Details

analyze2.8s (12.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample4.5s (19.3%)

Results

2.7s	14301×	body	128	invalid
1.7s	8256×	body	128	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify47.0ms (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

prune9.0ms (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

33.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	36.7b	(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)))))
▶	33.5b	(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))))))))

Status

Error

Program

36.7b

(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*)))))

▶

33.5b

(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))))))))

Compiler

Compiled 189 to 119 computations (37% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.6b	(*.f64 n (/.f64 l Om))
✓	6.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	11.0b	(.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)))))))
✓	21.2b	(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))))))))

series2.0s (8.7%)

Counts

4 → 216

Calls

4 calls:

1.5s	(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))))))))
426.0ms	(.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)))))))
36.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
14.0ms	(*.f64 n (/.f64 l Om))

rewrite73.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

84× egg-rr

Counts

4 → 84

Calls

2 calls:

71.0ms

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

0.0ms

()

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

simplify205.0ms (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

300 → 211

Iterations

Useful iterations: 1 (0.0ms)

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

prune409.0ms (1.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	196	15	211
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	197	16	213

Error

13.1b

Counts

213 → 16

Alt Table

Status	Error	Program
	38.3b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	60.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	62.5b	(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))))
	56.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	42.9b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (log.f64 (pow.f64 (exp.f64 n) (/.f64 l Om)))))))))
	57.9b	(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)))))))))
	57.9b	(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)))
✓	33.5b	(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))))))))
▶	33.7b	(pow.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)) 1/4) 2)
	48.1b	(.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)))
	41.7b	(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))))
	61.4b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	62.1b	(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))))
	44.3b	(.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))))
	41.4b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))

Compiler

Compiled 19111 to 10538 computations (44.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.6b	(*.f64 n (/.f64 l Om))
	6.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	11.0b	(.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))
✓	22.1b	(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)) 1/4)

series1.3s (5.6%)

Counts

2 → 144

Calls

2 calls:

914.0ms

(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)) 1/4)

382.0ms

(*.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))

rewrite67.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

35× egg-rr

Counts

2 → 35

Calls

2 calls:

66.0ms

((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)) 1/4) (*.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)))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	69
1	433	69
2	4860	69
3	5263	69
0	0	0
1	0	0

simplify258.0ms (1.1%)

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

179 → 195

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1449	28752
1	5113	28752

prune620.0ms (2.7%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	230	13	243
Fresh	3	11	14
Picked	1	0	1
Done	0	1	1
Total	234	25	259

Error

10.9b

Counts

259 → 25

Alt Table

Status	Error	Program
▶	38.3b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	44.4b	(pow.f64 (.f64 (pow.f64 (.f64 2 n) 1/4) (pow.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)) 1/4)) 2)
	38.5b	(pow.f64 (pow.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))) 1/4) 2)
	49.8b	(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)
	48.1b	(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)
	49.9b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t))))) 2)
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	62.5b	(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))))
	57.3b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 2 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))))) (.f64 2 (log.f64 (/.f64 -1 l)))))) 2)
	56.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	41.5b	(pow.f64 (pow.f64 (.f64 2 (.f64 n (*.f64 t U))) 1/4) 2)
	57.9b	(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)))))))))
	57.9b	(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)))
✓	33.5b	(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))))))))
	48.1b	(.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)))
	41.7b	(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))))
	44.3b	(.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))))
	52.7b	(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (-.f64 (+.f64 (.f64 2 (.f64 n t)) (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) U)) (pow.f64 Om 2)))) (.f64 4 (/.f64 (*.f64 n (pow.f64 l 2)) Om)))) (log.f64 U)))) 2)
	41.4b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	63.2b	(pow.f64 (-.f64 (fma.f64 1/2 (/.f64 (.f64 (.f64 l l) (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 2 (log.f64 (/.f64 -1 n))))))) (.f64 (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))) (.f64 n Om))) (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 2 (log.f64 (/.f64 -1 n))))))) (.f64 1/4 (/.f64 (.f64 t (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 2 (log.f64 (/.f64 -1 n))))))) (.f64 n (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))) 2)
	46.4b	(pow.f64 (pow.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 n n)) (.f64 Om Om)) (.f64 n (.f64 t U)))) (fma.f64 4 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om) (.f64 2 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 n n)) (.f64 Om Om))))) 1/4) 2)
	62.0b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.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 2 (log.f64 (/.f64 -1 n)))))) 2)
	51.9b	(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 2 (.f64 n U))) (neg.f64 (log.f64 t)))) 2)
	62.7b	(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)
	62.1b	(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))))

Compiler

Compiled 37446 to 21991 computations (41.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.7b	(/.f64 (*.f64 (pow.f64 l 2) U) Om)
✓	7.4b	(.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om))))
✓	8.5b	(*.f64 (pow.f64 l 2) U)
✓	16.5b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))

series517.0ms (2.2%)

