Details

analyze3.0s (17.2%)

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 (26.2%)

Results

2.7s	13908×	body	128	invalid
1.8s	8256×	body	128	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify28.0ms (0.2%)

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

29.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	29.9b	(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))))))))
	33.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))

Status

Error

Program

▶

29.9b

(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))))))))

33.3b

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

Compiler

Compiled 189 to 119 computations (37% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.6b	(*.f64 n (/.f64 l Om))
✓	6.0b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	10.0b	(.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)))))))
✓	18.8b	(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))))))))

series1.1s (6.4%)

Counts

4 → 216

Calls

4 calls:

777.0ms	(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))))))))
294.0ms	(.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)))))))
34.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
13.0ms	(*.f64 n (/.f64 l Om))

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

Calls

4 calls:

39.0ms	(*.f64 n (/.f64 l Om))
39.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
39.0ms	(.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)))))))
39.0ms	(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))))))))

simplify163.0ms (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`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	876	17039
1	3327	16151

Stop Event

1×	node limit

Counts

301 → 212

prune424.0ms (2.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	192	20	212
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	194	20	214

Error

15.1b

Counts

214 → 20

Alt Table

Status	Error	Program
▶	29.9b	(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))) 1/2)
	37.1b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	37.7b	(cbrt.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))
	30.1b	(.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))))
	43.1b	(-.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)))
	41.3b	(.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)))
	56.0b	(.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)))
	32.1b	(exp.f64 (log.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))))))
	56.3b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) Om)) (/.f64 (.f64 n (*.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) U))))
	60.0b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	56.4b	(+.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))))
	62.4b	(-.f64 (.f64 2 (/.f64 (.f64 (pow.f64 l 2) U) (.f64 Om (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)))))) (+.f64 (.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)))) (/.f64 (.f64 t U) (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))))))
	40.6b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	43.5b	(-.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)))))
	59.9b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (.f64 n (.f64 (pow.f64 l 2) U))) U))) (/.f64 (sqrt.f64 2) Om))
	57.3b	(-.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)))
	56.5b	(neg.f64 (+.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)))))
	55.1b	(.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))
	37.0b	(sqrt.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om))))
	30.1b	(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)

Compiler

Compiled 19651 to 10881 computations (44.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.6b	(*.f64 n (/.f64 l Om))
	6.0b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	10.2b	(.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))
✓	18.8b	(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))) 1/2)

series739.0ms (4.2%)

Counts

2 → 144

Calls

2 calls:

536.0ms

(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))) 1/2)

202.0ms

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

rewrite38.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

213×	`add-sqr-sqrt_binary64`
202×	`log1p-expm1-u_binary64`
202×	`expm1-log1p-u_binary64`
198×	`add-cbrt-cube_binary64`
197×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	65
1	431	65

Stop Event

1×	node limit

Counts

2 → 38

Calls

2 calls:

36.0ms

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

36.0ms

(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))) 1/2)

simplify167.0ms (1%)

Algorithm

1×	egg-herbie

Rules

721×	`*-commutative_binary64`
310×	`associate-r_binary64`
238×	`associate-/l*_binary64`
230×	`fma-def_binary64`
200×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1478	28217

Stop Event

1×	node limit

Counts

182 → 199

prune631.0ms (3.6%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	236	12	248
Fresh	6	13	19
Picked	0	1	1
Done	0	0	0
Total	242	26	268

