Details

analyze3.2s (15.3%)

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)

sample4.8s (23.2%)

Results

2.9s	14263×	body	128	invalid
1.9s	8256×	body	128	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify27.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

466×	`rules-20_binary64`
447×	`rules-11_binary64`
338×	`rules-6_binary64`
283×	`rules-9-rev_binary64`
272×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	42
1	49	40
2	194	40
3	1096	39
4	5144	39

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

31.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	36.3b	(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)))))
▶	31.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))))

Status

Error

Program

36.3b

(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*)))))

▶

31.5b

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

Compiler

Compiled 192 to 121 computations (37% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.4b	(*.f64 n (/.f64 l Om))
✓	9.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	9.3b	(.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))
✓	21.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))))

series1.3s (6.3%)

Counts

4 → 216

Calls

4 calls:

842.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))))
421.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))
35.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
14.0ms	(*.f64 n (/.f64 l Om))

rewrite90.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

223×	`add-sqr-sqrt_binary64`
212×	`log1p-expm1-u_binary64`
212×	`expm1-log1p-u_binary64`
205×	`add-cbrt-cube_binary64`
205×	`add-exp-log_binary64`

Counts

4 → 123

Calls

4 calls:

86.0ms	(*.f64 n (/.f64 l Om))
86.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
86.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))
86.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	92
1	496	92
2	4972	92
3	5240	92
0	0	0
1	0	0

simplify221.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

579×	`rules-21_binary64`
480×	`rules-14-rev_binary64`
404×	`rules-20_binary64`
193×	`rules-1_binary64`
160×	`rules-1-rev_binary64`

Counts

339 → 248

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	873	17324
1	3462	16606
2	5596	16606

prune519.0ms (2.5%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	226	22	248
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	227	23	250

Error

15.5b

Counts

250 → 23

Alt Table

Status	Error	Program
	36.7b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (/.f64 (.f64 n (*.f64 l U)) Om))))))
	57.3b	(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 (sqrt.f64 2) t) 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)))
	32.1b	(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))) 3)
	61.1b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	45.4b	(sqrt.f64 (-.f64 (.f64 2 (+.f64 (.f64 n (.f64 U t)) (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U* U))) (.f64 Om Om)))) (fma.f64 4 (.f64 n (/.f64 (.f64 (.f64 l l) U) Om)) (.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U U))) (*.f64 Om Om))))))
	41.4b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	38.7b	(sqrt.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om))))
	38.6b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	60.0b	(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) Om)) (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))))) (.f64 t (sqrt.f64 2)))) (.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) Om)) (/.f64 (.f64 n (*.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) U))) (sqrt.f64 2)))
	62.6b	(neg.f64 (.f64 U (sqrt.f64 (.f64 -2 (/.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 Om Om))))))
✓	31.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))))
	58.3b	(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 (sqrt.f64 2) t) 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))))
	61.6b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	42.0b	(sqrt.f64 (.f64 U (-.f64 (.f64 2 (+.f64 (.f64 n t) (.f64 (.f64 n n) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))) (.f64 4 (.f64 n (/.f64 (.f64 l l) Om))))))
	57.5b	(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)))
▶	31.7b	(pow.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))) 1/4) 2)
	40.8b	(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))) 3/2) 0) (+.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))) (+.f64 0 (.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))) 0))))
	41.7b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	40.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.f64 t (fma.f64 2 (/.f64 (.f64 l l) Om) (.f64 n (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))))))
	44.0b	(-.f64 (.f64 (sqrt.f64 (.f64 n (.f64 t U))) (sqrt.f64 2)) (.f64 (sqrt.f64 (/.f64 (.f64 n U) t)) (/.f64 (.f64 (pow.f64 l 2) (sqrt.f64 2)) Om)))
	60.8b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (.f64 n (.f64 (pow.f64 l 2) U))) U))) (/.f64 (sqrt.f64 2) Om))
	44.8b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (log.f64 (pow.f64 (exp.f64 (-.f64 U U)) (*.f64 n (/.f64 l Om)))))))))
	62.3b	(sqrt.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 2) n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))))

