Details

analyze9.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample426.0ms (1.8%)

Algorithm

1×

intervals

Results

338.0ms	133×	body	2048	valid
47.0ms	64×	body	1024	valid
9.0ms	256×	pre	128	true
7.0ms	7×	body	4096	valid
7.0ms	27×	body	512	valid
3.0ms	16×	body	256	valid
1.0ms	9×	body	128	valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify181.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	72	12
1	72	12

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

59.7b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.4b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
0.0b	(/.f64 1 (tan.f64 x))
0.0b	(/.f64 1 (tan.f64 x))
2.4b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite52.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_2424`
36×	`times-frac_binary64_2408`
35×	`*-un-lft-identity_binary64_2402`
19×	`add-cube-cbrt_binary64_2437`
14×	`cancel-sign-sub-inv_binary64_2368`
9×	`difference-of-squares_binary64_2371`
7×	`distribute-lft-out--_binary64_2354`
6×	`add-exp-log_binary64_2440` `div-inv_binary64_2399`
4×	`add-cbrt-cube_binary64_2438` `add-log-exp_binary64_2441`
3×	`associate-/r_binary64_2346` `pow1_binary64_2463` `associate-/l_binary64_2347`
2×	`div-exp_binary64_2453` `tan-quot_binary64_2561` `associate-/r/_binary64_2348`
1×	`cbrt-undiv_binary64_2436` `clear-num_binary64_2401` `inv-pow_binary64_2487` `frac-2neg_binary64_2413` `flip--_binary64_2377` `frac-sub_binary64_2411` `flip3--_binary64_2406` `rec-exp_binary64_2452` `diff-log_binary64_2494` `sub-neg_binary64_2395` `1-exp_binary64_2446` `pow-flip_binary64_2476`

Counts

2 → 74

Calls

4 calls:

33.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
7.0ms	(/.f64 1 (tan.f64 x))
0.0ms	(/.f64 1 (tan.f64 x))
0.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series239.0ms (1%)

Counts

2 → 11

Calls

2 calls:

140.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
99.0ms	(/.f64 1 (tan.f64 x))

Compiler

Compiled 171 to 140 computations (18.1% saved)

simplify148.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	5185	1101

prune160.0ms (0.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	1	86

Error

0.3b

Counts

86 → 1

Compiler

Compiled 1051 to 646 computations (38.5% saved)

localize13.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.3b	(*.f64 x 1/3)
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.0b	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
0.0b	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(*.f64 x 1/3)

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_2424`
15×	`associate-r_binary64_2342`
10×	`add-exp-log_binary64_2440`
9×	`*-un-lft-identity_binary64_2402` `add-cube-cbrt_binary64_2437`
7×	`add-cbrt-cube_binary64_2438`
6×	`associate-l_binary64_2343`
5×	`pow1_binary64_2463` `unswap-sqr_binary64_2370` `add-log-exp_binary64_2441`
4×	`prod-exp_binary64_2451` `unpow-prod-down_binary64_2481` `cube-prod_binary64_2430`
2×	`*-commutative_binary64_2333` `cbrt-unprod_binary64_2435` `sqr-pow_binary64_2374`
1×	`+-commutative_binary64_2332` `flip3-+_binary64_2405` `pow-prod-down_binary64_2473` `flip-+_binary64_2376` `cube-mult_binary64_2432` `pow-to-exp_binary64_2471` `unpow3_binary64_2468` `pow-exp_binary64_2470` `sum-log_binary64_2493`

Counts

3 → 60

Calls

6 calls:

11.0ms	(*.f64 1/45 (pow.f64 x 3))
11.0ms	(*.f64 x 1/3)
7.0ms	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
0.0ms	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
0.0ms	(*.f64 1/45 (pow.f64 x 3))

series216.0ms (0.9%)

Counts

3 → 12

Calls

3 calls:

122.0ms	(+.f64 (.f64 x 1/3) (.f64 1/45 (pow.f64 x 3)))
58.0ms	(*.f64 1/45 (pow.f64 x 3))
35.0ms	(*.f64 x 1/3)

Compiler

Compiled 175 to 157 computations (10.3% saved)

simplify175.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	4920	699
1	4920	699

prune147.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	7	73

Error

0.1b

Counts

73 → 7

Compiler

Compiled 1011 to 774 computations (23.4% saved)

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.4b	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
0.4b	(*.f64 x (sqrt.f64 1/3))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.0b	(+.f64 (.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3)) (*.f64 1/45 (pow.f64 x 3)))
0.0b	(+.f64 (.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3)) (*.f64 1/45 (pow.f64 x 3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.4b	(*.f64 x (sqrt.f64 1/3))
0.4b	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))

rewrite68.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_2424` `associate-r_binary64_2342`
16×	`add-exp-log_binary64_2440`
13×	`*-un-lft-identity_binary64_2402` `add-cbrt-cube_binary64_2438` `add-cube-cbrt_binary64_2437`
11×	`pow1_binary64_2463`
7×	`sqrt-prod_binary64_2418` `associate-l_binary64_2343` `prod-exp_binary64_2451`
6×	`unswap-sqr_binary64_2370` `add-log-exp_binary64_2441`
5×	`cbrt-unprod_binary64_2435`
4×	`pow-prod-down_binary64_2473` `unpow-prod-down_binary64_2481` `cube-prod_binary64_2430`
3×	`*-commutative_binary64_2333`
2×	`sqr-pow_binary64_2374`
1×	`+-commutative_binary64_2332` `flip3-+_binary64_2405` `flip-+_binary64_2376` `cube-mult_binary64_2432` `pow-to-exp_binary64_2471` `unpow3_binary64_2468` `pow-exp_binary64_2470` `sum-log_binary64_2493`

