Details

analyze3.4s (34.2%)

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)

sample85.0ms (0.9%)

Algorithm

1×

intervals

Results

46.0ms	248×	body	128	valid
4.0ms	4×	body	1024	valid
3.0ms	4×	body	512	valid
2.0ms	3×	body	1024	invalid
2.0ms	12×	body	128	invalid
1.0ms	4×	body	256	invalid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify180.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5097	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

Error

14.4b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize24.0ms (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	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.0b	(*.f64 K (+.f64 m n))
34.1b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite60.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_441`
15×	`*-un-lft-identity_binary64_419`
9×	`add-cube-cbrt_binary64_454`
7×	`add-exp-log_binary64_457` `pow1_binary64_480`
6×	`unpow-prod-down_binary64_498` `add-log-exp_binary64_458` `add-cbrt-cube_binary64_455`
4×	`cos-sum_binary64_553` `associate-r_binary64_359`
3×	`associate-l_binary64_360` `pow-unpow_binary64_496` `cancel-sign-sub-inv_binary64_385`
2×	`flip3-+_binary64_422` `difference-of-squares_binary64_388` `distribute-lft-out_binary64_370` `associate-*r/_binary64_361` `flip-+_binary64_393`
1×	`pow-prod-down_binary64_490` `times-frac_binary64_425` `sub-neg_binary64_412` `distribute-rgt-in_binary64_369` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow-exp_binary64_487` `sqr-pow_binary64_391` `sum-log_binary64_510` `distribute-lft-out--_binary64_371` `pow-to-exp_binary64_488` `distribute-lft-in_binary64_368` `*-commutative_binary64_350` `pow-pow_binary64_491` `unpow2_binary64_484` `+-commutative_binary64_349` `cos-diff_binary64_556`

Counts

4 → 68

Calls

4 calls:

19.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
16.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
10.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(*.f64 K (+.f64 m n))

series470.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
108.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
104.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
39.0ms	(*.f64 K (+.f64 m n))

simplify101.0ms (1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5100	1294

prune124.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	4	81

Error

1.6b

Counts

81 → 4

Compiler

Compiled 2790 to 1378 computations (50.6% saved)

localize12.0ms (0.1%)

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)

rewrite59.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_419`
13×	`add-sqr-sqrt_binary64_441`
10×	`add-log-exp_binary64_458`
6×	`unpow-prod-down_binary64_498` `add-cube-cbrt_binary64_454`
4×	`add-exp-log_binary64_457` `cancel-sign-sub-inv_binary64_385` `pow1_binary64_480`
3×	`difference-of-squares_binary64_388` `distribute-lft-out_binary64_370` `distribute-lft-out--_binary64_371` `add-cbrt-cube_binary64_455` `pow-unpow_binary64_496`
2×	`sum-log_binary64_510` `diff-log_binary64_511`
1×	`flip3-+_binary64_422` `times-frac_binary64_425` `sub-neg_binary64_412` `pow-exp_binary64_487` `sqr-pow_binary64_391` `flip3--_binary64_423` `pow-to-exp_binary64_488` `flip-+_binary64_393` `pow-pow_binary64_491` `associate--r+_binary64_355` `flip--_binary64_394` `unpow2_binary64_484` `+-commutative_binary64_349`

Counts

3 → 53

Calls

3 calls:

25.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
18.0ms	(-.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)

series460.0ms (4.6%)

Counts

3 → 9

Calls

3 calls:

234.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
162.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
65.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5488	1364

prune97.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	62	4	66

Error

1.6b

Counts

66 → 4

Compiler

Compiled 1634 to 907 computations (44.5% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 K)
0.6b	(cbrt.f64 K)
0.6b	(cbrt.f64 K)
34.0b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (+.f64 m n) (cbrt.f64 K))) 2) M))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_450`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
4×	`cos-sum_binary64_553` `add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
3×	`pow1/3_binary64_501` `cancel-sign-sub-inv_binary64_385`
1×	`sub-neg_binary64_412` `cos-diff_binary64_556`

Counts

4 → 45

Calls

4 calls:

