Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample19.0ms (0.5%)

Algorithm

1×

intervals

Results

5.0ms	49×	body	1024	valid
4.0ms	143×	body	128	valid
3.0ms	39×	body	512	valid
1.0ms	8×	body	2048	valid
1.0ms	17×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify144.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

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

27.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_776`
14×	`*-un-lft-identity_binary64_760` `add-sqr-sqrt_binary64_782`
6×	`cancel-sign-sub-inv_binary64_726`
5×	`add-cube-cbrt_binary64_795`
4×	`add-log-exp_binary64_799` `difference-of-squares_binary64_729`
3×	`distribute-lft-out--_binary64_712` `pow1_binary64_821`
2×	`distribute-lft-out_binary64_711` `add-exp-log_binary64_798` `sqrt-div_binary64_777` `add-cbrt-cube_binary64_796`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `flip3-+_binary64_763` `sqrt-pow1_binary64_778` `flip-+_binary64_734` `pow1/2_binary64_840` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

2 → 40

Calls

2 calls:

15.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 x 1))

series64.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

48.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
16.0ms	(sqrt.f64 (+.f64 x 1))

simplify88.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4936	794
1	4936	794

prune73.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	3	47

Error

0.1b

Counts

47 → 3

Compiler

Compiled 690 to 454 computations (34.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite45.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_760`
24×	`sqrt-prod_binary64_776`
21×	`distribute-lft-out_binary64_711`
18×	`times-frac_binary64_766`
16×	`add-sqr-sqrt_binary64_782`
15×	`add-cube-cbrt_binary64_795`
7×	`add-exp-log_binary64_798`
6×	`associate-/r*_binary64_704`
5×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `associate-/l*_binary64_705`
2×	`associate-/r/_binary64_706` `sqrt-div_binary64_777` `div-exp_binary64_811`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `inv-pow_binary64_845` `+-commutative_binary64_690` `sum-log_binary64_851` `rec-exp_binary64_810` `pow1/2_binary64_840` `clear-num_binary64_759` `1-exp_binary64_804` `pow-flip_binary64_834`

Counts

3 → 75

Calls

3 calls:

13.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
10.0ms	(sqrt.f64 (+.f64 x 1))

series75.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

33.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
23.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
18.0ms	(sqrt.f64 (+.f64 x 1))

simplify71.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4917	1530
1	4917	1530

prune128.0ms (3.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	79	8	87

Error

0.0b

Counts

87 → 8

Compiler

Compiled 1481 to 1051 computations (29% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
0.3b	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

rewrite119.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`sqrt-prod_binary64_776`
74×	`*-un-lft-identity_binary64_760`
37×	`pow1_binary64_821`
32×	`distribute-lft-out_binary64_711` `add-sqr-sqrt_binary64_782`
28×	`sqrt-div_binary64_777`
18×	`sqrt-pow1_binary64_778` `pow1/2_binary64_840`
17×	`add-exp-log_binary64_798`
16×	`add-cube-cbrt_binary64_795`
15×	`swap-sqr_binary64_727`
14×	`flip3-+_binary64_763` `flip-+_binary64_734` `pow-flip_binary64_834`
11×	`add-cbrt-cube_binary64_796`
10×	`pow-prod-up_binary64_830`
9×	`associate-r_binary64_700` `associate-l_binary64_701`
8×	`associate-/r/_binary64_706` `frac-times_binary64_770`
6×	`pow-sqr_binary64_733` `pow-prod-down_binary64_831`
4×	`unswap-sqr_binary64_728` `rem-sqrt-square_binary64_773` `associate-l/_binary64_703` `prod-exp_binary64_809` `add-log-exp_binary64_799` `associate-r/_binary64_702` `div-exp_binary64_811`
3×	`associate-/l*_binary64_705` `times-frac_binary64_766`
2×	`pow2_binary64_841` `cbrt-undiv_binary64_794` `pow-plus_binary64_823` `rec-exp_binary64_810` `cbrt-unprod_binary64_793` `1-exp_binary64_804`
1×	`frac-2neg_binary64_771` `rem-square-sqrt_binary64_772` `associate-/r_binary64_704` `div-inv_binary64_757` `inv-pow_binary64_845` `sqr-abs_binary64_775` `sqrt-unprod_binary64_780` `clear-num_binary64_759` `-commutative_binary64_691`

Counts

4 → 155

Calls

4 calls:

41.0ms	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
31.0ms	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
16.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series202.0ms (5%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
67.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
33.0ms	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
33.0ms	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

simplify116.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4900	3040
1	4900	3040

prune265.0ms (6.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	167	8	175

Error

0.0b

Counts

175 → 8

Compiler

Compiled 3647 to 2565 computations (29.7% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.3b	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

rewrite61.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64_760`
36×	`sqrt-prod_binary64_776`
33×	`distribute-lft-out_binary64_711`
12×	`pow1_binary64_821` `add-sqr-sqrt_binary64_782`
10×	`swap-sqr_binary64_727`
9×	`flip3-+_binary64_763` `add-cube-cbrt_binary64_795` `flip-+_binary64_734`
8×	`add-log-exp_binary64_799`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `associate-r_binary64_700` `associate-l_binary64_701`
4×	`frac-times_binary64_770`
2×	`associate-l/_binary64_703` `sqrt-div_binary64_777` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702`
1×	`pow2_binary64_841` `unswap-sqr_binary64_728` `rem-sqrt-square_binary64_773` `prod-exp_binary64_809` `distribute-lft-in_binary64_709` `sqrt-pow1_binary64_778` `pow-sqr_binary64_733` `pow-plus_binary64_823` `distribute-rgt-in_binary64_710` `cbrt-unprod_binary64_793` `pow1/2_binary64_840` `pow-prod-up_binary64_830` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 92

Calls

4 calls:

20.0ms	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
10.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 1 x))

series119.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
36.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
24.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
22.0ms	(sqrt.f64 (+.f64 1 x))

simplify104.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4916	1965
1	4916	1965

prune220.0ms (5.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	103	9	112

Error

0.0b

Counts

112 → 9

Compiler

Compiled 2307 to 1580 computations (31.5% saved)

regimes174.0ms (4.3%)

Accuracy

Total 0.2b remaining (92.2%)

Threshold costs 0.2b (92.2%)

Compiler

Compiled 1318 to 1073 computations (18.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.9s (47%)

Algorithm

1×

intervals

Results

356.0ms	2049×	body	1024	valid
205.0ms	4246×	body	128	valid
130.0ms	987×	body	512	valid
49.0ms	214×	body	2048	valid
44.0ms	504×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 631 to 516 computations (18.2% saved)

Details

analyze3.0ms (0.1%)

sample19.0ms (0.5%)

simplify144.0ms (3.5%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

rewrite27.0ms (0.7%)

series64.0ms (1.6%)

simplify88.0ms (2.2%)

prune73.0ms (1.8%)

localize6.0ms (0.2%)

rewrite45.0ms (1.1%)

series75.0ms (1.8%)

simplify71.0ms (1.7%)

prune128.0ms (3.1%)

localize9.0ms (0.2%)

rewrite119.0ms (2.9%)

series202.0ms (5%)

simplify116.0ms (2.9%)

prune265.0ms (6.5%)

localize12.0ms (0.3%)

rewrite61.0ms (1.5%)

series119.0ms (2.9%)

simplify104.0ms (2.6%)

prune220.0ms (5.4%)

regimes174.0ms (4.3%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.9s (47%)

Profiling