Details

analyze97.0ms (3%)

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)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	127×	body	128	valid
8.0ms	73×	body	1024	valid
2.0ms	31×	body	512	valid
1.0ms	22×	body	256	valid
0.0ms	3×	body	2048	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify10.0ms (0.3%)

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

Error

32.3b

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))
3.3b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_13393`
14×	`*-un-lft-identity_binary64_13377` `add-sqr-sqrt_binary64_13399`
6×	`cancel-sign-sub-inv_binary64_13343`
5×	`add-cube-cbrt_binary64_13412`
4×	`difference-of-squares_binary64_13346` `add-log-exp_binary64_13416`
3×	`distribute-lft-out--_binary64_13329` `pow1_binary64_13438`
2×	`sqrt-div_binary64_13394` `distribute-lft-out_binary64_13328` `add-exp-log_binary64_13415` `add-cbrt-cube_binary64_13413`
1×	`diff-log_binary64_13469` `pow1/2_binary64_13457` `flip3--_binary64_13381` `flip--_binary64_13352` `rem-sqrt-square_binary64_13390` `sqrt-pow1_binary64_13395` `flip-+_binary64_13351` `sub-neg_binary64_13370` `flip3-+_binary64_13380`

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 (1.6%)

Counts

2 → 6

Calls

2 calls:

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

simplify78.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4936	794
1	4936	794

prune47.0ms (1.4%)

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

Error

0.1b

Counts

47 → 3

Compiler

Compiled 699 to 459 computations (34.3% saved)

localize6.0ms (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)))

rewrite30.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_13377`
24×	`sqrt-prod_binary64_13393`
21×	`distribute-lft-out_binary64_13328`
18×	`times-frac_binary64_13383`
16×	`add-sqr-sqrt_binary64_13399`
15×	`add-cube-cbrt_binary64_13412`
7×	`add-exp-log_binary64_13415`
6×	`associate-/r*_binary64_13321`
5×	`pow1_binary64_13438` `add-log-exp_binary64_13416` `add-cbrt-cube_binary64_13413`
3×	`flip-+_binary64_13351` `associate-/l*_binary64_13322` `flip3-+_binary64_13380`
2×	`sqrt-div_binary64_13394` `div-exp_binary64_13428` `associate-/r/_binary64_13323`
1×	`+-commutative_binary64_13307` `div-inv_binary64_13374` `clear-num_binary64_13376` `pow-flip_binary64_13451` `sum-log_binary64_13468` `inv-pow_binary64_13462` `pow1/2_binary64_13457` `rec-exp_binary64_13427` `1-exp_binary64_13421` `rem-sqrt-square_binary64_13390` `cbrt-undiv_binary64_13411` `sqrt-pow1_binary64_13395` `frac-2neg_binary64_13388`

Counts

3 → 75

Calls

3 calls:

14.0ms	(/.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))

series67.0ms (2%)

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))

simplify61.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4917	1530
1	4917	1530

prune102.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	9	84
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	77	10	87

Error

Counts

87 → 10

Compiler

Compiled 1520 to 1083 computations (28.8% saved)

localize9.0ms (0.3%)

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)))))

rewrite122.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

310×	`*-un-lft-identity_binary64_13377`
290×	`sqrt-prod_binary64_13393`
172×	`times-frac_binary64_13383`
144×	`add-sqr-sqrt_binary64_13399`
116×	`distribute-lft-out_binary64_13328`
88×	`add-cube-cbrt_binary64_13412`
43×	`swap-sqr_binary64_13344`
31×	`pow1_binary64_13438`
27×	`associate-r_binary64_13317` `sqrt-pow1_binary64_13395` `associate-l_binary64_13318`
16×	`unswap-sqr_binary64_13345`
14×	`add-exp-log_binary64_13415` `associate-/r/_binary64_13323`
12×	`associate-/r*_binary64_13321`
11×	`pow-flip_binary64_13451` `inv-pow_binary64_13462`
10×	`add-cbrt-cube_binary64_13413`
9×	`div-inv_binary64_13374` `pow1/2_binary64_13457` `pow-prod-up_binary64_13447` `rem-sqrt-square_binary64_13390`
7×	`flip-+_binary64_13351` `flip3-+_binary64_13380`
6×	`associate-/l*_binary64_13322`
5×	`sqrt-div_binary64_13394` `pow-prod-down_binary64_13448` `pow-sqr_binary64_13350`
4×	`div-exp_binary64_13428` `add-log-exp_binary64_13416`
3×	`sqr-abs_binary64_13392`
2×	`clear-num_binary64_13376` `rec-exp_binary64_13427` `1-exp_binary64_13421` `cbrt-undiv_binary64_13411` `frac-2neg_binary64_13388`
1×	`prod-exp_binary64_13426` `associate-l/_binary64_13320` `cbrt-unprod_binary64_13410` `pow-plus_binary64_13440` `-commutative_binary64_13308` `frac-times_binary64_13387` `rem-square-sqrt_binary64_13389` `pow2_binary64_13458` `associate-*r/_binary64_13319` `sqrt-unprod_binary64_13397`

