Details

analyze15.0ms (0.2%)

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
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample18.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 29 to 26 computations (10.3% saved)

simplify103.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	21
1	22	21

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: 41.4b

Counts

2 → 1

Compiler

Compiled 28 to 22 computations (21.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.1b	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
38.5b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_19537`
19×	`times-frac_binary64_19521`
18×	`add-cube-cbrt_binary64_19550` `*-un-lft-identity_binary64_19515`
13×	`sqrt-prod_binary64_19531`
5×	`add-log-exp_binary64_19554` `add-cbrt-cube_binary64_19551` `add-exp-log_binary64_19553`
4×	`pow1_binary64_19576`
3×	`associate-/r_binary64_19459` `associate-/l_binary64_19460`
2×	`flip-+_binary64_19489` `associate-/l/_binary64_19462` `div-inv_binary64_19512` `rem-sqrt-square_binary64_19528` `flip3-+_binary64_19518`
1×	`sqrt-pow1_binary64_19533` `div-exp_binary64_19566` `clear-num_binary64_19514` `pow1/2_binary64_19595` `cbrt-undiv_binary64_19549` `sqrt-div_binary64_19532` `frac-2neg_binary64_19526` `+-commutative_binary64_19445` `sum-log_binary64_19606`

Counts

3 → 65

Calls

3 calls:

8.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
6.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series748.0ms (10.8%)

Counts

3 → 52

Calls

3 calls:

428.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
223.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
96.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 2213 to 2040 computations (7.8% saved)

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4962	2928
1	4962	2928

prune139.0ms (2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	100	17	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	17	118

Merged error: 39.0b

Counts

118 → 17

Compiler

Compiled 2619 to 1068 computations (59.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.4b	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
38.5b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`sqrt-prod_binary64_19531`
36×	`times-frac_binary64_19521`
33×	`add-sqr-sqrt_binary64_19537`
32×	`add-cube-cbrt_binary64_19550` `*-un-lft-identity_binary64_19515`
6×	`associate-/r_binary64_19459` `associate-/l_binary64_19460`
5×	`add-log-exp_binary64_19554` `add-cbrt-cube_binary64_19551` `add-exp-log_binary64_19553`
4×	`pow1_binary64_19576` `sqrt-div_binary64_19532`
3×	`flip-+_binary64_19489` `flip3-+_binary64_19518`
2×	`associate-/l/_binary64_19462`
1×	`sqrt-undiv_binary64_19536` `div-inv_binary64_19512` `sqrt-pow1_binary64_19533` `div-exp_binary64_19566` `clear-num_binary64_19514` `pow1/2_binary64_19595` `cbrt-undiv_binary64_19549` `rem-sqrt-square_binary64_19528` `frac-2neg_binary64_19526` `+-commutative_binary64_19445` `sum-log_binary64_19606`

Counts

3 → 89

Calls

3 calls:

10.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series852.0ms (12.3%)

Counts

3 → 55

Calls

3 calls:

460.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
288.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
104.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 3116 to 2757 computations (11.5% saved)

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5183	4622

prune165.0ms (2.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	133	11	144
Fresh	5	11	16
Picked	1	0	1
Done	0	0	0
Total	139	22	161

Merged error: 39.0b

Counts

161 → 22

Compiler

Compiled 3857 to 1594 computations (58.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 z z))) (sqrt.f64 3))
32.0b	(sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`sqrt-prod_binary64_19531`
36×	`times-frac_binary64_19521`
32×	`add-sqr-sqrt_binary64_19537`
31×	`add-cube-cbrt_binary64_19550` `*-un-lft-identity_binary64_19515`
6×	`associate-/r_binary64_19459` `associate-/l_binary64_19460`
4×	`add-cbrt-cube_binary64_19551` `sqrt-div_binary64_19532` `add-exp-log_binary64_19553`
3×	`pow1_binary64_19576`
2×	`flip-+_binary64_19489` `associate-/l/_binary64_19462` `add-log-exp_binary64_19554` `flip3-+_binary64_19518`
1×	`sqrt-undiv_binary64_19536` `div-inv_binary64_19512` `sqrt-pow1_binary64_19533` `div-exp_binary64_19566` `clear-num_binary64_19514` `pow1/2_binary64_19595` `cbrt-undiv_binary64_19549` `rem-sqrt-square_binary64_19528` `frac-2neg_binary64_19526`

Counts

2 → 78

Calls

2 calls:

8.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 z z))) (sqrt.f64 3))
4.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))

series263.0ms (3.8%)

