Details

analyze2.0ms (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)

sample25.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	67×	body	1024	valid
5.0ms	140×	body	128	valid
2.0ms	25×	body	512	valid
1.0ms	11×	body	2048	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify174.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0.1%)

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

Merged error: 29.1b

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))
2.8b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_14543`
14×	`add-sqr-sqrt_binary64_14549` `*-un-lft-identity_binary64_14527`
6×	`cancel-sign-sub-inv_binary64_14493`
5×	`add-cube-cbrt_binary64_14562`
4×	`add-log-exp_binary64_14566` `difference-of-squares_binary64_14496`
3×	`pow1_binary64_14588` `distribute-lft-out--_binary64_14479`
2×	`sqrt-div_binary64_14544` `add-exp-log_binary64_14565` `add-cbrt-cube_binary64_14563` `distribute-lft-out_binary64_14478`
1×	`flip-+_binary64_14501` `sqrt-pow1_binary64_14545` `flip3--_binary64_14531` `flip--_binary64_14502` `flip3-+_binary64_14530` `sub-neg_binary64_14520` `pow1/2_binary64_14607` `diff-log_binary64_14619` `rem-sqrt-square_binary64_14540`

Counts

2 → 40

Calls

2 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series99.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

72.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5005	794

prune73.0ms (2%)

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

Merged error: 0.1b

Counts

47 → 3

Compiler

Compiled 1029 to 725 computations (29.5% saved)

localize8.0ms (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)))

rewrite30.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_14527`
24×	`sqrt-prod_binary64_14543`
21×	`distribute-lft-out_binary64_14478`
18×	`times-frac_binary64_14533`
16×	`add-sqr-sqrt_binary64_14549`
15×	`add-cube-cbrt_binary64_14562`
7×	`add-exp-log_binary64_14565`
6×	`associate-/r*_binary64_14471`
5×	`pow1_binary64_14588` `add-cbrt-cube_binary64_14563` `add-log-exp_binary64_14566`
3×	`flip-+_binary64_14501` `flip3-+_binary64_14530` `associate-/l*_binary64_14472`
2×	`sqrt-div_binary64_14544` `associate-/r/_binary64_14473` `div-exp_binary64_14578`
1×	`sqrt-pow1_binary64_14545` `div-inv_binary64_14524` `pow-flip_binary64_14601` `+-commutative_binary64_14457` `rec-exp_binary64_14577` `cbrt-undiv_binary64_14561` `frac-2neg_binary64_14538` `inv-pow_binary64_14612` `pow1/2_binary64_14607` `sum-log_binary64_14618` `clear-num_binary64_14526` `1-exp_binary64_14571` `rem-sqrt-square_binary64_14540`

Counts

3 → 75

Calls

3 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series133.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

62.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
44.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify71.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4944	1516
1	4944	1516

prune193.0ms (5.2%)

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

Merged error: 0.0b

Counts

87 → 8

Compiler

Compiled 3028 to 2316 computations (23.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite69.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`sqrt-prod_binary64_14543`
70×	`add-sqr-sqrt_binary64_14549`
46×	`*-un-lft-identity_binary64_14527`
40×	`sqrt-pow1_binary64_14545`
32×	`sqrt-div_binary64_14544` `pow1_binary64_14588`
28×	`add-cube-cbrt_binary64_14562`
20×	`pow1/2_binary64_14607`
18×	`swap-sqr_binary64_14494`
12×	`rem-sqrt-square_binary64_14540`
10×	`associate-r_binary64_14467` `add-exp-log_binary64_14565` `associate-l_binary64_14468`
9×	`flip-+_binary64_14501` `flip3-+_binary64_14530` `pow-prod-up_binary64_14597` `unswap-sqr_binary64_14495` `times-frac_binary64_14533`
8×	`add-cbrt-cube_binary64_14563` `distribute-lft-out_binary64_14478`
5×	`pow-sqr_binary64_14500` `pow-prod-down_binary64_14598`
4×	`frac-times_binary64_14537` `sqr-abs_binary64_14542` `add-log-exp_binary64_14566`
3×	`associate-/l_binary64_14472` `associate-/r_binary64_14471`
2×	`associate-/r/_binary64_14473` `associate-l/_binary64_14470` `div-exp_binary64_14578` `associate-r/_binary64_14469`
1×	`pow-plus_binary64_14590` `div-inv_binary64_14524` `prod-exp_binary64_14576` `pow-flip_binary64_14601` `rec-exp_binary64_14577` `cbrt-undiv_binary64_14561` `sqrt-unprod_binary64_14547` `cbrt-unprod_binary64_14560` `frac-2neg_binary64_14538` `inv-pow_binary64_14612` `rem-square-sqrt_binary64_14539` `clear-num_binary64_14526` `*-commutative_binary64_14458` `1-exp_binary64_14571` `pow2_binary64_14608`

