Details

analyze3.0s (15%)

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)

sample4.5s (22.9%)

Results

2.8s	14781×	body	128	invalid
1.6s	8256×	body	128	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify24.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

515×	`fma-neg_binary64`
395×	`fma-def_binary64`
280×	`distribute-rgt-in_binary64`
276×	`distribute-lft-in_binary64`
245×	`associate-*r/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	42
1	58	40
2	192	40
3	983	38
4	4416	37

Stop Event

1×	node limit

Counts

1 → 2

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

30.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	35.2b	(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)))))
▶	30.2b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))

Status

Error

Program

35.2b

(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*)))))

▶

30.2b

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

Compiler

Compiled 189 to 119 computations (37% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.6b	(*.f64 n (/.f64 l Om))
✓	8.6b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	9.0b	(.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))
✓	20.3b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))

series1.1s (5.5%)

Counts

4 → 216

Calls

4 calls:

750.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
281.0ms	(.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))
33.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
11.0ms	(*.f64 n (/.f64 l Om))

rewrite45.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

223×	`add-sqr-sqrt_binary64`
211×	`log1p-expm1-u_binary64`
211×	`expm1-log1p-u_binary64`
210×	`add-cbrt-cube_binary64`
207×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	92
1	441	88

Stop Event

1×	node limit

Counts

4 → 85

Calls

4 calls:

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

simplify160.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	876	17039
1	3327	16151

Stop Event

1×	node limit

Counts

301 → 212

prune392.0ms (2%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	190	22	212
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	191	23	214

Error

11.4b

Counts

214 → 23

Alt Table

Status	Error	Program
▶	30.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	40.9b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (.f64 n t) U))) (.f64 (/.f64 (*.f64 l l) (/.f64 Om (sqrt.f64 2))) (sqrt.f64 (/.f64 n (/.f64 t U)))))
	42.3b	(-.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)))
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 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))))))) (sqrt.f64 2))
	58.9b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (.f64 l l) (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (*.f64 Om Om) U))))))))
	60.6b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	37.6b	(sqrt.f64 (.f64 2 (.f64 (*.f64 n t) U)))
	58.6b	(-.f64 (.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) -1/2) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U)))))) (.f64 (sqrt.f64 2) l)))
	59.0b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U)))))) (*.f64 (sqrt.f64 2) l)))
	61.1b	(.f64 (.f64 n (sqrt.f64 2)) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 l l) (/.f64 (*.f64 Om Om) U))))))
	61.7b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	58.4b	(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (pow.f64 Om 2)) (+.f64 (.f64 2 (/.f64 1 Om)) (/.f64 (.f64 n U) (pow.f64 Om 2)))))) (/.f64 (.f64 t (sqrt.f64 2)) l))) (.f64 (sqrt.f64 (.f64 n (.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 l (sqrt.f64 2))))
	62.7b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t)) (.f64 (*.f64 2 n) U))))
	57.6b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U)))))) (.f64 (sqrt.f64 2) l))
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	30.4b	(pow.f64 (pow.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 1/4) 2)
	36.5b	(sqrt.f64 (fma.f64 2 (.f64 (.f64 n t) U) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))
	37.7b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	42.3b	(.f64 (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) t)) (sqrt.f64 (.f64 (*.f64 2 n) U)))
	60.5b	(.f64 -1 (.f64 n (sqrt.f64 (.f64 -2 (.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)))))
	57.1b	(.f64 -1 (.f64 (sqrt.f64 (.f64 n (.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 l (sqrt.f64 2))))
	38.1b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	30.6b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))

Compiler

Compiled 19698 to 10872 computations (44.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.6b	(*.f64 n (/.f64 l Om))
	8.6b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	9.0b	(.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))
✓	20.3b	(sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t)))

series756.0ms (3.8%)

Counts

2 → 120

Calls

2 calls:

555.0ms

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

201.0ms

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

rewrite64.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

639×	`prod-diff_binary64`
184×	`add-sqr-sqrt_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`
171×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	62
1	362	62
2	4856	62

Stop Event

1×	node limit

Counts

2 → 45

Calls

2 calls:

63.0ms

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

63.0ms

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

simplify138.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

800×	`associate-/l*_binary64`
671×	`fma-def_binary64`
285×	`*-commutative_binary64`
153×	`+-commutative_binary64`
120×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	709	15123
1	2682	14256

Stop Event

1×	node limit

Counts

165 → 160

prune347.0ms (1.8%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	200	9	209
Fresh	8	13	21
Picked	0	1	1
Done	0	1	1
Total	208	24	232

