Details

analyze410.0ms (4.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5085	350
0	4	4
1	4	4

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)

sample127.0ms (1.5%)

Algorithm

1×

intervals

Results

42.0ms	140×	body	512	valid
31.0ms	316×	body	128	nan
19.0ms	49×	body	1024	valid
9.0ms	32×	body	256	valid
3.0ms	35×	body	128	valid

Compiler

Compiled 63 to 59 computations (6.3% saved)

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

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

4.6b

Counts

2 → 1

Compiler

Compiled 62 to 54 computations (12.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
1.9b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
4.4b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
4.5b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite53.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_10330` `sqrt-prod_binary64_10324`
40×	`*-un-lft-identity_binary64_10308`
24×	`cancel-sign-sub-inv_binary64_10274`
16×	`difference-of-squares_binary64_10277`
12×	`add-log-exp_binary64_10347` `add-cube-cbrt_binary64_10343` `distribute-lft-out--_binary64_10260`
4×	`flip--_binary64_10283` `sub-neg_binary64_10301` `distribute-lft-out_binary64_10259` `flip3--_binary64_10312` `pow1_binary64_10369` `add-cbrt-cube_binary64_10344` `add-exp-log_binary64_10346` `diff-log_binary64_10400`

Counts

4 → 96

Calls

4 calls:

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

series151.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
39.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
38.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
36.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5089	2235

prune234.0ms (2.7%)

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

0.6b

Counts

109 → 5

Compiler

Compiled 4432 to 2857 computations (35.5% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
1.9b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
4.4b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
4.5b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite59.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64_10308`
49×	`sqrt-prod_binary64_10324`
45×	`add-sqr-sqrt_binary64_10330`
21×	`add-cube-cbrt_binary64_10343`
19×	`distribute-lft-out_binary64_10259`
18×	`times-frac_binary64_10314` `cancel-sign-sub-inv_binary64_10274`
12×	`difference-of-squares_binary64_10277`
10×	`add-log-exp_binary64_10347`
9×	`distribute-lft-out--_binary64_10260`
8×	`add-exp-log_binary64_10346`
6×	`associate-/r*_binary64_10252` `add-cbrt-cube_binary64_10344`
5×	`pow1_binary64_10369`
3×	`flip--_binary64_10283` `associate-/l*_binary64_10253` `sub-neg_binary64_10301` `flip3--_binary64_10312` `diff-log_binary64_10400`
2×	`div-exp_binary64_10359` `associate-/r/_binary64_10254`
1×	`1-exp_binary64_10352` `inv-pow_binary64_10393` `clear-num_binary64_10307` `flip-+_binary64_10282` `rec-exp_binary64_10358` `flip3-+_binary64_10311` `div-inv_binary64_10305` `frac-2neg_binary64_10319` `cbrt-undiv_binary64_10342` `pow-flip_binary64_10382`

Counts

4 → 117

Calls

4 calls:

15.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
10.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
10.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

series145.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
38.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
38.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
30.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify99.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4886	2653
1	4886	2653

prune283.0ms (3.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	129	5	134

Error

0.0b

Counts

134 → 5

Compiler

Compiled 5471 to 3620 computations (33.8% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
1.9b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
4.5b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite61.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64_10308`
54×	`sqrt-prod_binary64_10324`
46×	`add-sqr-sqrt_binary64_10330`
36×	`times-frac_binary64_10314`
34×	`distribute-lft-out_binary64_10259`
30×	`add-cube-cbrt_binary64_10343`
12×	`associate-/r*_binary64_10252` `add-exp-log_binary64_10346` `cancel-sign-sub-inv_binary64_10274`
8×	`add-log-exp_binary64_10347` `add-cbrt-cube_binary64_10344` `difference-of-squares_binary64_10277`
6×	`associate-/l*_binary64_10253` `pow1_binary64_10369` `distribute-lft-out--_binary64_10260`
4×	`div-exp_binary64_10359` `associate-/r/_binary64_10254`
2×	`flip--_binary64_10283` `1-exp_binary64_10352` `sub-neg_binary64_10301` `inv-pow_binary64_10393` `clear-num_binary64_10307` `flip-+_binary64_10282` `flip3--_binary64_10312` `rec-exp_binary64_10358` `flip3-+_binary64_10311` `diff-log_binary64_10400` `div-inv_binary64_10305` `frac-2neg_binary64_10319` `cbrt-undiv_binary64_10342` `pow-flip_binary64_10382`