Counts

4 → 281

Calls

4 calls:

45.0ms	(*.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)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series144.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
32.0ms	(*.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)))
27.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify116.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5033	6769

prune515.0ms (15.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	292	1	293
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	294	9	303

Error

Counts

303 → 9

Compiler

Compiled 7470 to 5466 computations (26.8% saved)

localize12.0ms (0.4%)

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)))
0.5b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)

rewrite39.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64_13377`
28×	`sqrt-prod_binary64_13393`
13×	`distribute-lft-out_binary64_13328`
11×	`add-sqr-sqrt_binary64_13399`
9×	`add-cube-cbrt_binary64_13412` `unpow-prod-down_binary64_13456`
8×	`pow1_binary64_13438`
6×	`add-log-exp_binary64_13416`
5×	`add-exp-log_binary64_13415`
4×	`sqrt-div_binary64_13394` `add-cbrt-cube_binary64_13413`
3×	`pow-unpow_binary64_13454` `pow1/2_binary64_13457` `pow-pow_binary64_13449` `sqrt-pow1_binary64_13395` `flip-+_binary64_13351` `flip3-+_binary64_13380`
2×	`rem-sqrt-square_binary64_13390`
1×	`+-commutative_binary64_13307` `sum-log_binary64_13468` `pow-to-exp_binary64_13446` `sqrt-pow2_binary64_13396` `pow-exp_binary64_13445` `sqr-pow_binary64_13349`

Counts

4 → 74

Calls

4 calls:

11.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)
11.0ms	(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))

series143.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4)
37.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
21.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
16.0ms	(sqrt.f64 (+.f64 1 x))

simplify70.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4952	1657
1	4952	1657

prune108.0ms (3.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	86	9	95

Error

Counts

95 → 9

Compiler

Compiled 1804 to 1388 computations (23.1% saved)

regimes124.0ms (3.8%)

Accuracy

Total 0.2b remaining (95.7%)

Threshold costs 0.2b (95.7%)

Compiler

Compiled 1364 to 1121 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%)

sample1.3s (38.7%)

Algorithm

1×

intervals

Results

194.0ms	1926×	body	1024	valid
126.0ms	4351×	body	128	valid
82.0ms	1025×	body	512	valid
25.0ms	206×	body	2048	valid
25.0ms	492×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 672 to 555 computations (17.4% saved)

Details

analyze97.0ms (3%)

sample24.0ms (0.7%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite15.0ms (0.4%)

series52.0ms (1.6%)

simplify78.0ms (2.4%)

prune47.0ms (1.4%)

localize6.0ms (0.2%)

rewrite30.0ms (0.9%)

series67.0ms (2%)

simplify61.0ms (1.9%)

prune102.0ms (3.1%)

localize9.0ms (0.3%)

rewrite122.0ms (3.7%)

series144.0ms (4.4%)

simplify116.0ms (3.6%)

prune515.0ms (15.8%)

localize12.0ms (0.4%)

rewrite39.0ms (1.2%)

series143.0ms (4.4%)

simplify70.0ms (2.1%)

prune108.0ms (3.3%)

regimes124.0ms (3.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.3s (38.7%)

Profiling