Details

analyze806.0ms (4.8%)

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
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample50.0ms (0.3%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
2.0ms	18×	body	128	nan
2.0ms	18×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify681.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (575.0ms)

Iter	Nodes	Cost
0	4219	54
1	4219	54

prune16.0ms (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

Error

17.8b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize32.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) a)
0.1b	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b))
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
0.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
19.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
19.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
11×	`*-un-lft-identity_binary64_78`
8×	`add-log-exp_binary64_117`
7×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113`
6×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `difference-of-squares_binary64_47` `pow1/2_binary64_158`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `distribute-lft-out--_binary64_30` `diff-log_binary64_170` `distribute-lft-out_binary64_29` `sub-neg_binary64_71` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 59

Calls

8 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.0ms	(/.f64 (.f64 c 2) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b))

series698.0ms (4.2%)

Counts

4 → 60

Calls

4 calls:

228.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
226.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
146.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
98.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 3753 to 2796 computations (25.5% saved)

simplify113.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5494	2240

prune345.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	111	8	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	8	120

Error

6.3b

Counts

120 → 8

Compiler

Compiled 5029 to 2941 computations (41.5% saved)

localize26.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) a)
0.1b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
8.1b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
19.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
19.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
19.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_100`
9×	`sqrt-prod_binary64_94`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`pow1_binary64_139`
6×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
4×	`add-cbrt-cube_binary64_114` `flip3--_binary64_82` `flip--_binary64_53` `add-exp-log_binary64_116`
3×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158`
1×	`diff-log_binary64_170` `difference-of-squares_binary64_47` `sub-neg_binary64_71`

Counts

4 → 60

Calls

8 calls:

19.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.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)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.0ms	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

series797.0ms (4.8%)

Counts

4 → 52

Calls

4 calls:

315.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
214.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
149.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 4286 to 3084 computations (28% saved)

simplify137.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5332	1947

prune413.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	112	8	120

Error

6.3b

Counts

120 → 8

Compiler

Compiled 5828 to 3479 computations (40.3% saved)

localize43.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) a)
0.1b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
0.1b	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
19.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
19.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
19.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
19.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_94` `add-sqr-sqrt_binary64_100`
8×	`add-cube-cbrt_binary64_113` `sqrt-div_binary64_95` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `flip--_binary64_53` `add-exp-log_binary64_116` `pow1/2_binary64_158`

Counts

4 → 60

Calls

8 calls:

12.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.0ms	(sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

series735.0ms (4.4%)

Counts

4 → 48

Calls

4 calls:

219.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
205.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
166.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
144.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 6492 to 4364 computations (32.8% saved)

simplify90.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5040	1728

prune572.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	108	8	116

Error

6.3b

Counts

116 → 8

Compiler

Compiled 8603 to 5173 computations (39.9% saved)

localize55.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) a)
5.4b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
19.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_100`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-log-exp_binary64_117` `cbrt-prod_binary64_109`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `flip3--_binary64_82` `flip--_binary64_53` `add-exp-log_binary64_116`
3×	`sqrt-prod_binary64_94` `cancel-sign-sub-inv_binary64_44`
2×	`pow1/3_binary64_160` `sqrt-div_binary64_95`
1×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `pow1/2_binary64_158` `sub-neg_binary64_71`

Counts

4 → 55

Calls

8 calls:

17.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
8.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))) a)

series1.6s (9.7%)

Counts

4 → 60

Calls

4 calls:

611.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) b)
485.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
404.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
105.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 6391 to 4812 computations (24.7% saved)

simplify93.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5317	3355

prune440.0ms (2.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	113	10	123

Error

6.2b

Counts

123 → 10

Compiler

Compiled 6500 to 3907 computations (39.9% saved)

simplify40.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	431	2631
1	431	2631

regimes700.0ms (4.2%)

Accuracy

Total 1.3b remaining (19.9%)

Threshold costs 0b (0%)

Compiler

Compiled 5169 to 3570 computations (30.9% saved)

bsearch47.0ms (0.3%)

Steps

Iters	Range		Point
3	4.998262510207159e+126	6.356574971969715e+126	5.164708177196388e+126
6	-4.094168518393342e+62	-9.452236791432636e+61	-4.0595823059314417e+62

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	123	150
1	123	150

end0.0ms (0%)

sample8.0s (47.8%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
76.0ms	635×	body	128	nan
48.0ms	382×	body	128	invalid

Compiler

Compiled 5402 to 3710 computations (31.3% saved)

Pareto

0.36459644539555724

Details

analyze806.0ms (4.8%)

sample50.0ms (0.3%)

simplify681.0ms (4.1%)

prune16.0ms (0.1%)

localize32.0ms (0.2%)

rewrite32.0ms (0.2%)

series698.0ms (4.2%)

simplify113.0ms (0.7%)

prune345.0ms (2.1%)

localize26.0ms (0.2%)

rewrite34.0ms (0.2%)

series797.0ms (4.8%)

simplify137.0ms (0.8%)

prune413.0ms (2.5%)

localize43.0ms (0.3%)

rewrite35.0ms (0.2%)

series735.0ms (4.4%)

simplify90.0ms (0.5%)

prune572.0ms (3.4%)

localize55.0ms (0.3%)

rewrite44.0ms (0.3%)

series1.6s (9.7%)

simplify93.0ms (0.6%)

prune440.0ms (2.6%)

simplify40.0ms (0.2%)

regimes700.0ms (4.2%)

bsearch47.0ms (0.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.0s (47.8%)

Profiling