Details

analyze418.0ms (3.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
6.2%	93.6%	0.2%	5
6.2%	68.6%	25.1%	6
6.2%	49.9%	43.9%	7
6.2%	35.9%	57.9%	8
6.2%	25.3%	68.4%	9
6.2%	20.1%	73.7%	10
6.2%	15.7%	78.1%	11
6.2%	12%	81.7%	12
6.2%	9%	84.8%	13
6.2%	7.5%	86.3%	14

Compiler

Compiled 32 to 28 computations (12.5% saved)

sample162.0ms (1.2%)

Algorithm

1×

intervals

Results

57.0ms	144×	body	512	valid
42.0ms	312×	body	128	nan
22.0ms	48×	body	1024	valid
9.0ms	34×	body	256	valid
7.0ms	30×	body	128	valid

Compiler

Compiled 63 to 59 computations (6.3% saved)

simplify186.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5168	50

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

4.4b

Counts

2 → 1

Compiler

Compiled 62 to 54 computations (12.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.1b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
2.4b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
4.0b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite65.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`sqrt-prod_binary64_7937` `add-sqr-sqrt_binary64_7943`
40×	`*-un-lft-identity_binary64_7921`
24×	`cancel-sign-sub-inv_binary64_7887`
16×	`difference-of-squares_binary64_7890`
12×	`distribute-lft-out--_binary64_7873` `add-log-exp_binary64_7960` `add-cube-cbrt_binary64_7956`
4×	`flip3--_binary64_7925` `diff-log_binary64_8013` `add-cbrt-cube_binary64_7957` `distribute-lft-out_binary64_7872` `sub-neg_binary64_7914` `pow1_binary64_7982` `flip--_binary64_7896` `add-exp-log_binary64_7959`

Counts

4 → 96

Calls

4 calls:

17.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
12.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
9.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series246.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
65.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
63.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
45.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5089	2235

prune283.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	103	5	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	5	109

Error

0.2b

Counts

109 → 5

Compiler

Compiled 4441 to 2862 computations (35.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
2.4b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
4.0b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite103.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64_7921`
49×	`sqrt-prod_binary64_7937`
45×	`add-sqr-sqrt_binary64_7943`
21×	`add-cube-cbrt_binary64_7956`
19×	`distribute-lft-out_binary64_7872`
18×	`cancel-sign-sub-inv_binary64_7887` `times-frac_binary64_7927`
12×	`difference-of-squares_binary64_7890`
10×	`add-log-exp_binary64_7960`
9×	`distribute-lft-out--_binary64_7873`
8×	`add-exp-log_binary64_7959`
6×	`add-cbrt-cube_binary64_7957` `associate-/r*_binary64_7865`
5×	`pow1_binary64_7982`
3×	`flip3--_binary64_7925` `diff-log_binary64_8013` `sub-neg_binary64_7914` `associate-/l*_binary64_7866` `flip--_binary64_7896`
2×	`associate-/r/_binary64_7867` `div-exp_binary64_7972`
1×	`inv-pow_binary64_8006` `clear-num_binary64_7920` `frac-2neg_binary64_7932` `rec-exp_binary64_7971` `pow-flip_binary64_7995` `1-exp_binary64_7965` `cbrt-undiv_binary64_7955` `flip3-+_binary64_7924` `flip-+_binary64_7895` `div-inv_binary64_7918`

Counts

4 → 117

Calls

4 calls:

22.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
19.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
19.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
18.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

series162.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
43.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
35.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
35.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))

simplify126.0ms (1%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4900	2640
1	4900	2640

prune435.0ms (3.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	123	6	129
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	127	7	134

Error

0.1b

Counts

134 → 7

Compiler

Compiled 5570 to 3704 computations (33.5% saved)

