Details

analyze475.0ms (7.2%)

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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	32×	body	2048	valid
9.0ms	176×	body	128	valid
4.0ms	23×	body	1024	valid
4.0ms	12×	body	4096	valid
1.0ms	9×	body	512	valid
1.0ms	22×	body	128	nan
1.0ms	11×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify219.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 34.2b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.8b	(-.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))))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_435`
13×	`*-un-lft-identity_binary64_414`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
7×	`add-cube-cbrt_binary64_446`
6×	`times-frac_binary64_420` `difference-of-squares_binary64_383` `sqrt-prod_binary64_429` `associate-/l*_binary64_361`
5×	`pow1_binary64_472`
4×	`flip3--_binary64_418` `flip--_binary64_389`
3×	`distribute-lft-out--_binary64_368`
2×	`sqrt-div_binary64_430` `diff-log_binary64_503` `cbrt-undiv_binary64_445` `sub-neg_binary64_407` `associate-/l/_binary64_363` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `prod-exp_binary64_460` `frac-2neg_binary64_425` `pow1/2_binary64_491` `cbrt-unprod_binary64_444` `div-sub_binary64_419` `associate-/r*_binary64_360` `rem-sqrt-square_binary64_427`

Counts

4 → 70

Calls

4 calls:

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

series545.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
123.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
66.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4930	1975
1	4930	1975

prune129.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 7.0b

Counts

83 → 8

Compiler

Compiled 2080 to 1135 computations (45.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
1.0b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
1.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
25.1b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_435`
13×	`*-un-lft-identity_binary64_414`
9×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`add-log-exp_binary64_450`
7×	`add-cube-cbrt_binary64_446`
6×	`times-frac_binary64_420` `difference-of-squares_binary64_383` `sqrt-prod_binary64_429` `associate-/l*_binary64_361`
5×	`pow1_binary64_472`
3×	`distribute-lft-out--_binary64_368`
2×	`flip3--_binary64_418` `sqrt-div_binary64_430` `flip3-+_binary64_417` `cbrt-undiv_binary64_445` `flip-+_binary64_388` `flip--_binary64_389` `associate-/l/_binary64_363` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `+-commutative_binary64_346` `prod-exp_binary64_460` `sub-neg_binary64_407` `frac-2neg_binary64_425` `pow1/2_binary64_491` `cbrt-unprod_binary64_444` `sum-log_binary64_502` `div-sub_binary64_419` `associate-/r*_binary64_360` `rem-sqrt-square_binary64_427`

Counts

4 → 70

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
5.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series536.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (.f64 a 2))
130.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))
128.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
66.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4901	1956
1	4901	1956

prune93.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	82	8	90

Merged error: 6.8b

Counts

90 → 8

Compiler

Compiled 2056 to 1234 computations (40% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
3.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (.f64 a 2))
11.4b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
25.1b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
22×	`times-frac_binary64_420`
21×	`*-un-lft-identity_binary64_414`
17×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
13×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
12×	`add-sqr-sqrt_binary64_435`
11×	`add-cube-cbrt_binary64_446` `associate-/l*_binary64_361`
6×	`associate-/r/_binary64_362` `add-log-exp_binary64_450`
5×	`pow1_binary64_472` `flip3-+_binary64_417` `flip-+_binary64_388` `distribute-lft-out_binary64_367` `associate-/r*_binary64_360`
4×	`div-inv_binary64_411`
3×	`sqrt-prod_binary64_429`
2×	`clear-num_binary64_413` `sqrt-div_binary64_430` `frac-2neg_binary64_425`
1×	`sqrt-pow1_binary64_431` `+-commutative_binary64_346` `pow1/2_binary64_491` `associate-/l/_binary64_363` `sum-log_binary64_502` `rem-sqrt-square_binary64_427`

Counts

4 → 102

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
7.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series934.0ms (14.1%)

Counts

4 → 12

Calls

4 calls:

382.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
305.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))))) (.f64 a 2))
127.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
120.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5111	3121

prune154.0ms (2.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	114	8	122

Merged error: 6.7b

Counts

122 → 8

Compiler

Compiled 3250 to 1998 computations (38.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4))))))))
1.0b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
2.0b	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
25.1b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite77.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

