Details

analyze158.0ms (7.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	26
1	67	26
0	2	2
1	2	2

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 16 to 8 computations (50% saved)

sample13.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 31 to 17 computations (45.2% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	39	13
1	39	13

prune7.0ms (0.3%)

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

Error

0.0b

Counts

2 → 2

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

rewrite22.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp_binary64_16144`
10×	`sum-log_binary64_16196`
3×	`*-un-lft-identity_binary64_16105` `flip-+_binary64_16079` `add-cube-cbrt_binary64_16140` `add-sqr-sqrt_binary64_16127` `add-exp-log_binary64_16143` `+-commutative_binary64_16035` `flip3-+_binary64_16108` `pow1_binary64_16166` `add-cbrt-cube_binary64_16141`
2×	`associate-+l+_binary64_16038`

Counts

3 → 38

Calls

3 calls:

9.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series79.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

29.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
29.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
21.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify68.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5013	758

prune43.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	42	5	47
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	42	7	49

Error

0.0b

Counts

49 → 7

Compiler

Compiled 997 to 269 computations (73% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.2b	(.f64 y (.f64 y 3))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-exp-log_binary64_16143` `pow1_binary64_16166` `add-cbrt-cube_binary64_16141`
3×	`cbrt-unprod_binary64_16138` `pow-prod-down_binary64_16176` `prod-exp_binary64_16154` `associate-l_binary64_16046`
2×	`*-un-lft-identity_binary64_16105` `add-cube-cbrt_binary64_16140` `add-sqr-sqrt_binary64_16127`
1×	`add-log-exp_binary64_16144` `associate-r_binary64_16045` `*-commutative_binary64_16036`

Counts

1 → 18

Calls

1 calls:

5.0ms

(*.f64 y (*.f64 y 3))

series19.0ms (0.9%)

Counts

1 → 3

Calls

1 calls:

19.0ms

(*.f64 y (*.f64 y 3))

simplify64.0ms (3%)

Algorithm

1×	egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4830	166
1	4830	166

prune20.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	20	1	21
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	21	7	28

Error

0.0b

Counts

28 → 7

Compiler

Compiled 371 to 195 computations (47.4% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) (.f64 y y))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
6.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
6.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

rewrite46.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_16127`
24×	`sqrt-prod_binary64_16121`
21×	`pow1_binary64_16166`
16×	`sqrt-div_binary64_16122`
14×	`*-un-lft-identity_binary64_16105` `add-cube-cbrt_binary64_16140`
10×	`sqrt-pow1_binary64_16123` `pow1/2_binary64_16185`
9×	`flip-+_binary64_16079` `flip3-+_binary64_16108`
8×	`swap-sqr_binary64_16072`
6×	`add-exp-log_binary64_16143` `add-log-exp_binary64_16144` `associate-r_binary64_16045` `associate-l_binary64_16046` `add-cbrt-cube_binary64_16141`
5×	`pow-prod-up_binary64_16175`
4×	`rem-sqrt-square_binary64_16118` `frac-times_binary64_16115` `unswap-sqr_binary64_16073`
3×	`pow-sqr_binary64_16078` `pow-prod-down_binary64_16176`
2×	`associate-r/_binary64_16047` `associate-l/_binary64_16048`
1×	`rem-square-sqrt_binary64_16117` `cbrt-unprod_binary64_16138` `pow-plus_binary64_16168` `sum-log_binary64_16196` `+-commutative_binary64_16035` `*-commutative_binary64_16036` `prod-exp_binary64_16154` `sqrt-unprod_binary64_16125` `sqr-abs_binary64_16120` `pow2_binary64_16186`

Counts

4 → 99

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
12.0ms	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) (.f64 y y))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

series126.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
32.0ms	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) (.f64 y y))
31.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
29.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

simplify83.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4942	2032
1	4942	2032

prune93.0ms (4.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	111	7	118

Error

Counts

118 → 7

Compiler

Compiled 2928 to 550 computations (81.2% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 y y) 3)
0.3b	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) 3))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3))))
6.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))
6.5b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))

rewrite38.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_16127`
26×	`pow1_binary64_16166`
24×	`sqrt-prod_binary64_16121`
16×	`sqrt-div_binary64_16122`
15×	`*-un-lft-identity_binary64_16105` `add-cube-cbrt_binary64_16140`
11×	`add-exp-log_binary64_16143` `add-cbrt-cube_binary64_16141`
10×	`sqrt-pow1_binary64_16123` `pow1/2_binary64_16185`
9×	`associate-r_binary64_16045`
8×	`flip-+_binary64_16079` `swap-sqr_binary64_16072` `flip3-+_binary64_16108`
7×	`associate-l_binary64_16046`
6×	`pow-prod-down_binary64_16176`
5×	`pow-prod-up_binary64_16175` `unswap-sqr_binary64_16073`
4×	`rem-sqrt-square_binary64_16118` `cbrt-unprod_binary64_16138` `frac-times_binary64_16115` `add-log-exp_binary64_16144` `prod-exp_binary64_16154`
3×	`pow-sqr_binary64_16078`
2×	`associate-r/_binary64_16047` `associate-l/_binary64_16048` `*-commutative_binary64_16036`
1×	`rem-square-sqrt_binary64_16117` `pow-plus_binary64_16168` `sqrt-unprod_binary64_16125` `sqr-abs_binary64_16120` `pow2_binary64_16186`

Counts

4 → 107

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) 3))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3))))
6.0ms	(.f64 (.f64 y y) 3)
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))

series115.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))
32.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3)))
28.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 (.f64 y y) 3))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 y y) 3))))
20.0ms	(.f64 (.f64 y y) 3)

simplify103.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4898	1950
1	4898	1950

prune112.0ms (5.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	119	7	126

Error

Counts

126 → 7

Compiler

Compiled 2687 to 1326 computations (50.7% saved)

regimes187.0ms (8.6%)

Accuracy

Total 0.1b remaining (94.9%)

Threshold costs 0.1b (94.9%)

Compiler

Compiled 2356 to 1334 computations (43.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	10	13

end0.0ms (0%)

sample718.0ms (33.3%)

Algorithm

1×

intervals

Results

219.0ms	8000×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 498 to 284 computations (43% saved)

Details

analyze158.0ms (7.3%)

sample13.0ms (0.6%)

simplify7.0ms (0.3%)

prune7.0ms (0.3%)

localize7.0ms (0.3%)

rewrite22.0ms (1%)

series79.0ms (3.7%)

simplify68.0ms (3.1%)

prune43.0ms (2%)

localize6.0ms (0.3%)

rewrite6.0ms (0.3%)

series19.0ms (0.9%)

simplify64.0ms (3%)

prune20.0ms (0.9%)

localize10.0ms (0.5%)

rewrite46.0ms (2.1%)

series126.0ms (5.8%)

simplify83.0ms (3.8%)

prune93.0ms (4.3%)

localize8.0ms (0.4%)

rewrite38.0ms (1.7%)

series115.0ms (5.3%)

simplify103.0ms (4.8%)

prune112.0ms (5.2%)

regimes187.0ms (8.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample718.0ms (33.3%)

Profiling