Details

analyze211.0ms (6.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	7	20
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

Symmetry

(sort x y)

Compiler

Compiled 8 to 6 computations (25% saved)

sample23.0ms (0.7%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

prune3.0ms (0.1%)

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 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

3×	`add-log-exp_binary64_3527`
1×	`sum-log_binary64_3579` `pow1_binary64_3549` `add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524` `add-cube-cbrt_binary64_3523` `add-sqr-sqrt_binary64_3510` `flip3-+_binary64_3491` `*-un-lft-identity_binary64_3488` `flip-+_binary64_3462` `+-commutative_binary64_3418`

Counts

1 → 11

Calls

1 calls:

7.0ms

(+.f64 (*.f64 x x) (*.f64 y y))

Compiler

Compiled 178 to 40 computations (77.5% saved)

series122.0ms (3.8%)

Error

0.0b

Counts

1 → 12

Calls

1 calls:

109.0ms

(+.f64 (*.f64 x x) (*.f64 y y))

Compiler

Compiled 162 to 152 computations (6.2% saved)

simplify86.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4921	247
1	4921	247

prune16.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	21	2	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	3	24

Error

Counts

24 → 3

Compiler

Compiled 235 to 60 computations (74.5% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 y y) (.f64 x x))
0.0b	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 x x))))
5.6b	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
5.6b	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))

rewrite155.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

30×	`add-sqr-sqrt_binary64_3510`
24×	`sqrt-prod_binary64_3504`
21×	`pow1_binary64_3549`
16×	`sqrt-div_binary64_3505`
14×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
10×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506`
9×	`flip3-+_binary64_3491` `flip-+_binary64_3462`
8×	`swap-sqr_binary64_3455`
6×	`add-log-exp_binary64_3527` `add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524` `associate-l_binary64_3429` `associate-r_binary64_3428`
5×	`pow-prod-up_binary64_3558`
4×	`rem-sqrt-square_binary64_3501` `frac-times_binary64_3498` `unswap-sqr_binary64_3456`
3×	`pow-prod-down_binary64_3559` `pow-sqr_binary64_3461`
2×	`associate-l/_binary64_3431` `associate-r/_binary64_3430`
1×	`pow2_binary64_3569` `pow-plus_binary64_3551` `prod-exp_binary64_3537` `cbrt-unprod_binary64_3521` `sqrt-unprod_binary64_3508` `sqr-abs_binary64_3503` `rem-square-sqrt_binary64_3500` `*-commutative_binary64_3419` `sum-log_binary64_3579` `+-commutative_binary64_3418`

Counts

4 → 99

Calls

4 calls:

25.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 x x))))
7.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
7.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
4.0ms	(+.f64 (.f64 y y) (.f64 x x))

Compiler

Compiled 2841 to 321 computations (88.7% saved)

series382.0ms (12%)

Error

Counts

4 → 44

Calls

4 calls:

118.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 x x))) (sqrt.f64 (+.f64 (.f64 y y) (*.f64 x x))))
93.0ms	(+.f64 (.f64 y y) (.f64 x x))
77.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))
69.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 x x)))

Compiler

Compiled 1548 to 994 computations (35.8% saved)

simplify113.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4956	1897
1	4956	1897

prune106.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	143	3	146

Error

Counts

146 → 3

Compiler

Compiled 2501 to 456 computations (81.8% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 x x) (.f64 y y))
1.8b	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
33.5b	(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (-.f64 (.f64 x x) (.f64 y y)))

rewrite251.0ms (7.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

97×	`add-sqr-sqrt_binary64_3510`
70×	`difference-of-squares_binary64_3457`
56×	`times-frac_binary64_3494`
51×	`unpow-prod-down_binary64_3567`
49×	`*-un-lft-identity_binary64_3488`
37×	`sqr-pow_binary64_3460`
25×	`add-cube-cbrt_binary64_3523`
14×	`associate-/l*_binary64_3433`
12×	`distribute-lft-out--_binary64_3440`
8×	`cancel-sign-sub-inv_binary64_3454`
7×	`add-log-exp_binary64_3527`
5×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524`
4×	`flip3--_binary64_3492` `flip--_binary64_3463` `associate-/r*_binary64_3432`
3×	`pow1_binary64_3549`
2×	`associate-/l/_binary64_3435` `associate-/r/_binary64_3434` `diff-log_binary64_3580` `sub-neg_binary64_3481`
1×	`div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `frac-2neg_binary64_3499` `div-sub_binary64_3493` `clear-num_binary64_3487` `div-inv_binary64_3485`

Counts

3 → 133

Calls

3 calls:

22.0ms	(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (-.f64 (.f64 x x) (.f64 y y)))
8.0ms	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
4.0ms	(-.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 3861 to 1859 computations (51.9% saved)

series589.0ms (18.6%)

Error

Counts

3 → 36

Calls

3 calls:

272.0ms	(/.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (-.f64 (.f64 x x) (.f64 y y)))
190.0ms	(-.f64 (pow.f64 x 4) (pow.f64 y 4))
104.0ms	(-.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 990 to 743 computations (24.9% saved)

simplify98.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4940	3865
1	4940	3865

prune173.0ms (5.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	169	3	172

Error

Counts

172 → 3

Compiler

Compiled 3555 to 1317 computations (63% saved)

regimes131.0ms (4.1%)

Accuracy

Total 0.0b remaining (77.6%)

Threshold costs 0.0b (77.6%)

Compiler

Compiled 583 to 407 computations (30.2% saved)

bsearch0.0ms (0%)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	15
1	10	15

Remove

(sort x y)

Compiler

Compiled 20 to 16 computations (20% saved)

end0.0ms (0%)

sample647.0ms (20.4%)

Algorithm

1×

intervals

Results

222.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 121 to 87 computations (28.1% saved)

Details

analyze211.0ms (6.6%)

sample23.0ms (0.7%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

rewrite19.0ms (0.6%)

series122.0ms (3.8%)

simplify86.0ms (2.7%)

prune16.0ms (0.5%)

localize13.0ms (0.4%)

rewrite155.0ms (4.9%)

series382.0ms (12%)

simplify113.0ms (3.6%)

prune106.0ms (3.3%)

localize11.0ms (0.3%)

rewrite251.0ms (7.9%)

series589.0ms (18.6%)

simplify98.0ms (3.1%)

prune173.0ms (5.5%)

regimes131.0ms (4.1%)

bsearch0.0ms (0%)

simplify8.0ms (0.3%)

end0.0ms (0%)

sample647.0ms (20.4%)

Profiling