Error

9.2b

Counts

268 → 26

Alt Table

Status	Error	Program
	53.0b	(exp.f64 (.f64 1/2 (+.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))))
✓	29.9b	(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))) 1/2)
	41.4b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))) t)))
	37.1b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	49.3b	(pow.f64 (exp.f64 1/2) (+.f64 (log.f64 n) (log.f64 (+.f64 (.f64 (.f64 2 t) U) (.f64 -4 (/.f64 (.f64 l l) (/.f64 Om U)))))))
	40.6b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	37.7b	(cbrt.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))
	43.1b	(-.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)))
	41.3b	(.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)))
	45.7b	(pow.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 U U)) (.f64 Om Om)) (-.f64 (.f64 n (.f64 t U)) (fma.f64 2 (/.f64 n (/.f64 Om (.f64 U (.f64 l l)))) (/.f64 (.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 U U)) (.f64 Om Om)))))) 1/2)
	56.0b	(.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)))
	60.9b	(pow.f64 (.f64 2 (log.f64 (pow.f64 (exp.f64 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))) t))))) 1/2)
	52.6b	(pow.f64 (exp.f64 1/2) (-.f64 (log.f64 (.f64 (.f64 -2 n) U)) (log.f64 (/.f64 -1 t))))
	56.3b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) Om)) (/.f64 (.f64 n (*.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) U))))
	30.4b	(pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))) t)))) 2)) 1/2)
	52.5b	(exp.f64 (.f64 1/2 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t)))))
	62.4b	(-.f64 (.f64 2 (/.f64 (.f64 (pow.f64 l 2) U) (.f64 Om (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)))))) (+.f64 (.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)))) (/.f64 (.f64 t U) (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))))))
	57.5b	(pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 (.f64 Om Om) U))))))) (*.f64 -2 (log.f64 (/.f64 -1 l)))))
	30.6b	(pow.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))) t)))) 3)) 1/2)
	55.1b	(.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))
	57.6b	(pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 (.f64 Om Om) U))))))) (*.f64 -2 (neg.f64 (log.f64 l)))))
	37.0b	(sqrt.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om))))
	49.2b	(exp.f64 (.f64 1/2 (+.f64 (log.f64 n) (log.f64 (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))))
	43.5b	(-.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)))))
	59.9b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (.f64 n (.f64 (pow.f64 l 2) U))) U))) (/.f64 (sqrt.f64 2) Om))
▶	30.1b	(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)

Compiler

Compiled 36551 to 21322 computations (41.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.6b	(*.f64 n (/.f64 l Om))
	6.0b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
	10.2b	(.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))
✓	20.8b	(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)

series551.0ms (3.2%)

Counts

1 → 72

Calls

1 calls:

550.0ms

(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)

rewrite24.0ms (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:

23.0ms

(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)

simplify145.0ms (0.8%)

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

prune702.0ms (4%)

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	237	9	246
Fresh	0	24	24
Picked	1	0	1
Done	0	1	1
Total	238	34	272

Error

8.8b

Counts

272 → 34

Alt Table

Status	Error	Program
	53.0b	(exp.f64 (.f64 1/2 (+.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))))
✓	29.9b	(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))) 1/2)
	49.6b	(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (+.f64 (.f64 (.f64 2 t) U) (.f64 -4 (/.f64 (.f64 l l) (/.f64 Om U))))))) 2)
	41.4b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))) t)))
	37.1b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	49.3b	(pow.f64 (exp.f64 1/2) (+.f64 (log.f64 n) (log.f64 (+.f64 (.f64 (.f64 2 t) U) (.f64 -4 (/.f64 (.f64 l l) (/.f64 Om U)))))))
	40.6b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	49.2b	(exp.f64 (.f64 1/2 (+.f64 (log.f64 n) (log.f64 (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))))
	41.5b	(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)
▶	30.1b	(pow.f64 (.f64 1 (pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l)))) t)) 1/4)) 2)
	43.5b	(-.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)))))
	37.7b	(cbrt.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))
	43.1b	(-.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)))
	52.9b	(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 -2 (.f64 n U))) (log.f64 (/.f64 -1 t)))) 2)
	59.9b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (.f64 n (.f64 (pow.f64 l 2) U))) U))) (/.f64 (sqrt.f64 2) Om))
	41.3b	(.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)))
	45.7b	(pow.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 U U)) (.f64 Om Om)) (-.f64 (.f64 n (.f64 t U)) (fma.f64 2 (/.f64 n (/.f64 Om (.f64 U (.f64 l l)))) (/.f64 (.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 U U)) (.f64 Om Om)))))) 1/2)
	56.0b	(.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)))
	57.8b	(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 (log.f64 (/.f64 -1 l))))) 2)
	60.9b	(pow.f64 (.f64 2 (log.f64 (pow.f64 (exp.f64 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))) t))))) 1/2)
	52.6b	(pow.f64 (exp.f64 1/2) (-.f64 (log.f64 (.f64 (.f64 -2 n) U)) (log.f64 (/.f64 -1 t))))
	56.3b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) Om)) (/.f64 (.f64 n (*.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) U))))
	30.4b	(pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))) t)))) 2)) 1/2)
	52.5b	(exp.f64 (.f64 1/2 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t)))))
	62.4b	(-.f64 (.f64 2 (/.f64 (.f64 (pow.f64 l 2) U) (.f64 Om (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)))))) (+.f64 (.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)))) (/.f64 (.f64 t U) (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))))))
	57.5b	(pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 (.f64 Om Om) U))))))) (*.f64 -2 (log.f64 (/.f64 -1 l)))))
	30.6b	(pow.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))) t)))) 3)) 1/2)
	55.1b	(.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))
	57.6b	(pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 (.f64 Om Om) U))))))) (*.f64 -2 (neg.f64 (log.f64 l)))))
	53.2b	(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (+.f64 (.f64 2 (+.f64 (.f64 n t) (/.f64 (.f64 n n) (/.f64 (.f64 Om Om) (.f64 (.f64 l l) U))))) (.f64 -4 (/.f64 n (/.f64 Om (*.f64 l l)))))) (log.f64 U))) 2)
	37.0b	(sqrt.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om))))
	52.5b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t))))) 2)
	49.3b	(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 2 (.f64 n U))) (neg.f64 (log.f64 t)))) 2)
	53.0b	(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)

