Details

analyze3.1s (18%)

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 (27.2%)

Results

2.9s	14754×	body	128	invalid
1.7s	8256×	body	128	valid

Compiler

Compiled 70 to 48 computations (31.4% saved)

preprocess41.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

661×	`distribute-rgt-in_binary64`
501×	`fma-def_binary64`
356×	`cancel-sign-sub-inv_binary64`
251×	`distribute-rgt-neg-in_binary64`
235×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	170	672
1	563	640
2	2197	640
0	6	6

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 34 to 23 computations (32.4% 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

29.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	35.6b	(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)))))
▶	29.8b	(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

35.6b

(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*)))))

▶

29.8b

(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)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.7b	(*.f64 n (/.f64 l Om))
✓	6.5b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	9.6b	(.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)))))))
✓	18.6b	(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 (6.2%)

Counts

4 → 216

Calls

60 calls:

164.0ms	(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))))))))	U	0
94.0ms	(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))))))))	n	0
83.0ms	(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))))))))	U	inf
47.0ms	(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))))))))	U*	-inf
45.0ms	(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))))))))	U*	inf

rewrite41.0ms (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

simplify181.0ms (1.1%)

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

prune445.0ms (2.6%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	188	24	212
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	190	24	214

Error

15.0b

Counts

214 → 24

Alt Table

Status	Error	Program
	61.8b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	45.6b	(sqrt.f64 (+.f64 (fma.f64 2 (+.f64 (/.f64 (.f64 n n) (/.f64 (.f64 Om Om) (.f64 (.f64 l l) (.f64 U U)))) (.f64 (.f64 n t) U)) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)) (.f64 -2 (/.f64 (.f64 n n) (/.f64 (.f64 Om Om) (.f64 (.f64 l l) (.f64 U U)))))))
	29.8b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (pow.f64 (cbrt.f64 (*.f64 n (/.f64 l Om))) 3)))))))
▶	29.8b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 (.f64 (.f64 2 n) U) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	38.7b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (-.f64 t (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) Om)) (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) U))))
	30.1b	(.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))))))
	34.5b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 (/.f64 (.f64 l l) (/.f64 Om U)) -4))))
	62.8b	(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))))
	34.3b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	29.9b	(.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))))
	63.4b	(-.f64 (.f64 2 (.f64 (/.f64 (.f64 l l) Om) (/.f64 U (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))) (fma.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (/.f64 (.f64 U t) (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))))))
	43.0b	(.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)))
	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)))))) (neg.f64 (.f64 (sqrt.f64 2) l)))
	42.7b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (log.f64 (pow.f64 (pow.f64 (exp.f64 n) (/.f64 l Om)) (-.f64 U* U))))))))
	63.1b	(fma.f64 n (.f64 (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)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U))))) (-.f64 (.f64 1/2 (.f64 (sqrt.f64 2) t)) (/.f64 (.f64 l l) (/.f64 Om (sqrt.f64 2))))))
	30.8b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om)))))))
	60.6b	(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)))
	59.2b	(.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))
	61.8b	(.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))))))
	30.4b	(pow.f64 (cbrt.f64 (sqrt.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))))) 3)
	38.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	60.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	39.1b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	39.8b	(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))) 3/2) 1/3)

Compiler

Compiled 19873 to 10869 computations (45.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.7b	(*.f64 n (/.f64 l Om))
	6.5b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	10.8b	(.f64 (.f64 (.f64 2 n) U) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))
✓	18.6b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 (.f64 (.f64 2 n) U) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))

series748.0ms (4.4%)

Counts

2 → 108

Calls

33 calls:

107.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 (.f64 (.f64 2 n) U) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))	U	0
70.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 (.f64 (.f64 2 n) U) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))	n	0
45.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 (.f64 (.f64 2 n) U) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))	U	inf
44.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 (.f64 (.f64 2 n) U) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))	U	-inf
33.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 (.f64 (.f64 2 n) U) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))	U*	-inf

rewrite33.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

215×	`add-sqr-sqrt_binary64`
201×	`log1p-expm1-u_binary64`
201×	`expm1-log1p-u_binary64`
200×	`add-cbrt-cube_binary64`
199×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	76
1	427	69

Stop Event

1×	node limit

Counts

2 → 40

simplify159.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

704×	`associate-/l*_binary64`
544×	`fma-def_binary64`
274×	`*-commutative_binary64`
138×	`cancel-sign-sub-inv_binary64`
121×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	663	15528
1	2464	14472

Stop Event

1×	node limit

Counts

148 → 151

prune440.0ms (2.6%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	187	13	200
Fresh	9	14	23
Picked	1	0	1
Done	0	0	0
Total	197	27	224

Error

10.9b

Counts

224 → 27

Alt Table

Status	Error	Program
	61.8b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	45.6b	(sqrt.f64 (+.f64 (fma.f64 2 (+.f64 (/.f64 (.f64 n n) (/.f64 (.f64 Om Om) (.f64 (.f64 l l) (.f64 U U)))) (.f64 (.f64 n t) U)) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)) (.f64 -2 (/.f64 (.f64 n n) (/.f64 (.f64 Om Om) (.f64 (.f64 l l) (.f64 U U)))))))
	59.1b	(.f64 (sqrt.f64 (+.f64 (.f64 2 (-.f64 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 U U)) (/.f64 n (/.f64 (/.f64 Om (/.f64 (.f64 U U) Om)) n)))) (.f64 -4 (*.f64 (/.f64 n Om) U)))) (neg.f64 l))
	29.8b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (pow.f64 (cbrt.f64 (*.f64 n (/.f64 l Om))) 3)))))))
	38.7b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (-.f64 t (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) Om)) (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) U))))
	30.1b	(.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))))))
	34.5b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 (/.f64 (.f64 l l) (/.f64 Om U)) -4))))
	60.6b	(.f64 l (sqrt.f64 (+.f64 (.f64 2 (-.f64 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 U U)) (/.f64 n (/.f64 (/.f64 Om (/.f64 (.f64 U U) Om)) n)))) (.f64 -4 (*.f64 (/.f64 n Om) U)))))
	63.4b	(-.f64 (.f64 2 (.f64 (/.f64 (.f64 l l) Om) (/.f64 U (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))) (fma.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (/.f64 (.f64 U t) (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))))))
