Details

analyze2.4s (10.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5136	473
0	5	5
1	5	5

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)

sample44.0ms (0.2%)

Algorithm

1×

intervals

Results

24.0ms	250×	body	128	valid
1.0ms	3×	body	1024	valid
1.0ms	2×	body	1024	invalid
1.0ms	7×	body	128	invalid
1.0ms	3×	body	256	valid
0.0ms	1×	body	512	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify52.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5097	43

prune5.0ms (0%)

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

14.1b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize19.0ms (0.1%)

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 K (+.f64 m n))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
32.8b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite244.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

14.0b

Rules

16×	`add-sqr-sqrt_binary64_782`
15×	`*-un-lft-identity_binary64_760`
9×	`add-cube-cbrt_binary64_795`
7×	`pow1_binary64_821` `add-exp-log_binary64_798`
6×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839`
4×	`cos-sum_binary64_894` `associate-r_binary64_700`
3×	`cancel-sign-sub-inv_binary64_726` `pow-unpow_binary64_837` `associate-l_binary64_701`
2×	`difference-of-squares_binary64_729` `flip3-+_binary64_763` `associate-*r/_binary64_702` `flip-+_binary64_734` `distribute-lft-out_binary64_711`
1×	`cos-diff_binary64_897` `sub-neg_binary64_753` `times-frac_binary64_766` `distribute-lft-out--_binary64_712` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `*-commutative_binary64_691` `sum-log_binary64_851` `+-commutative_binary64_690`

Counts

4 → 68

Calls

4 calls:

15.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
11.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
6.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 2341 to 1174 computations (49.9% saved)

series1.9s (8.9%)

Error

1.2b

Counts

4 → 89

Calls

4 calls:

1.0s	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
454.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
202.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
147.0ms	(*.f64 K (+.f64 m n))

Compiler

Compiled 6334 to 4561 computations (28% saved)

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5399	2811

prune241.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	152	5	157
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	5	158

Error

1.2b

Counts

158 → 5

Compiler

Compiled 2998 to 1486 computations (50.4% saved)

localize14.0ms (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)

rewrite179.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

1.2b

Rules

17×	`*-un-lft-identity_binary64_760`
13×	`add-sqr-sqrt_binary64_782`
10×	`add-log-exp_binary64_799`
6×	`add-cube-cbrt_binary64_795` `unpow-prod-down_binary64_839`
4×	`pow1_binary64_821` `add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726`
3×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `pow-unpow_binary64_837` `add-cbrt-cube_binary64_796` `distribute-lft-out_binary64_711`
2×	`sum-log_binary64_851` `diff-log_binary64_852`
1×	`times-frac_binary64_766` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690` `flip3--_binary64_764` `sub-neg_binary64_753` `flip--_binary64_735` `associate--r+_binary64_696`

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))
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)

Compiler

Compiled 1512 to 783 computations (48.2% saved)

series2.6s (12.1%)

Error

1.2b

Counts

3 → 93

Calls

3 calls:

1.1s	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
965.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
444.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 5099 to 3833 computations (24.8% saved)

simplify72.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4966	3491
1	4966	3491

prune213.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	146	5	151

Error

1.2b

Counts

151 → 5

Compiler

Compiled 2246 to 1095 computations (51.2% saved)

localize19.0ms (0.1%)

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 (/.f64 (*.f64 m K) 2) M)
22.7b	(cos.f64 (-.f64 (/.f64 (*.f64 m K) 2) M))

rewrite222.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

15×	`add-sqr-sqrt_binary64_782`
14×	`*-un-lft-identity_binary64_760`
8×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799`
6×	`cancel-sign-sub-inv_binary64_726` `unpow-prod-down_binary64_839`
5×	`pow1_binary64_821` `add-exp-log_binary64_798`
4×	`cos-sum_binary64_894` `add-cbrt-cube_binary64_796`
3×	`difference-of-squares_binary64_729` `pow-unpow_binary64_837`
2×	`sub-neg_binary64_753` `distribute-lft-out--_binary64_712`
1×	`cos-diff_binary64_897` `diff-log_binary64_852` `flip3--_binary64_764` `flip--_binary64_735` `times-frac_binary64_766` `pow-pow_binary64_832` `pow-to-exp_binary64_829` `pow-exp_binary64_828` `unpow2_binary64_825` `sqr-pow_binary64_732` `sum-log_binary64_851` `flip3-+_binary64_763` `flip-+_binary64_734` `distribute-lft-out_binary64_711` `+-commutative_binary64_690`

Counts

4 → 61

Calls

4 calls:

