Details

analyze463.0ms (8.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample38.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	172×	body	128	valid
6.0ms	26×	body	2048	valid
5.0ms	27×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	18×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify225.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (0.1%)

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: 35.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_772`
13×	`*-un-lft-identity_binary64_751`
9×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
8×	`add-log-exp_binary64_787`
7×	`add-cube-cbrt_binary64_783`
6×	`times-frac_binary64_757` `sqrt-prod_binary64_766` `associate-/l*_binary64_698` `difference-of-squares_binary64_720`
5×	`pow1_binary64_809`
4×	`flip--_binary64_726` `flip3--_binary64_755`
3×	`distribute-lft-out--_binary64_705`
2×	`associate-/l/_binary64_700` `sqrt-div_binary64_767` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `sub-neg_binary64_744` `div-exp_binary64_799`
1×	`prod-exp_binary64_797` `div-sub_binary64_756` `rem-sqrt-square_binary64_764` `associate-/r*_binary64_697` `pow1/2_binary64_828` `div-inv_binary64_748` `frac-2neg_binary64_762` `cbrt-unprod_binary64_781` `clear-num_binary64_750` `sqrt-pow1_binary64_768`

Counts

4 → 70

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series506.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

202.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
117.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify75.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4930	1975
1	4930	1975

prune131.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 7.0b

Counts

83 → 9

Compiler

Compiled 2130 to 1163 computations (45.4% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_772`
10×	`*-un-lft-identity_binary64_751`
8×	`add-log-exp_binary64_787` `sqrt-prod_binary64_766`
6×	`add-cube-cbrt_binary64_783` `pow1_binary64_809`
4×	`flip--_binary64_726` `sqrt-div_binary64_767` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786` `flip3--_binary64_755` `difference-of-squares_binary64_720`
2×	`distribute-lft-out--_binary64_705` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `diff-log_binary64_840` `sub-neg_binary64_744` `sqrt-pow1_binary64_768`

Counts

4 → 58

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series483.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
126.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
118.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
109.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5072	1536

prune113.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	71	8	79

Merged error: 7.0b

Counts

79 → 8

Compiler

Compiled 2829 to 1535 computations (45.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_772`
10×	`*-un-lft-identity_binary64_751`
8×	`add-log-exp_binary64_787` `sqrt-prod_binary64_766`
6×	`add-cube-cbrt_binary64_783` `pow1_binary64_809`
4×	`flip--_binary64_726` `sqrt-div_binary64_767` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786` `flip3--_binary64_755` `difference-of-squares_binary64_720`
2×	`distribute-lft-out--_binary64_705` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `diff-log_binary64_840` `sub-neg_binary64_744` `sqrt-pow1_binary64_768`

Counts

4 → 58

Calls

4 calls:

12.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series474.0ms (9%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
114.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5072	1536

prune110.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	70	8	78

Merged error: 7.0b

Counts

78 → 8

Compiler

Compiled 2798 to 1514 computations (45.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_772`
10×	`sqrt-prod_binary64_766`
9×	`*-un-lft-identity_binary64_751`
7×	`add-cube-cbrt_binary64_783` `pow1_binary64_809`
6×	`add-log-exp_binary64_787` `sqrt-div_binary64_767`
4×	`flip--_binary64_726` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786` `flip3--_binary64_755`
3×	`rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `sqrt-pow1_binary64_768`
2×	`difference-of-squares_binary64_720`
1×	`distribute-lft-out--_binary64_705` `diff-log_binary64_840` `sub-neg_binary64_744`

Counts

4 → 59

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series451.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
115.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
107.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify72.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5072	1470

prune137.0ms (2.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	71	8	79

Merged error: 7.0b

Counts

79 → 8

Compiler

Compiled 3666 to 1927 computations (47.4% saved)

regimes160.0ms (3%)

Compiler: Compiled 609 to 432 computations (29.1% saved)

bsearch60.0ms (1.1%)

Steps

Iters	Range		Point
9	3.3524051650422195e-138	3.0996325530844213e-130	3.053015276645368e-130
8	-1.6249009059312762e+154	-3.534796202621665e+151	-2.598568989113781e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	52
1	93	52

end0.0ms (0%)

sample1.4s (27%)

Algorithm

1×

intervals

Results

294.0ms	1134×	body	2048	valid
261.0ms	5060×	body	128	valid
158.0ms	792×	body	1024	valid
131.0ms	417×	body	4096	valid
58.0ms	403×	body	512	valid
33.0ms	666×	body	128	nan
20.0ms	380×	body	128	invalid
19.0ms	194×	body	256	valid

Compiler

Compiled 296 to 206 computations (30.4% saved)

Details

analyze463.0ms (8.8%)

sample38.0ms (0.7%)

simplify225.0ms (4.3%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite41.0ms (0.8%)

series506.0ms (9.6%)

simplify75.0ms (1.4%)

prune131.0ms (2.5%)

localize16.0ms (0.3%)

rewrite34.0ms (0.7%)

series483.0ms (9.2%)

simplify71.0ms (1.3%)

prune113.0ms (2.1%)

localize14.0ms (0.3%)

rewrite38.0ms (0.7%)

series474.0ms (9%)

simplify71.0ms (1.3%)

prune110.0ms (2.1%)

localize17.0ms (0.3%)

rewrite33.0ms (0.6%)

series451.0ms (8.6%)

simplify72.0ms (1.4%)

prune137.0ms (2.6%)

regimes160.0ms (3%)

bsearch60.0ms (1.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (27%)

Profiling