Details

analyze13.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 23 to 15 computations (34.8% saved)

sample22.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify249.0ms (9.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5184	22

prune2.0ms (0.1%)

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: 22.3b

Counts

2 → 1

Compiler

Compiled 30 to 18 computations (40% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
22.1b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite25.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64_714`
7×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
5×	`flip-+_binary64_741` `flip3-+_binary64_770`
4×	`frac-times_binary64_777` `add-log-exp_binary64_806` `add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
3×	`associate-/r*_binary64_711` `times-frac_binary64_773` `flip--_binary64_742` `flip3--_binary64_771`
2×	`cbrt-undiv_binary64_801` `associate-/r/_binary64_713` `pow1_binary64_828` `associate-r/_binary64_709` `associate-l/_binary64_710` `div-exp_binary64_818`
1×	`frac-2neg_binary64_778` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `associate-/l*_binary64_712` `+-commutative_binary64_697` `sum-log_binary64_858` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

2 → 42

Calls

2 calls:

16.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))

series313.0ms (11.6%)

Counts

2 → 6

Calls

2 calls:

277.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
36.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify32.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5033	969

prune78.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	6	49

Merged error: 0.6b

Counts

49 → 6

Compiler

Compiled 1723 to 545 computations (68.4% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune4.0ms (0.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	1	1
Total	6	6

Merged error: 0.6b

Counts

6 → 6

Compiler

Compiled 56 to 30 computations (46.4% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.0b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
21.0b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
21.0b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite94.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64_789`
93×	`*-un-lft-identity_binary64_767`
90×	`times-frac_binary64_773`
55×	`add-cube-cbrt_binary64_802`
54×	`sqrt-prod_binary64_783`
36×	`associate-l_binary64_708`
30×	`associate-r_binary64_707`
18×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
13×	`distribute-lft-out_binary64_718`
10×	`sqrt-div_binary64_784`
9×	`unswap-sqr_binary64_735`
8×	`pow1_binary64_828`
6×	`associate-/r*_binary64_711` `associate-/r/_binary64_713` `flip-+_binary64_741` `distribute-lft-out--_binary64_719` `flip3-+_binary64_770` `difference-of-squares_binary64_736`
5×	`cbrt-undiv_binary64_801` `div-exp_binary64_818`
4×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816` `add-log-exp_binary64_806` `associate-/l*_binary64_712`
3×	`div-inv_binary64_764`
2×	`rem-sqrt-square_binary64_780` `associate-/l/_binary64_714` `pow1/2_binary64_847` `sqrt-pow1_binary64_785`
1×	`frac-2neg_binary64_778` `frac-times_binary64_777` `-commutative_binary64_698` `associate-r/_binary64_709` `associate-*l/_binary64_710` `pow-prod-down_binary64_838` `clear-num_binary64_766`

Counts

4 → 175

Calls

4 calls:

43.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
11.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series284.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
86.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
43.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
42.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify91.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4981	5627
1	4981	5627

prune160.0ms (5.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	187	6	193

Merged error: 0.6b

Counts

193 → 6

Compiler

Compiled 6398 to 608 computations (90.5% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.2b	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (+.f64 (.f64 x x) (*.f64 y y))))
21.2b	(/.f64 (+.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))

rewrite44.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_767`
28×	`add-sqr-sqrt_binary64_789`
25×	`times-frac_binary64_773`
21×	`add-cube-cbrt_binary64_802`
18×	`associate-r_binary64_707`
10×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
7×	`distribute-lft-out_binary64_718`
5×	`associate-l_binary64_708` `pow1_binary64_828` `add-log-exp_binary64_806`
4×	`associate-/r/_binary64_713` `flip-+_binary64_741` `associate-/l*_binary64_712` `flip3-+_binary64_770`
3×	`associate-/r*_binary64_711`
2×	`frac-times_binary64_777` `unswap-sqr_binary64_735` `associate-/l/_binary64_714` `cbrt-undiv_binary64_801` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `associate-*l/_binary64_710` `flip--_binary64_742` `div-exp_binary64_818` `div-inv_binary64_764` `flip3--_binary64_771`
1×	`frac-2neg_binary64_778` `-commutative_binary64_698` `distribute-lft-out--_binary64_719` `+-commutative_binary64_697` `sum-log_binary64_858` `associate-r/_binary64_709` `pow-prod-down_binary64_838` `clear-num_binary64_766` `difference-of-squares_binary64_736`

Counts

3 → 89

Calls

3 calls:

21.0ms	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (+.f64 (.f64 x x) (*.f64 y y))))
9.0ms	(/.f64 (+.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))
5.0ms	(+.f64 (.f64 x x) (.f64 y y))

series188.0ms (6.9%)

Counts

3 → 9

Calls

3 calls:

92.0ms	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (+.f64 (.f64 x x) (*.f64 y y))))
56.0ms	(/.f64 (+.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))
41.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify64.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5348	2173

prune68.0ms (2.5%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	98	6	104

Merged error: 0.6b

Counts

104 → 6

Compiler

Compiled 2245 to 324 computations (85.6% saved)

regimes92.0ms (3.4%)

Compiler: Compiled 250 to 152 computations (39.2% saved)

bsearch62.0ms (2.3%)

Steps

Iters	Range		Point
8	1.8297587729451786e-193	9.106967862748747e-191	1.8489230072387054e-193
9	7.54775606969044e-260	6.848554987354421e-255	6.780097591949427e-255
8	-3.378231746650949e-153	-5.900623004698139e-156	-5.983925060339704e-156
8	-7.770556217314213e+155	-1.454539525937534e+153	-1.360803354623427e+154

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	71
1	49	71

end0.0ms (0%)

sample783.0ms (28.9%)

Algorithm

1×

intervals

Results

303.0ms	8000×	body	128	valid
164.0ms	8000×	pre	128	true

Compiler

Compiled 180 to 107 computations (40.6% saved)

Details

analyze13.0ms (0.5%)

sample22.0ms (0.8%)

simplify249.0ms (9.2%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite25.0ms (0.9%)

series313.0ms (11.6%)

simplify32.0ms (1.2%)

prune78.0ms (2.9%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.2%)

prune4.0ms (0.1%)

localize14.0ms (0.5%)

rewrite94.0ms (3.5%)

series284.0ms (10.5%)

simplify91.0ms (3.4%)

prune160.0ms (5.9%)

localize9.0ms (0.3%)

rewrite44.0ms (1.6%)

series188.0ms (6.9%)

simplify64.0ms (2.3%)

prune68.0ms (2.5%)

regimes92.0ms (3.4%)

bsearch62.0ms (2.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample783.0ms (28.9%)

Profiling