Compiler

Compiled 37807 to 22362 computations (40.9% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.0b	(/.f64 n (/.f64 Om l))
✓	6.0b	(.f64 (-.f64 U U) (/.f64 n (/.f64 Om l)))
✓	10.0b	(.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 n (/.f64 Om l)))) t))
✓	20.8b	(pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 n (/.f64 Om l)))) t)) 1/4)

series845.0ms (4.8%)

Counts

4 → 240

Calls

4 calls:

538.0ms	(pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 n (/.f64 Om l)))) t)) 1/4)
262.0ms	(.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 n (/.f64 Om l)))) t))
32.0ms	(.f64 (-.f64 U U) (/.f64 n (/.f64 Om l)))
11.0ms	(/.f64 n (/.f64 Om l))

rewrite38.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

228×	`add-sqr-sqrt_binary64`
217×	`log1p-expm1-u_binary64`
217×	`expm1-log1p-u_binary64`
215×	`add-cbrt-cube_binary64`
213×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	89
1	460	89

Stop Event

1×	node limit

Counts

4 → 93

Calls

4 calls:

36.0ms	(/.f64 n (/.f64 Om l))
36.0ms	(.f64 (-.f64 U U) (/.f64 n (/.f64 Om l)))
36.0ms	(.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 n (/.f64 Om l)))) t))
36.0ms	(pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 n (/.f64 Om l)))) t)) 1/4)

simplify176.0ms (1%)

Algorithm

1×	egg-herbie

Rules

717×	`*-commutative_binary64`
302×	`associate-r_binary64`
254×	`fma-def_binary64`
227×	`associate-/l*_binary64`
208×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1477	29792

Stop Event

1×	node limit

Counts

333 → 271

prune671.0ms (3.8%)

Pruning

34 alts after pruning (32 fresh and 2 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	32	32
Picked	0	1	1
Done	0	1	1
Total	271	34	305