Error

8.4b

Counts

232 → 24

Alt Table

Status	Error	Program
	58.9b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (.f64 l l) (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (*.f64 Om Om) U))))))))
	60.6b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	41.9b	(.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 (.f64 n (.f64 U t))) (.f64 (/.f64 l (/.f64 Om l)) (sqrt.f64 (*.f64 (/.f64 n t) U)))))
	42.3b	(.f64 (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) t)) (sqrt.f64 (.f64 (*.f64 2 n) U)))
	37.6b	(sqrt.f64 (.f64 2 (.f64 (*.f64 n t) U)))
	58.6b	(-.f64 (.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) -1/2) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U)))))) (.f64 (sqrt.f64 2) l)))
	41.8b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U U) (/.f64 l Om)) n)) t)))))
	56.6b	(.f64 (sqrt.f64 2) (.f64 l (neg.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 Om (/.f64 U* Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om)))))))))))
	42.7b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U* U) (/.f64 l Om)) n)) t)) (sqrt.f64 (*.f64 n U))))
	57.1b	(.f64 -1 (.f64 (sqrt.f64 (.f64 n (.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 l (sqrt.f64 2))))
	32.3b	(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U* U) (/.f64 l Om)) n)) t))))) (cbrt.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U* U) (/.f64 l Om)) n)) t))))))
	57.3b	(.f64 (sqrt.f64 2) (.f64 l (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 Om (/.f64 U* Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om))))))))))
	59.0b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U)))))) (*.f64 (sqrt.f64 2) l)))
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
▶	30.4b	(pow.f64 (pow.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 1/4) 2)
	30.6b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))
	60.5b	(.f64 (sqrt.f64 2) (.f64 -1 (.f64 n (sqrt.f64 (.f64 -1 (.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))))))
✓	30.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	60.5b	(.f64 -1 (.f64 n (sqrt.f64 (.f64 -2 (.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)))))
	61.7b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	62.7b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t)) (.f64 (*.f64 2 n) U))))
	38.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (.f64 n (.f64 t U)) (.f64 2 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om)))))
	38.1b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	60.9b	(.f64 (sqrt.f64 2) (.f64 n (sqrt.f64 (.f64 U (-.f64 (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) U) (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) U))))))

Compiler

Compiled 19389 to 10161 computations (47.6% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.6b	(*.f64 n (/.f64 l Om))
	8.6b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
	9.0b	(.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))
✓	21.2b	(pow.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 1/4)

series520.0ms (2.6%)

Counts

1 → 72

Calls

1 calls:

519.0ms

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

rewrite27.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

215×	`add-sqr-sqrt_binary64`
205×	`log1p-expm1-u_binary64`
205×	`expm1-log1p-u_binary64`
203×	`add-cbrt-cube_binary64`
201×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	36
1	433	36

Stop Event

1×	node limit

Counts

1 → 18

Calls

1 calls:

26.0ms

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

simplify139.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

682×	`*-commutative_binary64`
284×	`associate-r_binary64`
251×	`fma-def_binary64`
215×	`associate-/l*_binary64`
200×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1412	24192

Stop Event

1×	node limit

Counts

90 → 152

prune596.0ms (3%)

Pruning

29 alts after pruning (26 fresh and 3 done)

	Pruned	Kept	Total
New	239	9	248
Fresh	4	17	21
Picked	0	1	1
Done	0	2	2
Total	243	29	272