	62.5b	(.f64 U (sqrt.f64 (.f64 (/.f64 n (/.f64 (/.f64 (.f64 Om Om) (.f64 l l)) n)) -2)))
	60.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	33.5b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 -2 (/.f64 (.f64 (+.f64 (.f64 2 l) (/.f64 (.f64 n (.f64 l U)) Om)) (.f64 n (*.f64 l U))) Om))))
	43.0b	(.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)))
	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)))))) (neg.f64 (.f64 (sqrt.f64 2) l)))
	35.1b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (/.f64 (.f64 (.f64 l (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))) (.f64 (*.f64 2 n) U)) Om)))
	38.6b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 U (/.f64 Om (+.f64 (.f64 (/.f64 n (/.f64 Om n)) (.f64 (.f64 l l) U)) (.f64 (.f64 (.f64 l l) n) -2)))))))
	42.7b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (log.f64 (pow.f64 (pow.f64 (exp.f64 n) (/.f64 l Om)) (-.f64 U* U))))))))
	40.2b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 (.f64 (-.f64 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) U)) Om) (.f64 2 (*.f64 n (pow.f64 l 2)))) U) Om))))
	62.4b	(fma.f64 (sqrt.f64 (/.f64 1 (.f64 2 (-.f64 (/.f64 (.f64 U U) (/.f64 (.f64 Om Om) (.f64 l l))) (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) (.f64 U U)))))) (.f64 U t) (fma.f64 (sqrt.f64 (.f64 2 (-.f64 (/.f64 (.f64 U U) (/.f64 (.f64 Om Om) (.f64 l l))) (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) (.f64 U U))))) n (.f64 (.f64 (sqrt.f64 (/.f64 1 (.f64 2 (-.f64 (/.f64 (.f64 U U) (/.f64 (.f64 Om Om) (.f64 l l))) (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) (.f64 U U)))))) (*.f64 (/.f64 l (/.f64 Om l)) U)) -2)))
	39.1b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	61.3b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 (.f64 l l) (.f64 n n)) (-.f64 (.f64 U U) (.f64 U U))))) Om)
	60.3b	(sqrt.f64 (-.f64 (.f64 2 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 (.f64 l l) (.f64 U U)))) (fma.f64 2 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 (.f64 l l) (.f64 U U))) (.f64 4 (/.f64 (.f64 (*.f64 l l) n) (/.f64 Om U))))))
▶	27.9b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) 1)))
	30.8b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om)))))))
	59.2b	(.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))
	29.9b	(pow.f64 (pow.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))))))) 1/4) 2)
	60.3b	(neg.f64 (fma.f64 (.f64 (/.f64 n l) (.f64 U t)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (-.f64 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 U U)) (/.f64 n (/.f64 (/.f64 Om (/.f64 (.f64 U U) Om)) n)))) (.f64 -4 (.f64 (/.f64 n Om) U))))) (.f64 l (sqrt.f64 (+.f64 (.f64 2 (-.f64 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 U U)) (/.f64 n (/.f64 (/.f64 Om (/.f64 (.f64 U U) Om)) n)))) (.f64 -4 (*.f64 (/.f64 n Om) U)))))))