Counts

4 → 169

Calls

4 calls:

22.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
19.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

series192.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
50.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
45.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
32.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

simplify71.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4969	2509
1	4969	2509

prune455.0ms (12.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	180	9	189

Merged error: 0.0b

Counts

189 → 9

Compiler

Compiled 4147 to 3152 computations (24% saved)

localize9.0ms (0.3%)

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

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_14549` `*-un-lft-identity_binary64_14527`
18×	`add-cube-cbrt_binary64_14562`
13×	`cbrt-prod_binary64_14558`
10×	`associate-r_binary64_14467` `add-exp-log_binary64_14565`
9×	`sqrt-prod_binary64_14543` `times-frac_binary64_14533`
8×	`add-cbrt-cube_binary64_14563`
7×	`pow1_binary64_14588`
6×	`cbrt-div_binary64_14559`
4×	`flip-+_binary64_14501` `flip3-+_binary64_14530` `add-log-exp_binary64_14566`
3×	`unswap-sqr_binary64_14495` `associate-/l_binary64_14472` `distribute-lft-out_binary64_14478` `associate-/r_binary64_14471` `associate-l_binary64_14468`
2×	`sqrt-div_binary64_14544` `associate-/r/_binary64_14473` `pow1/3_binary64_14609` `div-exp_binary64_14578` `associate-*r/_binary64_14469`
1×	`div-inv_binary64_14524` `prod-exp_binary64_14576` `pow-flip_binary64_14601` `rec-exp_binary64_14577` `cbrt-undiv_binary64_14561` `cbrt-unprod_binary64_14560` `frac-2neg_binary64_14538` `inv-pow_binary64_14612` `clear-num_binary64_14526` `*-commutative_binary64_14458` `1-exp_binary64_14571` `pow-prod-down_binary64_14598`

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)))
11.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
6.0ms	(cbrt.f64 (+.f64 1 x))
4.0ms	(cbrt.f64 (+.f64 1 x))

series738.0ms (19.7%)

Counts

4 → 12

Calls

4 calls:

578.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
76.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
43.0ms	(cbrt.f64 (+.f64 1 x))
40.0ms	(cbrt.f64 (+.f64 1 x))

simplify95.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4869	3063
1	4869	3063

prune243.0ms (6.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	101	10	111

Merged error: 0.0b

Counts

111 → 10

Compiler

Compiled 4284 to 3375 computations (21.2% saved)

regimes53.0ms (1.4%)

Compiler: Compiled 552 to 454 computations (17.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample869.0ms (23.2%)

Algorithm

1×

intervals

Results

208.0ms	2039×	body	1024	valid
124.0ms	4318×	body	128	valid
71.0ms	941×	body	512	valid
28.0ms	223×	body	2048	valid
27.0ms	479×	body	256	valid

Compiler

Compiled 294 to 244 computations (17% saved)

Details

analyze2.0ms (0.1%)

sample25.0ms (0.7%)

simplify174.0ms (4.7%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite20.0ms (0.5%)

series99.0ms (2.6%)

simplify62.0ms (1.6%)

prune73.0ms (2%)

localize8.0ms (0.2%)

rewrite30.0ms (0.8%)

series133.0ms (3.6%)

simplify71.0ms (1.9%)

prune193.0ms (5.2%)

localize8.0ms (0.2%)

rewrite69.0ms (1.8%)

series192.0ms (5.1%)

simplify71.0ms (1.9%)

prune455.0ms (12.2%)

localize9.0ms (0.3%)

rewrite40.0ms (1.1%)

series738.0ms (19.7%)

simplify95.0ms (2.5%)

prune243.0ms (6.5%)

regimes53.0ms (1.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample869.0ms (23.2%)

Profiling