Details

analyze12.0ms (0.3%)

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 12 to 11 computations (8.3% saved)

sample225.0ms (5.9%)

Algorithm

1×

intervals

Results

216.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify129.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	466	17
1	466	17

prune4.0ms (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

Merged error: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
6×	`associate-/l*_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `pow1_binary64` `associate-/r/_binary64`
3×	`add-log-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

3 → 100

Calls

3 calls:

11.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series58.0ms (1.5%)

Counts

3 → 9

Calls

3 calls:

23.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
21.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
13.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify71.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	6106	2062

prune134.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	107	3	110

Merged error: 0b

Counts

110 → 3

Compiler

Compiled 2011 to 1622 computations (19.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite118.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

714×	`times-frac_binary64`
690×	`*-un-lft-identity_binary64`
480×	`add-sqr-sqrt_binary64`
424×	`sqrt-prod_binary64`
286×	`add-cube-cbrt_binary64`
128×	`difference-of-squares_binary64`
106×	`distribute-lft-out_binary64`
64×	`distribute-lft-out--_binary64`
54×	`associate-/l*_binary64`
24×	`sqrt-div_binary64`
20×	`associate-/r/_binary64`
14×	`associate-/r*_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-/l/_binary64` `div-sub_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3--_binary64` `flip--_binary64`

Counts

4 → 513

Calls

4 calls:

25.0ms	(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x)))
10.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
3.0ms	(sqrt.f64 (+.f64 1 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

series72.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
14.0ms	(sqrt.f64 (+.f64 1 x))
13.0ms	(sqrt.f64 (+.f64 1 x))
13.0ms	(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x)))

simplify191.0ms (5%)

Algorithm

1×	egg-herbie

Counts

525 → 525

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5000	15882

prune1.3s (33.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	525	0	525
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	525	3	528

Merged error: 0b

Counts

528 → 3

Compiler

Compiled 14140 to 11517 computations (18.6% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`cbrt-prod_binary64`
44×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
18×	`cbrt-div_binary64`
15×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64`
11×	`pow1_binary64` `swap-sqr_binary64`
9×	`flip3--_binary64` `associate-r_binary64` `pow1/3_binary64` `associate-l_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 107

Calls

4 calls:

13.0ms	(*.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x)))
4.0ms	(cbrt.f64 (-.f64 1 x))
3.0ms	(cbrt.f64 (-.f64 1 x))
3.0ms	(cbrt.f64 (-.f64 1 x))

series111.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(cbrt.f64 (-.f64 1 x))
27.0ms	(*.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x)))
23.0ms	(cbrt.f64 (-.f64 1 x))
23.0ms	(cbrt.f64 (-.f64 1 x))

simplify67.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4886	1774
1	4886	1774

prune190.0ms (5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	119	3	122

Merged error: 0b

Counts

122 → 3

Compiler

Compiled 3295 to 2667 computations (19.1% saved)

regimes148.0ms (3.9%)

Compiler: Compiled 1664 to 1447 computations (13% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	21
1	24	21

end0.0ms (0%)

sample863.0ms (22.8%)

Algorithm

1×

intervals

Results

383.0ms

8000×

body

128

valid

Compiler

Compiled 335 to 293 computations (12.5% saved)

Details

analyze12.0ms (0.3%)

sample225.0ms (5.9%)

simplify129.0ms (3.4%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite38.0ms (1%)

series58.0ms (1.5%)

simplify71.0ms (1.9%)

prune134.0ms (3.6%)

localize10.0ms (0.3%)

rewrite118.0ms (3.1%)

series72.0ms (1.9%)

simplify191.0ms (5%)

prune1.3s (33.9%)

localize13.0ms (0.4%)

rewrite34.0ms (0.9%)

series111.0ms (2.9%)

simplify67.0ms (1.8%)

prune190.0ms (5%)

regimes148.0ms (3.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample863.0ms (22.8%)

Profiling