Compiler

Compiled 21432 to 11714 computations (45.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.7b	(*.f64 n (/.f64 l Om))
	6.5b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	11.0b	(.f64 (.f64 (*.f64 2 n) U) (/.f64 l Om))
✓	18.6b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) 1)))

series596.0ms (3.5%)

Counts

2 → 96

Calls

30 calls:

109.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) 1)))	U	0
69.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) 1)))	n	0
45.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) 1)))	U	-inf
43.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) 1)))	U	inf
37.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) 1)))	U*	inf

rewrite32.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

218×	`add-sqr-sqrt_binary64`
207×	`log1p-expm1-u_binary64`
207×	`expm1-log1p-u_binary64`
203×	`add-cbrt-cube_binary64`
201×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	57
1	453	50

Stop Event

1×	node limit

Counts

2 → 43

simplify136.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

652×	`associate-/l*_binary64`
565×	`associate-/r*_binary64`
536×	`fma-def_binary64`
243×	`*-commutative_binary64`
126×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	605	12907
1	2279	11803

Stop Event

1×	node limit

Counts

139 → 131

prune405.0ms (2.4%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	174	6	180
Fresh	7	19	26
Picked	1	0	1
Done	0	0	0
Total	182	25	207

Error

10.9b

Counts

207 → 25

Alt Table

Status	Error	Program
	61.8b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	45.6b	(sqrt.f64 (+.f64 (fma.f64 2 (+.f64 (/.f64 (.f64 n n) (/.f64 (.f64 Om Om) (.f64 (.f64 l l) (.f64 U U)))) (.f64 (.f64 n t) U)) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)) (.f64 -2 (/.f64 (.f64 n n) (/.f64 (.f64 Om Om) (.f64 (.f64 l l) (.f64 U U)))))))
	59.1b	(.f64 (sqrt.f64 (+.f64 (.f64 2 (-.f64 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 U U)) (/.f64 n (/.f64 (/.f64 Om (/.f64 (.f64 U U) Om)) n)))) (.f64 -4 (*.f64 (/.f64 n Om) U)))) (neg.f64 l))
	38.7b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (-.f64 t (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) Om)) (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) U))))
	62.2b	(fma.f64 (sqrt.f64 (/.f64 1/2 (-.f64 (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U)) (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U))))) (.f64 U t) (fma.f64 (sqrt.f64 (.f64 2 (-.f64 (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U)) (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U))))) n (.f64 (.f64 (sqrt.f64 (/.f64 1/2 (-.f64 (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U)) (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U))))) (/.f64 (.f64 l l) (/.f64 Om U))) -2)))
	30.1b	(.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 (.f64 2 (-.f64 (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U)) (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (*.f64 U U))))) n)
	34.5b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 (/.f64 (.f64 l l) (/.f64 Om U)) -4))))
	60.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	33.5b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 -2 (/.f64 (.f64 (+.f64 (.f64 2 l) (/.f64 (.f64 n (.f64 l U)) Om)) (.f64 n (*.f64 l U))) Om))))
	43.0b	(.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)))
	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)))))) (neg.f64 (.f64 (sqrt.f64 2) l)))
	42.7b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (log.f64 (pow.f64 (pow.f64 (exp.f64 n) (/.f64 l Om)) (-.f64 U* U))))))))
▶	27.9b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (pow.f64 (cbrt.f64 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) 3))) 1)))
	31.6b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 2 (.f64 (/.f64 n Om) (.f64 l U))) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) 1)))
	40.2b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 (.f64 (-.f64 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) U)) Om) (.f64 2 (*.f64 n (pow.f64 l 2)))) U) Om))))
	33.7b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 n) (.f64 U (/.f64 l Om))) 3)) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) 1)))
	39.1b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	61.3b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 (.f64 l l) (.f64 n n)) (-.f64 (.f64 U U) (.f64 U U))))) Om)
	60.3b	(sqrt.f64 (-.f64 (.f64 2 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 (.f64 l l) (.f64 U U)))) (fma.f64 2 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 (.f64 l l) (.f64 U U))) (.f64 4 (/.f64 (.f64 (*.f64 l l) n) (/.f64 Om U))))))
	63.4b	(-.f64 (.f64 2 (.f64 (/.f64 (.f64 l l) Om) (/.f64 U (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))) (fma.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (/.f64 (.f64 U t) (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))))))
	59.2b	(.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))
	60.6b	(.f64 l (sqrt.f64 (+.f64 (.f64 2 (-.f64 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 U U)) (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 U U)))) (.f64 -4 (/.f64 n (/.f64 Om U))))))
	29.9b	(pow.f64 (pow.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))))))) 1/4) 2)
	60.3b	(neg.f64 (fma.f64 (.f64 (/.f64 n l) (.f64 U t)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (-.f64 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 U U)) (/.f64 n (/.f64 (/.f64 Om (/.f64 (.f64 U U) Om)) n)))) (.f64 -4 (.f64 (/.f64 n Om) U))))) (.f64 l (sqrt.f64 (+.f64 (.f64 2 (-.f64 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 U U)) (/.f64 n (/.f64 (/.f64 Om (/.f64 (.f64 U U) Om)) n)))) (.f64 -4 (*.f64 (/.f64 n Om) U)))))))

Compiler

Compiled 20768 to 11381 computations (45.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	6.5b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
	11.0b	(.f64 (.f64 (*.f64 2 n) U) (/.f64 l Om))
✓	13.9b	(cbrt.f64 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))
✓	18.6b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (pow.f64 (cbrt.f64 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) 3))) 1)))

series538.0ms (3.1%)

Counts

2 → 34

Calls

33 calls:

