Details

analyze601.0ms (10.5%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample40.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	168×	body	128	valid
7.0ms	34×	body	2048	valid
3.0ms	19×	body	1024	valid
3.0ms	10×	body	4096	valid
2.0ms	19×	body	512	valid
1.0ms	21×	body	128	nan
1.0ms	6×	body	256	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify189.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	309	18
1	309	18

prune6.0ms (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: 34.2b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series486.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

189.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
124.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
121.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
52.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4975	2155
1	4975	2155

prune104.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 5.6b

Counts

95 → 9

Compiler

Compiled 2073 to 428 computations (79.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
3.5b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
8.8b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite67.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
156×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
32×	`distribute-lft-out_binary64`
21×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `div-inv_binary64` `flip-+_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`neg-sub0_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 217

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
9.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
6.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series863.0ms (15.1%)

Counts

4 → 12

Calls

4 calls:

383.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
266.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
111.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
102.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify111.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5322	8155

prune199.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	230	8	238

Merged error: 5.5b

Counts

238 → 8

Compiler

Compiled 6648 to 896 computations (86.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
15×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
12×	`distribute-lft-out_binary64`
10×	`associate-/l*_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `neg-mul-1_binary64`
4×	`associate-/r*_binary64`
3×	`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` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `distribute-frac-neg_binary64` `sum-log_binary64`

Counts

4 → 108

Calls

4 calls:

10.0ms	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
7.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series610.0ms (10.6%)

Counts

4 → 12

Calls

4 calls:

325.0ms	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
116.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
107.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
62.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5173	3058

prune104.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	119	9	128

Merged error: 5.5b

Counts

128 → 9

Compiler

Compiled 2905 to 719 computations (75.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 c)))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`associate-r_binary64` `add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64`
9×	`distribute-lft-neg-in_binary64` `add-cbrt-cube_binary64` `distribute-rgt-neg-in_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
4×	`associate-l_binary64` `prod-exp_binary64`
3×	`flip3-+_binary64` `neg-mul-1_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `div-exp_binary64` `flip--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 100

Calls

4 calls:

20.0ms	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 c)))
6.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series413.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 c)))
115.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
105.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
49.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4942	2348
1	4942	2348

prune98.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	112	9	121

Merged error: 5.5b

Counts

121 → 9

Compiler

Compiled 2554 to 853 computations (66.6% saved)

regimes146.0ms (2.5%)

Compiler: Compiled 447 to 327 computations (26.8% saved)

bsearch94.0ms (1.6%)

Steps

Iters	Range	Point
9	3.015956073754805e+145	2.7271454760193077e+153	2.6131658992292902e+152
8	-3.8589038659683565e-186	-2.7022059401101187e-190	-2.762899027788645e-190
7	-0.0008140605946641254	-2.0147283120525615e-05	-0.0008038623376922219

Iters

Range

Point

3.015956073754805e+145

2.7271454760193077e+153

2.6131658992292902e+152

-3.8589038659683565e-186

-2.7022059401101187e-190

-2.762899027788645e-190

-0.0008140605946641254

-2.0147283120525615e-05

-0.0008038623376922219

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	167	94
1	167	94

end0.0ms (0%)

sample1.2s (21.1%)

Algorithm

1×

intervals

Results

235.0ms	5230×	body	128	valid
227.0ms	1069×	body	2048	valid
122.0ms	436×	body	4096	valid
117.0ms	689×	body	1024	valid
47.0ms	386×	body	512	valid
31.0ms	732×	body	128	nan
16.0ms	190×	body	256	valid
12.0ms	258×	body	128	invalid

Compiler

Compiled 224 to 156 computations (30.4% saved)

Details

analyze601.0ms (10.5%)

sample40.0ms (0.7%)

simplify189.0ms (3.3%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite46.0ms (0.8%)

series486.0ms (8.5%)

simplify68.0ms (1.2%)

prune104.0ms (1.8%)

localize10.0ms (0.2%)

rewrite67.0ms (1.2%)

series863.0ms (15.1%)

simplify111.0ms (1.9%)

prune199.0ms (3.5%)

localize10.0ms (0.2%)

rewrite36.0ms (0.6%)

series610.0ms (10.6%)

simplify76.0ms (1.3%)

prune104.0ms (1.8%)

localize11.0ms (0.2%)

rewrite45.0ms (0.8%)

series413.0ms (7.2%)

simplify73.0ms (1.3%)

prune98.0ms (1.7%)

regimes146.0ms (2.5%)

bsearch94.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (21.1%)

Profiling