Compiler

Compiled 22473 to 12092 computations (46.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.4b	(*.f64 n (/.f64 l Om))
	9.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	9.3b	(.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))
✓	22.0b	(pow.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))) 1/4)

series881.0ms (4.2%)

Counts

2 → 144

Calls

2 calls:

591.0ms

(pow.f64 (*.f64 (*.f64 (*.f64 2 n) U) (-.f64 t (*.f64 (/.f64 l Om) (fma.f64 2 l (*.f64 (-.f64 U U*) (*.f64 n (/.f64 l Om))))))) 1/4)

289.0ms

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

rewrite83.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

217×	`add-sqr-sqrt_binary64`
207×	`log1p-expm1-u_binary64`
207×	`expm1-log1p-u_binary64`
200×	`add-cbrt-cube_binary64`
200×	`add-exp-log_binary64`

Counts

2 → 63

Calls

2 calls:

78.0ms

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

78.0ms

(pow.f64 (*.f64 (*.f64 (*.f64 2 n) U) (-.f64 t (*.f64 (/.f64 l Om) (fma.f64 2 l (*.f64 (-.f64 U U*) (*.f64 n (/.f64 l Om))))))) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	73
1	489	73
2	4904	73
3	5068	73
0	0	0
1	0	0

simplify268.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

709×	`rules-20_binary64`
276×	`rules-21_binary64`
255×	`fma-def_binary64`
216×	`rules-4_binary64`
207×	`rules-5-rev_binary64`

Counts

207 → 223

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1455	28998
1	5010	28998

prune733.0ms (3.5%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	278	7	285
Fresh	5	16	21
Picked	0	1	1
Done	0	1	1
Total	283	25	308

Error

10.5b

Counts

308 → 25

Alt Table

Status	Error	Program
	36.7b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (/.f64 (.f64 n (*.f64 l U)) Om))))))
	57.3b	(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 (sqrt.f64 2) t) 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)))
✓	31.7b	(pow.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))) 1/4) 2)
	48.0b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 2 (*.f64 n U))) (log.f64 (/.f64 1 t))))) 2)
▶	32.1b	(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))) 3)
	44.9b	(pow.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (log.f64 (pow.f64 (exp.f64 (-.f64 U U)) (.f64 n (/.f64 l Om)))))))) 1/4) 2)
	52.1b	(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (-.f64 (+.f64 (.f64 2 (.f64 n t)) (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) (.f64 4 (/.f64 (*.f64 n (pow.f64 l 2)) Om)))) (log.f64 U)))) 2)
	41.4b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	40.8b	(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))) 3/2) 0) (+.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))) (+.f64 0 (.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))) 0))))
	48.9b	(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om))))))) 2)
	62.6b	(neg.f64 (.f64 U (sqrt.f64 (.f64 -2 (/.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 Om Om))))))
✓	31.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))))
	38.8b	(pow.f64 (pow.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om))) 1/4) 2)
	60.8b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (.f64 n (.f64 (pow.f64 l 2) U))) U))) (/.f64 (sqrt.f64 2) Om))
	45.5b	(pow.f64 (pow.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 n n)) (.f64 Om Om)) (.f64 n (.f64 t U)))) (fma.f64 4 (.f64 n (/.f64 (.f64 U (.f64 l l)) Om)) (.f64 2 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 n n)) (.f64 Om Om))))) 1/4) 2)
	58.3b	(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 (sqrt.f64 2) t) 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))))
	61.6b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	42.0b	(sqrt.f64 (.f64 U (-.f64 (.f64 2 (+.f64 (.f64 n t) (.f64 (.f64 n n) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))) (.f64 4 (.f64 n (/.f64 (.f64 l l) Om))))))
	57.5b	(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)))
	51.0b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t))))) 2)
	38.6b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	41.7b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	40.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.f64 t (fma.f64 2 (/.f64 (.f64 l l) Om) (.f64 n (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))))))
	44.0b	(-.f64 (.f64 (sqrt.f64 (.f64 n (.f64 t U))) (sqrt.f64 2)) (.f64 (sqrt.f64 (/.f64 (.f64 n U) t)) (/.f64 (.f64 (pow.f64 l 2) (sqrt.f64 2)) Om)))
	62.3b	(sqrt.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 2) n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))))

