Details

analyze102.0ms (2.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11
0	1	1
1	1	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)

sample18.0ms (0.4%)

Algorithm

1×

intervals

Results

5.0ms	56×	body	1024	valid
4.0ms	138×	body	128	valid
3.0ms	38×	body	512	valid
1.0ms	9×	body	2048	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0%)

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

29.6b

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))
3.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_12029`
14×	`add-sqr-sqrt_binary64_12035` `*-un-lft-identity_binary64_12013`
6×	`cancel-sign-sub-inv_binary64_11979`
5×	`add-cube-cbrt_binary64_12048`
4×	`add-log-exp_binary64_12052` `difference-of-squares_binary64_11982`
3×	`pow1_binary64_12074` `distribute-lft-out--_binary64_11965`
2×	`distribute-lft-out_binary64_11964` `add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051` `sqrt-div_binary64_12030`
1×	`pow1/2_binary64_12093` `flip3-+_binary64_12016` `flip3--_binary64_12017` `flip-+_binary64_11987` `rem-sqrt-square_binary64_12026` `flip--_binary64_11988` `diff-log_binary64_12105` `sqrt-pow1_binary64_12031` `sub-neg_binary64_12006`

Counts

2 → 40

Calls

2 calls:

9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series54.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

37.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
17.0ms	(sqrt.f64 (+.f64 x 1))

simplify75.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4936	794
1	4936	794

prune50.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	4	47

Error

0.1b

Counts

47 → 4

Compiler

Compiled 730 to 483 computations (33.8% saved)

localize6.0ms (0.1%)

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))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_12013`
24×	`sqrt-prod_binary64_12029`
21×	`distribute-lft-out_binary64_11964`
18×	`times-frac_binary64_12019`
16×	`add-sqr-sqrt_binary64_12035`
15×	`add-cube-cbrt_binary64_12048`
7×	`add-exp-log_binary64_12051`
6×	`associate-/r*_binary64_11957`
5×	`add-cbrt-cube_binary64_12049` `add-log-exp_binary64_12052` `pow1_binary64_12074`
3×	`flip3-+_binary64_12016` `flip-+_binary64_11987` `associate-/l*_binary64_11958`
2×	`associate-/r/_binary64_11959` `div-exp_binary64_12064` `sqrt-div_binary64_12030`
1×	`pow1/2_binary64_12093` `+-commutative_binary64_11943` `sum-log_binary64_12104` `rec-exp_binary64_12063` `clear-num_binary64_12012` `pow-flip_binary64_12087` `div-inv_binary64_12010` `rem-sqrt-square_binary64_12026` `cbrt-undiv_binary64_12047` `inv-pow_binary64_12098` `frac-2neg_binary64_12024` `sqrt-pow1_binary64_12031` `1-exp_binary64_12057`

Counts

3 → 75

Calls

3 calls:

10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series66.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
21.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4917	1530
1	4917	1530

prune96.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	81	7	88

Error

0.0b

Counts

88 → 7

Compiler

Compiled 1459 to 1033 computations (29.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.0b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

rewrite60.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`sqrt-prod_binary64_12029`
70×	`add-sqr-sqrt_binary64_12035`
46×	`*-un-lft-identity_binary64_12013`
40×	`sqrt-pow1_binary64_12031`
32×	`pow1_binary64_12074` `sqrt-div_binary64_12030`
28×	`add-cube-cbrt_binary64_12048`
20×	`pow1/2_binary64_12093`
18×	`swap-sqr_binary64_11980`
12×	`rem-sqrt-square_binary64_12026`
10×	`associate-l_binary64_11954` `add-exp-log_binary64_12051` `associate-r_binary64_11953`
9×	`times-frac_binary64_12019` `pow-prod-up_binary64_12083` `flip3-+_binary64_12016` `unswap-sqr_binary64_11981` `flip-+_binary64_11987`
8×	`distribute-lft-out_binary64_11964` `add-cbrt-cube_binary64_12049`
5×	`pow-prod-down_binary64_12084` `pow-sqr_binary64_11986`
4×	`sqr-abs_binary64_12028` `add-log-exp_binary64_12052` `frac-times_binary64_12023`
3×	`associate-/r_binary64_11957` `associate-/l_binary64_11958`
2×	`associate-/r/_binary64_11959` `div-exp_binary64_12064` `associate-l/_binary64_11956` `associate-r/_binary64_11955`
1×	`rem-square-sqrt_binary64_12025` `rec-exp_binary64_12063` `*-commutative_binary64_11944` `pow-plus_binary64_12076` `clear-num_binary64_12012` `pow-flip_binary64_12087` `div-inv_binary64_12010` `cbrt-undiv_binary64_12047` `inv-pow_binary64_12098` `frac-2neg_binary64_12024` `cbrt-unprod_binary64_12046` `prod-exp_binary64_12062` `sqrt-unprod_binary64_12033` `1-exp_binary64_12057` `pow2_binary64_12094`

