Details

analyze463.0ms (7.8%)

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	167×	body	128	valid
8.0ms	32×	body	2048	valid
4.0ms	15×	body	4096	valid
4.0ms	23×	body	1024	valid
2.0ms	11×	body	512	valid
1.0ms	18×	body	128	invalid
1.0ms	17×	body	128	nan
1.0ms	8×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify237.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (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: 33.5b

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 (.f64 4 a) c)))) (.f64 2 a))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite40.0ms (0.7%)

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:

14.0ms	(/.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))

series499.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

197.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
122.0ms	(+.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)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5290	1826

prune466.0ms (7.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	72	11	83

Merged error: 5.7b

Counts

83 → 11

Compiler

Compiled 9321 to 6543 computations (29.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (/.f64 1/2 a))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_423`
19×	`add-sqr-sqrt_binary64_445`
13×	`add-cube-cbrt_binary64_458` `associate-r_binary64_363`
10×	`times-frac_binary64_429` `add-log-exp_binary64_462`
9×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
7×	`pow1_binary64_484`
5×	`associate-l_binary64_364`
4×	`distribute-lft-out_binary64_374`
3×	`flip-+_binary64_397` `sqrt-prod_binary64_439` `flip3-+_binary64_426`
2×	`sqrt-div_binary64_440` `frac-times_binary64_433` `prod-exp_binary64_472` `flip3--_binary64_427` `associate-*l/_binary64_366` `flip--_binary64_398` `unswap-sqr_binary64_391` `sum-log_binary64_514` `cbrt-unprod_binary64_456` `distribute-rgt-neg-in_binary64_381`
1×	`pow-prod-down_binary64_494` `sub-neg_binary64_416` `diff-log_binary64_515` `associate-+l-_binary64_358` `neg-log_binary64_516` `cancel-sign-sub-inv_binary64_389` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `neg-sub0_binary64_418` `associate-r/_binary64_365` `-commutative_binary64_354` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474`

Counts

4 → 80

Calls

4 calls:

18.0ms	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (/.f64 1/2 a))
10.0ms	(+.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)))

series521.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (/.f64 1/2 a))
139.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
61.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5238	2137

prune299.0ms (5.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	94	9	103

Merged error: 5.7b

Counts

103 → 9

Compiler

Compiled 6050 to 4089 computations (32.4% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_445`
12×	`*-un-lft-identity_binary64_423`
8×	`add-cube-cbrt_binary64_458` `sqrt-prod_binary64_439` `add-log-exp_binary64_462`
6×	`cancel-sign-sub-inv_binary64_389` `pow1_binary64_484`
4×	`sqrt-div_binary64_440` `flip3--_binary64_427` `add-exp-log_binary64_461` `difference-of-squares_binary64_392` `add-cbrt-cube_binary64_459` `flip--_binary64_398`
2×	`sub-neg_binary64_416` `diff-log_binary64_515` `rem-sqrt-square_binary64_436` `distribute-lft-out--_binary64_375` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`

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

series481.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
119.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4942	1554
1	4942	1554

prune123.0ms (2.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	76	9	85

Merged error: 5.7b

Counts

85 → 9

Compiler

Compiled 3012 to 1798 computations (40.3% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_445`
10×	`*-un-lft-identity_binary64_423` `sqrt-prod_binary64_439`
8×	`add-cube-cbrt_binary64_458`
7×	`pow1_binary64_484`
6×	`sqrt-div_binary64_440` `add-log-exp_binary64_462`
4×	`flip3--_binary64_427` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459` `flip--_binary64_398`
3×	`cancel-sign-sub-inv_binary64_389` `rem-sqrt-square_binary64_436` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`
2×	`difference-of-squares_binary64_392`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `distribute-lft-out--_binary64_375`

Counts

4 → 62

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(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	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series497.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
127.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4942	1479
1	4942	1479

prune148.0ms (2.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	74	9	83

Merged error: 5.7b

Counts

83 → 9

Compiler

Compiled 3952 to 2231 computations (43.5% saved)

regimes222.0ms (3.8%)

Compiler: Compiled 936 to 698 computations (25.4% saved)

bsearch61.0ms (1%)

Steps

Iters	Range		Point
8	1.6888427500450845e-49	1.8636184302889825e-45	1.8373918232904843e-47
8	-6.078197847532872e+152	-4.9104536583703805e+148	-1.0888578864056969e+151

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	93	52
1	93	52

end0.0ms (0%)

sample1.4s (23.3%)

Algorithm

1×

intervals

Results

277.0ms	1114×	body	2048	valid
273.0ms	5217×	body	128	valid
142.0ms	719×	body	1024	valid
122.0ms	406×	body	4096	valid
53.0ms	371×	body	512	valid
34.0ms	695×	body	128	nan
21.0ms	397×	body	128	invalid
17.0ms	173×	body	256	valid

Compiler

Compiled 277 to 204 computations (26.4% saved)

Details

analyze463.0ms (7.8%)

sample38.0ms (0.6%)

simplify237.0ms (4%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite40.0ms (0.7%)

series499.0ms (8.4%)

simplify57.0ms (1%)

prune466.0ms (7.9%)

localize14.0ms (0.2%)

rewrite45.0ms (0.8%)

series521.0ms (8.8%)

simplify67.0ms (1.1%)

prune299.0ms (5.1%)

localize16.0ms (0.3%)

rewrite35.0ms (0.6%)

series481.0ms (8.1%)

simplify65.0ms (1.1%)

prune123.0ms (2.1%)

localize21.0ms (0.4%)

rewrite33.0ms (0.6%)

series497.0ms (8.4%)

simplify63.0ms (1.1%)

prune148.0ms (2.5%)

regimes222.0ms (3.8%)

bsearch61.0ms (1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (23.3%)

Profiling