Details

analyze3.1s (16%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample118.0ms (0.6%)

Algorithm

1×

intervals

Results

49.0ms	373×	body	128	nan
29.0ms	256×	body	128	valid
5.0ms	43×	body	128	invalid

Compiler

Compiled 75 to 53 computations (29.3% saved)

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

515×	`fma-neg_binary64`
481×	`neg-mul-1_binary64`
395×	`fma-def_binary64`
358×	`cancel-sign-sub-inv_binary64`
348×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	42
1	58	40
2	182	40
3	757	38
4	2815	37
5	4555	37
6	4944	37

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.6b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	28.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	32.7b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))

Status

Error

Program

▶

28.6b

(sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))

32.7b

(sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (-.f64 (-.f64 t (*.f64 2 (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*)))))

Compiler

Compiled 161 to 103 computations (36% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.1b	(*.f64 n (/.f64 l Om))
7.9b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
9.7b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))
18.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))

rewrite309.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

21.4b

Rules

55×	`pow1_binary64`
33×	`pow-prod-down_binary64`
30×	`add-exp-log_binary64`
30×	`add-sqr-sqrt_binary64`
18×	`clear-num_binary64`

Counts

4 → 180

Calls

4 calls:

21.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
19.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))
15.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
15.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 5628 to 2199 computations (60.9% saved)

series770.0ms (4%)

Error

15.9b

Counts

4 → 95

Calls

4 calls:

358.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))
278.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
60.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
22.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 9545 to 6743 computations (29.4% saved)

simplify141.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

627×	`associate-r_binary64`
584×	`associate-l_binary64`
201×	`associate-/l*_binary64`
170×	`fma-def_binary64`
157×	`*-commutative_binary64`

Counts

275 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	446	8240
1	1270	7670
2	5314	7670

prune209.0ms (1.1%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	172	21	193
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	173	22	195

Error

12.5b

Counts

195 → 22

Alt Table

Status	Error	Program
	31.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))))
	33.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 U l)) Om)))))))
	55.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	62.2b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 U (.f64 (.f64 l l) U))) (.f64 Om Om))))
	58.2b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))) (/.f64 (.f64 t (sqrt.f64 2)) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	60.4b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (-.f64 U* U))) Om) (/.f64 U Om))))
	39.2b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (*.f64 t U))))
✓	28.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	61.7b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 2 (.f64 n U))) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t))))
	58.0b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (.f64 l l) (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))))))
	58.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 U (.f64 l l))) (*.f64 Om Om))))))))
▶	29.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))))
	36.3b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))
	40.8b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
	42.1b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 t U)))) (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (*.f64 n U) t))))
	29.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))))
	56.4b	(neg.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))) (/.f64 (.f64 t (sqrt.f64 2)) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))))
	57.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))
	36.3b	(sqrt.f64 (fma.f64 t (.f64 2 (.f64 n U)) (.f64 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om) -4)))
	62.4b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 t (sqrt.f64 2))) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))
	35.8b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) 3/2))
	60.6b	(.f64 (sqrt.f64 (.f64 n (.f64 n (.f64 (.f64 (.f64 l l) (-.f64 U* U)) U)))) (/.f64 (sqrt.f64 2) Om))

Compiler

Compiled 6277 to 2679 computations (57.3% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.7b	(.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))
9.7b	(.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))
18.1b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
18.1b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))

rewrite245.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

12.5b

Rules

56×	`pow1_binary64`
36×	`pow-prod-down_binary64`
28×	`add-sqr-sqrt_binary64`
24×	`add-exp-log_binary64`
18×	`add-cube-cbrt_binary64`

Counts

4 → 160

Calls

4 calls:

17.0ms	(.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))
17.0ms	(.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))
16.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
13.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))

Compiler

Compiled 8037 to 2849 computations (64.6% saved)

series1.4s (7.4%)

Error

12.5b

Counts

4 → 132

Calls

4 calls:

380.0ms	(.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))
350.0ms	(.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))
304.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
299.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))

