Details

analyze262.0ms (7.8%)

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 25 to 15 computations (40% saved)

sample25.0ms (0.7%)

Algorithm

1×

intervals

Results

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

Compiler

Compiled 44 to 26 computations (40.9% saved)

simplify173.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

917×	`times-frac_binary64`
687×	`unsub-neg_binary64`
552×	`sub-neg_binary64`
367×	`distribute-lft-neg-in_binary64`
317×	`associate-*l/_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	23	22
2	51	22
3	100	22
4	218	22
5	499	22
6	897	22
7	1954	22
8	2631	22
9	4334	22
10	3926	22
11	4140	22
12	4226	22
13	4228	22
14	4228	22
15	4979	22

prune5.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

21.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	21.2b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Compiler

Compiled 34 to 18 computations (47.1% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite58.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

20.9b

Rules

8×	`associate-/l/_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64` `frac-times_binary64`
3×	`times-frac_binary64` `flip3--_binary64` `flip--_binary64` `associate-/r*_binary64`

Counts

2 → 42

Calls

2 calls:

12.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 1156 to 190 computations (83.6% saved)

series65.0ms (1.9%)

Error

0.3b

Counts

2 → 24

Calls

2 calls:

30.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
27.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 579 to 415 computations (28.3% saved)

simplify53.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

945×	`distribute-rgt-in_binary64`
893×	`distribute-lft-in_binary64`
355×	`times-frac_binary64`
127×	`div-sub_binary64`
65×	`associate-l_binary64`

Counts

66 → 45

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1322
1	334	1124
2	1334	1122
3	5235	1122

prune30.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	3	46

Error

10.9b

Counts

46 → 3

Alt Table

Status	Error	Program
	28.2b	(+.f64 -1 (.f64 2 (/.f64 (.f64 x x) (*.f64 y y))))
✓	21.2b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
▶	21.4b	(/.f64 (.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (+.f64 x y)) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y))))

Compiler

Compiled 758 to 201 computations (73.5% saved)

localize12.0ms (0.3%)

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 x y))
20.4b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
20.4b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite151.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

10.9b

Rules

79×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
62×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`
40×	`sqrt-prod_binary64`

Counts

4 → 151

Calls

4 calls:

18.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) (+.f64 x y))
10.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 4725 to 581 computations (87.7% saved)

series179.0ms (5.3%)

Error

10.9b

Counts

4 → 59

Calls

4 calls:

40.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
39.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
37.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))) (+.f64 x y))
32.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))

Compiler

Compiled 3110 to 1754 computations (43.6% saved)

simplify177.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

569×	`distribute-rgt-in_binary64`
539×	`distribute-lft-in_binary64`
359×	`times-frac_binary64`
189×	`div-sub_binary64`
145×	`*-commutative_binary64`

Counts

210 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	214	5003
1	708	4735
2	1868	4727
3	4807	4727
4	5176	4727

prune83.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	140	3	143

Error

10.9b

Counts

143 → 3

Alt Table

Status	Error	Program
	28.2b	(+.f64 -1 (.f64 2 (/.f64 (.f64 x x) (*.f64 y y))))
✓	21.2b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
▶	21.8b	(/.f64 (.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (+.f64 y x))) (+.f64 x y)) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))

Compiler

Compiled 3569 to 655 computations (81.6% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (+.f64 y x))) (+.f64 x y))
20.4b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
20.4b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
20.6b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y))) (+.f64 y x)))

rewrite137.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

10.9b

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`flip3-+_binary64` `sqrt-div_binary64` `associate-/r/_binary64` `flip-+_binary64` `associate-l_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 107

Calls

4 calls:

18.0ms	(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (+.f64 y x))) (+.f64 x y))
13.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y))) (+.f64 y x)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
3.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 4899 to 555 computations (88.7% saved)

series176.0ms (5.2%)

Error

10.9b

Counts

4 → 59

Calls

4 calls:

40.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
40.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
35.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y))) (+.f64 y x)))
33.0ms	(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (+.f64 y x))) (+.f64 x y))

Compiler

Compiled 3638 to 1855 computations (49% saved)

simplify148.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

274×	`distribute-rgt-in_binary64`
264×	`distribute-lft-in_binary64`
207×	`associate-l_binary64`
201×	`associate-r_binary64`
186×	`+-commutative_binary64`

Counts

166 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	216	4402
1	767	3858
2	2860	3335
3	4815	3335
4	4964	3335

prune87.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	122	3	125

Error

10.9b

Counts

125 → 3

Alt Table

Status	Error	Program
▶	28.2b	(+.f64 -1 (.f64 2 (/.f64 (.f64 x x) (*.f64 y y))))
✓	21.2b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
✓	21.8b	(/.f64 (.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (+.f64 y x))) (+.f64 x y)) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))