Error

8.8b

Counts

305 → 34

Alt Table

Status	Error	Program
	53.0b	(exp.f64 (.f64 1/2 (+.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))))
✓	29.9b	(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))) 1/2)
	49.6b	(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 n) (log.f64 (+.f64 (.f64 (.f64 2 t) U) (.f64 -4 (/.f64 (.f64 l l) (/.f64 Om U))))))) 2)
	41.4b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))) t)))
	37.1b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	49.3b	(pow.f64 (exp.f64 1/2) (+.f64 (log.f64 n) (log.f64 (+.f64 (.f64 (.f64 2 t) U) (.f64 -4 (/.f64 (.f64 l l) (/.f64 Om U)))))))
	40.6b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	49.2b	(exp.f64 (.f64 1/2 (+.f64 (log.f64 n) (log.f64 (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))))
	41.5b	(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)
✓	30.1b	(pow.f64 (.f64 1 (pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l)))) t)) 1/4)) 2)
	43.5b	(-.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)))))
	37.7b	(cbrt.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))
	43.1b	(-.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)))
	52.9b	(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 -2 (.f64 n U))) (log.f64 (/.f64 -1 t)))) 2)
	59.9b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (.f64 n (.f64 (pow.f64 l 2) U))) U))) (/.f64 (sqrt.f64 2) Om))
	41.3b	(.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)))
	45.7b	(pow.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 U U)) (.f64 Om Om)) (-.f64 (.f64 n (.f64 t U)) (fma.f64 2 (/.f64 n (/.f64 Om (.f64 U (.f64 l l)))) (/.f64 (.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 U U)) (.f64 Om Om)))))) 1/2)
	56.0b	(.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)))
	57.8b	(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 (log.f64 (/.f64 -1 l))))) 2)
	60.9b	(pow.f64 (.f64 2 (log.f64 (pow.f64 (exp.f64 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))) t))))) 1/2)
	52.6b	(pow.f64 (exp.f64 1/2) (-.f64 (log.f64 (.f64 (.f64 -2 n) U)) (log.f64 (/.f64 -1 t))))
	56.3b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) Om)) (/.f64 (.f64 n (*.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) U))))
	30.4b	(pow.f64 (.f64 2 (pow.f64 (sqrt.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))) t)))) 2)) 1/2)
	52.5b	(exp.f64 (.f64 1/2 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t)))))
	62.4b	(-.f64 (.f64 2 (/.f64 (.f64 (pow.f64 l 2) U) (.f64 Om (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)))))) (+.f64 (.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)))) (/.f64 (.f64 t U) (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))))))
	57.5b	(pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 (.f64 Om Om) U))))))) (*.f64 -2 (log.f64 (/.f64 -1 l)))))
	30.6b	(pow.f64 (.f64 2 (pow.f64 (cbrt.f64 (.f64 n (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))) t)))) 3)) 1/2)
	55.1b	(.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))
	57.6b	(pow.f64 (exp.f64 1/2) (+.f64 (log.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 (.f64 Om Om) U))))))) (*.f64 -2 (neg.f64 (log.f64 l)))))
	53.2b	(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (+.f64 (.f64 2 (+.f64 (.f64 n t) (/.f64 (.f64 n n) (/.f64 (.f64 Om Om) (.f64 (.f64 l l) U))))) (.f64 -4 (/.f64 n (/.f64 Om (*.f64 l l)))))) (log.f64 U))) 2)
	37.0b	(sqrt.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om))))
	52.5b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t))))) 2)
	49.3b	(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 2 (.f64 n U))) (neg.f64 (log.f64 t)))) 2)
	53.0b	(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)

Compiler

Compiled 38072 to 22549 computations (40.8% saved)

regimes2.4s (13.5%)

Accuracy

Total 17.8b remaining (64.2%)

Threshold costs 0b (0%)

Counts

144 → 4

Compiler

Compiled 40634 to 27026 computations (33.5% saved)

bsearch340.0ms (1.9%)

Steps

Iters

Range

Point

1.7363098139445133e+126

6.785974751867613e+152

4.945578818309335e+151

2.015393873185818e-97

1.8740493083892768e-88

7.567777079365257e-90

-3.580989415709717e+148

-3.9127317395662955e+139

-1.9298476437970918e+146

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
12×	`+-commutative_binary64`
12×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	186
1	88	186
2	115	186
3	132	186
4	142	186
5	144	186

Stop Event

1×

saturated

end581.0ms (3.3%)

Compiler: Compiled 1437 to 968 computations (32.6% saved)

Details

analyze3.0s (17.2%)

sample4.6s (26.2%)

simplify28.0ms (0.2%)

prune4.0ms (0%)

localize24.0ms (0.1%)

series1.1s (6.4%)

rewrite41.0ms (0.2%)

simplify163.0ms (0.9%)

prune424.0ms (2.4%)

localize16.0ms (0.1%)

series739.0ms (4.2%)

rewrite38.0ms (0.2%)

simplify167.0ms (1%)

prune631.0ms (3.6%)

localize18.0ms (0.1%)

series551.0ms (3.2%)

rewrite24.0ms (0.1%)

simplify145.0ms (0.8%)

prune702.0ms (4%)

localize21.0ms (0.1%)

series845.0ms (4.8%)

rewrite38.0ms (0.2%)

simplify176.0ms (1%)

prune671.0ms (3.8%)

regimes2.4s (13.5%)

bsearch340.0ms (1.9%)

simplify6.0ms (0%)

end581.0ms (3.3%)

Profiling