Details

analyze97.0ms (4.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11
0	1	1
1	1	1

Search

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample27.0ms (1.1%)

Algorithm

1×

intervals

Results

11.0ms	64×	body	2048	valid
4.0ms	130×	body	128	valid
4.0ms	33×	body	1024	valid
2.0ms	19×	body	512	valid
1.0ms	10×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify11.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune6.0ms (0.3%)

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: 16.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.8b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms (0.3%)

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))

series16.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

12.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
4.0ms	(atan.f64 (+.f64 N 1))

simplify71.0ms (3%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4998	391
1	4998	391

prune22.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	2	31

Merged error: 0.4b

Counts

31 → 2

Compiler

Compiled 351 to 229 computations (34.8% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.4b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`pow1_binary64_2185` `add-log-exp_binary64_2163` `add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `add-exp-log_binary64_2162` `*-un-lft-identity_binary64_2124` `add-cbrt-cube_binary64_2160`

Counts

1 → 7

Calls

1 calls:

0.0ms

(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series8.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

8.0ms

(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify180.0ms (7.6%)

Algorithm

1×	egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 0 (172.0ms)

Iter	Nodes	Cost
0	4793	162
1	4793	162

prune16.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	7	3	10
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	8	4	12

Merged error: 0.3b

Counts

12 → 4

Compiler

Compiled 201 to 167 computations (16.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.6b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
13.5b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.5b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2146`
24×	`sqrt-prod_binary64_2140`
21×	`pow1_binary64_2185`
14×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
10×	`sqrt-pow1_binary64_2142` `pow1/2_binary64_2204`
8×	`swap-sqr_binary64_2091`
6×	`associate-l_binary64_2065` `associate-r_binary64_2064` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`pow-prod-up_binary64_2194`
4×	`unswap-sqr_binary64_2092` `rem-sqrt-square_binary64_2137` `add-log-exp_binary64_2163`
3×	`pow-prod-down_binary64_2195` `pow-sqr_binary64_2097`
1×	`sqrt-unprod_binary64_2144` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `rem-square-sqrt_binary64_2136` `pow2_binary64_2205` `sqr-abs_binary64_2139` `cbrt-unprod_binary64_2157`

Counts

4 → 83

Calls

4 calls:

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

series65.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
23.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
10.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
7.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))

simplify85.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5103	1475

prune124.0ms (5.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	93	6	99

Merged error: 0.3b

Counts

99 → 6

Compiler

Compiled 2091 to 1724 computations (17.6% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
13.5b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.5b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.5b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite31.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`sqrt-pow1_binary64_2142`
45×	`pow1_binary64_2185`
30×	`pow-prod-up_binary64_2194` `pow1/2_binary64_2204`
16×	`add-sqr-sqrt_binary64_2146`
14×	`sqrt-prod_binary64_2140`
9×	`add-cube-cbrt_binary64_2159` `add-exp-log_binary64_2162` `*-un-lft-identity_binary64_2124` `add-cbrt-cube_binary64_2160`
7×	`pow-prod-down_binary64_2195`
6×	`associate-l_binary64_2065` `pow-sqr_binary64_2097`
4×	`add-log-exp_binary64_2163`
3×	`rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
2×	`sqrt-unprod_binary64_2144` `unswap-sqr_binary64_2092` `swap-sqr_binary64_2091`
1×	`-commutative_binary64_2055` `associate-r*_binary64_2064`

Counts

4 → 85

Calls

4 calls:

17.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (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	(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)))))

series85.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
23.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
23.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))

simplify86.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4894	1397
1	4894	1397

prune151.0ms (6.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	97	6	103

Merged error: 0.3b

Counts

103 → 6

Compiler

Compiled 2677 to 2218 computations (17.1% saved)

regimes55.0ms (2.3%)

Compiler: Compiled 626 to 544 computations (13.1% 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 (49.7%)

Algorithm

1×

intervals

Results

374.0ms	2212×	body	2048	valid
140.0ms	3992×	body	128	valid
121.0ms	1016×	body	1024	valid
50.0ms	531×	body	512	valid
15.0ms	249×	body	256	valid

Compiler

Compiled 332 to 290 computations (12.7% saved)

Details

analyze97.0ms (4.1%)

sample27.0ms (1.1%)

simplify11.0ms (0.5%)

prune6.0ms (0.3%)

localize5.0ms (0.2%)

rewrite6.0ms (0.3%)

series16.0ms (0.7%)

simplify71.0ms (3%)

prune22.0ms (0.9%)

localize5.0ms (0.2%)

rewrite1.0ms (0%)

series8.0ms (0.3%)

simplify180.0ms (7.6%)

prune16.0ms (0.7%)

localize8.0ms (0.3%)

rewrite18.0ms (0.7%)

series65.0ms (2.8%)

simplify85.0ms (3.6%)

prune124.0ms (5.3%)

localize10.0ms (0.4%)

rewrite31.0ms (1.3%)

series85.0ms (3.6%)

simplify86.0ms (3.6%)

prune151.0ms (6.4%)

regimes55.0ms (2.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (49.7%)

Profiling