Details

analyze3.8s (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)

sample4.6s (19.6%)

Results

2.8s	14197×	body	128	invalid
1.7s	8256×	body	128	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify46.0ms (0.2%)

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 → 2

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

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
▶	32.0b	(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))))))))
	35.0b	(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

▶

32.0b

(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))))))))

35.0b

(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 189 to 119 computations (37% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.8b	(*.f64 n (/.f64 l Om))
✓	7.4b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	11.8b	(.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)))))))
✓	17.9b	(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))))))))

series1.2s (5.2%)

Counts

4 → 216

Calls

4 calls:

853.0ms	(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))))))))
318.0ms	(.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)))))))
37.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
13.0ms	(*.f64 n (/.f64 l Om))

rewrite75.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

223×	`add-sqr-sqrt_binary64`
211×	`log1p-expm1-u_binary64`
211×	`expm1-log1p-u_binary64`
207×	`add-log-exp_binary64`
206×	`add-cube-cbrt_binary64`

Counts

4 → 88

Calls

4 calls:

72.0ms	(*.f64 n (/.f64 l Om))
72.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
72.0ms	(.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)))))))
72.0ms	(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))))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	92
1	440	88
2	4849	88
3	5137	88
0	0	0
1	0	0

simplify218.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

734×	`fma-def_binary64`
405×	`*-commutative_binary64`
195×	`associate-r_binary64`
150×	`+-commutative_binary64`
147×	`associate-/l*_binary64`

Counts

304 → 215

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	876	17039
1	3084	16145
2	5020	16145

prune413.0ms (1.8%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	193	22	215
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	194	23	217

Error

11.9b

Counts

217 → 23

Alt Table

Status	Error	Program
	38.7b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	62.0b	(-.f64 (.f64 2 (/.f64 (.f64 (.f64 l l) U) (.f64 Om (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))))))))) (fma.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)))))) (/.f64 (.f64 U t) (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)))))))))
	58.1b	(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)))
	48.9b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))
	55.6b	(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)))))))))
	44.6b	(-.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 (.f64 n (sqrt.f64 2)) (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)) (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2))) U)))
	58.7b	(sqrt.f64 (.f64 2 (.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 (.f64 l l) U)) (*.f64 Om Om))))))))
	56.8b	(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))))
	41.7b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	62.3b	(sqrt.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 2) n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))
	33.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om)))))))
	43.3b	(sqrt.f64 (.f64 U (fma.f64 2 (fma.f64 n t (/.f64 (.f64 (.f64 (.f64 l l) U) (.f64 n n)) (.f64 Om Om))) (.f64 (/.f64 (.f64 n (.f64 l l)) Om) -4))))
	40.3b	(cbrt.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)) 3/2))
	35.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n (-.f64 U* U)) Om) l))))))
	60.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	38.7b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))
	35.0b	(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)))))
	44.5b	(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	62.3b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 (sqrt.f64 2) t)) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))
	60.9b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	41.6b	(sqrt.f64 (.f64 2 (.f64 n (*.f64 t U))))
▶	32.3b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 3))

Compiler

Compiled 19852 to 10927 computations (45% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	7.4b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	11.8b	(.f64 (.f64 (.f64 2 n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))
✓	17.9b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 3))
✓	19.0b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))

series2.0s (8.3%)

Counts

3 → 192

Calls

3 calls:

1.0s

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

646.0ms

(sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 3))

290.0ms

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

rewrite77.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

234×	`prod-diff_binary64`
219×	`add-sqr-sqrt_binary64`
208×	`log1p-expm1-u_binary64`
208×	`expm1-log1p-u_binary64`
204×	`add-cbrt-cube_binary64`

Counts

3 → 78

Calls

3 calls:

74.0ms

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

74.0ms

(sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 3))

74.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	103
1	448	103
2	4824	103
3	5213	103
0	0	0
1	0	0

simplify411.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

373×	`fma-def_binary64`
333×	`associate-/l*_binary64`
292×	`associate-*r/_binary64`
238×	`associate-/r*_binary64`
222×	`times-frac_binary64`

Counts

270 → 326

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2227	40919
1	5413	40919

prune1.0s (4.4%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	347	11	358
Fresh	5	17	22
Picked	1	0	1
Done	0	0	0
Total	353	28	381

