Details

analyze499.0ms (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)

sample204.0ms (1.3%)

Algorithm

1×

intervals

Results

78.0ms	154×	body	512	valid
47.0ms	257×	body	128	nan
38.0ms	55×	body	1024	valid
10.0ms	30×	body	256	valid
3.0ms	17×	body	128	valid

Compiler

Compiled 63 to 59 computations (6.3% saved)

simplify237.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5168	50

prune8.0ms (0.1%)

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

Merged error: 5.8b

Counts

2 → 1

Compiler

Compiled 62 to 54 computations (12.9% saved)

localize49.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
2.7b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
2.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.4b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

rewrite90.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_15445` `sqrt-prod_binary64_15439`
40×	`*-un-lft-identity_binary64_15423`
24×	`cancel-sign-sub-inv_binary64_15389`
16×	`difference-of-squares_binary64_15392`
12×	`add-cube-cbrt_binary64_15458` `distribute-lft-out--_binary64_15375` `add-log-exp_binary64_15462`
4×	`flip3--_binary64_15427` `pow1_binary64_15484` `distribute-lft-out_binary64_15374` `flip--_binary64_15398` `diff-log_binary64_15515` `add-exp-log_binary64_15461` `sub-neg_binary64_15416` `add-cbrt-cube_binary64_15459`

Counts

4 → 96

Calls

4 calls:

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

series260.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
65.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
63.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
62.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

simplify133.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5089	2235

prune405.0ms (2.6%)

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

Merged error: 1.1b

Counts

109 → 5

Compiler

Compiled 4431 to 2856 computations (35.5% saved)

localize54.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
2.7b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
2.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.4b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

rewrite102.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64_15423`
49×	`sqrt-prod_binary64_15439`
45×	`add-sqr-sqrt_binary64_15445`
21×	`add-cube-cbrt_binary64_15458`
19×	`distribute-lft-out_binary64_15374`
18×	`times-frac_binary64_15429` `cancel-sign-sub-inv_binary64_15389`
12×	`difference-of-squares_binary64_15392`
10×	`add-log-exp_binary64_15462`
9×	`distribute-lft-out--_binary64_15375`
8×	`add-exp-log_binary64_15461`
6×	`associate-/r*_binary64_15367` `add-cbrt-cube_binary64_15459`
5×	`pow1_binary64_15484`
3×	`flip3--_binary64_15427` `associate-/l*_binary64_15368` `flip--_binary64_15398` `diff-log_binary64_15515` `sub-neg_binary64_15416`
2×	`div-exp_binary64_15474` `associate-/r/_binary64_15369`
1×	`rec-exp_binary64_15473` `frac-2neg_binary64_15434` `1-exp_binary64_15467` `flip3-+_binary64_15426` `inv-pow_binary64_15508` `pow-flip_binary64_15497` `cbrt-undiv_binary64_15457` `flip-+_binary64_15397` `div-inv_binary64_15420` `clear-num_binary64_15422`

Counts

4 → 117

Calls

4 calls:

20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
18.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
18.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
17.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series246.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
66.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
62.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
51.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))

simplify139.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5092	2633

prune469.0ms (3%)

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

Merged error: 0.7b

Counts

134 → 5

Compiler

Compiled 5448 to 3606 computations (33.8% saved)

localize49.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
2.7b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
3.4b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

rewrite114.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64_15423`
54×	`sqrt-prod_binary64_15439`
46×	`add-sqr-sqrt_binary64_15445`
36×	`times-frac_binary64_15429`
34×	`distribute-lft-out_binary64_15374`
30×	`add-cube-cbrt_binary64_15458`
12×	`associate-/r*_binary64_15367` `add-exp-log_binary64_15461` `cancel-sign-sub-inv_binary64_15389`
8×	`difference-of-squares_binary64_15392` `add-cbrt-cube_binary64_15459` `add-log-exp_binary64_15462`
6×	`pow1_binary64_15484` `associate-/l*_binary64_15368` `distribute-lft-out--_binary64_15375`
4×	`div-exp_binary64_15474` `associate-/r/_binary64_15369`
2×	`rec-exp_binary64_15473` `frac-2neg_binary64_15434` `1-exp_binary64_15467` `flip3--_binary64_15427` `flip3-+_binary64_15426` `inv-pow_binary64_15508` `pow-flip_binary64_15497` `flip--_binary64_15398` `cbrt-undiv_binary64_15457` `flip-+_binary64_15397` `div-inv_binary64_15420` `clear-num_binary64_15422` `diff-log_binary64_15515` `sub-neg_binary64_15416`