15.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
8.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 m K) 2) M))
7.0ms	(-.f64 (/.f64 (*.f64 m K) 2) M)

Compiler

Compiled 2069 to 1112 computations (46.3% saved)

series1.8s (8.5%)

Error

1.2b

Counts

4 → 87

Calls

4 calls:

992.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l)
444.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
195.0ms	(-.f64 (/.f64 (*.f64 m K) 2) M)
88.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 m K) 2) M))

Compiler

Compiled 5360 to 4027 computations (24.9% saved)

simplify97.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4926	2649
1	4926	2649

prune220.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	148	5	153

Error

1.1b

Counts

153 → 5

Compiler

Compiled 2487 to 1312 computations (47.2% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K m) 2) M)
0.1b	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K m) 2) M)))
0.5b	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K m) 2) M))))
22.7b	(cos.f64 (-.f64 (/.f64 (*.f64 K m) 2) M))

rewrite251.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

13×	`add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
12×	`cos-sum_binary64_894` `cancel-sign-sub-inv_binary64_726`
11×	`add-cube-cbrt_binary64_795`
8×	`exp-diff_binary64_808`
7×	`add-log-exp_binary64_799`
6×	`exp-prod_binary64_812`
5×	`pow1_binary64_821`
4×	`sub-neg_binary64_753` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `log-pow_binary64_849` `log-div_binary64_847` `log-prod_binary64_846`
3×	`cos-diff_binary64_897`
2×	`exp-sum_binary64_806`
1×	`rem-log-exp_binary64_801` `rem-exp-log_binary64_800` `diff-log_binary64_852` `flip3--_binary64_764` `flip--_binary64_735` `difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712`

Counts

4 → 64

Calls

4 calls:

8.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K m) 2) M))))
8.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K m) 2) M)))
8.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K m) 2) M))
7.0ms	(-.f64 (/.f64 (*.f64 K m) 2) M)

Compiler

Compiled 2386 to 1306 computations (45.3% saved)

series860.0ms (4%)

Error

1.1b

Counts

4 → 45

Calls

4 calls:

419.0ms	(log.f64 (exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K m) 2) M))))
193.0ms	(-.f64 (/.f64 (*.f64 K m) 2) M)
137.0ms	(exp.f64 (cos.f64 (-.f64 (/.f64 (*.f64 K m) 2) M)))
93.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K m) 2) M))

Compiler

Compiled 2430 to 2042 computations (16% saved)

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4940	1665
1	4940	1665

prune182.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	109	5	114

Error

1.1b

Counts

114 → 5

Compiler

Compiled 1935 to 1072 computations (44.6% saved)

regimes8.1s (37.5%)

Accuracy

Total 3.2b remaining (71.9%)

Threshold costs 0b (0%)

Compiler

Compiled 95000 to 76647 computations (19.3% saved)

bsearch26.0ms (0.1%)

Steps

Iters	Range		Point
12	1.0	#hash((type . real) (value . NaN))	#hash((type . real) (value . NaN))

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	100	92
1	100	92

end3.0ms (0%)

Compiler: Compiled 60 to 38 computations (36.7% saved)

sample1.6s (7.5%)

Algorithm

1×

intervals

Results

784.0ms	7808×	body	128	valid
42.0ms	86×	body	1024	valid
35.0ms	87×	body	1024	invalid
30.0ms	87×	body	512	invalid
29.0ms	293×	body	128	invalid
19.0ms	60×	body	512	valid
14.0ms	24×	body	2048	invalid
9.0ms	45×	body	256	valid
9.0ms	46×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 261 to 213 computations (18.4% saved)

Details

analyze2.4s (10.9%)

sample44.0ms (0.2%)

simplify52.0ms (0.2%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite244.0ms (1.1%)

series1.9s (8.9%)

simplify68.0ms (0.3%)

prune241.0ms (1.1%)

localize14.0ms (0.1%)

rewrite179.0ms (0.8%)

series2.6s (12.1%)

simplify72.0ms (0.3%)

prune213.0ms (1%)

localize19.0ms (0.1%)

rewrite222.0ms (1%)

series1.8s (8.5%)

simplify97.0ms (0.4%)

prune220.0ms (1%)

localize26.0ms (0.1%)

rewrite251.0ms (1.2%)

series860.0ms (4%)

simplify76.0ms (0.4%)

prune182.0ms (0.8%)

regimes8.1s (37.5%)

bsearch26.0ms (0.1%)

simplify3.0ms (0%)

end3.0ms (0%)

sample1.6s (7.5%)

Profiling