Error

11.3b

Counts

381 → 28

Alt Table

Status	Error	Program
	35.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n (-.f64 U* U)) Om) l))))))
	42.0b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 n (*.f64 t U))) (cbrt.f64 2)) 3))
	56.8b	(neg.f64 (fma.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 t (.f64 l (sqrt.f64 2))) (.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))) U))) (.f64 l (sqrt.f64 2)))))
	60.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	62.5b	(sqrt.f64 (pow.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))) U)) (*.f64 2 (neg.f64 (log.f64 n)))))) (cbrt.f64 2)) 3))
	58.1b	(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)))
	48.9b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))
	62.3b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 (sqrt.f64 2) t)) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))
	60.5b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))) U)))))
	55.6b	(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)))))))))
	44.6b	(-.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 (.f64 n (sqrt.f64 2)) (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)) (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2))) U)))
▶	32.3b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (cbrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))
	53.0b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 2) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (*.f64 n U))) (log.f64 (/.f64 -1 t)))))) 3))
	60.9b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	58.7b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 (.f64 l l) U)) (*.f64 Om Om)))) U)))) 3))
	62.3b	(sqrt.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 2) n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))
	33.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om)))))))
	43.3b	(sqrt.f64 (.f64 U (fma.f64 2 (fma.f64 n t (/.f64 (.f64 (.f64 (.f64 l l) U) (.f64 n n)) (.f64 Om Om))) (.f64 (/.f64 (.f64 n (.f64 l l)) Om) -4))))
	40.3b	(cbrt.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)) 3/2))
	43.3b	(sqrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 n (*.f64 t U)) 1/3) (cbrt.f64 2)) 3))
	38.7b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))
	38.7b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	35.0b	(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)))))
	44.5b	(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	38.9b	(sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om)))) 3))
	54.2b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 2) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (*.f64 n U)) (log.f64 (/.f64 1 t)))))) 3))
	62.5b	(sqrt.f64 (pow.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) U)) (.f64 Om Om)))) (log.f64 (/.f64 -1 U))))) (cbrt.f64 2)) 3))

Compiler

Compiled 54005 to 31168 computations (42.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.9b	(.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))
	7.4b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	17.6b	(cbrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))
✓	17.9b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (cbrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))

series1.5s (6.2%)

Counts

3 → 192

Calls

3 calls:

647.0ms

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

642.0ms

(sqrt.f64 (pow.f64 (*.f64 (cbrt.f64 (*.f64 2 n)) (cbrt.f64 (*.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))

167.0ms

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

rewrite70.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

231×	`add-sqr-sqrt_binary64`
220×	`log1p-expm1-u_binary64`
220×	`expm1-log1p-u_binary64`
215×	`add-cbrt-cube_binary64`
214×	`add-cube-cbrt_binary64`

Counts

3 → 70

Calls

3 calls:

67.0ms

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

67.0ms

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

67.0ms

(sqrt.f64 (pow.f64 (*.f64 (cbrt.f64 (*.f64 2 n)) (cbrt.f64 (*.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	94
1	480	91
2	4856	91
3	4899	91
0	0	0
1	0	0

simplify322.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

365×	`associate-r_binary64`
343×	`fma-def_binary64`
274×	`associate-/l*_binary64`
242×	`associate-*r/_binary64`
206×	`associate-/r*_binary64`

Counts

262 → 318

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1910	35451
1	5250	35451

prune913.0ms (3.9%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	340	10	350
Fresh	4	23	27
Picked	1	0	1
Done	0	0	0
Total	345	33	378

