Details

analyze461.0ms (7.1%)

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 (0.6%)

Algorithm

1×

intervals

Results

9.0ms	35×	body	2048	valid
9.0ms	170×	body	128	valid
5.0ms	17×	body	4096	valid
4.0ms	20×	body	1024	valid
1.0ms	9×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	12×	body	128	invalid
0.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify403.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (303.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

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

Error

33.2b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_441`
14×	`*-un-lft-identity_binary64_419`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454`
6×	`times-frac_binary64_425` `difference-of-squares_binary64_388` `sqrt-prod_binary64_435` `associate-/l*_binary64_364`
5×	`pow1_binary64_480`
4×	`flip3--_binary64_423` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`
3×	`distribute-lft-out--_binary64_371`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `diff-log_binary64_511` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `associate-/r*_binary64_363` `rem-sqrt-square_binary64_432` `div-sub_binary64_424`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series616.0ms (9.5%)

Counts

4 → 62

Calls

4 calls:

184.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
173.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
136.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1859 to 1581 computations (15% saved)

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5536	2621

prune168.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	127	9	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	9	137

Error

6.7b

Counts

137 → 9

Compiler

Compiled 2837 to 1619 computations (42.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_441`
18×	`*-un-lft-identity_binary64_419`
14×	`add-cube-cbrt_binary64_454`
13×	`associate-r_binary64_359`
10×	`times-frac_binary64_425`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`add-log-exp_binary64_458`
7×	`pow1_binary64_480`
6×	`associate-l_binary64_360`
5×	`flip3--_binary64_423` `flip--_binary64_394` `sqrt-prod_binary64_435`
4×	`difference-of-squares_binary64_388` `cancel-sign-sub-inv_binary64_385`
2×	`associate-*l/_binary64_362` `sqrt-div_binary64_436` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `frac-times_binary64_429` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `distribute-lft-out--_binary64_371` `diff-log_binary64_511`
1×	`pow-prod-down_binary64_490` `pow1/2_binary64_499` `div-inv_binary64_416` `associate-r/_binary64_361` `-commutative_binary64_350` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 83

Calls

4 calls:

16.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series606.0ms (9.3%)

Counts

4 → 62

Calls

4 calls:

186.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
159.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
142.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 1859 to 1581 computations (15% saved)

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4954	2867
1	4954	2867

prune147.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	146	8	154

Error

6.7b

Counts

154 → 8

Compiler

Compiled 3000 to 1712 computations (42.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
24.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_441`
12×	`*-un-lft-identity_binary64_419`
8×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `sqrt-prod_binary64_435`
6×	`cancel-sign-sub-inv_binary64_385` `pow1_binary64_480`
4×	`sqrt-div_binary64_436` `difference-of-squares_binary64_388` `flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394`
2×	`sub-neg_binary64_412` `pow1/2_binary64_499` `distribute-lft-out--_binary64_371` `diff-log_binary64_511` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

4 → 64

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series557.0ms (8.5%)

Counts

4 → 60

Calls

4 calls:

151.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
140.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
139.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 3488 to 2664 computations (23.6% saved)

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5087	2180

prune180.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	124	8	132

Error

6.7b

Counts

132 → 8

Compiler

Compiled 4322 to 2462 computations (43% saved)

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	2	2
Total	8	8

Error

6.7b

Counts

8 → 8

Compiler

Compiled 0 to 0 computations (0% saved)

regimes840.0ms (12.9%)

Accuracy

Total 6.8b remaining (55.3%)

Threshold costs 0b (0%)

Compiler

Compiled 4408 to 3366 computations (23.6% saved)

bsearch49.0ms (0.8%)

Steps

Iters	Range		Point
6	6.756951728045913e+56	4.7942288744708346e+57	6.842931416474762e+56
7	-7.200445918492561e+72	-1.0185539658458724e+71	-7.0486931181595724e+72

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	48
1	90	48

end0.0ms (0%)

sample2.1s (32%)

Algorithm

1×

intervals

Results

283.0ms	1112×	body	2048	valid
274.0ms	5240×	body	128	valid
138.0ms	714×	body	1024	valid
126.0ms	422×	body	4096	valid
46.0ms	326×	body	512	valid
31.0ms	647×	body	128	nan
20.0ms	186×	body	256	valid
18.0ms	352×	body	128	invalid

Compiler

Compiled 1142 to 871 computations (23.7% saved)

Details

analyze461.0ms (7.1%)

sample38.0ms (0.6%)

simplify403.0ms (6.2%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite36.0ms (0.6%)

series616.0ms (9.5%)

simplify68.0ms (1%)

prune168.0ms (2.6%)

localize11.0ms (0.2%)

rewrite41.0ms (0.6%)

series606.0ms (9.3%)

simplify69.0ms (1.1%)

prune147.0ms (2.3%)

localize13.0ms (0.2%)

rewrite34.0ms (0.5%)

series557.0ms (8.5%)

simplify59.0ms (0.9%)

prune180.0ms (2.8%)

localize3.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune1.0ms (0%)

regimes840.0ms (12.9%)

bsearch49.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (32%)

Profiling