Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample12.0ms (0.8%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

128

valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify383.0ms (24.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (284.0ms)

Iter	Nodes	Cost
0	7521	9

prune2.0ms (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 12 to 10 computations (16.7% saved)

localize4.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite5.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`sqrt-prod_binary64_3504`
4×	`add-sqr-sqrt_binary64_3510`
3×	`*-un-lft-identity_binary64_3488`
2×	`difference-of-squares_binary64_3457` `sqrt-div_binary64_3505` `add-cube-cbrt_binary64_3523` `pow1_binary64_3549`
1×	`flip3--_binary64_3492` `add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `add-log-exp_binary64_3527` `pow1/2_binary64_3568` `flip--_binary64_3463` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501`

Counts

1 → 17

Calls

2 calls:

4.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series29.0ms (1.8%)

Counts

1 → 6

Calls

1 calls:

28.0ms

(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 77 to 73 computations (5.2% saved)

simplify142.0ms (9.2%)

Algorithm

1×	egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	4759	284
1	4759	284

prune26.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	22	1	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	2	24

Error

Counts

24 → 2

Compiler

Compiled 248 to 167 computations (32.7% saved)

localize9.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
0.0b	(sqrt.f64 (+.f64 1 (*.f64 x x)))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
0.0b	(sqrt.f64 (+.f64 1 (*.f64 x x)))

rewrite35.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`sqrt-prod_binary64_3504`
95×	`add-sqr-sqrt_binary64_3510`
80×	`*-un-lft-identity_binary64_3488`
78×	`times-frac_binary64_3494`
45×	`add-cube-cbrt_binary64_3523`
42×	`difference-of-squares_binary64_3457`
14×	`unpow-prod-down_binary64_3567` `sqr-pow_binary64_3460`
13×	`associate-/l*_binary64_3433`
7×	`distribute-lft-out--_binary64_3440`
6×	`associate-/r*_binary64_3432` `sqrt-div_binary64_3505`
4×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
3×	`pow1_binary64_3549`
2×	`associate-/l/_binary64_3435` `flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/r/_binary64_3434` `add-log-exp_binary64_3527`
1×	`clear-num_binary64_3487` `flip3--_binary64_3492` `sqrt-undiv_binary64_3509` `frac-2neg_binary64_3499` `pow1/2_binary64_3568` `flip--_binary64_3463` `sqrt-pow1_binary64_3506` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485` `rem-sqrt-square_binary64_3501`

Counts

2 → 129

Calls

4 calls:

16.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 x x)))
0.0ms	(sqrt.f64 (+.f64 1 (*.f64 x x)))
0.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))

series81.0ms (5.2%)

Counts

2 → 16

Calls

2 calls:

46.0ms	(sqrt.f64 (+.f64 1 (*.f64 x x)))
35.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 4))) (sqrt.f64 (+.f64 1 (*.f64 x x))))

Compiler

Compiled 296 to 266 computations (10.1% saved)

simplify99.0ms (6.4%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4942	4409
1	4942	4409

prune184.0ms (12%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	145	2	147

Error

Counts

147 → 2

Compiler

Compiled 3365 to 2292 computations (31.9% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	80
1	84	80

regimes48.0ms (3.1%)

Compiler: Compiled 250 to 224 computations (10.4% saved)

bsearch0.0ms (0%)

regimes16.0ms (1%)

Compiler: Compiled 28 to 30 computations (-7.1% saved)

bsearch0.0ms (0%)

regimes10.0ms (0.6%)

Accuracy

Total 0.0b remaining (95.5%)

Threshold costs 0.0b (95.5%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 14 to 13 computations (7.1% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	20
1	41	20

end0.0ms (0%)

sample445.0ms (28.9%)

Algorithm

1×

intervals

Results

187.0ms

8000×

body

128

valid

Compiler

Compiled 76 to 70 computations (7.9% saved)

Pareto

0.4740306792929222

Details

analyze3.0ms (0.2%)

sample12.0ms (0.8%)

simplify383.0ms (24.8%)

prune2.0ms (0.1%)

localize4.0ms (0.3%)

rewrite5.0ms (0.3%)

series29.0ms (1.8%)

simplify142.0ms (9.2%)

prune26.0ms (1.7%)

localize9.0ms (0.6%)

rewrite35.0ms (2.3%)

series81.0ms (5.2%)

simplify99.0ms (6.4%)

prune184.0ms (12%)

simplify4.0ms (0.2%)

regimes48.0ms (3.1%)

bsearch0.0ms (0%)

regimes16.0ms (1%)

bsearch0.0ms (0%)

regimes10.0ms (0.6%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample445.0ms (28.9%)

Profiling