Details

analyze151.0ms (3.5%)

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)

sample32.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms	80×	body	2048	valid
5.0ms	130×	body	128	valid
4.0ms	26×	body	1024	valid
1.0ms	11×	body	512	valid
1.0ms	9×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune6.0ms (0.1%)

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

12.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite46.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

10.8b

Rules

5×	`add-sqr-sqrt_binary64_2487` `*-un-lft-identity_binary64_2465`
4×	`add-log-exp_binary64_2504`
3×	`add-cube-cbrt_binary64_2500` `cancel-sign-sub-inv_binary64_2431`
2×	`pow1_binary64_2526` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
1×	`diff-atan_binary64_2622` `diff-log_binary64_2557` `flip3--_binary64_2469` `sub-neg_binary64_2458` `flip--_binary64_2440` `difference-of-squares_binary64_2434` `distribute-lft-out--_binary64_2417`

Counts

2 → 24

Calls

2 calls:

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

Compiler

Compiled 339 to 221 computations (34.8% saved)

series39.0ms (0.9%)

Error

12.0b

Counts

2 → 6

Calls

2 calls:

25.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))
12.0ms	(atan.f64 (+.f64 N 1))

Compiler

Compiled 91 to 78 computations (14.3% saved)

simplify67.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4998	391
1	4998	391

prune25.0ms (0.6%)

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

Error

0.3b

Counts

31 → 2

Compiler

Compiled 274 to 185 computations (32.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.3b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite60.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

6×	`add-sqr-sqrt_binary64_2487` `*-un-lft-identity_binary64_2465`
4×	`pow1_binary64_2526` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `add-cube-cbrt_binary64_2500` `associate-r_binary64_2405`
3×	`associate-l_binary64_2406`
2×	`add-log-exp_binary64_2504` `associate-*r/_binary64_2407`
1×	`pow-prod-down_binary64_2536` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `unswap-sqr_binary64_2433` `distribute-rgt-in_binary64_2415` `distribute-lft-in_binary64_2414` `flip3-+_binary64_2468` `flip-+_binary64_2439` `distribute-lft-out_binary64_2416` `*-commutative_binary64_2396`

Counts

2 → 30

Calls

2 calls:

9.0ms	(*.f64 N (+.f64 N 1))
0.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 435 to 334 computations (23.2% saved)

series77.0ms (1.8%)

Error

0.3b

Counts

2 → 9

Calls

2 calls:

54.0ms	(*.f64 N (+.f64 N 1))
18.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

Compiler

Compiled 157 to 140 computations (10.8% saved)

simplify69.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4927	392
1	4927	392

prune57.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	36	5	41

Error

0.3b

Counts

41 → 5

Compiler

Compiled 474 to 315 computations (33.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))
18.5b	(cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
18.5b	(cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
18.5b	(cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))

rewrite112.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

9×	`cbrt-prod_binary64_2496`
7×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487` `*-un-lft-identity_binary64_2465`
4×	`pow1_binary64_2526` `add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`pow1/3_binary64_2547`

Counts

4 → 40

Calls

4 calls:

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

Compiler

Compiled 1619 to 1045 computations (35.5% saved)

series676.0ms (15.5%)

Error

0.3b

Counts

4 → 12

Calls

4 calls:

225.0ms	(cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
209.0ms	(cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
205.0ms	(cbrt.f64 (atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N)))))
28.0ms	(atan2.f64 1 (+.f64 N (+.f64 1 (*.f64 N N))))

Compiler

Compiled 917 to 687 computations (25.1% saved)

simplify84.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4760	944
1	4760	944

prune105.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	52	5	57

Error

0.3b

Counts

57 → 5

Compiler

Compiled 1523 to 995 computations (34.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (pow.f64 N 3) N)
0.3b	(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (-.f64 N 1))))
5.2b	(/.f64 (-.f64 (pow.f64 N 3) N) (-.f64 N 1))

rewrite230.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

125×	`add-sqr-sqrt_binary64_2487`
79×	`*-un-lft-identity_binary64_2465`
63×	`times-frac_binary64_2471`
56×	`difference-of-squares_binary64_2434`
22×	`add-cube-cbrt_binary64_2500`
19×	`distribute-lft-out--_binary64_2417`
10×	`difference-of-sqr-1_binary64_2435`
9×	`unpow-prod-down_binary64_2544` `cube-prod_binary64_2493` `sqr-pow_binary64_2437` `unpow3_binary64_2531` `distribute-rgt-out--_binary64_2419` `associate-/l*_binary64_2410`
7×	`associate-/r*_binary64_2409`
5×	`add-exp-log_binary64_2503` `add-log-exp_binary64_2504` `add-cbrt-cube_binary64_2501`
3×	`pow1_binary64_2526` `flip3--_binary64_2469` `flip--_binary64_2440` `cancel-sign-sub-inv_binary64_2431`
2×	`associate-/l/_binary64_2412` `associate-/r/_binary64_2411`
1×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `frac-2neg_binary64_2476` `div-sub_binary64_2470` `clear-num_binary64_2464` `div-inv_binary64_2462` `diff-log_binary64_2557` `sub-neg_binary64_2458`

Counts

3 → 123

Calls

3 calls:

14.0ms	(/.f64 (-.f64 (pow.f64 N 3) N) (-.f64 N 1))
7.0ms	(-.f64 (pow.f64 N 3) N)
0.0ms	(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (-.f64 N 1))))

Compiler

Compiled 2132 to 1566 computations (26.5% saved)

series241.0ms (5.5%)

Error

0.3b

Counts

3 → 15

Calls

3 calls:

110.0ms	(/.f64 (-.f64 (pow.f64 N 3) N) (-.f64 N 1))
79.0ms	(-.f64 (pow.f64 N 3) N)
36.0ms	(atan2.f64 1 (+.f64 1 (/.f64 (-.f64 (pow.f64 N 3) N) (-.f64 N 1))))

Compiler

Compiled 376 to 319 computations (15.2% saved)

simplify88.0ms (2%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5000	2801

prune163.0ms (3.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	138	5	143

Error

0.3b

Counts

143 → 5

Compiler

Compiled 1545 to 1159 computations (25% saved)

regimes881.0ms (20.2%)

Accuracy

Total 0.0b remaining (7.5%)

Threshold costs 0.0b (7.5%)

Compiler

Compiled 6866 to 5546 computations (19.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	10	13

end1.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample1.1s (25.3%)

Algorithm

1×

intervals

Results

399.0ms	2174×	body	2048	valid
148.0ms	4102×	body	128	valid
132.0ms	990×	body	1024	valid
46.0ms	478×	body	512	valid
17.0ms	256×	body	256	valid

Compiler

Compiled 107 to 91 computations (15% saved)

Details

analyze151.0ms (3.5%)

sample32.0ms (0.7%)

simplify9.0ms (0.2%)

prune6.0ms (0.1%)

localize6.0ms (0.1%)

rewrite46.0ms (1.1%)

series39.0ms (0.9%)

simplify67.0ms (1.5%)

prune25.0ms (0.6%)

localize5.0ms (0.1%)

rewrite60.0ms (1.4%)

series77.0ms (1.8%)

simplify69.0ms (1.6%)

prune57.0ms (1.3%)

localize10.0ms (0.2%)

rewrite112.0ms (2.6%)

series676.0ms (15.5%)

simplify84.0ms (1.9%)

prune105.0ms (2.4%)

localize8.0ms (0.2%)

rewrite230.0ms (5.3%)

series241.0ms (5.5%)

simplify88.0ms (2%)

prune163.0ms (3.7%)

regimes881.0ms (20.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample1.1s (25.3%)

Profiling