Counts

4 → 138

Calls

4 calls:

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

series135.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
36.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
30.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
28.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4987	3097
1	4987	3097

prune361.0ms (4.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	149	6	155

Error

0.0b

Counts

155 → 6

Compiler

Compiled 6662 to 4503 computations (32.4% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
1.9b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite62.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64_10308`
47×	`sqrt-prod_binary64_10324`
37×	`distribute-lft-out_binary64_10259`
36×	`add-sqr-sqrt_binary64_10330` `times-frac_binary64_10314`
28×	`add-cube-cbrt_binary64_10343`
12×	`associate-/r*_binary64_10252` `add-exp-log_binary64_10346`
8×	`add-log-exp_binary64_10347` `add-cbrt-cube_binary64_10344`
6×	`associate-/l*_binary64_10253` `pow1_binary64_10369` `cancel-sign-sub-inv_binary64_10274`
4×	`div-exp_binary64_10359` `associate-/r/_binary64_10254` `difference-of-squares_binary64_10277`
3×	`flip-+_binary64_10282` `flip3-+_binary64_10311` `distribute-lft-out--_binary64_10260`
2×	`1-exp_binary64_10352` `inv-pow_binary64_10393` `clear-num_binary64_10307` `rec-exp_binary64_10358` `div-inv_binary64_10305` `frac-2neg_binary64_10319` `cbrt-undiv_binary64_10342` `pow-flip_binary64_10382`
1×	`sum-log_binary64_10399` `flip--_binary64_10283` `sub-neg_binary64_10301` `+-commutative_binary64_10238` `flip3--_binary64_10312` `diff-log_binary64_10400`

Counts

4 → 128

Calls

4 calls:

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

series117.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
30.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
27.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
20.0ms	(+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

simplify97.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4924	2809
1	4924	2809

prune349.0ms (4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	139	7	146

Error

0.0b

Counts

146 → 7

Compiler

Compiled 6208 to 4261 computations (31.4% saved)

regimes948.0ms (10.8%)

Accuracy

Total 0.1b remaining (71%)

Threshold costs 0.1b (71%)

Compiler

Compiled 14693 to 12638 computations (14% saved)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	62
1	41	62

Compiler

Compiled 78 to 70 computations (10.3% saved)

end0.0ms (0%)

sample4.7s (54.2%)

Algorithm

1×

intervals

Results

1.3s	4408×	body	512	valid
961.0ms	9614×	body	128	nan
699.0ms	1728×	body	1024	valid
200.0ms	1031×	body	256	valid
82.0ms	833×	body	128	valid

Compiler

Compiled 1127 to 971 computations (13.8% saved)

Details

analyze410.0ms (4.7%)

sample127.0ms (1.5%)

simplify44.0ms (0.5%)

prune4.0ms (0%)

localize22.0ms (0.2%)

rewrite53.0ms (0.6%)

series151.0ms (1.7%)

simplify71.0ms (0.8%)

prune234.0ms (2.7%)

localize24.0ms (0.3%)

rewrite59.0ms (0.7%)

series145.0ms (1.7%)

simplify99.0ms (1.1%)

prune283.0ms (3.2%)

localize28.0ms (0.3%)

rewrite61.0ms (0.7%)

series135.0ms (1.5%)

simplify91.0ms (1%)

prune361.0ms (4.1%)

localize26.0ms (0.3%)

rewrite62.0ms (0.7%)

series117.0ms (1.3%)

simplify97.0ms (1.1%)

prune349.0ms (4%)

regimes948.0ms (10.8%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample4.7s (54.2%)

Profiling