localize54.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
2.4b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite80.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64_7921`
54×	`sqrt-prod_binary64_7937`
46×	`add-sqr-sqrt_binary64_7943`
36×	`times-frac_binary64_7927`
34×	`distribute-lft-out_binary64_7872`
30×	`add-cube-cbrt_binary64_7956`
12×	`cancel-sign-sub-inv_binary64_7887` `associate-/r*_binary64_7865` `add-exp-log_binary64_7959`
8×	`add-log-exp_binary64_7960` `add-cbrt-cube_binary64_7957` `difference-of-squares_binary64_7890`
6×	`distribute-lft-out--_binary64_7873` `pow1_binary64_7982` `associate-/l*_binary64_7866`
4×	`associate-/r/_binary64_7867` `div-exp_binary64_7972`
2×	`flip3--_binary64_7925` `inv-pow_binary64_8006` `diff-log_binary64_8013` `clear-num_binary64_7920` `frac-2neg_binary64_7932` `sub-neg_binary64_7914` `rec-exp_binary64_7971` `pow-flip_binary64_7995` `1-exp_binary64_7965` `cbrt-undiv_binary64_7955` `flip3-+_binary64_7924` `flip--_binary64_7896` `flip-+_binary64_7895` `div-inv_binary64_7918`

Counts

4 → 138

Calls

4 calls:

20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
13.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series194.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
55.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
42.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
38.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))

simplify107.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4907	3091
1	4907	3091

prune552.0ms (4.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	151	6	157

Error

0.1b

Counts

157 → 6

Compiler

Compiled 6668 to 4510 computations (32.4% saved)

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
2.4b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite80.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`*-un-lft-identity_binary64_7921`
59×	`sqrt-prod_binary64_7937`
54×	`times-frac_binary64_7927`
49×	`distribute-lft-out_binary64_7872`
47×	`add-sqr-sqrt_binary64_7943`
39×	`add-cube-cbrt_binary64_7956`
18×	`associate-/r*_binary64_7865`
16×	`add-exp-log_binary64_7959`
10×	`add-cbrt-cube_binary64_7957`
9×	`associate-/l*_binary64_7866`
7×	`pow1_binary64_7982`
6×	`add-log-exp_binary64_7960` `cancel-sign-sub-inv_binary64_7887` `associate-/r/_binary64_7867` `div-exp_binary64_7972`
4×	`difference-of-squares_binary64_7890`
3×	`distribute-lft-out--_binary64_7873` `inv-pow_binary64_8006` `clear-num_binary64_7920` `frac-2neg_binary64_7932` `rec-exp_binary64_7971` `pow-flip_binary64_7995` `1-exp_binary64_7965` `cbrt-undiv_binary64_7955` `flip3-+_binary64_7924` `flip-+_binary64_7895` `div-inv_binary64_7918`
1×	`flip3--_binary64_7925` `diff-log_binary64_8013` `sub-neg_binary64_7914` `flip--_binary64_7896`

Counts

4 → 159

Calls

4 calls:

20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
17.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series158.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
42.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
36.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
30.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4891	3440
1	4891	3440

prune493.0ms (3.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	167	4	171
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	169	8	177

Error

0.0b

Counts

177 → 8

Compiler

Compiled 7563 to 5199 computations (31.3% saved)

regimes1.7s (13%)

Accuracy

Total 0.1b remaining (57.9%)

Threshold costs 0.1b (57.9%)

Compiler

Compiled 19829 to 16840 computations (15.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	62
1	41	62

end0.0ms (0%)

sample7.3s (55.4%)

Algorithm

1×

intervals

Results

2.0s	4427×	body	512	valid
1.4s	9958×	body	128	nan
1.0s	1737×	body	1024	valid
289.0ms	1000×	body	256	valid
121.0ms	836×	body	128	valid

Compiler

Compiled 1513 to 1287 computations (14.9% saved)

Details

analyze418.0ms (3.2%)

sample162.0ms (1.2%)

simplify186.0ms (1.4%)

prune4.0ms (0%)

localize23.0ms (0.2%)

rewrite65.0ms (0.5%)

series246.0ms (1.9%)

simplify92.0ms (0.7%)

prune283.0ms (2.1%)

localize23.0ms (0.2%)

rewrite103.0ms (0.8%)

series162.0ms (1.2%)

simplify126.0ms (1%)

prune435.0ms (3.3%)

localize54.0ms (0.4%)

rewrite80.0ms (0.6%)

series194.0ms (1.5%)

simplify107.0ms (0.8%)

prune552.0ms (4.2%)

localize38.0ms (0.3%)

rewrite80.0ms (0.6%)

series158.0ms (1.2%)

simplify93.0ms (0.7%)

prune493.0ms (3.7%)

regimes1.7s (13%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.3s (55.4%)

Profiling