Details

analyze592.0ms (11.9%)

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)

sample41.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	159×	body	128	valid
9.0ms	37×	body	2048	valid
5.0ms	31×	body	1024	valid
3.0ms	10×	body	4096	valid
2.0ms	13×	body	512	valid
1.0ms	22×	body	128	nan
0.0ms	6×	body	256	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify189.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	309	20
1	309	20

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 36.7b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
1.0b	(-.f64 (neg.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))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 89

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series445.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

141.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
126.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
117.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
60.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4922	2470
1	4922	2470

prune114.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	91	10	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	10	102

Merged error: 6.6b

Counts

102 → 10

Compiler

Compiled 2360 to 478 computations (79.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
1.0b	(-.f64 (neg.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))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite64.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
130×	`add-sqr-sqrt_binary64`
129×	`*-un-lft-identity_binary64`
77×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-rgt-neg-in_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `neg-log_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 175

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
11.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series465.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

197.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
117.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
99.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
52.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify89.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5004	5825

prune166.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	189	8	197

Merged error: 6.5b

Counts

197 → 8

Compiler

Compiled 4892 to 958 computations (80.4% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.5b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
14.7b	(/.f64 (*.f64 a c) a)
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 62

Calls

4 calls:

9.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
5.0ms	(/.f64 (*.f64 a c) a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series298.0ms (6%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
108.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
63.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
15.0ms	(/.f64 (*.f64 a c) a)

simplify67.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4953	967
1	4953	967

prune61.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	75	7	82

Merged error: 6.5b

Counts

82 → 7

Compiler

Compiled 1601 to 353 computations (78% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 (neg.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))
1.5b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `times-frac_binary64`
10×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r*_binary64` `pow1_binary64` `distribute-rgt-neg-in_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

14.0ms	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
9.0ms	(+.f64 (neg.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))

series645.0ms (12.9%)

Counts

4 → 12

Calls

4 calls:

359.0ms	(/.f64 c (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
125.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
109.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
53.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5433	1819

prune60.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	89	8	97

Merged error: 6.5b

Counts

97 → 8

Compiler

Compiled 1719 to 323 computations (81.2% saved)

regimes150.0ms (3%)

Compiler: Compiled 387 to 264 computations (31.8% saved)

bsearch75.0ms (1.5%)

Steps

Iters	Range		Point
8	1.1247184987748e+57	5.945267304394438e+60	5.867327981356101e+60
6	2.723802565587635e-281	1.1405275742133047e-280	5.128238380962619e-281
7	-5.2343157936136215e+138	-8.375339098837591e+136	-1.646116191344108e+138

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	84	73
1	84	73

end0.0ms (0%)

sample1.1s (23%)

Algorithm

1×

intervals

Results

236.0ms	5225×	body	128	valid
218.0ms	1076×	body	2048	valid
120.0ms	741×	body	1024	valid
97.0ms	384×	body	4096	valid
46.0ms	366×	body	512	valid
29.0ms	700×	body	128	nan
19.0ms	208×	body	256	valid
12.0ms	264×	body	128	invalid

Compiler

Compiled 190 to 125 computations (34.2% saved)

Details

analyze592.0ms (11.9%)

sample41.0ms (0.8%)

simplify189.0ms (3.8%)

prune4.0ms (0.1%)

localize18.0ms (0.4%)

rewrite43.0ms (0.9%)

series445.0ms (8.9%)

simplify77.0ms (1.5%)

prune114.0ms (2.3%)

localize11.0ms (0.2%)

rewrite64.0ms (1.3%)

series465.0ms (9.3%)

simplify89.0ms (1.8%)

prune166.0ms (3.3%)

localize14.0ms (0.3%)

rewrite28.0ms (0.6%)

series298.0ms (6%)

simplify67.0ms (1.4%)

prune61.0ms (1.2%)

localize10.0ms (0.2%)

rewrite40.0ms (0.8%)

series645.0ms (12.9%)

simplify69.0ms (1.4%)

prune60.0ms (1.2%)

regimes150.0ms (3%)

bsearch75.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (23%)

Profiling