273×	`times-frac_binary64_420`
135×	`*-un-lft-identity_binary64_414`
110×	`add-sqr-sqrt_binary64_435`
109×	`add-cube-cbrt_binary64_446`
38×	`add-exp-log_binary64_449`
35×	`associate-/r*_binary64_360`
29×	`associate-/r/_binary64_362`
23×	`div-exp_binary64_462`
18×	`add-cbrt-cube_binary64_447`
17×	`div-inv_binary64_411`
15×	`flip3-+_binary64_417` `flip-+_binary64_388`
13×	`distribute-lft-out_binary64_367`
9×	`cbrt-undiv_binary64_445`
8×	`add-log-exp_binary64_450`
6×	`pow1_binary64_472`
4×	`1-exp_binary64_455` `rec-exp_binary64_461`
3×	`prod-exp_binary64_460` `sqrt-prod_binary64_429` `associate-/l*_binary64_361`
2×	`sqrt-div_binary64_430` `+-commutative_binary64_346` `sum-log_binary64_502`
1×	`clear-num_binary64_413` `inv-pow_binary64_496` `pow-flip_binary64_485` `sqrt-pow1_binary64_431` `frac-2neg_binary64_425` `pow1/2_binary64_491` `cbrt-unprod_binary64_444` `rem-sqrt-square_binary64_427`

Counts

4 → 210

Calls

4 calls:

21.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4))))))))
7.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
5.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series655.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

364.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4))))))))
115.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
109.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))
67.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))

simplify102.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5026	8452

prune380.0ms (5.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	220	2	222
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	221	9	230

Merged error: 6.7b

Counts

230 → 9

Compiler

Compiled 7071 to 4671 computations (33.9% saved)

regimes339.0ms (5.1%)

Compiler: Compiled 543 to 456 computations (16% saved)

bsearch111.0ms (1.7%)

Steps

Iters	Range	Point
10	1.6829726428472436e+90	9.502704283103217e+100	7.7377607878944895e+96
9	-2.0073421179495267e-256	-1.6377269175435972e-261	-7.621813580046727e-260
9	-7.464578554549161e+98	-1.7868669415526677e+91	-1.3138164296877506e+98

Iters

Range

Point

1.6829726428472436e+90

9.502704283103217e+100

7.7377607878944895e+96

-2.0073421179495267e-256

-1.6377269175435972e-261

-7.621813580046727e-260

-7.464578554549161e+98

-1.7868669415526677e+91

-1.3138164296877506e+98

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	69	88
1	69	88

end0.0ms (0%)

sample1.4s (21.7%)

Algorithm

1×

intervals

Results

279.0ms	1093×	body	2048	valid
272.0ms	5224×	body	128	valid
144.0ms	712×	body	1024	valid
135.0ms	427×	body	4096	valid
54.0ms	362×	body	512	valid
35.0ms	654×	body	128	nan
20.0ms	389×	body	128	invalid
18.0ms	182×	body	256	valid

Compiler

Compiled 298 to 230 computations (22.8% saved)

Details

analyze475.0ms (7.2%)

sample39.0ms (0.6%)

simplify219.0ms (3.3%)

prune6.0ms (0.1%)

localize11.0ms (0.2%)

rewrite37.0ms (0.6%)

series545.0ms (8.2%)

simplify73.0ms (1.1%)

prune129.0ms (1.9%)

localize11.0ms (0.2%)

rewrite41.0ms (0.6%)

series536.0ms (8.1%)

simplify70.0ms (1.1%)

prune93.0ms (1.4%)

localize12.0ms (0.2%)

rewrite53.0ms (0.8%)

series934.0ms (14.1%)

simplify57.0ms (0.9%)

prune154.0ms (2.3%)

localize12.0ms (0.2%)

rewrite77.0ms (1.2%)

series655.0ms (9.9%)

simplify102.0ms (1.5%)

prune380.0ms (5.7%)

regimes339.0ms (5.1%)

bsearch111.0ms (1.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (21.7%)

Profiling