Compiler

Compiled 40463 to 23368 computations (42.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.4b	(*.f64 n (/.f64 l Om))
	9.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
	9.3b	(.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))
✓	21.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))

series798.0ms (3.8%)

Counts

1 → 48

Calls

1 calls:

797.0ms

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

rewrite68.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

206×	`add-sqr-sqrt_binary64`
194×	`log1p-expm1-u_binary64`
194×	`expm1-log1p-u_binary64`
189×	`add-cbrt-cube_binary64`
189×	`add-exp-log_binary64`

Counts

1 → 31

Calls

1 calls:

67.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	37
1	460	37
2	4900	37
3	5133	37
0	0	0
1	0	0

simplify149.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

570×	`rules-21_binary64`
468×	`rules-14-rev_binary64`
364×	`rules-20_binary64`
174×	`rules-1_binary64`
143×	`rules-1-rev_binary64`

Counts

79 → 117

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	800	11525
1	3186	10814
2	5178	10814

prune454.0ms (2.2%)

Pruning

29 alts after pruning (27 fresh and 2 done)

	Pruned	Kept	Total
New	237	7	244
Fresh	2	20	22
Picked	1	0	1
Done	0	2	2
Total	240	29	269

Error

10.5b

Counts

269 → 29

Alt Table

Status	Error	Program
✓	31.7b	(pow.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))) 1/4) 2)
	48.0b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 2 (*.f64 n U))) (log.f64 (/.f64 1 t))))) 2)
	44.9b	(pow.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (log.f64 (pow.f64 (exp.f64 (-.f64 U U)) (.f64 n (/.f64 l Om)))))))) 1/4) 2)
	52.1b	(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (-.f64 (+.f64 (.f64 2 (.f64 n t)) (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) (.f64 4 (/.f64 (*.f64 n (pow.f64 l 2)) Om)))) (log.f64 U)))) 2)
	41.4b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	40.8b	(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))) 3/2) 0) (+.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))) (+.f64 0 (.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))) 0))))
	48.9b	(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om))))))) 2)
	41.7b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	42.0b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))) 3)
	40.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.f64 t (fma.f64 2 (/.f64 (.f64 l l) Om) (.f64 n (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))))))
	44.3b	(pow.f64 (cbrt.f64 (-.f64 (.f64 (sqrt.f64 (.f64 n (.f64 t U))) (sqrt.f64 2)) (.f64 (sqrt.f64 (/.f64 (.f64 n U) t)) (/.f64 (.f64 (pow.f64 l 2) (sqrt.f64 2)) Om)))) 3)
	62.6b	(neg.f64 (.f64 U (sqrt.f64 (.f64 -2 (/.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 Om Om))))))
✓	31.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))))
	44.0b	(-.f64 (.f64 (sqrt.f64 (.f64 n (.f64 t U))) (sqrt.f64 2)) (.f64 (sqrt.f64 (/.f64 (.f64 n U) t)) (/.f64 (.f64 (pow.f64 l 2) (sqrt.f64 2)) Om)))
	56.9b	(pow.f64 (cbrt.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))) 3)
	38.8b	(pow.f64 (pow.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om))) 1/4) 2)
	60.8b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (.f64 n (.f64 (pow.f64 l 2) U))) U))) (/.f64 (sqrt.f64 2) Om))
	61.6b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	41.7b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))) 3)
	45.5b	(pow.f64 (pow.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 n n)) (.f64 Om Om)) (.f64 n (.f64 t U)))) (fma.f64 4 (.f64 n (/.f64 (.f64 U (.f64 l l)) Om)) (.f64 2 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 n n)) (.f64 Om Om))))) 1/4) 2)
	58.3b	(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 (sqrt.f64 2) t) 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))))
▶	37.1b	(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (/.f64 (.f64 n (.f64 l U)) Om))))))) 3)
	62.3b	(sqrt.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 2) n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))))
	57.6b	(pow.f64 (cbrt.f64 (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)))) 3)
	57.3b	(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 (sqrt.f64 2) t) 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)))
	51.0b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t))))) 2)
	38.6b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	58.4b	(pow.f64 (cbrt.f64 (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 (sqrt.f64 2) t) 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))))) 3)
	42.0b	(sqrt.f64 (.f64 U (-.f64 (.f64 2 (+.f64 (.f64 n t) (.f64 (.f64 n n) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))) (.f64 4 (.f64 n (/.f64 (.f64 l l) Om))))))