Compiler

Compiled 22742 to 14954 computations (34.2% saved)

simplify261.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

943×	`times-frac_binary64`
436×	`associate-r_binary64`
385×	`fma-neg_binary64`
374×	`associate-l_binary64`
274×	`*-commutative_binary64`

Counts

292 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	12006
1	913	11366
2	3630	11336
3	5636	11336

prune219.0ms (1.1%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	0	20	20
Picked	0	1	1
Done	0	1	1
Total	221	23	244

Error

12.5b

Counts

244 → 23

Alt Table

Status	Error	Program
	31.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))))
	33.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 U l)) Om)))))))
	55.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	62.2b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 U (.f64 (.f64 l l) U))) (.f64 Om Om))))
	58.2b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))) (/.f64 (.f64 t (sqrt.f64 2)) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	60.4b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (-.f64 U* U))) Om) (/.f64 U Om))))
	39.2b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (*.f64 t U))))
✓	28.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	61.7b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 2 (.f64 n U))) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t))))
	58.0b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (.f64 l l) (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))))))
	58.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 U (.f64 l l))) (*.f64 Om Om))))))))
✓	29.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))))
	36.3b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))
	40.8b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
	42.1b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 t U)))) (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (*.f64 n U) t))))
▶	29.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))))
	42.3b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 t U))))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))))
	56.4b	(neg.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))) (/.f64 (.f64 t (sqrt.f64 2)) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))))
	57.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))
	36.3b	(sqrt.f64 (fma.f64 t (.f64 2 (.f64 n U)) (.f64 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om) -4)))
	62.4b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 t (sqrt.f64 2))) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))
	35.8b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) 3/2))
	60.6b	(.f64 (sqrt.f64 (.f64 n (.f64 n (.f64 (.f64 (.f64 l l) (-.f64 U* U)) U)))) (/.f64 (sqrt.f64 2) Om))

Compiler

Compiled 10106 to 3902 computations (61.4% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

13.8b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))
13.8b	(cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t))
13.8b	(cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t))
18.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))))

rewrite214.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

12.5b

Rules

26×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`pow1/3_binary64`
12×	`log1p-expm1-u_binary64`
12×	`expm1-log1p-u_binary64`

Counts

4 → 136

Calls

4 calls:

18.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))))
12.0ms	(cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t))
12.0ms	(cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t))
11.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))

Compiler

Compiled 8280 to 2626 computations (68.3% saved)

series2.0s (10.2%)

Error

12.1b

Counts

4 → 116

Calls

4 calls:

682.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))))
385.0ms	(cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t))
382.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))
347.0ms	(cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t))

Compiler

Compiled 36156 to 23521 computations (34.9% saved)

simplify267.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

649×	`fma-def_binary64`
289×	`*-commutative_binary64`
276×	`associate-r_binary64`
231×	`associate-/l*_binary64`
215×	`times-frac_binary64`

Counts

252 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	13763
1	1245	11939
2	4218	11739
3	5022	11739

prune263.0ms (1.4%)

Pruning

26 alts after pruning (23 fresh and 3 done)

	Pruned	Kept	Total
New	183	3	186
Fresh	0	20	20
Picked	0	1	1
Done	0	2	2
Total	183	26	209

