Details

analyze234.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample23.0ms (0.1%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
0.0ms	12×	body	128	invalid

Compiler

Compiled 23 to 24 computations (-4.3% saved)

simplify167.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	105	16
1	105	16

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 7.4b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (*.f64 z z))
3.4b	(.f64 y (+.f64 1 (.f64 z z)))
5.3b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64_10193`
27×	`add-exp-log_binary64_10222`
21×	`add-sqr-sqrt_binary64_10208`
19×	`add-cube-cbrt_binary64_10219` `*-un-lft-identity_binary64_10187`
17×	`add-cbrt-cube_binary64_10220`
13×	`associate-/l*_binary64_10134`
12×	`div-exp_binary64_10235`
6×	`cbrt-undiv_binary64_10218`
5×	`prod-exp_binary64_10233` `pow1_binary64_10245` `add-log-exp_binary64_10223`
4×	`associate-*r/_binary64_10131`
3×	`associate-l_binary64_10130` `flip3-+_binary64_10190` `associate-r_binary64_10129` `flip-+_binary64_10161` `div-inv_binary64_10184` `cbrt-unprod_binary64_10217`
2×	`associate-/r/_binary64_10135` `rec-exp_binary64_10234` `1-exp_binary64_10228`
1×	`frac-2neg_binary64_10198` `associate-/l/_binary64_10136` `+-commutative_binary64_10119` `pow-prod-down_binary64_10255` `sum-log_binary64_10275` `associate-/r_binary64_10133` `-commutative_binary64_10120` `unswap-sqr_binary64_10155` `distribute-rgt-in_binary64_10139` `distribute-lft-in_binary64_10138` `clear-num_binary64_10186`

Counts

3 → 85

Calls

3 calls:

13.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
6.0ms	(.f64 y (+.f64 1 (.f64 z z)))
3.0ms	(+.f64 1 (*.f64 z z))

series210.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

95.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
70.0ms	(.f64 y (+.f64 1 (.f64 z z)))
45.0ms	(+.f64 1 (*.f64 z z))

simplify86.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4982	1456
1	4982	1456

prune106.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 5.4b

Counts

95 → 9

Compiler

Compiled 1645 to 1003 computations (39% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (*.f64 z z))
3.1b	(.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (+.f64 1 (.f64 z z))))
3.5b	(/.f64 (/.f64 1 x) (+.f64 1 (*.f64 z z)))

rewrite67.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

173×	`times-frac_binary64_10193`
127×	`add-sqr-sqrt_binary64_10208`
94×	`*-un-lft-identity_binary64_10187`
87×	`add-cube-cbrt_binary64_10219`
77×	`add-exp-log_binary64_10222`
45×	`associate-r_binary64_10129`
40×	`div-exp_binary64_10235`
29×	`add-cbrt-cube_binary64_10220`
20×	`prod-exp_binary64_10233`
13×	`associate-l_binary64_10130` `associate-/l*_binary64_10134`
12×	`cbrt-undiv_binary64_10218` `unswap-sqr_binary64_10155`
10×	`rec-exp_binary64_10234` `1-exp_binary64_10228` `div-inv_binary64_10184`
6×	`cbrt-unprod_binary64_10217`
5×	`pow1_binary64_10245` `add-log-exp_binary64_10223`
4×	`associate-/r/_binary64_10135`
3×	`flip3-+_binary64_10190` `associate-/r*_binary64_10133` `flip-+_binary64_10161`
1×	`frac-2neg_binary64_10198` `associate-r/_binary64_10131` `associate-/l/_binary64_10136` `frac-times_binary64_10197` `+-commutative_binary64_10119` `pow-prod-down_binary64_10255` `sum-log_binary64_10275` `-commutative_binary64_10120` `associate-*l/_binary64_10132` `clear-num_binary64_10186`

Counts

3 → 193

Calls

3 calls:

28.0ms	(.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (+.f64 1 (.f64 z z))))
9.0ms	(/.f64 (/.f64 1 x) (+.f64 1 (*.f64 z z)))
7.0ms	(+.f64 1 (*.f64 z z))

series239.0ms (1.3%)

Counts

3 → 9

Calls

3 calls:

98.0ms	(.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (+.f64 1 (.f64 z z))))
91.0ms	(/.f64 (/.f64 1 x) (+.f64 1 (*.f64 z z)))
50.0ms	(+.f64 1 (*.f64 z z))

simplify104.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4918	4413
1	4918	4413

prune224.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	202	9	211

Merged error: 5.4b

Counts

211 → 9

Compiler

Compiled 4422 to 2740 computations (38% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (*.f64 z z))
0.4b	(/.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) 1) (/.f64 y (/.f64 (/.f64 (cbrt.f64 1) x) (+.f64 1 (.f64 z z)))))
3.0b	(/.f64 y (/.f64 (/.f64 (cbrt.f64 1) x) (+.f64 1 (*.f64 z z))))
3.5b	(/.f64 (/.f64 (cbrt.f64 1) x) (+.f64 1 (*.f64 z z)))

rewrite707.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Rules

7655×	`times-frac_binary64_10193`
2916×	`add-sqr-sqrt_binary64_10208` `add-cube-cbrt_binary64_10219` `*-un-lft-identity_binary64_10187`
792×	`cbrt-prod_binary64_10215`
349×	`div-inv_binary64_10184`
296×	`associate-/r*_binary64_10133`
104×	`add-exp-log_binary64_10222`
75×	`div-exp_binary64_10235`
68×	`associate-/r/_binary64_10135`
59×	`add-cbrt-cube_binary64_10220`
47×	`cbrt-undiv_binary64_10218`
32×	`associate-/l*_binary64_10134`
30×	`flip3-+_binary64_10190` `flip-+_binary64_10161`
8×	`1-exp_binary64_10228` `prod-exp_binary64_10233`
6×	`add-log-exp_binary64_10223`
4×	`pow1_binary64_10245` `cbrt-unprod_binary64_10217`
3×	`frac-2neg_binary64_10198` `clear-num_binary64_10186`
2×	`associate-/l/_binary64_10136`
1×	`+-commutative_binary64_10119` `sum-log_binary64_10275`