Compiler

Compiled 23352 to 12961 computations (44.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(.f64 n (.f64 l U))
✓	6.3b	(/.f64 (.f64 n (.f64 l U)) Om)
✓	9.9b	(.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (/.f64 (.f64 n (.f64 l U)) Om)))))
✓	16.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (/.f64 (.f64 n (.f64 l U)) Om))))))

series545.0ms (2.6%)

Counts

4 → 104

Calls

4 calls:

352.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (/.f64 (.f64 n (.f64 l U)) Om))))))
160.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (/.f64 (.f64 n (.f64 l U)) Om)))))
25.0ms	(/.f64 (.f64 n (.f64 l U)) Om)
8.0ms	(.f64 n (.f64 l U))

rewrite100.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

237×	`prod-diff_binary64`
191×	`add-sqr-sqrt_binary64`
178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`
175×	`add-cbrt-cube_binary64`

Counts

4 → 151

Calls

4 calls:

93.0ms	(.f64 n (.f64 l U))
93.0ms	(/.f64 (.f64 n (.f64 l U)) Om)
93.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (/.f64 (.f64 n (.f64 l U)) Om)))))
93.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (/.f64 (.f64 n (.f64 l U)) Om))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	83
1	429	83
2	4881	83
3	5192	83
0	0	0
1	0	0

simplify136.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

738×	`rules-20_binary64`
704×	`fma-def_binary64`
539×	`rules-13_binary64`
368×	`rules-14-rev_binary64`
327×	`rules-21_binary64`

Counts

255 → 247

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	554	10025
1	2170	9450
2	6237	9450

prune346.0ms (1.7%)

Pruning

30 alts after pruning (28 fresh and 2 done)

	Pruned	Kept	Total
New	243	4	247
Fresh	2	24	26
Picked	1	0	1
Done	0	2	2
Total	246	30	276