120.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (pow.f64 (cbrt.f64 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) 3))) 1)))	U	0
67.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (pow.f64 (cbrt.f64 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) 3))) 1)))	U*	0
31.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (pow.f64 (cbrt.f64 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) 3))) 1)))	t	inf
30.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (pow.f64 (cbrt.f64 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) 3))) 1)))	t	-inf
28.0ms	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (pow.f64 (cbrt.f64 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) 3))) 1)))	n	-inf

rewrite30.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

234×	`add-sqr-sqrt_binary64`
226×	`log1p-expm1-u_binary64`
226×	`expm1-log1p-u_binary64`
220×	`add-cbrt-cube_binary64`
217×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	59
1	514	59

Stop Event

1×	node limit

Counts

2 → 46

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
439×	`unswap-sqr_binary64`
322×	`associate-r_binary64`
238×	`associate-l_binary64`
184×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	3753
1	846	3715
2	3313	3703

Stop Event

1×	node limit

Counts

80 → 96

prune248.0ms (1.5%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	5	19	24
Picked	0	1	1
Done	0	0	0
Total	153	23	176

Error

10.4b

Counts

176 → 23

Alt Table

Status	Error	Program
	45.6b	(sqrt.f64 (+.f64 (fma.f64 2 (+.f64 (/.f64 (.f64 n n) (/.f64 (.f64 Om Om) (.f64 (.f64 l l) (.f64 U U)))) (.f64 (.f64 n t) U)) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)) (.f64 -2 (/.f64 (.f64 n n) (/.f64 (.f64 Om Om) (.f64 (.f64 l l) (.f64 U U)))))))
	58.4b	(neg.f64 (fma.f64 l (sqrt.f64 (.f64 (.f64 (/.f64 n Om) U) -4)) (.f64 (/.f64 n (sqrt.f64 (.f64 (*.f64 (/.f64 n Om) U) -4))) (/.f64 U (/.f64 l t)))))
	38.7b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (-.f64 t (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) Om)) (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) U))))
	62.2b	(fma.f64 (sqrt.f64 (/.f64 1/2 (-.f64 (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U)) (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U))))) (.f64 U t) (fma.f64 (sqrt.f64 (.f64 2 (-.f64 (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U)) (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U))))) n (.f64 (.f64 (sqrt.f64 (/.f64 1/2 (-.f64 (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U)) (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U))))) (/.f64 (.f64 l l) (/.f64 Om U))) -2)))
	57.2b	(.f64 (sqrt.f64 (.f64 (*.f64 (/.f64 n Om) U) -4)) (neg.f64 l))
	30.1b	(.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 (.f64 2 (-.f64 (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (.f64 U U)) (.f64 (/.f64 l (/.f64 (.f64 Om Om) l)) (*.f64 U U))))) n)
	34.5b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 (/.f64 (.f64 l l) (/.f64 Om U)) -4))))
	60.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	33.5b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 -2 (/.f64 (.f64 (+.f64 (.f64 2 l) (/.f64 (.f64 n (.f64 l U)) Om)) (.f64 n (*.f64 l U))) Om))))
✓	27.9b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (pow.f64 (cbrt.f64 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) 3))) 1)))
	31.6b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (.f64 2 (.f64 (/.f64 n Om) (.f64 l U))) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) 1)))
	40.2b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 (.f64 (-.f64 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) U)) Om) (.f64 2 (*.f64 n (pow.f64 l 2)))) U) Om))))
	33.7b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (pow.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 n) (.f64 U (/.f64 l Om))) 3)) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) 1)))
	39.1b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	61.3b	(/.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 (.f64 l l) (.f64 n n)) (-.f64 (.f64 U U) (.f64 U U))))) Om)
	58.9b	(.f64 l (sqrt.f64 (.f64 (*.f64 (/.f64 n Om) U) -4)))
	60.3b	(sqrt.f64 (-.f64 (.f64 2 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 (.f64 l l) (.f64 U U)))) (fma.f64 2 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 (.f64 l l) (.f64 U U))) (.f64 4 (/.f64 (.f64 (*.f64 l l) n) (/.f64 Om U))))))
	63.4b	(-.f64 (.f64 2 (.f64 (/.f64 (.f64 l l) Om) (/.f64 U (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))) (fma.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (/.f64 (.f64 U t) (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 l l) (/.f64 (.f64 Om Om) U)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))))))
	43.0b	(.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)))
	59.2b	(.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))
	29.9b	(pow.f64 (pow.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))))))) 1/4) 2)
	60.3b	(neg.f64 (fma.f64 (.f64 (/.f64 n l) (.f64 U t)) (sqrt.f64 (/.f64 1 (+.f64 (.f64 2 (-.f64 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 U U)) (/.f64 n (/.f64 (/.f64 Om (/.f64 (.f64 U U) Om)) n)))) (.f64 -4 (.f64 (/.f64 n Om) U))))) (.f64 l (sqrt.f64 (+.f64 (.f64 2 (-.f64 (.f64 (/.f64 n (/.f64 (.f64 Om Om) n)) (.f64 U U)) (/.f64 n (/.f64 (/.f64 Om (/.f64 (.f64 U U) Om)) n)))) (.f64 -4 (*.f64 (/.f64 n Om) U)))))))

