Details

analyze450.0ms (4.5%)

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
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 (0.4%)

Algorithm

1×

intervals

Results

11.0ms	176×	body	128	valid
7.0ms	30×	body	2048	valid
5.0ms	28×	body	1024	valid
2.0ms	6×	body	4096	valid
2.0ms	11×	body	512	valid
1.0ms	17×	body	128	nan
1.0ms	14×	body	128	invalid
0.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify229.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune9.0ms (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: 32.0b

Counts

2 → 2

Compiler

Compiled 82 to 67 computations (18.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_423`
10×	`add-log-exp_binary64_462`
9×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
8×	`add-sqr-sqrt_binary64_445`
7×	`add-cube-cbrt_binary64_458`
6×	`distribute-lft-out_binary64_374`
5×	`times-frac_binary64_429` `pow1_binary64_484` `associate-/l*_binary64_368`
3×	`sqrt-prod_binary64_439` `distribute-rgt-neg-in_binary64_381`
2×	`sqrt-div_binary64_440` `flip-+_binary64_397` `associate-+l-_binary64_358` `neg-sub0_binary64_418` `flip3--_binary64_427` `associate-/l/_binary64_370` `flip3-+_binary64_426` `flip--_binary64_398` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `sum-log_binary64_514`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `neg-log_binary64_516` `cancel-sign-sub-inv_binary64_389` `prod-exp_binary64_472` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `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 → 70

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
10.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series497.0ms (5%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
115.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5290	1826

prune418.0ms (4.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	75	9	84

Merged error: 6.3b

Counts

84 → 9

Compiler

Compiled 8049 to 5739 computations (28.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.7b	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
10.5b	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite73.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
34×	`times-frac_binary64_429` `add-sqr-sqrt_binary64_445`
33×	`*-un-lft-identity_binary64_423`
17×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
14×	`associate-/l*_binary64_368`
13×	`add-cube-cbrt_binary64_458` `prod-exp_binary64_472` `cbrt-unprod_binary64_456`
11×	`sqrt-prod_binary64_439`
10×	`distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392`
8×	`add-log-exp_binary64_462` `associate-/r*_binary64_367`
6×	`cancel-sign-sub-inv_binary64_389` `associate-/r/_binary64_369`
5×	`pow1_binary64_484` `flip3--_binary64_427` `flip--_binary64_398` `distribute-rgt-neg-in_binary64_381`
4×	`div-inv_binary64_420`
2×	`sqrt-div_binary64_440` `diff-log_binary64_515` `clear-num_binary64_422` `frac-2neg_binary64_434`
1×	`sub-neg_binary64_416` `associate--l-_binary64_361` `neg-log_binary64_516` `rem-sqrt-square_binary64_436` `neg-sub0_binary64_418` `associate-/l/_binary64_370` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`

Counts

4 → 125

Calls

4 calls:

24.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
16.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series951.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

384.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
320.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
131.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify103.0ms (1%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4940	4228
1	4940	4228

prune394.0ms (3.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	1	6	7
Picked	1	0	1
Done	1	0	1
Total	136	10	146

Merged error: 6.2b

Counts

146 → 10

Compiler

Compiled 8181 to 5363 computations (34.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.7b	(/.f64 (.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
2.8b	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite76.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
35×	`add-sqr-sqrt_binary64_445`
34×	`*-un-lft-identity_binary64_423`
27×	`associate-r_binary64_363`
23×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
22×	`times-frac_binary64_429`
18×	`add-cube-cbrt_binary64_458`
16×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
10×	`sqrt-prod_binary64_439` `pow1_binary64_484`
8×	`distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392` `add-log-exp_binary64_462`
6×	`cancel-sign-sub-inv_binary64_389`
4×	`distribute-rgt-neg-in_binary64_381`
3×	`pow-prod-down_binary64_494` `flip3--_binary64_427` `flip--_binary64_398`
2×	`sqrt-div_binary64_440` `diff-log_binary64_515` `associate-*r/_binary64_365` `associate-/r/_binary64_369` `div-inv_binary64_420`
1×	`sub-neg_binary64_416` `associate-l_binary64_364` `associate--l-_binary64_361` `neg-log_binary64_516` `rem-sqrt-square_binary64_436` `neg-sub0_binary64_418` `associate-/l/_binary64_370` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `associate-/l_binary64_368` `associate-/r*_binary64_367`