Error

12.1b

Counts

209 → 26

Alt Table

Status	Error	Program
▶	31.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))))
	33.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 U l)) Om)))))))
	55.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	62.3b	(.f64 (sqrt.f64 (.f64 n U)) (.f64 (sqrt.f64 2) (exp.f64 (fma.f64 1/3 (fma.f64 (log.f64 Om) -2 (log.f64 (.f64 n (.f64 (.f64 l l) (-.f64 U* U))))) (.f64 1/6 (fma.f64 (log.f64 Om) -2 (log.f64 (.f64 n (.f64 (.f64 l l) (-.f64 U* U))))))))))
	62.2b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 U (.f64 (.f64 l l) U))) (.f64 Om Om))))
	58.2b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))) (/.f64 (.f64 t (sqrt.f64 2)) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	61.5b	(.f64 (sqrt.f64 (.f64 n U)) (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 (log.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om)))) (.f64 (log.f64 l) 2)) 1/2))))
	57.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))
	60.4b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (-.f64 U* U))) Om) (/.f64 U Om))))
	39.2b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (*.f64 t U))))
✓	28.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	61.7b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 2 (.f64 n U))) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t))))
	58.0b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (.f64 l l) (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))))))
	58.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 U (.f64 l l))) (*.f64 Om Om))))))))
✓	29.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))))
	36.3b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))
	40.8b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
	42.1b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 t U)))) (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (*.f64 n U) t))))
✓	29.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))))
	42.3b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 t U))))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))))
	56.4b	(neg.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))) (/.f64 (.f64 t (sqrt.f64 2)) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))))
	36.3b	(sqrt.f64 (fma.f64 t (.f64 2 (.f64 n U)) (.f64 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om) -4)))
	62.4b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 t (sqrt.f64 2))) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))
	60.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (fma.f64 1/3 (/.f64 (.f64 t (pow.f64 (exp.f64 1/3) (fma.f64 (log.f64 (/.f64 -1 l)) -2 (log.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om))))))) (.f64 (.f64 l l) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om))))) (pow.f64 (exp.f64 1/3) (fma.f64 (log.f64 (/.f64 -1 l)) -2 (log.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om))))))) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))))
	35.8b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) 3/2))
	60.6b	(.f64 (sqrt.f64 (.f64 n (.f64 n (.f64 (.f64 (.f64 l l) (-.f64 U* U)) U)))) (/.f64 (sqrt.f64 2) Om))

Compiler

Compiled 15330 to 5354 computations (65.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.5b	(.f64 (-.f64 U U) (/.f64 l Om))
7.0b	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
8.0b	(.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
18.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))))

rewrite278.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

10.6b

Rules

55×	`pow1_binary64`
33×	`pow-prod-down_binary64`
30×	`add-exp-log_binary64`
30×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`

Counts

4 → 171

Calls

4 calls:

57.0ms	(.f64 (-.f64 U U) (/.f64 l Om))
19.0ms	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
18.0ms	(.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
12.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))))

Compiler

Compiled 4868 to 1848 computations (62% saved)

series795.0ms (4.1%)

Error

12.1b

Counts

4 → 104

Calls

4 calls:

328.0ms	(.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
306.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))))
62.0ms	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
43.0ms	(.f64 (-.f64 U U) (/.f64 l Om))

Compiler

Compiled 10023 to 6992 computations (30.2% saved)

simplify186.0ms (1%)

Algorithm

1×	egg-herbie

Rules

605×	`associate-r_binary64`
542×	`associate-l_binary64`
350×	`fma-neg_binary64`
208×	`associate-/l*_binary64`
157×	`*-commutative_binary64`

Counts

275 → 192

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	433	7575
1	1232	7129
2	4975	7127
3	5213	7127

prune181.0ms (0.9%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	2	20	22
Picked	0	1	1
Done	2	1	3
Total	193	25	218