Counts

4 → 169

Calls

4 calls:

17.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
17.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

series103.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

38.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
24.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
24.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
16.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

simplify74.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4892	2509
1	4892	2509

prune207.0ms (4.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	181	7	188

Error

0.0b

Counts

188 → 7

Compiler

Compiled 3469 to 2598 computations (25.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
0.3b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

rewrite156.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

448×	`sqrt-prod_binary64_12029`
414×	`times-frac_binary64_12019`
411×	`*-un-lft-identity_binary64_12013`
254×	`add-sqr-sqrt_binary64_12035`
215×	`add-cube-cbrt_binary64_12048`
110×	`distribute-lft-out_binary64_11964`
44×	`sqrt-div_binary64_12030`
36×	`associate-/l*_binary64_11958`
34×	`sqrt-pow1_binary64_12031`
30×	`pow1_binary64_12074`
19×	`add-exp-log_binary64_12051`
18×	`associate-/r/_binary64_11959` `pow1/2_binary64_12093` `swap-sqr_binary64_11980`
16×	`flip3-+_binary64_12016` `flip-+_binary64_11987`
15×	`associate-/r*_binary64_11957`
13×	`add-cbrt-cube_binary64_12049`
10×	`associate-l_binary64_11954` `associate-r_binary64_11953`
9×	`pow-prod-up_binary64_12083` `unswap-sqr_binary64_11981` `div-inv_binary64_12010` `rem-sqrt-square_binary64_12026`
8×	`div-exp_binary64_12064`
5×	`pow-prod-down_binary64_12084` `pow-sqr_binary64_11986`
4×	`sqr-abs_binary64_12028` `add-log-exp_binary64_12052` `cbrt-undiv_binary64_12047` `frac-times_binary64_12023`
3×	`pow-flip_binary64_12087`
2×	`rec-exp_binary64_12063` `clear-num_binary64_12012` `associate-l/_binary64_11956` `frac-2neg_binary64_12024` `associate-r/_binary64_11955` `1-exp_binary64_12057`
1×	`rem-square-sqrt_binary64_12025` `*-commutative_binary64_11944` `pow-plus_binary64_12076` `inv-pow_binary64_12098` `cbrt-unprod_binary64_12046` `prod-exp_binary64_12062` `associate-/l/_binary64_11960` `sqrt-unprod_binary64_12033` `pow2_binary64_12094`

Counts

4 → 425

Calls

4 calls:

39.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
17.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
12.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
9.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series143.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
45.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
32.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
16.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

simplify221.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

437 → 437

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4908	14356
1	4908	14356

prune1.1s (26.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	435	2	437
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	437	7	444

Error

Counts

444 → 7

Compiler

Compiled 13110 to 9680 computations (26.2% saved)

regimes148.0ms (3.5%)

Accuracy

Total 0.2b remaining (95%)

Threshold costs 0.2b (95%)

Compiler

Compiled 1790 to 1474 computations (17.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.4s (33%)

Algorithm

1×

intervals

Results

202.0ms	1985×	body	1024	valid
117.0ms	4282×	body	128	valid
74.0ms	986×	body	512	valid
29.0ms	233×	body	2048	valid
25.0ms	514×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 872 to 721 computations (17.3% saved)

Details

analyze102.0ms (2.4%)

sample18.0ms (0.4%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite15.0ms (0.3%)

series54.0ms (1.3%)

simplify75.0ms (1.8%)

prune50.0ms (1.2%)

localize6.0ms (0.1%)

rewrite26.0ms (0.6%)

series66.0ms (1.6%)

simplify63.0ms (1.5%)

prune96.0ms (2.2%)

localize8.0ms (0.2%)

rewrite60.0ms (1.4%)

series103.0ms (2.4%)

simplify74.0ms (1.7%)

prune207.0ms (4.9%)

localize13.0ms (0.3%)

rewrite156.0ms (3.7%)

series143.0ms (3.3%)

simplify221.0ms (5.2%)

prune1.1s (26.7%)

regimes148.0ms (3.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.4s (33%)

Profiling