Details

analyze465.0ms (3.8%)

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)

sample40.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	173×	body	128	valid
6.0ms	24×	body	2048	valid
5.0ms	25×	body	1024	valid
4.0ms	15×	body	4096	valid
1.0ms	10×	body	512	valid
1.0ms	9×	body	256	valid
1.0ms	17×	body	128	invalid
1.0ms	17×	body	128	nan

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify399.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (304.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune7.0ms (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

Error

33.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

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))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite151.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

33.3b

Rules

21×	`add-sqr-sqrt_binary64_782`
14×	`*-un-lft-identity_binary64_760`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799` `add-cube-cbrt_binary64_795`
6×	`sqrt-prod_binary64_776` `difference-of-squares_binary64_729` `times-frac_binary64_766` `associate-/l*_binary64_705`
5×	`pow1_binary64_821`
4×	`flip3--_binary64_764` `flip--_binary64_735` `cancel-sign-sub-inv_binary64_726`
3×	`distribute-lft-out--_binary64_712`
2×	`sqrt-div_binary64_777` `diff-log_binary64_852` `sub-neg_binary64_753` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `associate-/l/_binary64_707`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `frac-2neg_binary64_771` `div-sub_binary64_765` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/r*_binary64_704`

Counts

4 → 74

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2100 to 1088 computations (48.2% saved)

series731.0ms (6%)

Error

7.7b

Counts

4 → 69

Calls

4 calls:

229.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
155.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
147.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
137.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3046 to 2313 computations (24.1% saved)

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4973	2790
1	4973	2790

prune154.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	129	14	143
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	14	144

Error

7.6b

Counts

144 → 14

Compiler

Compiled 2983 to 1581 computations (47% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite937.0ms (7.7%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Rules

693×	`times-frac_binary64_766`
439×	`add-sqr-sqrt_binary64_782`
364×	`*-un-lft-identity_binary64_760`
290×	`add-cube-cbrt_binary64_795`
74×	`difference-of-squares_binary64_729`
71×	`associate-/r*_binary64_704`
40×	`sqrt-prod_binary64_776`
37×	`distribute-lft-out--_binary64_712`
25×	`add-exp-log_binary64_798`
17×	`div-inv_binary64_757`
15×	`div-exp_binary64_811`
13×	`add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799`
6×	`pow1_binary64_821` `cbrt-undiv_binary64_794`
5×	`associate-/r/_binary64_706`
4×	`cancel-sign-sub-inv_binary64_726`
3×	`flip3--_binary64_764` `flip--_binary64_735` `1-exp_binary64_804` `rec-exp_binary64_810` `associate-/l*_binary64_705`
2×	`sqrt-div_binary64_777` `diff-log_binary64_852` `sub-neg_binary64_753`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `inv-pow_binary64_845` `pow-flip_binary64_834` `frac-2neg_binary64_771` `clear-num_binary64_759`

Counts

4 → 356

Calls

4 calls:

27.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 14021 to 8305 computations (40.8% saved)

series768.0ms (6.3%)

Error

7.6b

Counts

4 → 69

Calls

4 calls:

229.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
171.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
163.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
147.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3308 to 2575 computations (22.2% saved)

simplify192.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4955	17097
1	4955	17097

prune813.0ms (6.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	422	3	425
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	427	12	439

Error

7.6b

Counts

439 → 12

Compiler

Compiled 13678 to 7588 computations (44.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite134.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Rules

28×	`add-sqr-sqrt_binary64_782`
18×	`*-un-lft-identity_binary64_760`
14×	`add-cube-cbrt_binary64_795`
13×	`associate-r_binary64_700`
10×	`times-frac_binary64_766`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799`
7×	`pow1_binary64_821`
6×	`associate-l_binary64_701`
5×	`flip3--_binary64_764` `flip--_binary64_735` `sqrt-prod_binary64_776`
4×	`difference-of-squares_binary64_729` `cancel-sign-sub-inv_binary64_726`
2×	`sqrt-div_binary64_777` `diff-log_binary64_852` `sub-neg_binary64_753` `distribute-lft-out--_binary64_712` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `frac-times_binary64_770` `unswap-sqr_binary64_728` `associate-*l/_binary64_703`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `pow-prod-down_binary64_831` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `associate-r/_binary64_702` `div-inv_binary64_757` `-commutative_binary64_691`

