Details

analyze282.0ms (7.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

sample53.0ms (1.4%)

Algorithm

1×

intervals

Results

15.0ms	108×	body	320	valid
10.0ms	284×	pre	80	true
9.0ms	93×	body	160	valid
4.0ms	20×	body	640	valid
2.0ms	35×	body	80	valid
1.0ms	28×	body	80	nan

simplify250.0ms (6.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (247.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 51.3b

Counts

2 → 1

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
24.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 70

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series80.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))) b) (.f64 a 2.0))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))) b)
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))

simplify51.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4921	1309
1	4921	1309

prune115.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	4	83

Merged error: 0.1b

Counts

83 → 4

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
0.2b	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
0.2b	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))

rewrite45.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64`
78×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
36×	`associate-/l*_binary64`
20×	`distribute-lft-out_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
8×	`add-log-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64`
2×	`cbrt-unprod_binary64` `neg-sub0_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 155

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
10.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))

series157.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
53.0ms	(/.f64 (/.f64 (neg.f64 (.f64 (.f64 4.0 a) c)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c))))) (.f64 a 2.0))
20.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))

simplify61.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4978	3969
1	4978	3969

prune301.0ms (7.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	161	6	167
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	165	6	171

Merged error: 0b

Counts

171 → 6

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
0.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series104.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
18.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))

simplify69.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4930	1299
1	4930	1299

prune126.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	83	6	89

Merged error: 0b

Counts

89 → 6

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
0.0b	(/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))
0.3b	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a)))))))

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64`
4×	`associate-/r*_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 104

Calls

4 calls:

14.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a)))))))
9.0ms	(/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))

series120.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(.f64 c (/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4.0 a)))))))
32.0ms	(/.f64 1 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a))))
11.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4.0 a)))

simplify74.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4911	1733
1	4911	1733

prune161.0ms (4.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	116	6	122

Merged error: 0b

Counts

122 → 6

regimes163.0ms (4.3%)

Accuracy

Total 0.1b remaining (80%)

Threshold costs 0.1b (80%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	19
1	84	19

end0.0ms (0%)

sample1.5s (38.3%)

Algorithm

1×

intervals

Results

520.0ms	3575×	body	320	valid
291.0ms	3024×	body	160	valid
262.0ms	8840×	pre	80	true
94.0ms	501×	body	640	valid
47.0ms	900×	body	80	valid
40.0ms	840×	body	80	nan

Details

analyze282.0ms (7.4%)

sample53.0ms (1.4%)

simplify250.0ms (6.5%)

prune7.0ms (0.2%)

localize10.0ms (0.3%)

rewrite33.0ms (0.9%)

series80.0ms (2.1%)

simplify51.0ms (1.3%)

prune115.0ms (3%)

localize13.0ms (0.3%)

rewrite45.0ms (1.2%)

series157.0ms (4.1%)

simplify61.0ms (1.6%)

prune301.0ms (7.9%)

localize12.0ms (0.3%)

rewrite28.0ms (0.7%)

series104.0ms (2.7%)

simplify69.0ms (1.8%)

prune126.0ms (3.3%)

localize14.0ms (0.4%)

rewrite35.0ms (0.9%)

series120.0ms (3.1%)

simplify74.0ms (1.9%)

prune161.0ms (4.2%)

regimes163.0ms (4.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.5s (38.3%)

Profiling