Details

analyze260.0ms (3.1%)

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)

sample125.0ms (1.5%)

Algorithm

1×

intervals

Results

43.0ms	145×	body	512	valid
32.0ms	303×	body	128	nan
20.0ms	50×	body	1024	valid
8.0ms	41×	body	256	valid
2.0ms	20×	body	128	valid

Compiler

Compiled 63 to 59 computations (6.3% saved)

simplify141.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

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

4.2b

Counts

2 → 1

Compiler

Compiled 62 to 54 computations (12.9% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.6b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
2.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
4.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`sqrt-prod_binary64_13734` `add-sqr-sqrt_binary64_13740`
40×	`*-un-lft-identity_binary64_13718`
24×	`cancel-sign-sub-inv_binary64_13684`
16×	`difference-of-squares_binary64_13687`
12×	`add-log-exp_binary64_13757` `distribute-lft-out--_binary64_13670` `add-cube-cbrt_binary64_13753`
4×	`pow1_binary64_13779` `add-cbrt-cube_binary64_13754` `distribute-lft-out_binary64_13669` `sub-neg_binary64_13711` `diff-log_binary64_13810` `add-exp-log_binary64_13756` `flip3--_binary64_13722` `flip--_binary64_13693`

Counts

4 → 96

Calls

4 calls:

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

series148.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
38.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
37.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
33.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

simplify77.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5089	2235

prune245.0ms (2.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Error

0.3b

Counts

109 → 8

Compiler

Compiled 4570 to 2970 computations (35% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
2.6b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
2.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

rewrite53.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64_13718`
49×	`sqrt-prod_binary64_13734`
45×	`add-sqr-sqrt_binary64_13740`
21×	`add-cube-cbrt_binary64_13753`
19×	`distribute-lft-out_binary64_13669`
18×	`times-frac_binary64_13724` `cancel-sign-sub-inv_binary64_13684`
12×	`difference-of-squares_binary64_13687`
10×	`add-log-exp_binary64_13757`
9×	`distribute-lft-out--_binary64_13670`
8×	`add-exp-log_binary64_13756`
6×	`associate-/r*_binary64_13662` `add-cbrt-cube_binary64_13754`
5×	`pow1_binary64_13779`
3×	`sub-neg_binary64_13711` `diff-log_binary64_13810` `associate-/l*_binary64_13663` `flip3--_binary64_13722` `flip--_binary64_13693`
2×	`associate-/r/_binary64_13664` `div-exp_binary64_13769`
1×	`rec-exp_binary64_13768` `frac-2neg_binary64_13729` `flip3-+_binary64_13721` `1-exp_binary64_13762` `pow-flip_binary64_13792` `flip-+_binary64_13692` `clear-num_binary64_13717` `inv-pow_binary64_13803` `cbrt-undiv_binary64_13752` `div-inv_binary64_13715`

Counts

4 → 117

Calls

4 calls:

11.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
8.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

series140.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
37.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
35.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
28.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4886	2653
1	4886	2653

prune309.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	130	7	137

Error

0.3b

Counts

137 → 7

Compiler

Compiled 5564 to 3695 computations (33.6% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
2.6b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
3.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

rewrite60.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64_13718`
54×	`sqrt-prod_binary64_13734`
46×	`add-sqr-sqrt_binary64_13740`
36×	`times-frac_binary64_13724`
34×	`distribute-lft-out_binary64_13669`
30×	`add-cube-cbrt_binary64_13753`
12×	`associate-/r*_binary64_13662` `add-exp-log_binary64_13756` `cancel-sign-sub-inv_binary64_13684`
8×	`difference-of-squares_binary64_13687` `add-log-exp_binary64_13757` `add-cbrt-cube_binary64_13754`
6×	`pow1_binary64_13779` `associate-/l*_binary64_13663` `distribute-lft-out--_binary64_13670`
4×	`associate-/r/_binary64_13664` `div-exp_binary64_13769`
2×	`rec-exp_binary64_13768` `frac-2neg_binary64_13729` `flip3-+_binary64_13721` `1-exp_binary64_13762` `sub-neg_binary64_13711` `diff-log_binary64_13810` `pow-flip_binary64_13792` `flip-+_binary64_13692` `flip3--_binary64_13722` `flip--_binary64_13693` `clear-num_binary64_13717` `inv-pow_binary64_13803` `cbrt-undiv_binary64_13752` `div-inv_binary64_13715`