Counts

4 → 2246

Calls

4 calls:

91.0ms	(/.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) 1) (/.f64 y (/.f64 (/.f64 (cbrt.f64 1) x) (+.f64 1 (.f64 z z)))))
21.0ms	(/.f64 y (/.f64 (/.f64 (cbrt.f64 1) x) (+.f64 1 (*.f64 z z))))
11.0ms	(/.f64 (/.f64 (cbrt.f64 1) x) (+.f64 1 (*.f64 z z)))
3.0ms	(+.f64 1 (*.f64 z z))

series339.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(/.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) 1) (/.f64 y (/.f64 (/.f64 (cbrt.f64 1) x) (+.f64 1 (.f64 z z)))))
94.0ms	(/.f64 y (/.f64 (/.f64 (cbrt.f64 1) x) (+.f64 1 (*.f64 z z))))
94.0ms	(/.f64 (/.f64 (cbrt.f64 1) x) (+.f64 1 (*.f64 z z)))
43.0ms	(+.f64 1 (*.f64 z z))

simplify992.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

2258 → 2258

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5742	126367

prune11.7s (63.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	2258	0	2258
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	2258	9	2267

Merged error: 5.4b

Counts

2267 → 9

Compiler

Compiled 89039 to 60185 computations (32.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (/.f64 1 x))
0.5b	(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
1.4b	(/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (*.f64 z z)))
5.6b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (*.f64 z z))))

rewrite113.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64_10193`
205×	`add-sqr-sqrt_binary64_10208`
190×	`cbrt-prod_binary64_10215`
147×	`*-un-lft-identity_binary64_10187`
135×	`add-cube-cbrt_binary64_10219`
70×	`associate-r_binary64_10129`
29×	`add-exp-log_binary64_10222`
26×	`unswap-sqr_binary64_10155`
23×	`associate-l_binary64_10130`
19×	`add-cbrt-cube_binary64_10220`
18×	`swap-sqr_binary64_10154`
17×	`div-inv_binary64_10184`
16×	`associate-/l*_binary64_10134`
13×	`pow1_binary64_10245`
9×	`prod-exp_binary64_10233` `cbrt-unprod_binary64_10217`
8×	`cbrt-undiv_binary64_10218` `div-exp_binary64_10235`
7×	`pow1/3_binary64_10266`
6×	`cbrt-div_binary64_10216`
4×	`associate-/r/_binary64_10135` `add-log-exp_binary64_10223`
3×	`pow-prod-down_binary64_10255` `associate-/r*_binary64_10133`
2×	`associate-r/_binary64_10131` `frac-times_binary64_10197` `flip3-+_binary64_10190` `-commutative_binary64_10120` `flip-+_binary64_10161` `pow-prod-up_binary64_10254` `pow-sqr_binary64_10160` `associate-*l/_binary64_10132`
1×	`frac-2neg_binary64_10198` `pow2_binary64_10265` `associate-/l/_binary64_10136` `pow-plus_binary64_10247` `clear-num_binary64_10186`

Counts

4 → 286

Calls

4 calls:

36.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (*.f64 z z))))
15.0ms	(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
10.0ms	(/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (*.f64 z z)))
3.0ms	(cbrt.f64 (/.f64 1 x))

series673.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (*.f64 z z)))
165.0ms	(*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x)))
151.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (+.f64 1 (*.f64 z z))))
145.0ms	(cbrt.f64 (/.f64 1 x))

simplify113.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4972	7319
1	4972	7319

prune614.0ms (3.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	297	1	298
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	298	9	307

Merged error: 4.7b

Counts

307 → 9

Compiler

Compiled 8795 to 5971 computations (32.1% saved)

regimes484.0ms (2.6%)

Compiler: Compiled 5072 to 4280 computations (15.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	16
1	12	16

end0.0ms (0%)

sample1.2s (6.3%)

Algorithm

1×

intervals

Results

295.0ms	8000×	body	128	valid
16.0ms	465×	body	128	invalid

Compiler

Compiled 664 to 552 computations (16.9% saved)

Details

analyze234.0ms (1.3%)

sample23.0ms (0.1%)

simplify167.0ms (0.9%)

prune3.0ms (0%)

localize7.0ms (0%)

rewrite29.0ms (0.2%)

series210.0ms (1.1%)

simplify86.0ms (0.5%)

prune106.0ms (0.6%)

localize8.0ms (0%)

rewrite67.0ms (0.4%)

series239.0ms (1.3%)

simplify104.0ms (0.6%)

prune224.0ms (1.2%)

localize13.0ms (0.1%)

rewrite707.0ms (3.8%)

series339.0ms (1.8%)

simplify992.0ms (5.4%)

prune11.7s (63.5%)

localize11.0ms (0.1%)

rewrite113.0ms (0.6%)

series673.0ms (3.6%)

simplify113.0ms (0.6%)

prune614.0ms (3.3%)

regimes484.0ms (2.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (6.3%)

Profiling