Compiler

Compiled 9376 to 5017 computations (46.5% saved)

regimes3.6s (21.1%)

Accuracy

Total 13.1b remaining (52.4%)

Threshold costs 0b (0%)

Counts

200 → 3

Compiler

Compiled 60594 to 38234 computations (36.9% saved)

bsearch13.0ms (0.1%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms

(*.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*))))

0.0ms

(*.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*))))

Steps

Iters	Point		Range
#hash((type . real) (value . +inf))	∈ [	#hash((type . real) (value . +inf))	,	#hash((type . real) (value . NaN))	]
0.0	∈ [	0.0	,	1.8638726419268474e-292	]

Compiler

Compiled 33 to 22 computations (33.3% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

37×	`*-commutative_binary64`
19×	`+-commutative_binary64`
18×	`sub-neg_binary64`
16×	`neg-sub0_binary64`
16×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	205
1	95	205
2	126	205
3	149	205
4	179	205
5	201	205
6	211	205
7	221	205
8	227	205
9	230	205
10	231	205

Stop Event

1×

saturated

end420.0ms (2.5%)

Stop Event

1×

fuel

Compiler

Compiled 1258 to 692 computations (45% saved)

Iter	Nodes	Cost
0	58	205
1	95	205
2	126	205
3	149	205
4	179	205
5	201	205
6	211	205
7	221	205
8	227	205
9	230	205
10	231	205

Iter	Nodes	Cost
0	58	205
1	95	205
2	126	205
3	149	205
4	179	205
5	201	205
6	211	205
7	221	205
8	227	205
9	230	205
10	231	205

Details

analyze3.1s (18%)

sample4.6s (27.2%)

preprocess41.0ms (0.2%)

simplify24.0ms (0.1%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series1.1s (6.2%)

rewrite41.0ms (0.2%)

simplify181.0ms (1.1%)

prune445.0ms (2.6%)

localize17.0ms (0.1%)

series748.0ms (4.4%)

rewrite33.0ms (0.2%)

simplify159.0ms (0.9%)

prune440.0ms (2.6%)

localize20.0ms (0.1%)

series596.0ms (3.5%)

rewrite32.0ms (0.2%)

simplify136.0ms (0.8%)

prune405.0ms (2.4%)

localize19.0ms (0.1%)

series538.0ms (3.1%)

rewrite30.0ms (0.2%)

simplify71.0ms (0.4%)

prune248.0ms (1.5%)

regimes3.6s (21.1%)

bsearch13.0ms (0.1%)

simplify11.0ms (0.1%)

end420.0ms (2.5%)

Profiling

Iter	Nodes	Cost
0	58	205
1	95	205
2	126	205
3	149	205
4	179	205
5	201	205
6	211	205
7	221	205
8	227	205
9	230	205
10	231	205