Counts

4 → 138

Calls

4 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
9.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series132.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
33.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
30.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
28.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify116.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4908	3094
1	4908	3094

prune378.0ms (4.5%)

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 6656 to 4497 computations (32.4% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
3.2b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

rewrite61.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`*-un-lft-identity_binary64_13718`
59×	`sqrt-prod_binary64_13734`
54×	`times-frac_binary64_13724`
49×	`distribute-lft-out_binary64_13669`
47×	`add-sqr-sqrt_binary64_13740`
39×	`add-cube-cbrt_binary64_13753`
18×	`associate-/r*_binary64_13662`
16×	`add-exp-log_binary64_13756`
10×	`add-cbrt-cube_binary64_13754`
9×	`associate-/l*_binary64_13663`
7×	`pow1_binary64_13779`
6×	`add-log-exp_binary64_13757` `associate-/r/_binary64_13664` `div-exp_binary64_13769` `cancel-sign-sub-inv_binary64_13684`
4×	`difference-of-squares_binary64_13687`
3×	`rec-exp_binary64_13768` `frac-2neg_binary64_13729` `flip3-+_binary64_13721` `1-exp_binary64_13762` `pow-flip_binary64_13792` `flip-+_binary64_13692` `clear-num_binary64_13717` `inv-pow_binary64_13803` `cbrt-undiv_binary64_13752` `distribute-lft-out--_binary64_13670` `div-inv_binary64_13715`
1×	`sub-neg_binary64_13711` `diff-log_binary64_13810` `flip3--_binary64_13722` `flip--_binary64_13693`

Counts

4 → 159

Calls

4 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

series125.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
33.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
29.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
27.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4946	3465
1	4946	3465

prune432.0ms (5.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	171	6	177

Error

0.0b

Counts

177 → 6

Compiler

Compiled 7579 to 5206 computations (31.3% saved)

regimes819.0ms (9.7%)

Accuracy

Total 0.0b remaining (50.3%)

Threshold costs 0.0b (50.3%)

Compiler

Compiled 12590 to 10861 computations (13.7% 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%)

sample4.5s (53.1%)

Algorithm

1×

intervals

Results

1.3s	4402×	body	512	valid
959.0ms	9591×	body	128	nan
680.0ms	1711×	body	1024	valid
199.0ms	1022×	body	256	valid
86.0ms	865×	body	128	valid

Compiler

Compiled 957 to 827 computations (13.6% saved)

Details

analyze260.0ms (3.1%)

sample125.0ms (1.5%)

simplify141.0ms (1.7%)

prune4.0ms (0%)

localize22.0ms (0.3%)

rewrite51.0ms (0.6%)

series148.0ms (1.7%)

simplify77.0ms (0.9%)

prune245.0ms (2.9%)

localize24.0ms (0.3%)

rewrite53.0ms (0.6%)

series140.0ms (1.6%)

simplify93.0ms (1.1%)

prune309.0ms (3.6%)

localize25.0ms (0.3%)

rewrite60.0ms (0.7%)

series132.0ms (1.6%)

simplify116.0ms (1.4%)

prune378.0ms (4.5%)

localize27.0ms (0.3%)

rewrite61.0ms (0.7%)

series125.0ms (1.5%)

simplify102.0ms (1.2%)

prune432.0ms (5.1%)

regimes819.0ms (9.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.5s (53.1%)

Profiling