Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 13 to 13 computations (0% saved)

sample40.0ms (0.7%)

Algorithm

1×

intervals

Results

25.0ms	97×	body	1280	valid
5.0ms	129×	body	80	valid
3.0ms	19×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	46	15
1	46	15

prune4.0ms (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

Merged error: 15.1b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.9b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
8×	`sqrt-prod_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 34

Calls

2 calls:

9.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

series23.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

12.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
11.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

simplify91.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5087	763

prune39.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	3	41

Merged error: 14.6b

Counts

41 → 3

Compiler

Compiled 683 to 624 computations (8.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.4b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
44×	`times-frac_binary64`
29×	`distribute-lft-out_binary64`
18×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
16×	`difference-of-squares_binary64`
8×	`distribute-lft-out--_binary64`
6×	`associate-/r_binary64` `associate-/l_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 95

Calls

3 calls:

17.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

series51.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

32.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
11.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
8.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify95.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4980	3292
1	4980	3292

prune147.0ms (2.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	104	3	107

Merged error: 14.5b

Counts

107 → 3

Compiler

Compiled 2980 to 2682 computations (10% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.2b	(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.5b	(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite138.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

217×	`*-un-lft-identity_binary64`
188×	`times-frac_binary64`
147×	`add-sqr-sqrt_binary64`
89×	`distribute-lft-out_binary64`
81×	`add-cube-cbrt_binary64`
48×	`sqrt-prod_binary64`
16×	`associate-/l*_binary64`
12×	`associate-/r*_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
8×	`associate-/r/_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`distribute-rgt-out--_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 204

Calls

4 calls:

94.0ms	(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
15.0ms	(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
11.0ms	(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

series118.0ms (2%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
28.0ms	(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
21.0ms	(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
12.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

simplify129.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4986	8113
1	4986	8113

prune626.0ms (10.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	215	4	219

Merged error: 14.3b

Counts

219 → 4

Compiler

Compiled 8892 to 8028 computations (9.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
0.5b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
0.5b	(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
0.6b	(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite224.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Rules

319×	`times-frac_binary64`
306×	`*-un-lft-identity_binary64`
256×	`add-sqr-sqrt_binary64`
217×	`sqrt-prod_binary64`
142×	`add-cube-cbrt_binary64`
104×	`distribute-lft-out_binary64`
27×	`associate-/r*_binary64`
19×	`associate-/l*_binary64`
16×	`distribute-lft-out--_binary64`
15×	`add-exp-log_binary64` `difference-of-squares_binary64` `div-inv_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/r/_binary64` `sqrt-div_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `div-exp_binary64`
5×	`flip3-+_binary64` `cbrt-undiv_binary64` `flip-+_binary64`
3×	`distribute-rgt-out--_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-flip_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `inv-pow_binary64` `rec-exp_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 315

Calls

4 calls:

160.0ms	(-.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
20.0ms	(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
13.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
12.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

series155.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(-.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))
41.0ms	(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
26.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
23.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

simplify193.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

327 → 327

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4944	13386
1	4944	13386

prune2.1s (36.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	324	3	327
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	326	5	331

Merged error: 14.3b

Counts

331 → 5

Compiler

Compiled 18777 to 17166 computations (8.6% saved)

regimes55.0ms (0.9%)

Compiler: Compiled 536 to 498 computations (7.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	68
1	44	68

end0.0ms (0%)

sample1.5s (25.2%)

Algorithm

1×

intervals

Results

623.0ms	2910×	body	1280	valid
151.0ms	4021×	body	80	valid
104.0ms	609×	body	640	valid
37.0ms	299×	body	320	valid
12.0ms	161×	body	160	valid

Compiler

Compiled 321 to 300 computations (6.5% saved)

Details

analyze1.0ms (0%)

sample40.0ms (0.7%)

simplify14.0ms (0.2%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

rewrite16.0ms (0.3%)

series23.0ms (0.4%)

simplify91.0ms (1.6%)

prune39.0ms (0.7%)

localize10.0ms (0.2%)

rewrite34.0ms (0.6%)

series51.0ms (0.9%)

simplify95.0ms (1.6%)

prune147.0ms (2.5%)

localize10.0ms (0.2%)

rewrite138.0ms (2.3%)

series118.0ms (2%)

simplify129.0ms (2.2%)

prune626.0ms (10.7%)

localize13.0ms (0.2%)

rewrite224.0ms (3.8%)

series155.0ms (2.6%)

simplify193.0ms (3.3%)

prune2.1s (36.6%)

regimes55.0ms (0.9%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.5s (25.2%)

Profiling