Error

6.2b

Counts

272 → 29

Alt Table

Status	Error	Program
	50.1b	(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 -2 (.f64 n U))) (log.f64 (/.f64 -1 t)))) 2)
✓	30.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	49.1b	(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 2 (.f64 n U))) (neg.f64 (log.f64 t)))) 2)
	60.6b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	41.9b	(.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 (.f64 n (.f64 U t))) (.f64 (/.f64 l (/.f64 Om l)) (sqrt.f64 (*.f64 (/.f64 n t) U)))))
	42.3b	(.f64 (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) t)) (sqrt.f64 (.f64 (*.f64 2 n) U)))
	60.9b	(pow.f64 (fma.f64 1/4 (.f64 t (pow.f64 (/.f64 n (/.f64 (pow.f64 (-.f64 (/.f64 n (/.f64 (.f64 Om Om) (.f64 (.f64 l l) U))) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 n (/.f64 (.f64 Om Om) (.f64 U (.f64 l l)))))) 3) (.f64 2 U))) 1/4)) (pow.f64 (.f64 2 (.f64 (.f64 n U) (-.f64 (/.f64 n (/.f64 (.f64 Om Om) (.f64 (.f64 l l) U))) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 n (/.f64 (.f64 Om Om) (.f64 U (*.f64 l l)))))))) 1/4)) 2)
	37.6b	(sqrt.f64 (.f64 2 (.f64 (*.f64 n t) U)))
	58.6b	(-.f64 (.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) -1/2) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U)))))) (.f64 (sqrt.f64 2) l)))
	59.9b	(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 2 (.f64 (.f64 n (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))) U))) (.f64 -2 (neg.f64 (log.f64 l))))) 2)
	41.8b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U U) (/.f64 l Om)) n)) t)))))
	56.6b	(.f64 (sqrt.f64 2) (.f64 l (neg.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 Om (/.f64 U* Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om)))))))))))
	32.3b	(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U* U) (/.f64 l Om)) n)) t))))) (cbrt.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U* U) (/.f64 l Om)) n)) t))))))
	57.3b	(.f64 (sqrt.f64 2) (.f64 l (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 Om (/.f64 U* Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om))))))))))
	59.0b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U)))))) (*.f64 (sqrt.f64 2) l)))
	55.2b	(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)
	38.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (.f64 n (.f64 t U)) (.f64 2 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om)))))
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
✓	30.4b	(pow.f64 (pow.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 1/4) 2)
	42.4b	(pow.f64 (.f64 (pow.f64 (.f64 2 (.f64 n U)) 1/4) (pow.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 n (/.f64 Om l)))) t) 1/4)) 2)
	47.3b	(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)
▶	30.6b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))
	32.0b	(pow.f64 (.f64 (pow.f64 2 1/4) (pow.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 n (/.f64 Om l)))) t))) 1/4)) 2)
	60.9b	(.f64 (sqrt.f64 2) (.f64 n (sqrt.f64 (.f64 U (-.f64 (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) U) (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) U))))))
	49.7b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t))))) 2)
	60.5b	(.f64 -1 (.f64 n (sqrt.f64 (.f64 -2 (.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)))))
	57.1b	(.f64 -1 (.f64 (sqrt.f64 (.f64 n (.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 l (sqrt.f64 2))))
	61.7b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	38.1b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))

Compiler

Compiled 37572 to 22088 computations (41.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	8.6b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
	9.0b	(.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))
✓	9.0b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 2))
✓	21.4b	(cbrt.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))

series1.8s (9%)

Counts

2 → 144

Calls

2 calls:

889.0ms

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

887.0ms

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

rewrite36.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

212×	`add-sqr-sqrt_binary64`
199×	`log1p-expm1-u_binary64`
199×	`expm1-log1p-u_binary64`
198×	`add-cbrt-cube_binary64`
196×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	70
1	443	70

Stop Event

1×	node limit

Counts

2 → 58

Calls

2 calls:

35.0ms

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

35.0ms

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

simplify292.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

493×	`associate-r_binary64`
290×	`fma-def_binary64`
253×	`associate-/l*_binary64`
227×	`associate-*r/_binary64`
218×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1695	50865

Stop Event

1×	node limit

Counts

202 → 166

prune1.4s (6.9%)

Pruning

29 alts after pruning (25 fresh and 4 done)

	Pruned	Kept	Total
New	485	0	485
Fresh	0	25	25
Picked	0	1	1
Done	0	3	3
Total	485	29	514