Counts

4 → 85

Calls

8 calls:

15.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3)) (*.f64 1/45 (pow.f64 x 3)))
14.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
13.0ms	(*.f64 1/45 (pow.f64 x 3))
11.0ms	(*.f64 x (sqrt.f64 1/3))
0.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3)) (*.f64 1/45 (pow.f64 x 3)))

series390.0ms (1.7%)

Counts

4 → 15

Calls

4 calls:

173.0ms	(+.f64 (.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3)) (*.f64 1/45 (pow.f64 x 3)))
103.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
58.0ms	(*.f64 1/45 (pow.f64 x 3))
56.0ms	(*.f64 x (sqrt.f64 1/3))

Compiler

Compiled 316 to 292 computations (7.6% saved)

simplify149.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	4914	941
1	4914	941

prune214.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	96	11	107

Error

0.0b

Counts

107 → 11

Compiler

Compiled 1717 to 1408 computations (18% saved)

localize24.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.4b	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
0.3b	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.0b	(+.f64 (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 1/45 (pow.f64 x 3)))
0.0b	(+.f64 (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 1/45 (pow.f64 x 3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.3b	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
0.4b	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

rewrite82.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`associate-r_binary64_2342`
29×	`add-sqr-sqrt_binary64_2424`
24×	`add-exp-log_binary64_2440`
15×	`*-un-lft-identity_binary64_2402` `add-cube-cbrt_binary64_2437`
13×	`sqrt-prod_binary64_2418` `add-cbrt-cube_binary64_2438` `prod-exp_binary64_2451`
12×	`unpow-prod-down_binary64_2481`
8×	`unswap-sqr_binary64_2370`
7×	`associate-l_binary64_2343`
6×	`pow1_binary64_2463` `add-log-exp_binary64_2441`
5×	`cbrt-unprod_binary64_2435`
4×	`sqr-pow_binary64_2374` `cube-prod_binary64_2430`
3×	`*-commutative_binary64_2333` `pow-to-exp_binary64_2471` `pow-exp_binary64_2470`
1×	`+-commutative_binary64_2332` `flip3-+_binary64_2405` `pow-prod-down_binary64_2473` `flip-+_binary64_2376` `cube-mult_binary64_2432` `unpow3_binary64_2468` `sum-log_binary64_2493`

Counts

4 → 96

Calls

8 calls:

19.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
18.0ms	(+.f64 (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 1/45 (pow.f64 x 3)))
13.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
12.0ms	(*.f64 1/45 (pow.f64 x 3))
0.0ms	(+.f64 (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 1/45 (pow.f64 x 3)))

series513.0ms (2.2%)

Counts

4 → 15

Calls

4 calls:

197.0ms	(+.f64 (.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3))) (*.f64 1/45 (pow.f64 x 3)))
160.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))
87.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
69.0ms	(*.f64 1/45 (pow.f64 x 3))

Compiler

Compiled 358 to 334 computations (6.7% saved)

simplify167.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	4873	1199
1	4873	1199

prune273.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	7	2	9
Picked	1	0	1
Done	0	1	1
Total	116	6	122

Error

Counts

122 → 6

Compiler

Compiled 2003 to 1693 computations (15.5% saved)

simplify44.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	518	1277
1	518	1277

regimes293.0ms (1.2%)

Accuracy

Total 0.4b remaining (88.5%)

Threshold costs 0.4b (88.5%)

Compiler

Compiled 1687 to 1428 computations (15.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	36
1	21	36

end0.0ms (0%)

sample19.6s (82.8%)

Algorithm

1×

intervals

Results

10.3s	4016×	body	2048	valid
1.3s	1976×	body	1024	valid
266.0ms	8000×	pre	128	true
250.0ms	1030×	body	512	valid
216.0ms	220×	body	4096	valid
80.0ms	503×	body	256	valid
21.0ms	255×	body	128	valid

Compiler

Compiled 2531 to 2138 computations (15.5% saved)

Pareto

0.2840521673582935

Details

analyze9.0ms (0%)

sample426.0ms (1.8%)

simplify181.0ms (0.8%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite52.0ms (0.2%)

series239.0ms (1%)

simplify148.0ms (0.6%)

prune160.0ms (0.7%)

localize13.0ms (0.1%)

rewrite38.0ms (0.2%)

series216.0ms (0.9%)

simplify175.0ms (0.7%)

prune147.0ms (0.6%)

localize17.0ms (0.1%)

rewrite68.0ms (0.3%)

series390.0ms (1.7%)

simplify149.0ms (0.6%)

prune214.0ms (0.9%)

localize24.0ms (0.1%)

rewrite82.0ms (0.3%)

series513.0ms (2.2%)

simplify167.0ms (0.7%)

prune273.0ms (1.2%)

simplify44.0ms (0.2%)

regimes293.0ms (1.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample19.6s (82.8%)

Profiling