Counts

4 → 138

Calls

4 calls:

20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
19.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
17.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
17.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series220.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
59.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
52.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
48.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify197.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	4908	3094
1	4908	3094

prune601.0ms (3.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	151	4	155

Merged error: 0.4b

Counts

155 → 4

Compiler

Compiled 6554 to 4416 computations (32.6% saved)

localize53.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
2.7b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite122.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`*-un-lft-identity_binary64_15423`
59×	`sqrt-prod_binary64_15439`
54×	`times-frac_binary64_15429`
49×	`distribute-lft-out_binary64_15374`
47×	`add-sqr-sqrt_binary64_15445`
39×	`add-cube-cbrt_binary64_15458`
18×	`associate-/r*_binary64_15367`
16×	`add-exp-log_binary64_15461`
10×	`add-cbrt-cube_binary64_15459`
9×	`associate-/l*_binary64_15368`
7×	`pow1_binary64_15484`
6×	`div-exp_binary64_15474` `associate-/r/_binary64_15369` `add-log-exp_binary64_15462` `cancel-sign-sub-inv_binary64_15389`
4×	`difference-of-squares_binary64_15392`
3×	`rec-exp_binary64_15473` `frac-2neg_binary64_15434` `1-exp_binary64_15467` `flip3-+_binary64_15426` `inv-pow_binary64_15508` `pow-flip_binary64_15497` `cbrt-undiv_binary64_15457` `flip-+_binary64_15397` `div-inv_binary64_15420` `distribute-lft-out--_binary64_15375` `clear-num_binary64_15422`
1×	`flip3--_binary64_15427` `flip--_binary64_15398` `diff-log_binary64_15515` `sub-neg_binary64_15416`

Counts

4 → 159

Calls

4 calls:

24.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
19.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
17.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series228.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
61.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
54.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
51.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify143.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4957	3453
1	4957	3453

prune660.0ms (4.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	170	5	175

Merged error: 0.0b

Counts

175 → 5

Compiler

Compiled 7571 to 5203 computations (31.3% saved)

regimes1.6s (10.1%)

Compiler: Compiled 12591 to 10890 computations (13.5% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	62
1	41	62

end0.0ms (0%)

sample8.6s (55.6%)

Algorithm

1×

intervals

Results

2.4s	4319×	body	512	valid
1.8s	9685×	body	128	nan
1.4s	1793×	body	1024	valid
368.0ms	989×	body	256	valid
167.0ms	899×	body	128	valid

Compiler

Compiled 982 to 850 computations (13.4% saved)

Details

analyze499.0ms (3.2%)

sample204.0ms (1.3%)

simplify237.0ms (1.5%)

prune8.0ms (0.1%)

localize49.0ms (0.3%)

rewrite90.0ms (0.6%)

series260.0ms (1.7%)

simplify133.0ms (0.9%)

prune405.0ms (2.6%)

localize54.0ms (0.3%)

rewrite102.0ms (0.7%)

series246.0ms (1.6%)

simplify139.0ms (0.9%)

prune469.0ms (3%)

localize49.0ms (0.3%)

rewrite114.0ms (0.7%)

series220.0ms (1.4%)

simplify197.0ms (1.3%)

prune601.0ms (3.9%)

localize53.0ms (0.3%)

rewrite122.0ms (0.8%)

series228.0ms (1.5%)

simplify143.0ms (0.9%)

prune660.0ms (4.3%)

regimes1.6s (10.1%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.6s (55.6%)

Profiling