Details

analyze268.0ms (3%)

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)

sample121.0ms (1.3%)

Algorithm

1×

intervals

Results

44.0ms	149×	body	512	valid
30.0ms	286×	body	128	nan
21.0ms	53×	body	1024	valid
5.0ms	26×	body	256	valid
3.0ms	28×	body	128	valid

Compiler

Compiled 63 to 59 computations (6.3% saved)

simplify209.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

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

Merged error: 5.9b

Counts

2 → 1

Compiler

Compiled 62 to 54 computations (12.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.6b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
2.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.4b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.7b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_12141` `sqrt-prod_binary64_12135`
40×	`*-un-lft-identity_binary64_12119`
24×	`cancel-sign-sub-inv_binary64_12085`
16×	`difference-of-squares_binary64_12088`
12×	`distribute-lft-out--_binary64_12071` `add-log-exp_binary64_12158` `add-cube-cbrt_binary64_12154`
4×	`sub-neg_binary64_12112` `flip3--_binary64_12123` `distribute-lft-out_binary64_12070` `flip--_binary64_12094` `pow1_binary64_12180` `add-exp-log_binary64_12157` `add-cbrt-cube_binary64_12155` `diff-log_binary64_12211`

Counts

4 → 96

Calls

4 calls:

13.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
11.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
11.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
10.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

series264.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
67.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
66.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
64.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify86.0ms (1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5136	2211

prune535.0ms (5.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	7	109

Merged error: 0.3b

Counts

109 → 7

Compiler

Compiled 10376 to 7856 computations (24.3% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
2.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.4b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.7b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64_12119`
49×	`sqrt-prod_binary64_12135`
45×	`add-sqr-sqrt_binary64_12141`
21×	`add-cube-cbrt_binary64_12154`
19×	`distribute-lft-out_binary64_12070`
18×	`cancel-sign-sub-inv_binary64_12085` `times-frac_binary64_12125`
12×	`difference-of-squares_binary64_12088`
10×	`add-log-exp_binary64_12158`
9×	`distribute-lft-out--_binary64_12071`
8×	`add-exp-log_binary64_12157`
6×	`associate-/r*_binary64_12063` `add-cbrt-cube_binary64_12155`
5×	`pow1_binary64_12180`
3×	`sub-neg_binary64_12112` `flip3--_binary64_12123` `flip--_binary64_12094` `diff-log_binary64_12211` `associate-/l*_binary64_12064`
2×	`div-exp_binary64_12170` `associate-/r/_binary64_12065`
1×	`flip-+_binary64_12093` `cbrt-undiv_binary64_12153` `inv-pow_binary64_12204` `pow-flip_binary64_12193` `clear-num_binary64_12118` `rec-exp_binary64_12169` `frac-2neg_binary64_12130` `1-exp_binary64_12163` `div-inv_binary64_12116` `flip3-+_binary64_12122`

Counts

4 → 117

Calls

4 calls:

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

series264.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
69.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
66.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
57.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5112	2622

prune434.0ms (4.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Merged error: 0.1b

Counts

136 → 8

Compiler

Compiled 8360 to 6060 computations (27.5% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
3.4b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.7b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64_12119`
54×	`sqrt-prod_binary64_12135`
46×	`add-sqr-sqrt_binary64_12141`
36×	`times-frac_binary64_12125`
34×	`distribute-lft-out_binary64_12070`
30×	`add-cube-cbrt_binary64_12154`
12×	`cancel-sign-sub-inv_binary64_12085` `associate-/r*_binary64_12063` `add-exp-log_binary64_12157`
8×	`difference-of-squares_binary64_12088` `add-log-exp_binary64_12158` `add-cbrt-cube_binary64_12155`
6×	`distribute-lft-out--_binary64_12071` `pow1_binary64_12180` `associate-/l*_binary64_12064`
4×	`div-exp_binary64_12170` `associate-/r/_binary64_12065`
2×	`flip-+_binary64_12093` `cbrt-undiv_binary64_12153` `inv-pow_binary64_12204` `sub-neg_binary64_12112` `pow-flip_binary64_12193` `flip3--_binary64_12123` `clear-num_binary64_12118` `flip--_binary64_12094` `rec-exp_binary64_12169` `frac-2neg_binary64_12130` `1-exp_binary64_12163` `div-inv_binary64_12116` `flip3-+_binary64_12122` `diff-log_binary64_12211`