Error

6.2b

Counts

514 → 29

Alt Table

Status	Error	Program
	50.1b	(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 -2 (.f64 n U))) (log.f64 (/.f64 -1 t)))) 2)
✓	30.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	49.1b	(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 2 (.f64 n U))) (neg.f64 (log.f64 t)))) 2)
	60.6b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	41.9b	(.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 (.f64 n (.f64 U t))) (.f64 (/.f64 l (/.f64 Om l)) (sqrt.f64 (*.f64 (/.f64 n t) U)))))
	42.3b	(.f64 (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) t)) (sqrt.f64 (.f64 (*.f64 2 n) U)))
	60.9b	(pow.f64 (fma.f64 1/4 (.f64 t (pow.f64 (/.f64 n (/.f64 (pow.f64 (-.f64 (/.f64 n (/.f64 (.f64 Om Om) (.f64 (.f64 l l) U))) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 n (/.f64 (.f64 Om Om) (.f64 U (.f64 l l)))))) 3) (.f64 2 U))) 1/4)) (pow.f64 (.f64 2 (.f64 (.f64 n U) (-.f64 (/.f64 n (/.f64 (.f64 Om Om) (.f64 (.f64 l l) U))) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 n (/.f64 (.f64 Om Om) (.f64 U (*.f64 l l)))))))) 1/4)) 2)
	37.6b	(sqrt.f64 (.f64 2 (.f64 (*.f64 n t) U)))
	58.6b	(-.f64 (.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) -1/2) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U)))))) (.f64 (sqrt.f64 2) l)))
	59.9b	(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 2 (.f64 (.f64 n (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))) U))) (.f64 -2 (neg.f64 (log.f64 l))))) 2)
	41.8b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U U) (/.f64 l Om)) n)) t)))))
	56.6b	(.f64 (sqrt.f64 2) (.f64 l (neg.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 Om (/.f64 U* Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om)))))))))))
	32.3b	(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U* U) (/.f64 l Om)) n)) t))))) (cbrt.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U* U) (/.f64 l Om)) n)) t))))))
	57.3b	(.f64 (sqrt.f64 2) (.f64 l (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 Om (/.f64 U* Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om))))))))))
	59.0b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 n (/.f64 (.f64 Om Om) U)))))) (*.f64 (sqrt.f64 2) l)))
	55.2b	(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)
	38.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (.f64 n (.f64 t U)) (.f64 2 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om)))))
✓	30.2b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
✓	30.4b	(pow.f64 (pow.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 1/4) 2)
	42.4b	(pow.f64 (.f64 (pow.f64 (.f64 2 (.f64 n U)) 1/4) (pow.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 n (/.f64 Om l)))) t) 1/4)) 2)
	47.3b	(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)
✓	30.6b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))
	32.0b	(pow.f64 (.f64 (pow.f64 2 1/4) (pow.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 n (/.f64 Om l)))) t))) 1/4)) 2)
	60.9b	(.f64 (sqrt.f64 2) (.f64 n (sqrt.f64 (.f64 U (-.f64 (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) U) (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) U))))))
	49.7b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t))))) 2)
	60.5b	(.f64 -1 (.f64 n (sqrt.f64 (.f64 -2 (.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)))))
	57.1b	(.f64 -1 (.f64 (sqrt.f64 (.f64 n (.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 l (sqrt.f64 2))))
	61.7b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	38.1b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))

Compiler

Compiled 89048 to 48853 computations (45.1% saved)

regimes3.2s (16.3%)

Accuracy

Total 21.0b remaining (71.6%)

Threshold costs 0b (0%)

Counts

154 → 8

Compiler

Compiled 47130 to 30698 computations (34.9% saved)

bsearch662.0ms (3.4%)

Steps

Iters	Range		Point
10	5.567301452334803e+171	3.422588066441456e+183	1.0079913196216918e+181
5	-6.160762907369153e-266	-1.6097783187243604e-266	-4.5557220936498896e-266
7	-4.147707722749587e-113	-7.629977169521692e-115	-9.579590953786636e-114
6	-3.5531888468767614e-82	-2.6153871548663725e-83	-2.66377957353005e-83
9	-2.5527779983166847e+121	-2.204301060343935e+114	-4.362243388401799e+119
9	-1.2192746087189854e+160	-3.2907393441687557e+153	-5.438743501710158e+153
11	-7.046149514903014e+251	-8.337690454827196e+227	-2.0626575918686287e+228

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

57×	`*-commutative_binary64`
27×	`+-commutative_binary64`
24×	`sub-neg_binary64`
21×	`neg-sub0_binary64`
20×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	342
1	168	342
2	204	342
3	250	342
4	292	342
5	317	342
6	326	342
7	329	342
8	330	342

Stop Event

1×

saturated

end540.0ms (2.7%)

Compiler: Compiled 1542 to 966 computations (37.4% saved)

Iter	Nodes	Cost
0	114	342
1	168	342
2	204	342
3	250	342
4	292	342
5	317	342
6	326	342
7	329	342
8	330	342

Iter	Nodes	Cost
0	114	342
1	168	342
2	204	342
3	250	342
4	292	342
5	317	342
6	326	342
7	329	342
8	330	342

Details

analyze3.0s (15%)

sample4.5s (22.9%)

simplify24.0ms (0.1%)

prune4.0ms (0%)

localize16.0ms (0.1%)

series1.1s (5.5%)

rewrite45.0ms (0.2%)

simplify160.0ms (0.8%)

prune392.0ms (2%)

localize17.0ms (0.1%)

series756.0ms (3.8%)

rewrite64.0ms (0.3%)

simplify138.0ms (0.7%)

prune347.0ms (1.8%)

localize18.0ms (0.1%)

series520.0ms (2.6%)

rewrite27.0ms (0.1%)

simplify139.0ms (0.7%)

prune596.0ms (3%)

localize19.0ms (0.1%)

series1.8s (9%)

rewrite36.0ms (0.2%)

simplify292.0ms (1.5%)

prune1.4s (6.9%)

regimes3.2s (16.3%)

bsearch662.0ms (3.4%)

simplify17.0ms (0.1%)

end540.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	114	342
1	168	342
2	204	342
3	250	342
4	292	342
5	317	342
6	326	342
7	329	342
8	330	342