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)

sample21.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	82×	body	1024	valid
4.0ms	123×	body	128	valid
2.0ms	30×	body	512	valid
1.0ms	8×	body	2048	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify99.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune8.0ms (0.2%)

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

Merged error: 33.4b

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))
3.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_11688`
14×	`add-sqr-sqrt_binary64_11694` `*-un-lft-identity_binary64_11672`
6×	`cancel-sign-sub-inv_binary64_11638`
5×	`add-cube-cbrt_binary64_11707`
4×	`add-log-exp_binary64_11711` `difference-of-squares_binary64_11641`
3×	`pow1_binary64_11733` `distribute-lft-out--_binary64_11624`
2×	`sqrt-div_binary64_11689` `add-exp-log_binary64_11710` `distribute-lft-out_binary64_11623` `add-cbrt-cube_binary64_11708`
1×	`rem-sqrt-square_binary64_11685` `pow1/2_binary64_11752` `flip-+_binary64_11646` `flip3-+_binary64_11675` `sqrt-pow1_binary64_11690` `flip3--_binary64_11676` `flip--_binary64_11647` `sub-neg_binary64_11665` `diff-log_binary64_11764`

Counts

2 → 40

Calls

2 calls:

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

series52.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

38.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 x 1))

simplify81.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4936	794
1	4936	794

prune48.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	2	47

Merged error: 0.2b

Counts

47 → 2

Compiler

Compiled 680 to 445 computations (34.6% saved)

localize7.0ms (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))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_11672`
24×	`sqrt-prod_binary64_11688`
21×	`distribute-lft-out_binary64_11623`
18×	`times-frac_binary64_11678`
16×	`add-sqr-sqrt_binary64_11694`
15×	`add-cube-cbrt_binary64_11707`
7×	`add-exp-log_binary64_11710`
6×	`associate-/r*_binary64_11616`
5×	`pow1_binary64_11733` `add-log-exp_binary64_11711` `add-cbrt-cube_binary64_11708`
3×	`flip-+_binary64_11646` `flip3-+_binary64_11675` `associate-/l*_binary64_11617`
2×	`sqrt-div_binary64_11689` `associate-/r/_binary64_11618` `div-exp_binary64_11723`
1×	`rem-sqrt-square_binary64_11685` `cbrt-undiv_binary64_11706` `inv-pow_binary64_11757` `clear-num_binary64_11671` `1-exp_binary64_11716` `sum-log_binary64_11763` `pow-flip_binary64_11746` `pow1/2_binary64_11752` `sqrt-pow1_binary64_11690` `+-commutative_binary64_11602` `frac-2neg_binary64_11683` `div-inv_binary64_11669` `rec-exp_binary64_11722`

Counts

3 → 75

Calls

3 calls:

11.0ms	(/.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))

series74.0ms (2%)

Counts

3 → 9

Calls

3 calls:

36.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
23.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
15.0ms	(sqrt.f64 (+.f64 x 1))

simplify60.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4917	1530
1	4917	1530

prune95.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	77	9	86

Merged error: 0.0b

Counts

86 → 9

Compiler

Compiled 1511 to 1075 computations (28.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_11694` `*-un-lft-identity_binary64_11672`
18×	`add-cube-cbrt_binary64_11707`
13×	`cbrt-prod_binary64_11703`
10×	`associate-r_binary64_11612` `add-exp-log_binary64_11710`
9×	`sqrt-prod_binary64_11688` `times-frac_binary64_11678`
8×	`add-cbrt-cube_binary64_11708`
7×	`pow1_binary64_11733`
6×	`cbrt-div_binary64_11704`
4×	`add-log-exp_binary64_11711` `flip-+_binary64_11646` `flip3-+_binary64_11675`
3×	`associate-/r_binary64_11616` `unswap-sqr_binary64_11640` `distribute-lft-out_binary64_11623` `associate-l_binary64_11613` `associate-/l_binary64_11617`
2×	`sqrt-div_binary64_11689` `associate-/r/_binary64_11618` `div-exp_binary64_11723` `associate-*r/_binary64_11614` `pow1/3_binary64_11754`
1×	`cbrt-undiv_binary64_11706` `cbrt-unprod_binary64_11705` `inv-pow_binary64_11757` `clear-num_binary64_11671` `1-exp_binary64_11716` `pow-flip_binary64_11746` `prod-exp_binary64_11721` `frac-2neg_binary64_11683` `div-inv_binary64_11669` `*-commutative_binary64_11603` `pow-prod-down_binary64_11743` `rec-exp_binary64_11722`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
9.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

series415.0ms (11.1%)

