Details

analyze468.0ms (7%)

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	166×	body	128	valid
8.0ms	30×	body	2048	valid
5.0ms	24×	body	1024	valid
4.0ms	12×	body	4096	valid
3.0ms	16×	body	512	valid
1.0ms	8×	body	256	valid
1.0ms	10×	body	128	invalid
1.0ms	10×	body	128	nan

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify224.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 36.3b

Counts

2 → 1

Compiler

Compiled 66 to 54 computations (18.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.1b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_445`
21×	`*-un-lft-identity_binary64_423`
10×	`add-log-exp_binary64_462`
9×	`add-cube-cbrt_binary64_458` `sqrt-prod_binary64_439` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
7×	`times-frac_binary64_429` `cancel-sign-sub-inv_binary64_389` `associate-/l*_binary64_368`
6×	`distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392`
5×	`pow1_binary64_484`
4×	`flip3--_binary64_427` `flip--_binary64_398`
3×	`diff-log_binary64_515` `distribute-rgt-neg-in_binary64_381`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `associate-/l/_binary64_370` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
1×	`associate--l-_binary64_361` `neg-log_binary64_516` `prod-exp_binary64_472` `rem-sqrt-square_binary64_436` `neg-sub0_binary64_418` `div-sub_binary64_428` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `associate-/r*_binary64_367` `cbrt-unprod_binary64_456`

Counts

4 → 82

Calls

4 calls:

15.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
11.0ms	(-.f64 (neg.f64 b) (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	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series460.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
123.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5923	2287

prune481.0ms (7.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	84	10	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Merged error: 6.5b

Counts

95 → 10

Compiler

Compiled 9728 to 6404 computations (34.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.9b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b)) (.f64 2 a))
10.4b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite88.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
30×	`times-frac_binary64_429`
28×	`add-sqr-sqrt_binary64_445`
19×	`*-un-lft-identity_binary64_423`
17×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
13×	`prod-exp_binary64_472` `associate-/l*_binary64_368` `cbrt-unprod_binary64_456`
11×	`add-cube-cbrt_binary64_458`
8×	`difference-of-squares_binary64_392`
7×	`sqrt-prod_binary64_439` `associate-/r*_binary64_367`
6×	`associate-/r/_binary64_369` `add-log-exp_binary64_462`
5×	`pow1_binary64_484` `flip3--_binary64_427` `flip--_binary64_398`
4×	`distribute-lft-out--_binary64_375` `div-inv_binary64_420`
2×	`sqrt-div_binary64_440` `clear-num_binary64_422` `frac-2neg_binary64_434`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `rem-sqrt-square_binary64_436` `associate-/l/_binary64_370` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`

Counts

4 → 110

Calls

4 calls:

50.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b)) (.f64 2 a))
15.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series868.0ms (13%)

Counts

4 → 12

Calls

4 calls:

376.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
312.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b)) (.f64 2 a))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4973	3511
1	4973	3511

prune280.0ms (4.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	123	9	132

Merged error: 6.5b

Counts

132 → 9

Compiler

Compiled 5978 to 3680 computations (38.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_445`
27×	`*-un-lft-identity_binary64_423`
18×	`times-frac_binary64_429`
17×	`add-cube-cbrt_binary64_458`
10×	`difference-of-squares_binary64_392`
8×	`sqrt-prod_binary64_439` `add-log-exp_binary64_462`
6×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459` `associate-/r*_binary64_367`
5×	`pow1_binary64_484` `distribute-lft-out--_binary64_375`
4×	`cancel-sign-sub-inv_binary64_389` `flip3--_binary64_427` `flip--_binary64_398`
3×	`associate-/l*_binary64_368`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `diff-log_binary64_515` `associate-/r/_binary64_369`
1×	`rem-sqrt-square_binary64_436` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474`

Counts

4 → 85

Calls

4 calls:

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

series668.0ms (10%)

Counts

4 → 12

Calls

4 calls:

360.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b))
133.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4886	2453
1	4886	2453

prune159.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	97	9	106

Merged error: 6.5b

Counts

106 → 9

Compiler

Compiled 3471 to 2105 computations (39.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite58.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_429`
122×	`add-sqr-sqrt_binary64_445`
95×	`*-un-lft-identity_binary64_423`
69×	`add-cube-cbrt_binary64_458`
26×	`difference-of-squares_binary64_392`
22×	`associate-/r*_binary64_367`
16×	`sqrt-prod_binary64_439`
15×	`add-exp-log_binary64_461`
13×	`distribute-lft-out--_binary64_375`
9×	`add-cbrt-cube_binary64_459`
8×	`add-log-exp_binary64_462`
7×	`div-exp_binary64_474`
6×	`pow1_binary64_484`
5×	`div-inv_binary64_420`
4×	`cancel-sign-sub-inv_binary64_389`
3×	`flip3--_binary64_427` `flip--_binary64_398` `associate-/l*_binary64_368` `cbrt-undiv_binary64_457`
2×	`rec-exp_binary64_473` `1-exp_binary64_467` `sqrt-div_binary64_440` `sub-neg_binary64_416` `diff-log_binary64_515`
1×	`rem-sqrt-square_binary64_436` `associate-/r/_binary64_369` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow-flip_binary64_497` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `inv-pow_binary64_508`

Counts

4 → 156

Calls

4 calls:

14.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) c))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series539.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

232.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) c))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
60.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4979	5518
1	4979	5518

prune238.0ms (3.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	168	9	177

Merged error: 6.5b

Counts

177 → 9

Compiler

Compiled 5232 to 2970 computations (43.2% saved)

regimes101.0ms (1.5%)

Compiler: Compiled 522 to 408 computations (21.8% saved)

bsearch109.0ms (1.6%)

Steps

Iters	Range		Point
6	3.453198629799523e+50	2.437223188812816e+51	2.404688834790521e+51
10	6.859135451625387e-140	3.0996325530844213e-130	6.924914397486699e-140
9	-1.8084373769306673e+109	-7.821142621831562e+100	-5.193186085288575e+108

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	146	120
1	146	120

end0.0ms (0%)

sample1.4s (21.3%)

Algorithm

1×

intervals

Results

280.0ms	5243×	body	128	valid
277.0ms	1092×	body	2048	valid
150.0ms	719×	body	1024	valid
129.0ms	415×	body	4096	valid
54.0ms	369×	body	512	valid
34.0ms	684×	body	128	nan
23.0ms	392×	body	128	invalid
16.0ms	162×	body	256	valid

Compiler

Compiled 310 to 222 computations (28.4% saved)

Details

analyze468.0ms (7%)

sample38.0ms (0.6%)

simplify224.0ms (3.3%)

prune5.0ms (0.1%)

localize12.0ms (0.2%)

rewrite43.0ms (0.6%)

series460.0ms (6.9%)

simplify67.0ms (1%)

prune481.0ms (7.2%)

localize13.0ms (0.2%)

rewrite88.0ms (1.3%)

series868.0ms (13%)

simplify91.0ms (1.4%)

prune280.0ms (4.2%)

localize13.0ms (0.2%)

rewrite41.0ms (0.6%)

series668.0ms (10%)

simplify73.0ms (1.1%)

prune159.0ms (2.4%)

localize14.0ms (0.2%)

rewrite58.0ms (0.9%)

series539.0ms (8.1%)

simplify109.0ms (1.6%)

prune238.0ms (3.6%)

regimes101.0ms (1.5%)

bsearch109.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (21.3%)

Profiling