Details

analyze2.5s (23.6%)

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)

sample47.0ms (0.4%)

Algorithm

1×

intervals

Results

25.0ms	255×	body	128	valid
1.0ms	3×	body	1024	invalid
1.0ms	11×	body	128	invalid
1.0ms	1×	body	1024	valid
1.0ms	2×	body	512	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5097	43

prune6.0ms (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

17.0b

Counts

2 → 1

Compiler

Compiled 56 to 44 computations (21.4% saved)

localize19.0ms (0.2%)

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 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
35.3b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite180.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

17.0b

Rules

20×	`*-un-lft-identity_binary64_1101`
18×	`add-sqr-sqrt_binary64_1123`
11×	`add-log-exp_binary64_1140`
10×	`cancel-sign-sub-inv_binary64_1067`
9×	`add-cube-cbrt_binary64_1136`
6×	`unpow-prod-down_binary64_1180`
5×	`pow1_binary64_1162` `add-exp-log_binary64_1139`
4×	`cos-sum_binary64_1235` `add-cbrt-cube_binary64_1137` `difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053`
3×	`sub-neg_binary64_1094` `pow-unpow_binary64_1178` `diff-log_binary64_1193`
2×	`flip3--_binary64_1105` `flip--_binary64_1076` `distribute-lft-out_binary64_1052`
1×	`cos-diff_binary64_1238` `times-frac_binary64_1107` `pow-pow_binary64_1173` `pow-to-exp_binary64_1170` `pow-exp_binary64_1169` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `sum-log_binary64_1192` `associate--r+_binary64_1037`

Counts

4 → 69

Calls

4 calls:

17.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
9.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))
8.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)

Compiler

Compiled 2698 to 1339 computations (50.4% saved)

series2.1s (19.5%)

Error

0.2b

Counts

4 → 94

Calls

4 calls:

985.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
448.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
366.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
147.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Compiler

Compiled 7998 to 5476 computations (31.5% saved)

simplify77.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4975	3444
1	4975	3444

prune259.0ms (2.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	2	164

Error

0.2b

Counts

164 → 2

Compiler

Compiled 5296 to 2482 computations (53.1% saved)

localize14.0ms (0.1%)

Local error

Found 2 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	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite88.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

14×	`*-un-lft-identity_binary64_1101`
12×	`add-sqr-sqrt_binary64_1123`
7×	`add-log-exp_binary64_1140`
6×	`unpow-prod-down_binary64_1180`
5×	`add-cube-cbrt_binary64_1136`
4×	`cancel-sign-sub-inv_binary64_1067`
3×	`difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053` `pow-unpow_binary64_1178` `pow1_binary64_1162` `add-exp-log_binary64_1139`
2×	`add-cbrt-cube_binary64_1137` `diff-log_binary64_1193` `distribute-lft-out_binary64_1052`
1×	`times-frac_binary64_1107` `pow-pow_binary64_1173` `pow-to-exp_binary64_1170` `pow-exp_binary64_1169` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `sum-log_binary64_1192` `flip3--_binary64_1105` `sub-neg_binary64_1094` `flip--_binary64_1076` `associate--r+_binary64_1037`

Counts

2 → 41

Calls

2 calls:

16.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 1264 to 653 computations (48.3% saved)

series1.5s (13.6%)

Error

0.2b

Counts

2 → 60

Calls

2 calls:

943.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
432.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Compiler

Compiled 4104 to 2868 computations (30.1% saved)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4969	2463
1	4969	2463

prune133.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	101	2	103

Error

0.2b

Counts

103 → 2

Compiler

Compiled 2561 to 1157 computations (54.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 1/2 (.f64 K n))
0.0b	(-.f64 (.f64 1/2 (.f64 K n)) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
24.0b	(cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))

rewrite146.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

14×	`add-sqr-sqrt_binary64_1123`
11×	`*-un-lft-identity_binary64_1101`
10×	`pow1_binary64_1162` `add-exp-log_binary64_1139`
9×	`add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`
6×	`cancel-sign-sub-inv_binary64_1067` `add-log-exp_binary64_1140` `unpow-prod-down_binary64_1180`
4×	`cos-sum_binary64_1235`
3×	`pow-unpow_binary64_1178` `pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `associate-l_binary64_1042`
2×	`sub-neg_binary64_1094` `difference-of-squares_binary64_1070`
1×	`cos-diff_binary64_1238` `times-frac_binary64_1107` `distribute-lft-out--_binary64_1053` `pow-pow_binary64_1173` `pow-to-exp_binary64_1170` `pow-exp_binary64_1169` `unpow2_binary64_1166` `sqr-pow_binary64_1073` `diff-log_binary64_1193` `flip3--_binary64_1105` `flip--_binary64_1076` `associate-r_binary64_1041` `*-commutative_binary64_1032`

Counts

4 → 65

Calls

4 calls:

10.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
7.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))
5.0ms	(-.f64 (.f64 1/2 (.f64 K n)) M)
5.0ms	(.f64 1/2 (.f64 K n))

Compiler

Compiled 2224 to 1198 computations (46.1% saved)

series875.0ms (8.2%)

Error

0.2b

Counts

4 → 60

Calls

4 calls:

421.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
198.0ms	(-.f64 (.f64 1/2 (.f64 K n)) M)
92.0ms	(.f64 1/2 (.f64 K n))
80.0ms	(cos.f64 (-.f64 (.f64 1/2 (.f64 K n)) M))

Compiler

Compiled 4539 to 3212 computations (29.2% saved)

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5221	1780

prune190.0ms (1.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	125	2	127

Error

0.2b

Counts

127 → 2

Compiler

Compiled 3697 to 1840 computations (50.2% saved)

regimes372.0ms (3.5%)

Accuracy

Total 0.2b remaining (11.3%)

Threshold costs 0.2b (11.3%)

Compiler

Compiled 3296 to 3210 computations (2.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	31
1	62	31

end0.0ms (0%)

sample2.0s (18.8%)

Algorithm

1×

intervals

Results

806.0ms	7830×	body	128	valid
39.0ms	94×	body	1024	invalid
35.0ms	70×	body	1024	valid
34.0ms	294×	body	128	invalid
26.0ms	86×	body	512	invalid
18.0ms	55×	body	512	valid
11.0ms	52×	body	256	invalid
9.0ms	44×	body	256	valid
8.0ms	15×	body	2048	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 588 to 566 computations (3.7% saved)

Details

analyze2.5s (23.6%)

sample47.0ms (0.4%)

simplify52.0ms (0.5%)

prune6.0ms (0.1%)

localize19.0ms (0.2%)

rewrite180.0ms (1.7%)

series2.1s (19.5%)

simplify77.0ms (0.7%)

prune259.0ms (2.4%)

localize14.0ms (0.1%)

rewrite88.0ms (0.8%)

series1.5s (13.6%)

simplify66.0ms (0.6%)

prune133.0ms (1.2%)

localize18.0ms (0.2%)

rewrite146.0ms (1.4%)

series875.0ms (8.2%)

simplify74.0ms (0.7%)

prune190.0ms (1.8%)

regimes372.0ms (3.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (18.8%)

Profiling