21.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (+.f64 m n) (cbrt.f64 K))) 2) M))
1.0ms	(cbrt.f64 K)
1.0ms	(cbrt.f64 K)
1.0ms	(cbrt.f64 K)

series492.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (cbrt.f64 K)) (*.f64 (+.f64 m n) (cbrt.f64 K))) 2) M))
116.0ms	(cbrt.f64 K)
108.0ms	(cbrt.f64 K)
94.0ms	(cbrt.f64 K)

simplify107.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4915	603
1	4915	603

prune108.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	53	8	61

Error

1.5b

Counts

61 → 8

Compiler

Compiled 2379 to 1117 computations (53% saved)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 K)
0.6b	(cbrt.f64 K)
0.6b	(cbrt.f64 K)
34.1b	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (.f64 (.f64 (cbrt.f64 (cbrt.f64 K)) (cbrt.f64 (cbrt.f64 K))) (cbrt.f64 (cbrt.f64 K)))) (*.f64 (+.f64 m n) (cbrt.f64 K))) 2) M))

rewrite51.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_450`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
4×	`cos-sum_binary64_553` `add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
3×	`pow1/3_binary64_501` `cancel-sign-sub-inv_binary64_385`
1×	`sub-neg_binary64_412` `cos-diff_binary64_556`

Counts

4 → 45

Calls

4 calls:

32.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (.f64 (.f64 (cbrt.f64 (cbrt.f64 K)) (cbrt.f64 (cbrt.f64 K))) (cbrt.f64 (cbrt.f64 K)))) (*.f64 (+.f64 m n) (cbrt.f64 K))) 2) M))
2.0ms	(cbrt.f64 K)
2.0ms	(cbrt.f64 K)
2.0ms	(cbrt.f64 K)

series495.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(cos.f64 (-.f64 (/.f64 (.f64 (.f64 (cbrt.f64 K) (.f64 (.f64 (cbrt.f64 (cbrt.f64 K)) (cbrt.f64 (cbrt.f64 K))) (cbrt.f64 (cbrt.f64 K)))) (*.f64 (+.f64 m n) (cbrt.f64 K))) 2) M))
126.0ms	(cbrt.f64 K)
96.0ms	(cbrt.f64 K)
87.0ms	(cbrt.f64 K)

simplify41.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5283	585

prune114.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	1	4	5
Picked	0	1	1
Done	1	1	2
Total	57	8	65

Error

1.5b

Counts

65 → 8

Compiler

Compiled 2532 to 1024 computations (59.6% saved)

regimes480.0ms (4.8%)

Accuracy

Total 0.3b remaining (20.2%)

Threshold costs 0.3b (20.2%)

Compiler

Compiled 4550 to 3348 computations (26.4% 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%)

sample2.9s (28.6%)

Algorithm

1×

intervals

Results

1.2s	7831×	body	128	valid
53.0ms	91×	body	1024	invalid
50.0ms	323×	body	128	invalid
47.0ms	70×	body	1024	valid
40.0ms	89×	body	512	invalid
30.0ms	64×	body	512	valid
16.0ms	55×	body	256	invalid
14.0ms	17×	body	2048	invalid
10.0ms	33×	body	256	valid
2.0ms	2×	body	2048	valid

Compiler

Compiled 794 to 587 computations (26.1% saved)

Details

analyze3.4s (34.2%)

sample85.0ms (0.9%)

simplify180.0ms (1.8%)

prune9.0ms (0.1%)

localize24.0ms (0.2%)

rewrite60.0ms (0.6%)

series470.0ms (4.7%)

simplify101.0ms (1%)

prune124.0ms (1.2%)

localize12.0ms (0.1%)

rewrite59.0ms (0.6%)

series460.0ms (4.6%)

simplify63.0ms (0.6%)

prune97.0ms (1%)

localize24.0ms (0.2%)

rewrite29.0ms (0.3%)

series492.0ms (4.9%)

simplify107.0ms (1.1%)

prune108.0ms (1.1%)

localize28.0ms (0.3%)

rewrite51.0ms (0.5%)

series495.0ms (4.9%)

simplify41.0ms (0.4%)

prune114.0ms (1.1%)

regimes480.0ms (4.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (28.6%)

Profiling