Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample26.0ms (1%)

Algorithm

1×

intervals

Results

11.0ms	68×	body	2048	valid
5.0ms	140×	body	128	valid
4.0ms	30×	body	1024	valid
1.0ms	16×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify106.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

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

Error

13.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
0.8b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163`
3×	`cancel-sign-sub-inv_binary64_2090` `add-cube-cbrt_binary64_2159`
2×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
1×	`flip--_binary64_2099` `difference-of-squares_binary64_2093` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `diff-log_binary64_2216` `diff-atan_binary64_2281` `sub-neg_binary64_2117`

Counts

2 → 24

Calls

2 calls:

4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
1.0ms	(atan.f64 (+.f64 N 1))

series28.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

18.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
9.0ms	(atan.f64 (+.f64 N 1))

Compiler

Compiled 108 to 96 computations (11.1% saved)

simplify72.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4886	409
1	4886	409

prune29.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	3	31

Error

0.7b

Counts

31 → 3

Compiler

Compiled 402 to 272 computations (32.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.7b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
4×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159` `associate-r_binary64_2064` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`associate-l_binary64_2065`
2×	`add-log-exp_binary64_2163` `associate-*r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `distribute-lft-out_binary64_2075` `prod-exp_binary64_2173` `distribute-rgt-in_binary64_2074` `flip3-+_binary64_2127` `flip-+_binary64_2098` `distribute-lft-in_binary64_2073` `cbrt-unprod_binary64_2157`

Counts

2 → 30

Calls

2 calls:

7.0ms	(*.f64 N (+.f64 N 1))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series52.0ms (2.1%)

Counts

2 → 9

Calls

2 calls:

37.0ms	(*.f64 N (+.f64 N 1))
15.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 143 to 131 computations (8.4% saved)

simplify80.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4937	404
1	4937	404

prune44.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	35	7	42

Error

0.7b

Counts

42 → 7

Compiler

Compiled 595 to 458 computations (23% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 N)
0.5b	(cbrt.f64 N)
0.5b	(cbrt.f64 N)
0.7b	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 N) (cbrt.f64 N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_2155`
7×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
4×	`pow1_binary64_2185` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`pow1/3_binary64_2206`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)
1.0ms	(cbrt.f64 N)
1.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 N) (cbrt.f64 N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))))

series300.0ms (11.8%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt.f64 N)
93.0ms	(cbrt.f64 N)
89.0ms	(cbrt.f64 N)
23.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 N) (cbrt.f64 N)) (*.f64 (+.f64 1 N) (cbrt.f64 N)))))

Compiler

Compiled 430 to 352 computations (18.1% saved)

simplify132.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4905	429
1	4905	429

prune51.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	52	7	59

Error

0.7b

Counts

59 → 7

Compiler

Compiled 1047 to 627 computations (40.1% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.7b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
14.8b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
14.8b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_2146`
6×	`sqrt-prod_binary64_2140` `pow1_binary64_2185` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
2×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204`

Counts

4 → 40

Calls

4 calls:

1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

series104.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
33.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
19.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
17.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

Compiler

Compiled 568 to 496 computations (12.7% saved)

simplify101.0ms (4%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4938	910
1	4938	910

prune74.0ms (2.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	4	4
Picked	0	1	1
Done	1	1	2
Total	51	8	59

Error

0.7b

Counts

59 → 8

Compiler

Compiled 1376 to 1122 computations (18.5% saved)

regimes74.0ms (2.9%)

Accuracy

Total 0.1b remaining (14.2%)

Threshold costs 0.1b (14.2%)

Compiler

Compiled 728 to 608 computations (16.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	13
1	11	13

end0.0ms (0%)

sample1.2s (47%)

Algorithm

1×

intervals

Results

364.0ms	2107×	body	2048	valid
135.0ms	4194×	body	128	valid
111.0ms	958×	body	1024	valid
44.0ms	485×	body	512	valid
16.0ms	256×	body	256	valid

Compiler

Compiled 368 to 309 computations (16% saved)

Details

analyze1.0ms (0.1%)

sample26.0ms (1%)

simplify106.0ms (4.2%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite6.0ms (0.2%)

series28.0ms (1.1%)

simplify72.0ms (2.9%)

prune29.0ms (1.1%)

localize6.0ms (0.2%)

rewrite9.0ms (0.4%)

series52.0ms (2.1%)

simplify80.0ms (3.2%)

prune44.0ms (1.7%)

localize10.0ms (0.4%)

rewrite9.0ms (0.3%)

series300.0ms (11.8%)

simplify132.0ms (5.2%)

prune51.0ms (2%)

localize10.0ms (0.4%)

rewrite7.0ms (0.3%)

series104.0ms (4.1%)

simplify101.0ms (4%)

prune74.0ms (2.9%)

regimes74.0ms (2.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (47%)

Profiling