Error

10.6b

Counts

218 → 25

Alt Table

Status	Error	Program
	31.0b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))))
	33.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 U l)) Om)))))))
	55.5b	(neg.f64 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	62.3b	(.f64 (sqrt.f64 (.f64 n U)) (.f64 (sqrt.f64 2) (exp.f64 (fma.f64 1/3 (fma.f64 (log.f64 Om) -2 (log.f64 (.f64 n (.f64 (.f64 l l) (-.f64 U* U))))) (.f64 1/6 (fma.f64 (log.f64 Om) -2 (log.f64 (.f64 n (.f64 (.f64 l l) (-.f64 U* U))))))))))
	62.2b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 U (.f64 (.f64 l l) U))) (.f64 Om Om))))
	58.2b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))) (/.f64 (.f64 t (sqrt.f64 2)) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	61.5b	(.f64 (sqrt.f64 (.f64 n U)) (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 (log.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om)))) (.f64 (log.f64 l) 2)) 1/2))))
	57.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))
	60.4b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (-.f64 U* U))) Om) (/.f64 U Om))))
	39.2b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (*.f64 t U))))
	61.7b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 2 (.f64 n U))) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t))))
	58.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 U (.f64 l l))) (*.f64 Om Om))))))))
	40.8b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
	42.1b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 t U)))) (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (*.f64 n U) t))))
	31.1b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) t))))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t)))))) (cbrt.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))
	60.6b	(.f64 (sqrt.f64 (.f64 n (.f64 n (.f64 (.f64 (.f64 l l) (-.f64 U* U)) U)))) (/.f64 (sqrt.f64 2) Om))
	43.7b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	29.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))))
	56.4b	(neg.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))) (/.f64 (.f64 t (sqrt.f64 2)) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))))
	36.3b	(sqrt.f64 (fma.f64 t (.f64 2 (.f64 n U)) (.f64 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om) -4)))
	30.7b	(.f64 (pow.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t))) 1/4) (pow.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))) 1/4))
	62.4b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 t (sqrt.f64 2))) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))
	60.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (fma.f64 1/3 (/.f64 (.f64 t (pow.f64 (exp.f64 1/3) (fma.f64 (log.f64 (/.f64 -1 l)) -2 (log.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om))))))) (.f64 (.f64 l l) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om))))) (pow.f64 (exp.f64 1/3) (fma.f64 (log.f64 (/.f64 -1 l)) -2 (log.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om))))))) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))))))))
	36.3b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))
	35.8b	(cbrt.f64 (pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) 3/2))

Compiler

Compiled 4895 to 2090 computations (57.3% saved)

regimes3.9s (20.1%)

Accuracy

Total 15.5b remaining (55.6%)

Threshold costs 0b (0%)

Compiler

Compiled 67666 to 40370 computations (40.3% saved)

bsearch230.0ms (1.2%)

Steps

Iters	Range		Point
9	8.825303102569469e+148	5.812260815476856e+156	2.914456406777243e+149
7	-1.3161936169998671e+194	-3.5282010883285005e+192	-4.3244787979006757e+192

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
15×	`+-commutative_binary64`
13×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	139
1	68	139
2	92	139
3	115	139
4	134	139
5	142	139
6	145	139
7	146	139
8	145	139

end1.0ms (0%)

Compiler: Compiled 98 to 54 computations (44.9% saved)

sample4.1s (21.2%)

Algorithm

1×

intervals

Results

1.5s	13172×	body	128	nan
931.0ms	8000×	body	128	valid
147.0ms	1207×	body	128	invalid

Compiler

Compiled 1250 to 714 computations (42.9% saved)

Iter	Nodes	Cost
0	43	139
1	68	139
2	92	139
3	115	139
4	134	139
5	142	139
6	145	139
7	146	139
8	145	139

Iter	Nodes	Cost
0	43	139
1	68	139
2	92	139
3	115	139
4	134	139
5	142	139
6	145	139
7	146	139
8	145	139

Details

analyze3.1s (16%)

sample118.0ms (0.6%)

simplify56.0ms (0.3%)

prune4.0ms (0%)

localize18.0ms (0.1%)

rewrite309.0ms (1.6%)

series770.0ms (4%)

simplify141.0ms (0.7%)

prune209.0ms (1.1%)

localize23.0ms (0.1%)

rewrite245.0ms (1.3%)

series1.4s (7.4%)

simplify261.0ms (1.4%)

prune219.0ms (1.1%)

localize33.0ms (0.2%)

rewrite214.0ms (1.1%)

series2.0s (10.2%)

simplify267.0ms (1.4%)

prune263.0ms (1.4%)

localize19.0ms (0.1%)

rewrite278.0ms (1.4%)

series795.0ms (4.1%)

simplify186.0ms (1%)

prune181.0ms (0.9%)

regimes3.9s (20.1%)

bsearch230.0ms (1.2%)

simplify12.0ms (0.1%)

end1.0ms (0%)

sample4.1s (21.2%)

Profiling

Iter	Nodes	Cost
0	43	139
1	68	139
2	92	139
3	115	139
4	134	139
5	142	139
6	145	139
7	146	139
8	145	139