Details

analyze2.4s (24.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample47.0ms (0.5%)

Algorithm

1×

intervals

Results

27.0ms	251×	body	128	valid
1.0ms	3×	body	512	valid
1.0ms	10×	body	128	invalid
1.0ms	2×	body	1024	valid
1.0ms	2×	body	256	invalid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify209.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5353	43

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 18.5b

Counts

2 → 1

Compiler

Compiled 113 to 89 computations (21.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
36.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite61.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_789`
14×	`*-un-lft-identity_binary64_767`
8×	`add-log-exp_binary64_806` `add-cube-cbrt_binary64_802`
6×	`unpow-prod-down_binary64_846` `cancel-sign-sub-inv_binary64_733`
5×	`add-exp-log_binary64_805` `pow1_binary64_828`
4×	`cos-sum_binary64_901` `add-cbrt-cube_binary64_803`
3×	`pow-unpow_binary64_844` `difference-of-squares_binary64_736`
2×	`sub-neg_binary64_760` `distribute-lft-out--_binary64_719`
1×	`pow-to-exp_binary64_836` `distribute-lft-out_binary64_718` `sqr-pow_binary64_739` `pow-exp_binary64_835` `times-frac_binary64_773` `flip-+_binary64_741` `diff-log_binary64_859` `unpow2_binary64_832` `+-commutative_binary64_697` `sum-log_binary64_858` `cos-diff_binary64_904` `flip3-+_binary64_770` `flip--_binary64_742` `flip3--_binary64_771` `pow-pow_binary64_839`

Counts

4 → 61

Calls

4 calls:

21.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
10.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

series584.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

237.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
146.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
107.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
93.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4999	1379
1	4999	1379

prune158.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Merged error: 1.1b

Counts

74 → 3

Compiler

Compiled 3552 to 1975 computations (44.4% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite54.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_767`
13×	`add-sqr-sqrt_binary64_789`
10×	`add-log-exp_binary64_806`
6×	`unpow-prod-down_binary64_846` `add-cube-cbrt_binary64_802`
4×	`add-exp-log_binary64_805` `pow1_binary64_828` `cancel-sign-sub-inv_binary64_733`
3×	`distribute-lft-out_binary64_718` `pow-unpow_binary64_844` `distribute-lft-out--_binary64_719` `add-cbrt-cube_binary64_803` `difference-of-squares_binary64_736`
2×	`diff-log_binary64_859` `sum-log_binary64_858`
1×	`pow-to-exp_binary64_836` `sqr-pow_binary64_739` `pow-exp_binary64_835` `sub-neg_binary64_760` `times-frac_binary64_773` `flip-+_binary64_741` `unpow2_binary64_832` `associate--r+_binary64_703` `+-commutative_binary64_697` `flip3-+_binary64_770` `flip--_binary64_742` `flip3--_binary64_771` `pow-pow_binary64_839`

Counts

3 → 53

Calls

3 calls:

19.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
18.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series603.0ms (6.1%)

Counts

3 → 9

Calls

3 calls:

262.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
233.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
107.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify47.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5091	1364

prune103.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	62	3	65

Merged error: 1.1b

Counts

65 → 3

Compiler

Compiled 2183 to 1300 computations (40.4% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

16.9b	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.9b	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.9b	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
45.1b	(cos.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cbrt-prod_binary64_798`
13×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767`
7×	`add-cube-cbrt_binary64_802`
6×	`cbrt-div_binary64_799`
4×	`add-exp-log_binary64_805` `pow1_binary64_828` `add-log-exp_binary64_806` `add-cbrt-cube_binary64_803`
3×	`pow1/3_binary64_849` `distribute-lft-out--_binary64_719` `flip--_binary64_742` `flip3--_binary64_771` `difference-of-squares_binary64_736`

Counts

4 → 52

Calls

4 calls:

10.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
10.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
9.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(cos.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

series1.5s (15.4%)

Counts

4 → 12

Calls

4 calls:

456.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
452.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
448.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
168.0ms	(cos.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5266	1475

prune175.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	62	5	67

Merged error: 1.1b

Counts

67 → 5

Compiler

Compiled 4474 to 2340 computations (47.7% saved)

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

16.9b	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.9b	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
16.9b	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
46.0b	(cos.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))))

rewrite72.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cbrt-prod_binary64_798`
13×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767`
7×	`add-cube-cbrt_binary64_802`
6×	`cbrt-div_binary64_799`
4×	`add-exp-log_binary64_805` `pow1_binary64_828` `add-log-exp_binary64_806` `add-cbrt-cube_binary64_803`
3×	`pow1/3_binary64_849` `distribute-lft-out--_binary64_719` `flip--_binary64_742` `flip3--_binary64_771` `difference-of-squares_binary64_736`

Counts

4 → 52

Calls

4 calls:

31.0ms	(cos.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))))
10.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
10.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
10.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series1.6s (15.9%)

Counts

4 → 12

Calls

4 calls:

461.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
456.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
449.0ms	(cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
206.0ms	(cos.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)) (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M))) (cbrt.f64 (cbrt.f64 (-.f64 (/.f64 (.f64 K (+.f64 m n)) 2) M)))) (cbrt.f64 (cbrt.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))))

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4929	1385
1	4929	1385

prune200.0ms (2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	64	5	69

Merged error: 1.0b

Counts

69 → 5

Compiler

Compiled 5584 to 2881 computations (48.4% saved)

regimes112.0ms (1.1%)

Compiler: Compiled 1370 to 945 computations (31% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	26
1	62	26

end0.0ms (0%)

sample1.6s (16.6%)

Algorithm

1×

intervals

Results

882.0ms	7836×	body	128	valid
38.0ms	77×	body	1024	valid
35.0ms	318×	body	128	invalid
34.0ms	72×	body	1024	invalid
31.0ms	83×	body	512	invalid
19.0ms	55×	body	512	valid
13.0ms	18×	body	2048	invalid
11.0ms	49×	body	256	invalid
7.0ms	32×	body	256	valid

Compiler

Compiled 319 to 224 computations (29.8% saved)

Details

analyze2.4s (24.2%)

sample47.0ms (0.5%)

simplify209.0ms (2.1%)

prune8.0ms (0.1%)

localize22.0ms (0.2%)

rewrite61.0ms (0.6%)

series584.0ms (5.9%)

simplify68.0ms (0.7%)

prune158.0ms (1.6%)

localize16.0ms (0.2%)

rewrite54.0ms (0.5%)

series603.0ms (6.1%)

simplify47.0ms (0.5%)

prune103.0ms (1%)

localize27.0ms (0.3%)

rewrite44.0ms (0.4%)

series1.5s (15.4%)

simplify62.0ms (0.6%)

prune175.0ms (1.8%)

localize36.0ms (0.4%)

rewrite72.0ms (0.7%)

series1.6s (15.9%)

simplify62.0ms (0.6%)

prune200.0ms (2%)

regimes112.0ms (1.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.6s (16.6%)

Profiling