Counts

4 → 12

Calls

4 calls:

323.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
40.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
28.0ms	(cbrt.f64 (+.f64 1 x))
24.0ms	(cbrt.f64 (+.f64 1 x))

simplify80.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4944	3191
1	4944	3191

prune186.0ms (5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	100	11	111

Merged error: 0.0b

Counts

111 → 11

Compiler

Compiled 3161 to 2445 computations (22.7% 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))))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(*.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)))))

rewrite120.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

310×	`*-un-lft-identity_binary64_11672`
290×	`sqrt-prod_binary64_11688`
172×	`times-frac_binary64_11678`
144×	`add-sqr-sqrt_binary64_11694`
116×	`distribute-lft-out_binary64_11623`
88×	`add-cube-cbrt_binary64_11707`
43×	`swap-sqr_binary64_11639`
31×	`pow1_binary64_11733`
27×	`associate-r_binary64_11612` `sqrt-pow1_binary64_11690` `associate-l_binary64_11613`
16×	`unswap-sqr_binary64_11640`
14×	`associate-/r/_binary64_11618` `add-exp-log_binary64_11710`
12×	`associate-/r*_binary64_11616`
11×	`inv-pow_binary64_11757` `pow-flip_binary64_11746`
10×	`add-cbrt-cube_binary64_11708`
9×	`rem-sqrt-square_binary64_11685` `pow1/2_binary64_11752` `pow-prod-up_binary64_11742` `div-inv_binary64_11669`
7×	`flip-+_binary64_11646` `flip3-+_binary64_11675`
6×	`associate-/l*_binary64_11617`
5×	`sqrt-div_binary64_11689` `pow-sqr_binary64_11645` `pow-prod-down_binary64_11743`
4×	`div-exp_binary64_11723` `add-log-exp_binary64_11711`
3×	`sqr-abs_binary64_11687`
2×	`cbrt-undiv_binary64_11706` `clear-num_binary64_11671` `1-exp_binary64_11716` `frac-2neg_binary64_11683` `rec-exp_binary64_11722`
1×	`rem-square-sqrt_binary64_11684` `cbrt-unprod_binary64_11705` `frac-times_binary64_11682` `associate-l/_binary64_11615` `sqrt-unprod_binary64_11692` `associate-r/_binary64_11614` `pow2_binary64_11753` `prod-exp_binary64_11721` `*-commutative_binary64_11603` `pow-plus_binary64_11735`

Counts

4 → 281

Calls

4 calls:

43.0ms	(*.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)))))
15.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(/.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))))

series144.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
34.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
33.0ms	(*.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)))))
29.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify109.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5033	6769

prune501.0ms (13.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	288	5	293
Fresh	3	5	8
Picked	1	0	1
Done	0	2	2
Total	292	12	304

Merged error: 0.0b

Counts

304 → 12

Compiler

Compiled 7328 to 5349 computations (27% saved)

regimes140.0ms (3.8%)

Compiler: Compiled 1677 to 1378 computations (17.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample1.4s (37.1%)

Algorithm

1×

intervals

Results

204.0ms	2027×	body	1024	valid
123.0ms	4300×	body	128	valid
83.0ms	1004×	body	512	valid
30.0ms	213×	body	2048	valid
23.0ms	456×	body	256	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 819 to 675 computations (17.6% saved)

Details

analyze3.0ms (0.1%)

sample21.0ms (0.6%)

simplify99.0ms (2.6%)

prune8.0ms (0.2%)

localize5.0ms (0.1%)

rewrite15.0ms (0.4%)

series52.0ms (1.4%)

simplify81.0ms (2.2%)

prune48.0ms (1.3%)

localize7.0ms (0.2%)

rewrite28.0ms (0.7%)

series74.0ms (2%)

simplify60.0ms (1.6%)

prune95.0ms (2.6%)

localize10.0ms (0.3%)

rewrite35.0ms (0.9%)

series415.0ms (11.1%)

simplify80.0ms (2.1%)

prune186.0ms (5%)

localize9.0ms (0.2%)

rewrite120.0ms (3.2%)

series144.0ms (3.9%)

simplify109.0ms (2.9%)

prune501.0ms (13.4%)

regimes140.0ms (3.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.4s (37.1%)

Profiling