Counts

4 → 83

Calls

4 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2366 to 1240 computations (47.6% saved)

series706.0ms (5.8%)

Error

7.6b

Counts

4 → 69

Calls

4 calls:

208.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
165.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
152.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
131.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3046 to 2313 computations (24.1% saved)

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5062	3036

prune149.0ms (1.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	149	3	152
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	152	12	164

Error

7.6b

Counts

164 → 12

Compiler

Compiled 3167 to 1673 computations (47.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sqrt.f64 1/2) a)
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite133.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Rules

26×	`add-sqr-sqrt_binary64_782`
23×	`*-un-lft-identity_binary64_760`
21×	`add-cube-cbrt_binary64_795`
18×	`times-frac_binary64_766`
16×	`sqrt-prod_binary64_776`
8×	`add-log-exp_binary64_799`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `associate-/l*_binary64_705`
5×	`pow1_binary64_821`
4×	`cancel-sign-sub-inv_binary64_726`
3×	`flip3--_binary64_764` `flip--_binary64_735` `associate-/r*_binary64_704`
2×	`sqrt-div_binary64_777` `diff-log_binary64_852` `sub-neg_binary64_753` `difference-of-squares_binary64_729`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `distribute-lft-out--_binary64_712` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757`

Counts

4 → 83

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(/.f64 (sqrt.f64 1/2) a)

Compiler

Compiled 2435 to 1472 computations (39.5% saved)

series536.0ms (4.4%)

Error

7.6b

Counts

4 → 55

Calls

4 calls:

153.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
149.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
147.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
32.0ms	(/.f64 (sqrt.f64 1/2) a)

Compiler

Compiled 3035 to 2438 computations (19.7% saved)

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4924	2095
1	4924	2095

prune160.0ms (1.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	139	11	150

Error

7.4b

Counts

150 → 11

Compiler

Compiled 3239 to 1982 computations (38.8% saved)

regimes1.8s (15.1%)

Accuracy

Total 4.4b remaining (44.3%)

Threshold costs 0b (0%)

Compiler

Compiled 11700 to 8798 computations (24.8% saved)

bsearch54.0ms (0.4%)

Steps

Iters	Range		Point
6	4.506395671377052e-64	4.207723813353611e-63	1.7464220447169885e-63
8	-2.975373334087326e+126	-4.944510384907234e+123	-2.0362182003131042e+126

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	52
1	93	52

end0.0ms (0%)

sample3.6s (29.4%)

Algorithm

1×

intervals

Results

283.0ms	5199×	body	128	valid
278.0ms	1118×	body	2048	valid
147.0ms	729×	body	1024	valid
136.0ms	429×	body	4096	valid
50.0ms	347×	body	512	valid
34.0ms	654×	body	128	nan
20.0ms	396×	body	128	invalid
20.0ms	178×	body	256	valid

Compiler

Compiled 3010 to 2256 computations (25% saved)

Details

analyze465.0ms (3.8%)

sample40.0ms (0.3%)

simplify399.0ms (3.3%)

prune7.0ms (0.1%)

localize11.0ms (0.1%)

rewrite151.0ms (1.2%)

series731.0ms (6%)

simplify70.0ms (0.6%)

prune154.0ms (1.3%)

localize12.0ms (0.1%)

rewrite937.0ms (7.7%)

series768.0ms (6.3%)

simplify192.0ms (1.6%)

prune813.0ms (6.7%)

localize11.0ms (0.1%)

rewrite134.0ms (1.1%)

series706.0ms (5.8%)

simplify57.0ms (0.5%)

prune149.0ms (1.2%)

localize13.0ms (0.1%)

rewrite133.0ms (1.1%)

series536.0ms (4.4%)

simplify67.0ms (0.6%)

prune160.0ms (1.3%)

regimes1.8s (15.1%)

bsearch54.0ms (0.4%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.6s (29.4%)

Profiling