Details

analyze95.0ms (1.9%)

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)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	150×	body	128	valid
6.0ms	61×	body	1024	valid
2.0ms	26×	body	512	valid
1.0ms	15×	body	256	valid
1.0ms	4×	body	2048	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

26.4b

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))
2.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite63.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

25.3b

Rules

15×	`sqrt-prod_binary64_776`
14×	`add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
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×	`pow1_binary64_821` `distribute-lft-out--_binary64_712`
2×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `distribute-lft-out_binary64_711` `sqrt-div_binary64_777`
1×	`diff-log_binary64_852` `flip3--_binary64_764` `sub-neg_binary64_753` `flip--_binary64_735` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `flip3-+_binary64_763` `flip-+_binary64_734` `rem-sqrt-square_binary64_773`

Counts

2 → 40

Calls

2 calls:

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

Compiler

Compiled 571 to 370 computations (35.2% saved)

series55.0ms (1.1%)

Error

25.7b

Counts

2 → 9

Calls

2 calls:

29.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
16.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 245 to 193 computations (21.2% saved)

simplify38.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4932	589
1	4932	589

prune47.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Error

0.1b

Counts

50 → 3

Compiler

Compiled 592 to 389 computations (34.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite109.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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×	`pow1_binary64_821` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `associate-/l*_binary64_705`
2×	`div-exp_binary64_811` `associate-/r/_binary64_706` `sqrt-div_binary64_777`
1×	`inv-pow_binary64_845` `pow-flip_binary64_834` `1-exp_binary64_804` `rec-exp_binary64_810` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `sum-log_binary64_851` `+-commutative_binary64_690` `pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773`

Counts

3 → 75

Calls

3 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 1268 to 926 computations (27% saved)

series54.0ms (1.1%)

Error

0.1b

Counts

3 → 12

Calls

3 calls:

18.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
16.0ms	(sqrt.f64 (+.f64 1 x))
14.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 268 to 232 computations (13.4% saved)

simplify93.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4859	1227
1	4859	1227

prune86.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	82	8	90

Error

0.0b

Counts

90 → 8

Compiler

Compiled 1333 to 976 computations (26.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite813.0ms (16.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

310×	`*-un-lft-identity_binary64_760`
290×	`sqrt-prod_binary64_776`
172×	`times-frac_binary64_766`
144×	`add-sqr-sqrt_binary64_782`
116×	`distribute-lft-out_binary64_711`
88×	`add-cube-cbrt_binary64_795`
43×	`swap-sqr_binary64_727`
31×	`pow1_binary64_821`
27×	`sqrt-pow1_binary64_778` `associate-l_binary64_701` `associate-r_binary64_700`
16×	`unswap-sqr_binary64_728`
14×	`add-exp-log_binary64_798` `associate-/r/_binary64_706`
12×	`associate-/r*_binary64_704`
11×	`inv-pow_binary64_845` `pow-flip_binary64_834`
10×	`add-cbrt-cube_binary64_796`
9×	`pow1/2_binary64_840` `pow-prod-up_binary64_830` `rem-sqrt-square_binary64_773` `div-inv_binary64_757`
7×	`flip3-+_binary64_763` `flip-+_binary64_734`
6×	`associate-/l*_binary64_705`
5×	`pow-prod-down_binary64_831` `sqrt-div_binary64_777` `pow-sqr_binary64_733`
4×	`add-log-exp_binary64_799` `div-exp_binary64_811`
3×	`sqr-abs_binary64_775`
2×	`1-exp_binary64_804` `rec-exp_binary64_810` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`pow2_binary64_841` `pow-plus_binary64_823` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `sqrt-unprod_binary64_780` `rem-square-sqrt_binary64_772` `frac-times_binary64_770` `associate-l/_binary64_703` `associate-r/_binary64_702` `*-commutative_binary64_691`

Counts

4 → 281

Calls

4 calls:

46.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 9177 to 6931 computations (24.5% saved)

series96.0ms (2%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
21.0ms	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
21.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 545 to 477 computations (12.5% saved)

simplify122.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5824	5963

prune486.0ms (9.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	288	5	293
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	293	8	301

Error

Counts

301 → 8

Compiler

Compiled 7018 to 5189 computations (26.1% saved)

localize11.0ms (0.2%)

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))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.4b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)

rewrite127.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`*-un-lft-identity_binary64_760`
28×	`sqrt-prod_binary64_776`
13×	`distribute-lft-out_binary64_711`
11×	`add-sqr-sqrt_binary64_782`
9×	`add-cube-cbrt_binary64_795` `unpow-prod-down_binary64_839`
8×	`pow1_binary64_821`
6×	`add-log-exp_binary64_799`
5×	`add-exp-log_binary64_798`
4×	`add-cbrt-cube_binary64_796` `sqrt-div_binary64_777`
3×	`pow-unpow_binary64_837` `pow1/2_binary64_840` `pow-pow_binary64_832` `sqrt-pow1_binary64_778` `flip3-+_binary64_763` `flip-+_binary64_734`
2×	`rem-sqrt-square_binary64_773`
1×	`pow-to-exp_binary64_829` `pow-exp_binary64_828` `sqrt-pow2_binary64_779` `sqr-pow_binary64_732` `sum-log_binary64_851` `+-commutative_binary64_690`

Counts

4 → 74

Calls

4 calls:

10.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)
9.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 1600 to 1258 computations (21.4% saved)

series100.0ms (2%)

Error

Counts

4 → 15

Calls

4 calls:

29.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)
22.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
19.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
18.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 576 to 534 computations (7.3% saved)

simplify41.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5081	1146

prune96.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	89	8	97

Error

Counts

97 → 8

Compiler

Compiled 1523 to 1214 computations (20.3% saved)

regimes243.0ms (5%)

Accuracy

Total 0.2b remaining (97.9%)

Threshold costs 0.2b (97.9%)

Compiler

Compiled 2966 to 2380 computations (19.8% 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%)

sample2.1s (42%)

Algorithm

1×

intervals

Results

211.0ms	2072×	body	1024	valid
125.0ms	4249×	body	128	valid
77.0ms	987×	body	512	valid
28.0ms	482×	body	256	valid
27.0ms	210×	body	2048	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 1456 to 1171 computations (19.6% saved)

Details

analyze95.0ms (1.9%)

sample26.0ms (0.5%)

simplify10.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite63.0ms (1.3%)

series55.0ms (1.1%)

simplify38.0ms (0.8%)

prune47.0ms (1%)

localize6.0ms (0.1%)

rewrite109.0ms (2.2%)

series54.0ms (1.1%)

simplify93.0ms (1.9%)

prune86.0ms (1.8%)

localize9.0ms (0.2%)

rewrite813.0ms (16.6%)

series96.0ms (2%)

simplify122.0ms (2.5%)

prune486.0ms (9.9%)

localize11.0ms (0.2%)

rewrite127.0ms (2.6%)

series100.0ms (2%)

simplify41.0ms (0.8%)

prune96.0ms (2%)

regimes243.0ms (5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.1s (42%)

Profiling