Details

analyze348.0ms (7.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5007	54
0	2	2
1	2	2

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
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 43 to 37 computations (14% saved)

simplify56.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5241	29

prune5.0ms (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

Error

15.7b

Counts

2 → 2

Compiler

Compiled 59 to 47 computations (20.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.7b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
6.5b	(-.f64 (.f64 b b) (.f64 a a))
8.3b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite117.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`times-frac_binary64_425`
178×	`add-sqr-sqrt_binary64_441`
153×	`*-un-lft-identity_binary64_419`
121×	`add-cube-cbrt_binary64_454`
58×	`associate-l_binary64_360`
46×	`difference-of-squares_binary64_388`
40×	`cancel-sign-sub-inv_binary64_385`
22×	`div-inv_binary64_416`
19×	`associate-r_binary64_359`
18×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
14×	`distribute-rgt-in_binary64_369` `distribute-lft-out--_binary64_371` `distribute-lft-in_binary64_368`
13×	`associate-/l*_binary64_364`
8×	`add-log-exp_binary64_458`
6×	`flip3--_binary64_423` `flip--_binary64_394` `pow1_binary64_480` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
4×	`sub-neg_binary64_412` `associate-/r/_binary64_365` `associate-/r*_binary64_363`
3×	`unswap-sqr_binary64_387` `frac-times_binary64_429` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-*r/_binary64_361` `frac-sub_binary64_428`
2×	`diff-log_binary64_511`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `clear-num_binary64_418` `-commutative_binary64_350` `frac-2neg_binary64_430` `associate-/l/_binary64_366`

Counts

4 → 270

Calls

4 calls:

51.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
15.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))

series114.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))
33.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
23.0ms	(-.f64 (.f64 b b) (.f64 a a))
10.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))

simplify118.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5154	7997

prune372.0ms (7.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	273	9	282
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	275	9	284

Error

0.0b

Counts

284 → 9

Compiler

Compiled 8377 to 4000 computations (52.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`times-frac_binary64_425`
79×	`*-un-lft-identity_binary64_419`
60×	`add-exp-log_binary64_457`
51×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
39×	`add-cbrt-cube_binary64_455`
29×	`div-exp_binary64_470`
19×	`prod-exp_binary64_468`
17×	`cbrt-undiv_binary64_453`
14×	`distribute-lft-out_binary64_370` `associate-/l*_binary64_364`
10×	`cbrt-unprod_binary64_452`
7×	`div-inv_binary64_416`
6×	`1-exp_binary64_463`
5×	`associate-/r*_binary64_363`
2×	`clear-num_binary64_418` `add-log-exp_binary64_458` `associate-/r/_binary64_365` `frac-2neg_binary64_430` `pow1_binary64_480` `associate-/l/_binary64_366`
1×	`flip3-+_binary64_422` `associate-*l/_binary64_362` `flip-+_binary64_393`

Counts

2 → 122

Calls

2 calls:

14.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
8.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series82.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

47.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
35.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify63.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5189	2615

prune129.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	129	8	137

Error

Counts

137 → 8

Compiler

Compiled 2603 to 1301 computations (50% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
0.3b	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
0.3b	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

rewrite109.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

621×	`times-frac_binary64_425`
410×	`*-un-lft-identity_binary64_419`
278×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
202×	`add-exp-log_binary64_457`
120×	`div-exp_binary64_470`
71×	`associate-/r*_binary64_363`
66×	`distribute-lft-out_binary64_370`
62×	`add-cbrt-cube_binary64_455`
61×	`prod-exp_binary64_468`
35×	`1-exp_binary64_463`
31×	`cbrt-undiv_binary64_453`
28×	`div-inv_binary64_416`
15×	`rec-exp_binary64_469`
13×	`cbrt-unprod_binary64_452`
8×	`associate-/l*_binary64_364`
6×	`associate-/r/_binary64_365`
4×	`pow1_binary64_480`
3×	`clear-num_binary64_418` `add-log-exp_binary64_458` `frac-2neg_binary64_430` `associate-/l/_binary64_366`
1×	`flip3-+_binary64_422` `associate-*l/_binary64_362` `inv-pow_binary64_504` `pow-flip_binary64_493` `flip-+_binary64_393`

Counts

3 → 408

Calls

3 calls:

31.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
17.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))
8.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))

series114.0ms (2.3%)

Counts

3 → 9

Calls

3 calls:

44.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
40.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
29.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

simplify156.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4963	10043
1	4963	10043

prune456.0ms (9.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	417	0	417
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	417	8	425

Error

Counts

425 → 8

Compiler

Compiled 9601 to 4937 computations (48.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (*.f64 b a))
0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

rewrite52.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

331×	`times-frac_binary64_425`
215×	`*-un-lft-identity_binary64_419`
135×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
71×	`associate-/l*_binary64_364`
40×	`distribute-lft-out_binary64_370`
28×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
17×	`div-inv_binary64_416`
15×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
6×	`associate-/r/_binary64_365`
5×	`associate-/r*_binary64_363`
3×	`flip3-+_binary64_422` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `flip-+_binary64_393`
2×	`clear-num_binary64_418` `add-log-exp_binary64_458` `frac-2neg_binary64_430` `pow1_binary64_480` `associate-/l/_binary64_366`

Counts

2 → 226

Calls

2 calls:

18.0ms	(/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (*.f64 b a))
8.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series75.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

41.0ms	(/.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) (*.f64 b a))
34.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify108.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4977	5513
1	4977	5513

prune213.0ms (4.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	230	2	232
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	232	8	240

Error

Counts

240 → 8

Compiler

Compiled 4724 to 2159 computations (54.3% saved)

regimes347.0ms (7.1%)

Accuracy

Total 0.3b remaining (99.3%)

Threshold costs 0.3b (99.3%)

Compiler

Compiled 4586 to 3321 computations (27.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	20
1	15	20

end0.0ms (0%)

sample1.7s (35.7%)

Algorithm

1×

intervals

Results

440.0ms	8000×	body	128	valid
19.0ms	351×	body	128	invalid

Compiler

Compiled 1527 to 1106 computations (27.6% saved)

Details

analyze348.0ms (7.2%)

sample22.0ms (0.5%)

simplify56.0ms (1.2%)

prune5.0ms (0.1%)

localize12.0ms (0.2%)

rewrite117.0ms (2.4%)

series114.0ms (2.3%)

simplify118.0ms (2.4%)

prune372.0ms (7.6%)

localize8.0ms (0.2%)

rewrite35.0ms (0.7%)

series82.0ms (1.7%)

simplify63.0ms (1.3%)

prune129.0ms (2.6%)

localize9.0ms (0.2%)

rewrite109.0ms (2.2%)

series114.0ms (2.3%)

simplify156.0ms (3.2%)

prune456.0ms (9.4%)

localize7.0ms (0.1%)

rewrite52.0ms (1.1%)

series75.0ms (1.5%)

simplify108.0ms (2.2%)

prune213.0ms (4.4%)

regimes347.0ms (7.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.7s (35.7%)

Profiling