Details

analyze452.0ms (6.5%)

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 (0.6%)

Algorithm

1×

intervals

Results

9.0ms	171×	body	128	valid
8.0ms	34×	body	2048	valid
5.0ms	28×	body	1024	valid
3.0ms	11×	body	4096	valid
1.0ms	24×	body	128	nan
1.0ms	7×	body	512	valid
0.0ms	5×	body	256	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify237.0ms (3.4%)

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: 34.4b

Counts

2 → 1

Compiler

Compiled 66 to 54 computations (18.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4 a) c)
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.1b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_423` `pow1_binary64_484` `add-log-exp_binary64_462`
9×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
7×	`add-sqr-sqrt_binary64_445`
6×	`add-cube-cbrt_binary64_458`
3×	`pow-prod-down_binary64_494` `sqrt-prod_binary64_439` `prod-exp_binary64_472` `associate-r_binary64_363` `cbrt-unprod_binary64_456`
2×	`sqrt-div_binary64_440` `distribute-lft-out_binary64_374` `flip3--_binary64_427` `flip--_binary64_398` `sum-log_binary64_514`
1×	`sub-neg_binary64_416` `associate-l_binary64_364` `flip-+_binary64_397` `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` `*-commutative_binary64_354` `flip3-+_binary64_426` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `distribute-rgt-neg-in_binary64_381`

Counts

4 → 60

Calls

4 calls:

10.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
6.0ms	(.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)))

series338.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
117.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
27.0ms	(.f64 (.f64 4 a) c)

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5357	1184

prune283.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	9	73

Merged error: 12.9b

Counts

73 → 9

Compiler

Compiled 5496 to 3854 computations (29.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.7b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.4b	(/.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))
8.1b	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite68.0ms (1%)

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:

19.0ms	(/.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))
17.0ms	(/.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)))

series996.0ms (14.3%)

Counts

4 → 12

Calls

4 calls:

415.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
319.0ms	(/.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))
137.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify103.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4940	4228
1	4940	4228

prune557.0ms (8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	128	9	137
Fresh	6	1	7
Picked	1	0	1
Done	0	1	1
Total	135	11	146

Merged error: 8.2b

Counts

146 → 11

Compiler

Compiled 11846 to 8040 computations (32.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
1.7b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.4b	(/.f64 (.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))) a)
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite70.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_445`
36×	`*-un-lft-identity_binary64_423`
34×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
27×	`associate-r_binary64_363`
24×	`times-frac_binary64_429`
20×	`add-cube-cbrt_binary64_458`
12×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
10×	`sqrt-prod_binary64_439` `pow1_binary64_484`
9×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
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` `associate-/r*_binary64_367`
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`

Counts

4 → 113

Calls

4 calls:

20.0ms	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
19.0ms	(/.f64 (.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))) a)
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series1.0s (14.7%)

Counts

4 → 12

Calls

4 calls:

416.0ms	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
324.0ms	(/.f64 (.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))) a)
145.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
136.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4937	3223
1	4937	3223

prune346.0ms (5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	7	2	9
Picked	0	1	1
Done	0	1	1
Total	126	10	136

Merged error: 8.1b

Counts

136 → 10

Compiler

Compiled 7248 to 4787 computations (34% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4 a) c)
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.7b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
23.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_445`
12×	`*-un-lft-identity_binary64_423`
10×	`pow1_binary64_484` `add-log-exp_binary64_462`
9×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
8×	`add-cube-cbrt_binary64_458`
7×	`sqrt-prod_binary64_439` `cancel-sign-sub-inv_binary64_389`
3×	`pow-prod-down_binary64_494` `diff-log_binary64_515` `prod-exp_binary64_472` `flip3--_binary64_427` `associate-r_binary64_363` `flip--_binary64_398` `cbrt-unprod_binary64_456`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392`
1×	`associate-l_binary64_364` `associate--l-_binary64_361` `neg-log_binary64_516` `rem-sqrt-square_binary64_436` `neg-sub0_binary64_418` `*-commutative_binary64_354` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `distribute-rgt-neg-in_binary64_381`

Counts

4 → 68

Calls

4 calls:

11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
6.0ms	(.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)))

series341.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
119.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
29.0ms	(.f64 (.f64 4 a) c)

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5591	1423

prune112.0ms (1.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	3	4	7
Picked	0	1	1
Done	0	2	2
Total	82	8	90

Merged error: 7.2b

Counts

90 → 8

Compiler

Compiled 2318 to 1466 computations (36.8% saved)

regimes182.0ms (2.6%)

Compiler: Compiled 616 to 506 computations (17.9% saved)

bsearch109.0ms (1.6%)

Steps

Iters	Range	Point
8	6.787489049073195e+118	7.133955408180205e+122	5.525835260688754e+121
9	2.173626231849138e-227	1.6620553427918547e-219	7.131198222427231e-227
8	-1.6407368404235515e+56	-3.3624292403433257e+53	-1.6236541306877014e+56

Iters

Range

Point

6.787489049073195e+118

7.133955408180205e+122

5.525835260688754e+121

2.173626231849138e-227

1.6620553427918547e-219

7.131198222427231e-227

-1.6407368404235515e+56

-3.3624292403433257e+53

-1.6236541306877014e+56

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	112	112
1	112	112

end0.0ms (0%)

sample1.4s (19.6%)

Algorithm

1×

intervals

Results

287.0ms	5258×	body	128	valid
274.0ms	1104×	body	2048	valid
136.0ms	682×	body	1024	valid
123.0ms	398×	body	4096	valid
53.0ms	372×	body	512	valid
33.0ms	662×	body	128	nan
19.0ms	360×	body	128	invalid
18.0ms	186×	body	256	valid

Compiler

Compiled 237 to 182 computations (23.2% saved)

Details

analyze452.0ms (6.5%)

sample38.0ms (0.6%)

simplify237.0ms (3.4%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite30.0ms (0.4%)

series338.0ms (4.9%)

simplify65.0ms (0.9%)

prune283.0ms (4.1%)

localize13.0ms (0.2%)

rewrite68.0ms (1%)

series996.0ms (14.3%)

simplify103.0ms (1.5%)

prune557.0ms (8%)

localize14.0ms (0.2%)

rewrite70.0ms (1%)

series1.0s (14.7%)

simplify81.0ms (1.2%)

prune346.0ms (5%)

localize13.0ms (0.2%)

rewrite32.0ms (0.5%)

series341.0ms (4.9%)

simplify69.0ms (1%)

prune112.0ms (1.6%)

regimes182.0ms (2.6%)

bsearch109.0ms (1.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (19.6%)

Profiling