Compiler

Compiled 3826 to 768 computations (79.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 2 (/.f64 (.f64 x x) (*.f64 y y)))
23.6b	(/.f64 (.f64 x x) (.f64 y y))

rewrite63.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

4.9b

Rules

32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`prod-exp_binary64` `cbrt-unprod_binary64`
8×	`div-exp_binary64` `cbrt-undiv_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`associate-r_binary64`

Counts

2 → 51

Calls

2 calls:

8.0ms	(.f64 2 (/.f64 (.f64 x x) (*.f64 y y)))
6.0ms	(/.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 939 to 356 computations (62.1% saved)

series48.0ms (1.4%)

Error

10.9b

Counts

2 → 12

Calls

2 calls:

23.0ms	(.f64 2 (/.f64 (.f64 x x) (*.f64 y y)))
23.0ms	(/.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 325 to 275 computations (15.4% saved)

simplify100.0ms (3%)

Algorithm

1×	egg-herbie

Rules

720×	`times-frac_binary64`
468×	`associate-*l/_binary64`
415×	`associate-*r/_binary64`
414×	`associate-/l*_binary64`
389×	`associate-l_binary64`

Counts

63 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	1129
1	185	815
2	681	766
3	3583	713
4	4910	713
5	4982	713
6	4967	713

prune23.0ms (0.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	41	5	46
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	42	7	49

Error

4.9b

Counts

49 → 7

Alt Table

Status	Error	Program
	21.2b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
	21.8b	(/.f64 (.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (+.f64 y x))) (+.f64 x y)) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
	22.0b	(+.f64 -1 (.f64 2 (/.f64 (.f64 x (/.f64 x y)) y)))
	44.5b	(+.f64 -1 (.f64 2 (exp.f64 (.f64 2 (log.f64 (/.f64 x y))))))
	22.2b	(+.f64 -1 (*.f64 2 (/.f64 x (/.f64 y (/.f64 x y)))))
	22.0b	(+.f64 -1 (.f64 2 (.f64 (fabs.f64 (/.f64 x y)) (fabs.f64 (/.f64 x y)))))
	44.5b	(+.f64 -1 (exp.f64 (+.f64 (*.f64 2 (log.f64 (/.f64 x y))) (log.f64 2))))

Compiler

Compiled 311 to 180 computations (42.1% saved)

regimes291.0ms (8.6%)

Accuracy

Total 0.9b remaining (16.1%)

Threshold costs 0.9b (16.1%)

Compiler

Compiled 2812 to 1409 computations (49.9% saved)

bsearch49.0ms (1.4%)

Steps

Iters	Range		Point
8	1.4750413923448963e-169	3.1366203260892765e-166	4.82726859401974e-168
5	2.081952674602606e-197	5.1490603514502835e-197	5.0918618588880355e-197
7	-6.503975820444618e-201	-6.625783095730193e-203	-3.6861139043320025e-201
7	-3.295835945949844e-176	-4.2752574898770984e-178	-1.7556393841525514e-177
1	-4.902021561468657e+154	-1.74946235443502e+150	-3.034508079287107e+152

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	126
1	49	126
2	52	126
3	54	126
4	55	126
5	54	126

end2.0ms (0.1%)

Compiler: Compiled 88 to 43 computations (51.1% saved)

sample939.0ms (27.8%)

Algorithm

1×

intervals

Results

312.0ms	8000×	body	128	valid
164.0ms	8000×	pre	128	true

Compiler

Compiled 235 to 132 computations (43.8% saved)

Details

analyze262.0ms (7.8%)

sample25.0ms (0.7%)

simplify173.0ms (5.1%)

prune5.0ms (0.2%)

localize9.0ms (0.3%)

rewrite58.0ms (1.7%)

series65.0ms (1.9%)

simplify53.0ms (1.6%)

prune30.0ms (0.9%)

localize12.0ms (0.3%)

rewrite151.0ms (4.5%)

series179.0ms (5.3%)

simplify177.0ms (5.3%)

prune83.0ms (2.5%)

localize14.0ms (0.4%)

rewrite137.0ms (4.1%)

series176.0ms (5.2%)

simplify148.0ms (4.4%)

prune87.0ms (2.6%)

localize7.0ms (0.2%)

rewrite63.0ms (1.9%)

series48.0ms (1.4%)

simplify100.0ms (3%)

prune23.0ms (0.7%)

regimes291.0ms (8.6%)

bsearch49.0ms (1.4%)

simplify7.0ms (0.2%)

end2.0ms (0.1%)

sample939.0ms (27.8%)

Profiling