Counts

2 → 30

Calls

2 calls:

163.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 z z))) (sqrt.f64 3))
100.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))

Compiler

Compiled 785 to 761 computations (3.1% saved)

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5052	2650

prune125.0ms (1.8%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	96	12	108
Fresh	4	17	21
Picked	1	0	1
Done	0	0	0
Total	101	29	130

Merged error: 26.4b

Counts

130 → 29

Compiler

Compiled 2377 to 1162 computations (51.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y y) (*.f64 z z))))) (sqrt.f64 3))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y y) (*.f64 z z)))))
32.0b	(sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))
32.0b	(sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))

rewrite62.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`sqrt-prod_binary64_19531`
62×	`add-sqr-sqrt_binary64_19537`
52×	`sqrt-div_binary64_19532`
34×	`sqrt-pow1_binary64_19533`
29×	`pow1_binary64_19576`
22×	`add-cube-cbrt_binary64_19550` `*-un-lft-identity_binary64_19515`
18×	`pow1/2_binary64_19595`
15×	`swap-sqr_binary64_19482`
14×	`flip-+_binary64_19489` `flip3-+_binary64_19518`
11×	`add-cbrt-cube_binary64_19551` `add-exp-log_binary64_19553`
10×	`rem-sqrt-square_binary64_19528`
9×	`associate-l_binary64_19456` `pow-prod-up_binary64_19585` `associate-r_binary64_19455` `unswap-sqr_binary64_19483`
8×	`associate-/l/_binary64_19462` `frac-times_binary64_19525`
6×	`times-frac_binary64_19521` `associate-/r*_binary64_19459`
5×	`pow-sqr_binary64_19488` `pow-prod-down_binary64_19586`
4×	`associate-r/_binary64_19457` `associate-l/_binary64_19458` `add-log-exp_binary64_19554` `sqr-abs_binary64_19530`
2×	`cbrt-unprod_binary64_19548` `div-exp_binary64_19566` `cbrt-undiv_binary64_19549` `sqrt-unprod_binary64_19535` `prod-exp_binary64_19564`
1×	`rem-square-sqrt_binary64_19527` `sqrt-undiv_binary64_19536` `div-inv_binary64_19512` `clear-num_binary64_19514` `associate-/l_binary64_19460` `pow-plus_binary64_19578` `-commutative_binary64_19446` `pow2_binary64_19596` `frac-2neg_binary64_19526`

Counts

4 → 153

Calls

4 calls:

18.0ms	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y y) (*.f64 z z))))) (sqrt.f64 3))
17.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y y) (*.f64 z z)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))

series496.0ms (7.2%)

Counts

4 → 60

Calls

4 calls:

177.0ms	(/.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y y) (*.f64 z z))))) (sqrt.f64 3))
108.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y y) (*.f64 z z)))))
107.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))
104.0ms	(sqrt.f64 (+.f64 (.f64 y y) (.f64 z z)))

Compiler

Compiled 1951 to 1735 computations (11.1% saved)

simplify101.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4979	3893
1	4979	3893

prune195.0ms (2.8%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	209	4	213
Fresh	1	27	28
Picked	0	1	1
Done	0	0	0
Total	210	32	242

Merged error: 26.3b

Counts

242 → 32

Compiler

Compiled 4763 to 1601 computations (66.4% saved)

regimes1.7s (24.5%)

Compiler: Compiled 13595 to 10295 computations (24.3% saved)

bsearch3.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	48
1	22	48

end0.0ms (0%)

sample1.6s (22.9%)

Algorithm

1×

intervals

Results

368.0ms

8000×

body

128

valid

Compiler

Compiled 1148 to 878 computations (23.5% saved)

Details

analyze15.0ms (0.2%)

sample18.0ms (0.3%)

simplify103.0ms (1.5%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite24.0ms (0.4%)

series748.0ms (10.8%)

simplify90.0ms (1.3%)

prune139.0ms (2%)

localize10.0ms (0.1%)

rewrite28.0ms (0.4%)

series852.0ms (12.3%)

simplify67.0ms (1%)

prune165.0ms (2.4%)

localize7.0ms (0.1%)

rewrite20.0ms (0.3%)

series263.0ms (3.8%)

simplify72.0ms (1%)

prune125.0ms (1.8%)

localize13.0ms (0.2%)

rewrite62.0ms (0.9%)

series496.0ms (7.2%)

simplify101.0ms (1.5%)

prune195.0ms (2.8%)

regimes1.7s (24.5%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.6s (22.9%)

Profiling