Details

analyze353.0ms (3.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	25%	57.9%	7
18%	20.3%	61.8%	8
18.3%	16.4%	65.3%	9
18.5%	13.7%	67.8%	10
18.6%	11.5%	69.9%	11
18.7%	10%	71.3%	12
18.7%	8.9%	72.4%	13
18.7%	8.2%	73.1%	14

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.4s (36.8%)

Results

1.4s	8256×	body	128	valid
1.2s	1451×	body	1024	invalid
403.0ms	712×	body	512	invalid
177.0ms	1155×	body	128	invalid
120.0ms	352×	body	256	invalid

Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

672×	`associate-/l*_binary64`
625×	`associate-/r*_binary64`
461×	`div-sub_binary64`
445×	`distribute-frac-neg_binary64`
288×	`distribute-rgt-neg-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	65	22
3	129	22
4	280	22
5	634	20
6	1332	20
7	3121	20
8	4914	20
9	4550	20

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 97 to 77 computations (20.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.3b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
✓	0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

series502.0ms (5.4%)

Counts

3 → 48

Calls

3 calls:

277.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
222.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms	(.f64 (.f64 2 (PI.f64)) n)

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`

Counts

3 → 108

Calls

3 calls:

11.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
4.0ms	(.f64 (.f64 2 (PI.f64)) n)

simplify124.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

405×	`distribute-rgt-in_binary64`
399×	`distribute-lft-in_binary64`
243×	`fma-neg_binary64`
211×	`associate-/l*_binary64`
162×	`associate-l_binary64`

Counts

156 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	4057
1	428	3712
2	1390	3636
3	4506	3636
4	4960	3636

prune215.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	161	7	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	163	7	170

Error

0.0b

Counts

170 → 7

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
	0.5b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 (.f64 (.f64 2 (PI.f64)) (.f64 (cbrt.f64 n) (cbrt.f64 n))) (cbrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
	0.5b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))

Compiler

Compiled 4217 to 2742 computations (35% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
✓	0.2b	(.f64 n (.f64 2 (PI.f64)))
	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.4b	(/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))))

series112.0ms (1.2%)

Counts

3 → 12

Calls

3 calls:

76.0ms

(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))

33.0ms

(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))

3.0ms

(*.f64 n (*.f64 2 (PI.f64)))

rewrite59.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

308×	`times-frac_binary64`
140×	`*-un-lft-identity_binary64`
140×	`add-sqr-sqrt_binary64`
140×	`add-cube-cbrt_binary64`
130×	`sqrt-prod_binary64`

Counts

3 → 267

Calls

3 calls:

11.0ms

(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))

5.0ms

(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))

5.0ms

(*.f64 n (*.f64 2 (PI.f64)))

simplify367.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

725×	`associate-/r*_binary64`
365×	`fma-neg_binary64`
297×	`associate-/r/_binary64`
237×	`associate-/l/_binary64`
218×	`*-commutative_binary64`

Counts

279 → 383

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	365	12747
1	735	12412
2	2603	12184
3	3405	12184
4	4878	12184
5	5156	12184

prune536.0ms (5.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	410	1	411
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	411	7	418

Error

Counts

418 → 7

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
▶	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
	0.5b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 (.f64 (.f64 2 (PI.f64)) (.f64 (cbrt.f64 n) (cbrt.f64 n))) (cbrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
	0.7b	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (cbrt.f64 k)) (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))

Compiler

Compiled 14349 to 8787 computations (38.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 k))
✓	0.2b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
✓	0.3b	(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
✓	0.3b	(/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n))

series494.0ms (5.3%)

Counts

4 → 48

Calls

4 calls:

256.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
229.0ms	(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
5.0ms	(sqrt.f64 (/.f64 1 k))
4.0ms	(/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n))

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`times-frac_binary64`
78×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`
50×	`add-exp-log_binary64`

Counts

4 → 187

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
6.0ms	(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
5.0ms	(/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n))
2.0ms	(sqrt.f64 (/.f64 1 k))

simplify122.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

519×	`times-frac_binary64`
329×	`distribute-rgt-in_binary64`
320×	`distribute-lft-in_binary64`
220×	`associate-l_binary64`
202×	`associate-r_binary64`

Counts

235 → 288

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	312	5342
1	686	4831
2	2219	4803
3	4947	4803

prune352.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	288	7	295

Error

Counts

295 → 7

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
	0.6b	(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
✓	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
▶	0.5b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 (.f64 (.f64 2 (PI.f64)) (.f64 (cbrt.f64 n) (cbrt.f64 n))) (cbrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
	0.7b	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (cbrt.f64 k)) (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))

Compiler

Compiled 7660 to 5696 computations (25.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2))
✓	0.3b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
✓	0.3b	(.f64 (.f64 2 (PI.f64)) (sqrt.f64 n))
✓	0.4b	(.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n))

series380.0ms (4.1%)

Counts

4 → 36

Calls

4 calls:

205.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
160.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2))
9.0ms	(.f64 (.f64 2 (PI.f64)) (sqrt.f64 n))
6.0ms	(.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64`
36×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`

Counts

4 → 140

Calls

4 calls:

9.0ms	(.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n))
7.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2))
5.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms	(.f64 (.f64 2 (PI.f64)) (sqrt.f64 n))

simplify133.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

310×	`distribute-rgt-in_binary64`
304×	`distribute-lft-in_binary64`
274×	`associate-l_binary64`
250×	`fma-neg_binary64`
244×	`exp-sum_binary64`

Counts

176 → 195

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	4334
1	486	4010
2	1568	3878
3	4371	3878
4	5191	3878

prune227.0ms (2.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	195	7	202

Error

Counts

202 → 7

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (.f64 n (*.f64 2 (PI.f64))))))
	0.6b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
✓	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
✓	0.5b	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n)) (sqrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.8b	(/.f64 (pow.f64 (.f64 (.f64 (.f64 2 (PI.f64)) (.f64 (cbrt.f64 n) (cbrt.f64 n))) (cbrt.f64 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
	0.7b	(.f64 (/.f64 (pow.f64 (.f64 n (.f64 2 (PI.f64))) (.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (.f64 n (.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
	0.7b	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 n (PI.f64))) (.f64 k -1/2)) (/.f64 (sqrt.f64 (cbrt.f64 k)) (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 n (PI.f64))))))))

Compiler

Compiled 5329 to 3009 computations (43.5% saved)

regimes1.6s (16.7%)

Accuracy

Total 0.3b remaining (82.1%)

Threshold costs 0.3b (82.1%)

Counts

268 → 1

Compiler

Compiled 28960 to 22024 computations (24% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	38
1	30	38
2	29	38

end140.0ms (1.5%)

Compiler: Compiled 218 to 162 computations (25.7% saved)

Details

analyze353.0ms (3.8%)

sample3.4s (36.8%)

simplify56.0ms (0.6%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series502.0ms (5.4%)

rewrite26.0ms (0.3%)

simplify124.0ms (1.3%)

prune215.0ms (2.3%)

localize11.0ms (0.1%)

series112.0ms (1.2%)

rewrite59.0ms (0.6%)

simplify367.0ms (3.9%)

prune536.0ms (5.8%)

localize12.0ms (0.1%)

series494.0ms (5.3%)

rewrite42.0ms (0.5%)

simplify122.0ms (1.3%)

prune352.0ms (3.8%)

localize16.0ms (0.2%)

series380.0ms (4.1%)

rewrite38.0ms (0.4%)

simplify133.0ms (1.4%)

prune227.0ms (2.4%)

regimes1.6s (16.7%)

simplify2.0ms (0%)

end140.0ms (1.5%)

Profiling