Error

10.6b

Counts

378 → 33

Alt Table

Status	Error	Program
	35.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n (-.f64 U* U)) Om) l))))))
	56.8b	(neg.f64 (fma.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 t (.f64 l (sqrt.f64 2))) (.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))) U))) (.f64 l (sqrt.f64 2)))))
	44.8b	(.f64 (pow.f64 (cbrt.f64 (.f64 2 n)) 3/2) (pow.f64 (cbrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 3/2))
	63.0b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)))) (log.f64 (/.f64 -1 U)))))) 3))
	60.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	62.5b	(sqrt.f64 (pow.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))) U)) (*.f64 2 (neg.f64 (log.f64 n)))))) (cbrt.f64 2)) 3))
	38.7b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))
	62.2b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (cbrt.f64 (log.f64 (pow.f64 (exp.f64 U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))) 3))
	38.7b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	34.0b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))))
	59.1b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))) U)) (.f64 2 (log.f64 (/.f64 -1 l))))))) 3))
	58.1b	(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)))
	61.4b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 (-.f64 (/.f64 (.f64 n U) (pow.f64 Om 2)) (+.f64 (.f64 2 (/.f64 1 Om)) (/.f64 (.f64 n U) (pow.f64 Om 2)))) U)) (*.f64 2 (log.f64 (/.f64 1 l))))))) 3))
	48.9b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))
	62.3b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 (sqrt.f64 2) t)) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))
	53.6b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (pow.f64 (*.f64 t U) 1/3)) 3))
	60.5b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))) U)))))
	55.6b	(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)))))))))
	44.6b	(-.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 (.f64 n (sqrt.f64 2)) (sqrt.f64 (.f64 (-.f64 (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)) (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2))) U)))
▶	32.0b	(pow.f64 (pow.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 1/4) 2)
	53.0b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 2) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (*.f64 n U))) (log.f64 (/.f64 -1 t)))))) 3))
	62.3b	(sqrt.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 2) n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))
	33.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om)))))))
	57.6b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (pow.f64 (exp.f64 1/3) (-.f64 (log.f64 U) (neg.f64 (log.f64 t))))) 3))
	62.5b	(sqrt.f64 (pow.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) U)) (.f64 Om Om)))) (log.f64 (/.f64 -1 U))))) (cbrt.f64 2)) 3))
	43.3b	(sqrt.f64 (.f64 U (fma.f64 2 (fma.f64 n t (/.f64 (.f64 (.f64 (.f64 l l) U) (.f64 n n)) (.f64 Om Om))) (.f64 (/.f64 (.f64 n (.f64 l l)) Om) -4))))
	40.3b	(cbrt.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)) 3/2))
	35.0b	(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)))))
	44.5b	(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	60.9b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	38.9b	(sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om)))) 3))
	58.8b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (exp.f64 (*.f64 1/3 (-.f64 (log.f64 (neg.f64 U)) (log.f64 (/.f64 -1 t)))))) 3))

Compiler

Compiled 49347 to 28089 computations (43.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.9b	(.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))
✓	7.2b	(.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))
	7.4b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	18.8b	(pow.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 1/4)

series904.0ms (3.8%)

Counts

2 → 144

Calls

2 calls:

591.0ms

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

312.0ms

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

rewrite69.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

234×	`prod-diff_binary64`
216×	`add-sqr-sqrt_binary64`
205×	`log1p-expm1-u_binary64`
205×	`expm1-log1p-u_binary64`
201×	`add-log-exp_binary64`

Counts

2 → 38

Calls

2 calls:

68.0ms

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

68.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	69
1	433	69
2	4866	69
3	5269	69
0	0	0
1	0	0

simplify273.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

705×	`*-commutative_binary64`
298×	`associate-r_binary64`
254×	`fma-def_binary64`
220×	`associate-/l*_binary64`
206×	`associate-*r/_binary64`

Counts

182 → 198

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1449	28755
1	5113	28755

prune682.0ms (2.9%)

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	269	7	276
Fresh	6	26	32
Picked	0	1	1
Done	0	0	0
Total	275	34	309

