pow1_binary64` `frac-sub_binary64`
4×	`associate-/r_binary64` `associate-r_binary64` `associate-/r/_binary64` `associate-l/_binary64`
3×	`associate-/l*_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `associate-+r+_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 127

Calls

4 calls:

23.0ms	(+.f64 (-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x)) (.f64 (/.f64 1.0 (-.f64 (.f64 x x) (*.f64 1.0 1.0))) (+.f64 x 1.0)))
17.0ms	(-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x))
13.0ms	(.f64 (/.f64 1.0 (-.f64 (.f64 x x) (*.f64 1.0 1.0))) (+.f64 x 1.0))
6.0ms	(/.f64 1.0 (-.f64 (.f64 x x) (.f64 1.0 1.0)))

series35.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(+.f64 (-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x)) (.f64 (/.f64 1.0 (-.f64 (.f64 x x) (*.f64 1.0 1.0))) (+.f64 x 1.0)))
5.0ms	(/.f64 1.0 (-.f64 (.f64 x x) (.f64 1.0 1.0)))
5.0ms	(.f64 (/.f64 1.0 (-.f64 (.f64 x x) (*.f64 1.0 1.0))) (+.f64 x 1.0))
4.0ms	(-.f64 (/.f64 1.0 (+.f64 x 1.0)) (/.f64 2.0 x))

simplify49.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5018	3165

prune266.0ms (10.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	138	4	142

Merged error: 0.1b

Counts

142 → 4

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 1.0 x) (.f64 (+.f64 1.0 x) 2.0))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1.0) (-.f64 (.f64 1.0 x) (.f64 (+.f64 1.0 x) 2.0))) (.f64 1.0 (.f64 x (+.f64 1.0 x)))) (.f64 (-.f64 x 1.0) (*.f64 x (+.f64 1.0 x))))
0.1b	(.f64 (-.f64 x 1.0) (.f64 x (+.f64 1.0 x)))
18.5b	(+.f64 (.f64 (-.f64 x 1.0) (-.f64 (.f64 1.0 x) (.f64 (+.f64 1.0 x) 2.0))) (.f64 1.0 (*.f64 x (+.f64 1.0 x))))

rewrite64.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`associate-*r/_binary64`
32×	`frac-add_binary64`
31×	`flip3--_binary64` `flip--_binary64`
24×	`flip3-+_binary64` `flip-+_binary64` `frac-times_binary64`
18×	`associate-/l/_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-*l/_binary64`
9×	`*-un-lft-identity_binary64` `pow1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64` `associate-/r/_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-unprod_binary64` `prod-exp_binary64`
5×	`associate-l_binary64`
4×	`associate-+r+_binary64`
3×	`pow-prod-down_binary64` `sub-neg_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`associate-+l+_binary64`
1×	`associate-/r_binary64` `diff-log_binary64` `associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 125

Calls

4 calls:

29.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1.0) (-.f64 (.f64 1.0 x) (.f64 (+.f64 1.0 x) 2.0))) (.f64 1.0 (.f64 x (+.f64 1.0 x)))) (.f64 (-.f64 x 1.0) (*.f64 x (+.f64 1.0 x))))
13.0ms	(+.f64 (.f64 (-.f64 x 1.0) (-.f64 (.f64 1.0 x) (.f64 (+.f64 1.0 x) 2.0))) (.f64 1.0 (*.f64 x (+.f64 1.0 x))))
10.0ms	(.f64 (-.f64 x 1.0) (.f64 x (+.f64 1.0 x)))
4.0ms	(-.f64 (.f64 1.0 x) (.f64 (+.f64 1.0 x) 2.0))

series26.0ms (1%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(.f64 (-.f64 x 1.0) (.f64 x (+.f64 1.0 x)))
8.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1.0) (-.f64 (.f64 1.0 x) (.f64 (+.f64 1.0 x) 2.0))) (.f64 1.0 (.f64 x (+.f64 1.0 x)))) (.f64 (-.f64 x 1.0) (*.f64 x (+.f64 1.0 x))))
5.0ms	(-.f64 (.f64 1.0 x) (.f64 (+.f64 1.0 x) 2.0))
2.0ms	(+.f64 (.f64 (-.f64 x 1.0) (-.f64 (.f64 1.0 x) (.f64 (+.f64 1.0 x) 2.0))) (.f64 1.0 (*.f64 x (+.f64 1.0 x))))

simplify54.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5001	4194

prune378.0ms (15%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	136	5	141

Merged error: 0.1b

Counts

141 → 5

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 (-.f64 x 1.0) (.f64 x (+.f64 1.0 x)))
0.2b	(/.f64 2.0 (.f64 (-.f64 x 1.0) (.f64 x (+.f64 1.0 x))))

rewrite24.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 63

Calls

2 calls:

12.0ms	(/.f64 2.0 (.f64 (-.f64 x 1.0) (.f64 x (+.f64 1.0 x))))
10.0ms	(.f64 (-.f64 x 1.0) (.f64 x (+.f64 1.0 x)))

series18.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

11.0ms	(.f64 (-.f64 x 1.0) (.f64 x (+.f64 1.0 x)))
7.0ms	(/.f64 2.0 (.f64 (-.f64 x 1.0) (.f64 x (+.f64 1.0 x))))

simplify37.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5018	916

prune86.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	2	0	2
Picked	1	0	1
Done	1	1	2
Total	69	5	74

Merged error: 0.0b

Counts

74 → 5

regimes32.0ms (1.3%)

Accuracy

Total 0.1b remaining (82%)

Threshold costs 0.1b (82%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms (0%)

sample895.0ms (35.6%)

Algorithm

1×

intervals

Results

318.0ms	1826×	body	640	valid
186.0ms	4210×	body	80	valid
118.0ms	558×	body	1280	valid
117.0ms	940×	body	320	valid
42.0ms	466×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze6.0ms (0.2%)

sample26.0ms (1%)

simplify67.0ms (2.7%)

prune4.0ms (0.2%)

localize9.0ms (0.3%)

rewrite66.0ms (2.6%)

series24.0ms (0.9%)

simplify52.0ms (2.1%)

prune197.0ms (7.8%)

localize12.0ms (0.5%)

rewrite65.0ms (2.6%)

series35.0ms (1.4%)

simplify49.0ms (1.9%)

prune266.0ms (10.6%)

localize13.0ms (0.5%)

rewrite64.0ms (2.6%)

series26.0ms (1%)

simplify54.0ms (2.2%)

prune378.0ms (15%)

localize7.0ms (0.3%)

rewrite24.0ms (1%)

series18.0ms (0.7%)

simplify37.0ms (1.5%)

prune86.0ms (3.4%)

regimes32.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample895.0ms (35.6%)

Profiling