Details

analyze776.0ms (5.5%)

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
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 20 to 16 computations (20% saved)

sample85.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	55×	body	1024	invalid
18.0ms	60×	body	1024	valid
11.0ms	153×	body	128	valid
7.0ms	32×	body	512	valid
6.0ms	28×	body	512	invalid
2.0ms	14×	body	256	invalid
2.0ms	10×	body	256	valid
1.0ms	17×	body	128	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify97.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune4.0ms (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

Error

0.3b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite149.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

40×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
32×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
22×	`sqrt-prod_binary64_435` `associate-r_binary64_359`
10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
6×	`associate-/r*_binary64_363`
5×	`pow1_binary64_480` `add-log-exp_binary64_458`
3×	`associate-/l_binary64_364` `unswap-sqr_binary64_387` `associate-l*_binary64_360`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-inv_binary64_416` `flip3-+_binary64_422` `associate-/l/_binary64_366` `flip-+_binary64_393` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

3 → 94

Calls

3 calls:

12.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
7.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2362 to 862 computations (63.5% saved)

series764.0ms (5.5%)

Error

0.3b

Counts

3 → 42

Calls

3 calls:

428.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
194.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
97.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1676 to 1476 computations (11.9% saved)

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5044	2993

prune152.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	126	10	136
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	10	138

Error

Counts

138 → 10

Compiler

Compiled 2943 to 1208 computations (59% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
0.5b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
6.8b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.8b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite727.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

540×	`times-frac_binary64_425`
429×	`sqrt-prod_binary64_435`
297×	`add-sqr-sqrt_binary64_441`
295×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
48×	`associate-/r*_binary64_363`
22×	`sqrt-div_binary64_436`
17×	`associate-/r/_binary64_365`
12×	`associate-/l*_binary64_364`
11×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `flip3-+_binary64_422` `flip-+_binary64_393`
9×	`div-inv_binary64_416`
6×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`sqrt-undiv_binary64_440`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `frac-2neg_binary64_430` `clear-num_binary64_418` `associate-/l/_binary64_366`

Counts

4 → 411

Calls

4 calls:

21.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
10.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 18617 to 4886 computations (73.8% saved)

series651.0ms (4.6%)

Error

Counts

4 → 60

Calls

4 calls:

188.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
137.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
134.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
130.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 3524 to 2508 computations (28.8% saved)

simplify196.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

471 → 471

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5064	18741

prune595.0ms (4.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	470	1	471
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	472	9	481

Error

Counts

481 → 9

Compiler

Compiled 16205 to 4897 computations (69.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
0.2b	(/.f64 2 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
6.8b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.9b	(sqrt.f64 (/.f64 2 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))

rewrite333.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

190×	`times-frac_binary64_425`
180×	`sqrt-prod_binary64_435`
118×	`add-sqr-sqrt_binary64_441`
114×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
21×	`associate-/r*_binary64_363`
19×	`associate-/r/_binary64_365`
11×	`flip3-+_binary64_422` `flip-+_binary64_393`
10×	`div-inv_binary64_416`
9×	`associate-/l*_binary64_364`
8×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
6×	`pow1_binary64_480` `sqrt-div_binary64_436`
4×	`add-log-exp_binary64_458`
3×	`rem-sqrt-square_binary64_432`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `frac-2neg_binary64_430` `clear-num_binary64_418` `associate-/l/_binary64_366`
1×	`sqrt-undiv_binary64_440`

Counts

4 → 219

Calls

4 calls:

14.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
6.0ms	(sqrt.f64 (/.f64 2 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
5.0ms	(/.f64 2 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 8975 to 2399 computations (73.3% saved)

series614.0ms (4.4%)

Error

Counts

4 → 54

Calls

4 calls:

196.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
141.0ms	(sqrt.f64 (/.f64 2 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
129.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
93.0ms	(/.f64 2 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3134 to 2279 computations (27.3% saved)

simplify171.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4947	10143
1	4947	10143

prune332.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	273	9	282

Error

Counts

282 → 9

Compiler

Compiled 9400 to 2878 computations (69.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
0.1b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
0.2b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

rewrite517.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

195×	`times-frac_binary64_425`
111×	`add-sqr-sqrt_binary64_441`
94×	`cbrt-prod_binary64_450`
91×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
67×	`associate-r_binary64_359`
47×	`sqrt-prod_binary64_435`
32×	`add-exp-log_binary64_457`
22×	`div-inv_binary64_416`
20×	`add-cbrt-cube_binary64_455`
12×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
10×	`associate-/l_binary64_364` `associate-/r_binary64_363`
7×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `unswap-sqr_binary64_387`
6×	`pow1_binary64_480` `add-log-exp_binary64_458`
3×	`associate-/l/_binary64_366` `associate-l_binary64_360`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418` `flip3-+_binary64_422` `flip-+_binary64_393`
1×	`pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 225

Calls

4 calls:

30.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
14.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
10.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 8603 to 5119 computations (40.5% saved)

series1.4s (10.1%)

Error

Counts

4 → 54

Calls

4 calls:

639.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
425.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
193.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
101.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 2750 to 2514 computations (8.6% saved)

simplify123.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4964	8773
1	4964	8773

prune444.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	279	0	279
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	279	9	288

Error

Counts

288 → 9

Compiler

Compiled 8199 to 4567 computations (44.3% saved)

regimes1.4s (10%)

Accuracy

Total 0.7b remaining (96.3%)

Threshold costs 0.7b (96.3%)

Compiler

Compiled 16871 to 12399 computations (26.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	34
1	16	34

end0.0ms (0%)

sample4.3s (31%)

Algorithm

1×

intervals

Results

588.0ms	1838×	body	1024	valid
470.0ms	1520×	body	1024	invalid
370.0ms	4800×	body	128	valid
218.0ms	914×	body	512	valid
184.0ms	829×	body	512	invalid
70.0ms	442×	body	256	valid
61.0ms	398×	body	256	invalid
53.0ms	627×	body	128	invalid
3.0ms	6×	body	2048	valid

Compiler

Compiled 2136 to 1565 computations (26.7% saved)

Details

analyze776.0ms (5.5%)

sample85.0ms (0.6%)

simplify97.0ms (0.7%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite149.0ms (1.1%)

series764.0ms (5.5%)

simplify68.0ms (0.5%)

prune152.0ms (1.1%)

localize15.0ms (0.1%)

rewrite727.0ms (5.2%)

series651.0ms (4.6%)

simplify196.0ms (1.4%)

prune595.0ms (4.2%)

localize14.0ms (0.1%)

rewrite333.0ms (2.4%)

series614.0ms (4.4%)

simplify171.0ms (1.2%)

prune332.0ms (2.4%)

localize13.0ms (0.1%)

rewrite517.0ms (3.7%)

series1.4s (10.1%)

simplify123.0ms (0.9%)

prune444.0ms (3.2%)

regimes1.4s (10%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.3s (31%)

Profiling