Details

analyze160.0ms (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)

sample64.0ms (0.8%)

Algorithm

1×

intervals

Results

28.0ms	65×	body	1024	valid
10.0ms	129×	body	128	valid
10.0ms	38×	body	512	valid
4.0ms	19×	body	256	valid
2.0ms	5×	body	2048	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune4.0ms (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

31.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
3.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite25.0ms (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:

15.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 x 1))

series78.0ms (0.9%)

Counts

2 → 9

Calls

2 calls:

49.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
28.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 170 to 142 computations (16.5% saved)

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4932	589
1	4932	589

prune75.0ms (0.9%)

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 583 to 384 computations (34.1% saved)

localize23.0ms (0.3%)

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)))

rewrite46.0ms (0.5%)

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:

18.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
13.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 x 1))

series85.0ms (1%)

Counts

3 → 12

Calls

3 calls:

30.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
29.0ms	(sqrt.f64 (+.f64 x 1))
25.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 182 to 168 computations (7.7% saved)

simplify441.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4911	1227
1	4911	1227

prune144.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	82	8	90

Error

0.0b

Counts

90 → 8

Compiler

Compiled 1309 to 958 computations (26.8% saved)

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite63.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_12035` `*-un-lft-identity_binary64_12013`
18×	`add-cube-cbrt_binary64_12048`
13×	`cbrt-prod_binary64_12044`
10×	`add-exp-log_binary64_12051` `associate-r_binary64_11953`
9×	`times-frac_binary64_12019` `sqrt-prod_binary64_12029`
8×	`add-cbrt-cube_binary64_12049`
7×	`pow1_binary64_12074`
6×	`cbrt-div_binary64_12045`
4×	`flip3-+_binary64_12016` `add-log-exp_binary64_12052` `flip-+_binary64_11987`
3×	`distribute-lft-out_binary64_11964` `associate-/r_binary64_11957` `unswap-sqr_binary64_11981` `associate-l_binary64_11954` `associate-/l_binary64_11958`
2×	`associate-/r/_binary64_11959` `div-exp_binary64_12064` `pow1/3_binary64_12095` `associate-*r/_binary64_11955` `sqrt-div_binary64_12030`
1×	`rec-exp_binary64_12063` `*-commutative_binary64_11944` `clear-num_binary64_12012` `pow-flip_binary64_12087` `div-inv_binary64_12010` `pow-prod-down_binary64_12084` `cbrt-undiv_binary64_12047` `inv-pow_binary64_12098` `frac-2neg_binary64_12024` `cbrt-unprod_binary64_12046` `prod-exp_binary64_12062` `1-exp_binary64_12057`

Counts

4 → 90

Calls

4 calls:

24.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
16.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
5.0ms	(cbrt.f64 (+.f64 1 x))
5.0ms	(cbrt.f64 (+.f64 1 x))

series468.0ms (5.6%)

Counts

4 → 30

Calls

4 calls:

175.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
126.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
85.0ms	(cbrt.f64 (+.f64 1 x))
83.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 1101 to 969 computations (12% saved)

simplify161.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	4840	2640
1	4840	2640

prune278.0ms (3.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	120	8	128

Error

0.0b

Counts

128 → 8

Compiler

Compiled 2938 to 2261 computations (23% saved)

localize43.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite244.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

742×	`*-un-lft-identity_binary64_12013`
700×	`sqrt-prod_binary64_12029`
594×	`times-frac_binary64_12019`
280×	`distribute-lft-out_binary64_11964`
254×	`add-sqr-sqrt_binary64_12035`
252×	`add-cube-cbrt_binary64_12048`
36×	`associate-/l*_binary64_11958`
28×	`sqrt-div_binary64_12030`
24×	`associate-/r/_binary64_11959`
18×	`associate-/r*_binary64_11957`
17×	`add-exp-log_binary64_12051`
14×	`flip3-+_binary64_12016` `flip-+_binary64_11987`
12×	`div-inv_binary64_12010`
11×	`add-cbrt-cube_binary64_12049`
8×	`div-exp_binary64_12064` `pow1_binary64_12074`
4×	`add-log-exp_binary64_12052` `cbrt-undiv_binary64_12047`
3×	`pow1/2_binary64_12093` `pow-flip_binary64_12087` `sqrt-pow1_binary64_12031`
2×	`rec-exp_binary64_12063` `clear-num_binary64_12012` `rem-sqrt-square_binary64_12026` `frac-2neg_binary64_12024` `1-exp_binary64_12057`
1×	`inv-pow_binary64_12098` `associate-/l/_binary64_11960`

Counts

4 → 453

Calls

4 calls:

55.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
20.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
14.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
13.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series163.0ms (2%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
45.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
38.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
34.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Compiler

Compiled 408 to 368 computations (9.8% saved)

simplify380.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4875	14766
1	4875	14766

prune1.5s (18%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	461	4	465
Fresh	2	3	5
Picked	1	0	1
Done	1	1	2
Total	465	8	473

Error

Counts

473 → 8

Compiler

Compiled 11336 to 8340 computations (26.4% saved)

regimes288.0ms (3.5%)

Accuracy

Total 0.2b remaining (96.1%)

Threshold costs 0.2b (96.1%)

Compiler

Compiled 1851 to 1516 computations (18.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample3.5s (41.7%)

Algorithm

1×

intervals

Results

718.0ms	2033×	body	1024	valid
342.0ms	4240×	body	128	valid
263.0ms	1003×	body	512	valid
98.0ms	217×	body	2048	valid
83.0ms	507×	body	256	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 910 to 747 computations (17.9% saved)

Details

analyze160.0ms (1.9%)

sample64.0ms (0.8%)

simplify17.0ms (0.2%)

prune4.0ms (0%)

localize16.0ms (0.2%)

rewrite25.0ms (0.3%)

series78.0ms (0.9%)

simplify64.0ms (0.8%)

prune75.0ms (0.9%)

localize23.0ms (0.3%)

rewrite46.0ms (0.5%)

series85.0ms (1%)

simplify441.0ms (5.3%)

prune144.0ms (1.7%)

localize31.0ms (0.4%)

rewrite63.0ms (0.8%)

series468.0ms (5.6%)

simplify161.0ms (1.9%)

prune278.0ms (3.3%)

localize43.0ms (0.5%)

rewrite244.0ms (2.9%)

series163.0ms (2%)

simplify380.0ms (4.6%)

prune1.5s (18%)

regimes288.0ms (3.5%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.5s (41.7%)

Profiling