Error

7.9b

Counts

309 → 34

Alt Table

Status	Error	Program
	35.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n (-.f64 U* U)) Om) l))))))
	56.8b	(neg.f64 (fma.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 t (.f64 l (sqrt.f64 2))) (.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))) U))) (.f64 l (sqrt.f64 2)))))
	44.8b	(.f64 (pow.f64 (cbrt.f64 (.f64 2 n)) 3/2) (pow.f64 (cbrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 3/2))
	63.0b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)))) (log.f64 (/.f64 -1 U)))))) 3))
	38.7b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))
	49.0b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t))))) 2)
	38.7b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	49.4b	(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)
	34.0b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))))
	59.1b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))) U)) (.f64 2 (log.f64 (/.f64 -1 l))))))) 3))
	58.1b	(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)))
	62.0b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) (log.f64 (/.f64 1 U*))))) 2)
	61.4b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 (-.f64 (/.f64 (.f64 n U) (pow.f64 Om 2)) (+.f64 (.f64 2 (/.f64 1 Om)) (/.f64 (.f64 n U) (pow.f64 Om 2)))) U)) (*.f64 2 (log.f64 (/.f64 1 l))))))) 3))
	48.9b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))
	60.1b	(pow.f64 (pow.f64 (.f64 (.f64 2 n) (/.f64 (.f64 n (.f64 (.f64 l l) (.f64 U* U))) (*.f64 Om Om))) 1/4) 2)
	44.5b	(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	62.3b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 (sqrt.f64 2) t)) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))
	53.6b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (pow.f64 (*.f64 t U) 1/3)) 3))
	60.5b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))) U)))))
	55.6b	(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)))))))))
	44.6b	(-.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)))
✓	32.0b	(pow.f64 (pow.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 1/4) 2)
	53.0b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 2) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (neg.f64 (*.f64 n U))) (log.f64 (/.f64 -1 t)))))) 3))
	61.8b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 2 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)))))) (*.f64 2 (neg.f64 (log.f64 n)))))) 2)
	49.0b	(pow.f64 (.f64 (pow.f64 (.f64 (.f64 2 n) U) 1/4) (pow.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t) 1/4)) 2)
	58.8b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (exp.f64 (*.f64 1/3 (-.f64 (log.f64 (neg.f64 U)) (log.f64 (/.f64 -1 t)))))) 3))
	62.3b	(sqrt.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 2) n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))
	51.3b	(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)
	33.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om)))))))
	43.3b	(sqrt.f64 (.f64 U (fma.f64 2 (fma.f64 n t (/.f64 (.f64 (.f64 (.f64 l l) U) (.f64 n n)) (.f64 Om Om))) (.f64 (/.f64 (.f64 n (.f64 l l)) Om) -4))))
	40.3b	(cbrt.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)) 3/2))
	35.0b	(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)))))
	60.9b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	38.9b	(sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om)))) 3))

Compiler

Compiled 37678 to 22078 computations (41.4% saved)

regimes3.8s (16.2%)

Accuracy

Total 20.3b remaining (68.7%)

Threshold costs 0b (0%)

Counts

166 → 5

Compiler

Compiled 49074 to 32866 computations (33% saved)

bsearch364.0ms (1.6%)

Steps

Iters	Range		Point
12	6.551271705977295e+182	1.1434994557764313e+223	1.654663879281347e+185
5	4.180981210236647e-8	8.536167494363952e-8	4.516470951330459e-8
5	2.766523468094321e-270	1.1440080722651625e-267	6.904723308845628e-270
7	-1.2882920736355296e+103	-2.3724113429795934e+101	-1.268193104122423e+103

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative_binary64`
16×	`+-commutative_binary64`
14×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	275
1	95	275
2	126	275
3	152	275
4	166	275
5	170	275
6	169	275

end730.0ms (3.1%)

Compiler: Compiled 1577 to 981 computations (37.8% saved)

Details

analyze3.8s (16%)

sample4.6s (19.6%)

simplify46.0ms (0.2%)

prune4.0ms (0%)

localize16.0ms (0.1%)

series1.2s (5.2%)

rewrite75.0ms (0.3%)

simplify218.0ms (0.9%)

prune413.0ms (1.8%)

localize17.0ms (0.1%)

series2.0s (8.3%)

rewrite77.0ms (0.3%)

simplify411.0ms (1.7%)

prune1.0s (4.4%)

localize20.0ms (0.1%)

series1.5s (6.2%)

rewrite70.0ms (0.3%)

simplify322.0ms (1.4%)

prune913.0ms (3.9%)

localize18.0ms (0.1%)

series904.0ms (3.8%)

rewrite69.0ms (0.3%)

simplify273.0ms (1.2%)

prune682.0ms (2.9%)

regimes3.8s (16.2%)

bsearch364.0ms (1.6%)

simplify9.0ms (0%)

end730.0ms (3.1%)

Profiling