Details

analyze2.4s (37.6%)

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)

sample48.0ms (0.7%)

Algorithm

1×

intervals

Results

25.0ms	249×	body	80	valid
2.0ms	4×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	9×	body	80	invalid
1.0ms	3×	body	320	invalid
1.0ms	1×	body	1280	invalid
1.0ms	1×	body	640	invalid
0.0ms	2×	body	160	invalid
0.0ms	1×	body	320	valid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5364	43

prune9.0ms (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: 13.1b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize26.0ms (0.4%)

Local error

Found 4 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 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
35.4b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
9×	`add-log-exp_binary64`
8×	`add-cube-cbrt_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
4×	`associate-r_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `cos-diff_binary64` `prod-exp_binary64` `cos-sum_binary64` `times-frac_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 69

Calls

4 calls:

16.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
12.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
7.0ms	(*.f64 K (+.f64 m n))

series88.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
23.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
17.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms	(*.f64 K (+.f64 m n))

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4962	1487
1	4962	1487

prune102.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	5	82

Merged error: 1.4b

Counts

82 → 5

Compiler

Compiled 2860 to 1420 computations (50.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
0.0b	(-.f64 (/.f64 (+.f64 m n) 2) M)
0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.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 (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`add-log-exp_binary64`
6×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64` `difference-of-squares_binary64`
4×	`add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
3×	`pow-unpow_binary64` `diff-log_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `times-frac_binary64` `flip--_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `associate--r+_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 63

Calls

4 calls:

16.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
14.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

series100.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
37.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
6.0ms	(-.f64 (/.f64 (+.f64 m n) 2) M)

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5067	1586

prune73.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	75	5	80

Merged error: 1.4b

Counts

80 → 5

Compiler

Compiled 2010 to 1114 computations (44.6% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 m n))
0.6b	(cbrt.f64 (+.f64 m n))
0.6b	(cbrt.f64 (+.f64 m n))
35.1b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n))) 2) M))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-div_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `cos-diff_binary64` `cos-sum_binary64`

Counts

4 → 51

Calls

4 calls:

18.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n))) 2) M))
3.0ms	(cbrt.f64 (+.f64 m n))
3.0ms	(cbrt.f64 (+.f64 m n))
3.0ms	(cbrt.f64 (+.f64 m n))

series122.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(cbrt.f64 (+.f64 m n))
30.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (*.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (+.f64 m n))) 2) M))
30.0ms	(cbrt.f64 (+.f64 m n))
30.0ms	(cbrt.f64 (+.f64 m n))

simplify85.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4894	897
1	4894	897

prune81.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	61	7	68

Merged error: 1.4b

Counts

68 → 7

Compiler

Compiled 2894 to 1262 computations (56.4% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 m n))
0.6b	(cbrt.f64 (+.f64 m n))
0.6b	(cbrt.f64 (+.f64 m n))
35.5b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 m n))) (cbrt.f64 (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (cbrt.f64 (+.f64 m n))))) 2) M))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-div_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `cos-diff_binary64` `cos-sum_binary64`

Counts

4 → 51

Calls

4 calls:

31.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 m n))) (cbrt.f64 (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (cbrt.f64 (+.f64 m n))))) 2) M))
3.0ms	(cbrt.f64 (+.f64 m n))
3.0ms	(cbrt.f64 (+.f64 m n))
3.0ms	(cbrt.f64 (+.f64 m n))

series122.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 K (.f64 (cbrt.f64 (+.f64 m n)) (cbrt.f64 (+.f64 m n)))) (.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 m n))) (cbrt.f64 (cbrt.f64 (+.f64 m n)))) (cbrt.f64 (cbrt.f64 (+.f64 m n))))) 2) M))
30.0ms	(cbrt.f64 (+.f64 m n))
29.0ms	(cbrt.f64 (+.f64 m n))
29.0ms	(cbrt.f64 (+.f64 m n))

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5604	861

prune65.0ms (1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	63	7	70

Merged error: 1.3b

Counts

70 → 7

Compiler

Compiled 3385 to 1209 computations (64.3% saved)

regimes307.0ms (4.8%)

Compiler: Compiled 1305 to 930 computations (28.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	26
1	63	26

end0.0ms (0%)

sample2.2s (34.2%)

Algorithm

1×

intervals

Results

831.0ms	7820×	body	80	valid
47.0ms	83×	body	1280	invalid
37.0ms	88×	body	640	invalid
36.0ms	75×	body	640	valid
32.0ms	45×	body	1280	valid
29.0ms	291×	body	80	invalid
19.0ms	61×	body	320	invalid
12.0ms	38×	body	320	valid
6.0ms	30×	body	160	invalid
5.0ms	22×	body	160	valid
4.0ms	4×	body	2560	invalid

Compiler

Compiled 306 to 221 computations (27.8% saved)

Details

analyze2.4s (37.6%)

sample48.0ms (0.7%)

simplify63.0ms (1%)

prune9.0ms (0.1%)

localize26.0ms (0.4%)

rewrite45.0ms (0.7%)

series88.0ms (1.4%)

simplify89.0ms (1.4%)

prune102.0ms (1.6%)

localize13.0ms (0.2%)

rewrite54.0ms (0.8%)

series100.0ms (1.6%)

simplify89.0ms (1.4%)

prune73.0ms (1.2%)

localize27.0ms (0.4%)

rewrite30.0ms (0.5%)

series122.0ms (1.9%)

simplify85.0ms (1.3%)

prune81.0ms (1.3%)

localize33.0ms (0.5%)

rewrite43.0ms (0.7%)

series122.0ms (1.9%)

simplify77.0ms (1.2%)

prune65.0ms (1%)

regimes307.0ms (4.8%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (34.2%)

Profiling