Counts

4 → 138

Calls

4 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
10.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

series242.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
68.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
55.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
51.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))

simplify77.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4904	3046
1	4904	3046

prune454.0ms (5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	150	8	158

Merged error: 0.1b

Counts

158 → 8

Compiler

Compiled 8321 to 5920 computations (28.9% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
3.7b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

rewrite73.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`*-un-lft-identity_binary64_12119`
59×	`sqrt-prod_binary64_12135`
54×	`times-frac_binary64_12125`
49×	`distribute-lft-out_binary64_12070`
47×	`add-sqr-sqrt_binary64_12141`
39×	`add-cube-cbrt_binary64_12154`
18×	`associate-/r*_binary64_12063`
16×	`add-exp-log_binary64_12157`
10×	`add-cbrt-cube_binary64_12155`
9×	`associate-/l*_binary64_12064`
7×	`pow1_binary64_12180`
6×	`div-exp_binary64_12170` `add-log-exp_binary64_12158` `cancel-sign-sub-inv_binary64_12085` `associate-/r/_binary64_12065`
4×	`difference-of-squares_binary64_12088`
3×	`flip-+_binary64_12093` `cbrt-undiv_binary64_12153` `inv-pow_binary64_12204` `pow-flip_binary64_12193` `distribute-lft-out--_binary64_12071` `clear-num_binary64_12118` `rec-exp_binary64_12169` `frac-2neg_binary64_12130` `1-exp_binary64_12163` `div-inv_binary64_12116` `flip3-+_binary64_12122`
1×	`sub-neg_binary64_12112` `flip3--_binary64_12123` `flip--_binary64_12094` `diff-log_binary64_12211`

Counts

4 → 159

Calls

4 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

series240.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))
66.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
55.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t)))
51.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4987	3450
1	4987	3450

prune686.0ms (7.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	172	7	179

Merged error: 0.0b

Counts

179 → 7

Compiler

Compiled 9330 to 6689 computations (28.3% saved)

regimes359.0ms (4%)

Compiler: Compiled 4280 to 3692 computations (13.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	62
1	41	62

end0.0ms (0%)

sample4.2s (47.1%)

Algorithm

1×

intervals

Results

1.4s	4436×	body	512	valid
1.0s	9728×	body	128	nan
704.0ms	1677×	body	1024	valid
223.0ms	1040×	body	256	valid
89.0ms	847×	body	128	valid

Compiler

Compiled 420 to 363 computations (13.6% saved)

Details

analyze268.0ms (3%)

sample121.0ms (1.3%)

simplify209.0ms (2.3%)

prune4.0ms (0%)

localize22.0ms (0.2%)

rewrite57.0ms (0.6%)

series264.0ms (2.9%)

simplify86.0ms (1%)

prune535.0ms (5.9%)

localize28.0ms (0.3%)

rewrite57.0ms (0.6%)

series264.0ms (2.9%)

simplify76.0ms (0.8%)

prune434.0ms (4.8%)

localize28.0ms (0.3%)

rewrite63.0ms (0.7%)

series242.0ms (2.7%)

simplify77.0ms (0.9%)

prune454.0ms (5%)

localize27.0ms (0.3%)

rewrite73.0ms (0.8%)

series240.0ms (2.7%)

simplify80.0ms (0.9%)

prune686.0ms (7.6%)

regimes359.0ms (4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.2s (47.1%)

Profiling