Error

10.5b

Counts

276 → 30

Alt Table

Status	Error	Program
✓	31.7b	(pow.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))) 1/4) 2)
	48.0b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 2 (*.f64 n U))) (log.f64 (/.f64 1 t))))) 2)
	59.2b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 n (.f64 U (fma.f64 n (/.f64 U (.f64 Om Om)) (/.f64 2 Om)))))) (neg.f64 (*.f64 l (sqrt.f64 2))))) 3)
	52.1b	(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (-.f64 (+.f64 (.f64 2 (.f64 n t)) (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) (.f64 4 (/.f64 (*.f64 n (pow.f64 l 2)) Om)))) (log.f64 U)))) 2)
	41.4b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	36.9b	(pow.f64 (cbrt.f64 (sqrt.f64 (fabs.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (/.f64 (.f64 n (.f64 U l)) Om)))))))) 3)
	40.8b	(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))) 3/2) 0) (+.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))) (+.f64 0 (.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))) 0))))
	48.9b	(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 n) (log.f64 (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om))))))) 2)
	41.7b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	42.0b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))) 3)
	40.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.f64 t (fma.f64 2 (/.f64 (.f64 l l) Om) (.f64 n (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))))))
	44.3b	(pow.f64 (cbrt.f64 (-.f64 (.f64 (sqrt.f64 (.f64 n (.f64 t U))) (sqrt.f64 2)) (.f64 (sqrt.f64 (/.f64 (.f64 n U) t)) (/.f64 (.f64 (pow.f64 l 2) (sqrt.f64 2)) Om)))) 3)
	38.4b	(pow.f64 (cbrt.f64 (exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (/.f64 (.f64 n (.f64 U l)) Om))))))))) 3)
	62.6b	(neg.f64 (.f64 U (sqrt.f64 (.f64 -2 (/.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 Om Om))))))
✓	31.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 2 l) (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))))))
	44.0b	(-.f64 (.f64 (sqrt.f64 (.f64 n (.f64 t U))) (sqrt.f64 2)) (.f64 (sqrt.f64 (/.f64 (.f64 n U) t)) (/.f64 (.f64 (pow.f64 l 2) (sqrt.f64 2)) Om)))
	56.9b	(pow.f64 (cbrt.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))) 3)
	44.9b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (/.f64 (.f64 n (.f64 U l)) Om))))))) 3)
	38.8b	(pow.f64 (pow.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om))) 1/4) 2)
	60.8b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (.f64 n (.f64 (pow.f64 l 2) U))) U))) (/.f64 (sqrt.f64 2) Om))
	61.6b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	41.7b	(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))) 3)
	45.5b	(pow.f64 (pow.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 n n)) (.f64 Om Om)) (.f64 n (.f64 t U)))) (fma.f64 4 (.f64 n (/.f64 (.f64 U (.f64 l l)) Om)) (.f64 2 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 n n)) (.f64 Om Om))))) 1/4) 2)
	58.3b	(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 (sqrt.f64 2) t) 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	(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 (sqrt.f64 2) t) 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)))
	51.0b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t))))) 2)
	38.6b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	58.4b	(pow.f64 (cbrt.f64 (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 (sqrt.f64 2) t) 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))))) 3)
	42.0b	(sqrt.f64 (.f64 U (-.f64 (.f64 2 (+.f64 (.f64 n t) (.f64 (.f64 n n) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))) (.f64 4 (.f64 n (/.f64 (.f64 l l) Om))))))
	62.3b	(sqrt.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 2) n) U) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 2 l (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))))

Compiler

Compiled 17909 to 10004 computations (44.1% saved)

regimes5.0s (23.8%)

Accuracy

Total 18.0b remaining (62.1%)

Threshold costs 0b (0%)

Counts

207 → 7

Compiler

Compiled 64626 to 42594 computations (34.1% saved)

bsearch460.0ms (2.2%)

Steps

Iters	Range		Point
9	1.7144866038215244e+147	1.505503524694323e+152	1.0929684051149698e+148
6	3.4455479151883626e+106	1.9932005309408237e+107	1.9647608470229247e+107
6	4.321882449013399e+53	6.647823029798716e+54	6.458348500382844e+54
8	1.6203010716718168e-122	3.6226991104622533e-118	1.996995397456292e-122
3	4.461333025751657e-261	6.219888100730681e-261	5.890159024172114e-261
9	-3.6625970117205837e+93	-4.113052109771031e+87	-4.315335066187473e+92

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	286
1	68	286

end592.0ms (2.8%)

Compiler: Compiled 1517 to 936 computations (38.3% saved)

Details

analyze3.2s (15.3%)

sample4.8s (23.2%)

simplify27.0ms (0.1%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series1.3s (6.3%)

rewrite90.0ms (0.4%)

simplify221.0ms (1.1%)

prune519.0ms (2.5%)

localize18.0ms (0.1%)

series881.0ms (4.2%)

rewrite83.0ms (0.4%)

simplify268.0ms (1.3%)

prune733.0ms (3.5%)

localize17.0ms (0.1%)

series798.0ms (3.8%)

rewrite68.0ms (0.3%)

simplify149.0ms (0.7%)

prune454.0ms (2.2%)

localize17.0ms (0.1%)

series545.0ms (2.6%)

rewrite100.0ms (0.5%)

simplify136.0ms (0.7%)

prune346.0ms (1.7%)

regimes5.0s (23.8%)

bsearch460.0ms (2.2%)

simplify4.0ms (0%)

end592.0ms (2.8%)

Profiling