Counts

4 → 119

Calls

4 calls:

23.0ms	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
21.0ms	(/.f64 (.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series956.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

385.0ms	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
325.0ms	(/.f64 (.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
121.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

simplify103.0ms (1%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4901	3363
1	4901	3363

prune196.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	131	10	141

Merged error: 6.2b

Counts

141 → 10

Compiler

Compiled 4337 to 2603 computations (40% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1 (/.f64 1/2 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.7b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
22.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite145.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

834×	`times-frac_binary64_429`
487×	`add-sqr-sqrt_binary64_445`
486×	`*-un-lft-identity_binary64_423`
338×	`add-cube-cbrt_binary64_458`
86×	`associate-/r*_binary64_367`
74×	`distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392`
43×	`sqrt-prod_binary64_439`
37×	`distribute-rgt-neg-in_binary64_381`
29×	`associate-/r/_binary64_369`
25×	`add-exp-log_binary64_461`
17×	`div-inv_binary64_420`
15×	`flip3--_binary64_427` `flip--_binary64_398` `div-exp_binary64_474`
13×	`add-cbrt-cube_binary64_459`
10×	`add-log-exp_binary64_462`
7×	`cancel-sign-sub-inv_binary64_389`
6×	`pow1_binary64_484` `cbrt-undiv_binary64_457`
3×	`rec-exp_binary64_473` `1-exp_binary64_467` `diff-log_binary64_515` `associate-/l*_binary64_368`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416`
1×	`associate--l-_binary64_361` `neg-log_binary64_516` `rem-sqrt-square_binary64_436` `neg-sub0_binary64_418` `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 → 422

Calls

4 calls:

34.0ms	(/.f64 1 (/.f64 1/2 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
14.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series668.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

363.0ms	(/.f64 1 (/.f64 1/2 (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
122.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify210.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

434 → 434

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4942	19878
1	4942	19878

prune1.0s (10.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	432	2	434
Fresh	2	6	8
Picked	1	0	1
Done	1	0	1
Total	436	8	444

Merged error: 6.2b

Counts

444 → 8

Compiler

Compiled 16873 to 10238 computations (39.3% saved)

regimes991.0ms (9.9%)

Compiler: Compiled 5104 to 4012 computations (21.4% saved)

bsearch116.0ms (1.2%)

Steps

Iters	Range		Point
11	1.533617338164353e+90	3.5739920072306705e+109	7.247767303097121e+99
8	-2.349509325897326e-294	-6.21723965058882e-297	-3.715355009492806e-296
8	-4.630209800779741e+87	-1.2404399109580175e+85	-4.563634741252048e+87

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	84
1	117	84

end0.0ms (0%)

sample2.2s (22.2%)

Algorithm

1×

intervals

Results

300.0ms	1206×	body	2048	valid
269.0ms	5148×	body	128	valid
138.0ms	708×	body	1024	valid
127.0ms	412×	body	4096	valid
53.0ms	358×	body	512	valid
33.0ms	679×	body	128	nan
21.0ms	399×	body	128	invalid
16.0ms	168×	body	256	valid

Compiler

Compiled 1327 to 1034 computations (22.1% saved)

Details

analyze450.0ms (4.5%)

sample38.0ms (0.4%)

simplify229.0ms (2.3%)

prune9.0ms (0.1%)

localize11.0ms (0.1%)

rewrite41.0ms (0.4%)

series497.0ms (5%)

simplify59.0ms (0.6%)

prune418.0ms (4.2%)

localize13.0ms (0.1%)

rewrite73.0ms (0.7%)

series951.0ms (9.5%)

simplify103.0ms (1%)

prune394.0ms (3.9%)

localize14.0ms (0.1%)

rewrite76.0ms (0.8%)

series956.0ms (9.5%)

simplify103.0ms (1%)

prune196.0ms (2%)

localize13.0ms (0.1%)

rewrite145.0ms (1.4%)

series668.0ms (6.7%)

simplify210.0ms (2.1%)

prune1.0s (10.2%)

regimes991.0ms (9.9%)

bsearch116.0ms (1.2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.2s (22.2%)

Profiling