Counts

4 → 72

Calls

4 calls:

382.0ms	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
103.0ms	(.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om))))
24.0ms	(/.f64 (*.f64 (pow.f64 l 2) U) Om)
8.0ms	(*.f64 (pow.f64 l 2) U)

rewrite88.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

107× egg-rr

Counts

4 → 107

Calls

2 calls:

86.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	69
1	369	65
2	4584	65
3	5004	65
0	0	0
1	0	0

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

933×	`associate-/r*_binary64`
300×	`fma-def_binary64`
250×	`associate-/r/_binary64`
180×	`cancel-sign-sub-inv_binary64`
137×	`unswap-sqr_binary64`

Counts

179 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2724
1	414	2608
2	1627	2496
3	5036	2496

prune201.0ms (0.9%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	138	12	150
Fresh	3	20	23
Picked	1	0	1
Done	0	1	1
Total	142	33	175

Error

8.7b

Counts

175 → 33

Alt Table

Status	Error	Program
	48.7b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (pow.f64 (/.f64 l (sqrt.f64 (/.f64 Om U))) 2)))))
	62.0b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.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 2 (log.f64 (/.f64 -1 n)))))) 2)
	43.4b	(pow.f64 (pow.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4))) 3/2) 1/3)
	58.1b	(neg.f64 (.f64 l (sqrt.f64 (.f64 -4 (/.f64 (*.f64 n U) Om)))))
	44.4b	(pow.f64 (.f64 (pow.f64 (.f64 2 n) 1/4) (pow.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)) 1/4)) 2)
	49.8b	(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)
	48.1b	(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)
	49.9b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t))))) 2)
	51.1b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (.f64 (/.f64 (.f64 l (sqrt.f64 U)) (pow.f64 (cbrt.f64 Om) 2)) (/.f64 (*.f64 l (sqrt.f64 U)) (cbrt.f64 Om)))))))
	58.8b	(.f64 (sqrt.f64 (.f64 -4 (/.f64 (*.f64 n U) Om))) l)
	51.9b	(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 2 (.f64 n U))) (neg.f64 (log.f64 t)))) 2)
▶	38.6b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (.f64 l l)) Om) -4)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4))))))
	58.8b	(sqrt.f64 (.f64 -4 (/.f64 (.f64 n (*.f64 (pow.f64 l 2) U)) Om)))
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	62.5b	(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))))
	57.3b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 2 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))))) (.f64 2 (log.f64 (/.f64 -1 l)))))) 2)
	56.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	39.3b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (expm1.f64 (log1p.f64 (/.f64 (.f64 U (.f64 l l)) Om)))))))
	52.2b	(sqrt.f64 (cbrt.f64 (pow.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4))) 3)))
	41.5b	(pow.f64 (pow.f64 (.f64 2 (.f64 n (*.f64 t U))) 1/4) 2)
	57.9b	(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)))))))))
	57.9b	(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)))
✓	33.5b	(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))))))))
	47.0b	(sqrt.f64 (sqrt.f64 (pow.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4))) 2)))
	48.1b	(.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)))
	41.7b	(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))))
	44.3b	(.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))))
	52.7b	(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)
	51.0b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (.f64 (.f64 l (sqrt.f64 U)) (.f64 (.f64 l (sqrt.f64 U)) (/.f64 1 Om)))))))
	63.2b	(pow.f64 (-.f64 (fma.f64 1/2 (/.f64 (.f64 (.f64 l l) (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 2 (log.f64 (/.f64 -1 n))))))) (.f64 (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))) (.f64 n Om))) (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 2 (log.f64 (/.f64 -1 n))))))) (.f64 1/4 (/.f64 (.f64 t (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 2 (log.f64 (/.f64 -1 n))))))) (.f64 n (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))) 2)
	46.4b	(pow.f64 (pow.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 n n)) (.f64 Om Om)) (.f64 n (.f64 t U)))) (fma.f64 4 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om) (.f64 2 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 n n)) (.f64 Om Om))))) 1/4) 2)
	62.7b	(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)
	62.1b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 n) (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (.f64 l l)) Om) -4)))))

Compiler

Compiled 6496 to 3479 computations (46.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.1b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4)))) 2))
✓	7.4b	(.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4)))
✓	8.5b	(.f64 U (.f64 l l))
✓	19.1b	(cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4))))

series3.6s (15.7%)

Counts

4 → 204

Calls

4 calls:

1.8s	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4)))) 2))
1.7s	(cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4))))
92.0ms	(.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4)))
8.0ms	(.f64 U (.f64 l l))

rewrite76.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

89× egg-rr

Counts

4 → 89

Calls

2 calls:

73.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	80
1	351	80
2	4134	80
3	4987	80
0	0	0
1	0	0

simplify156.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

563×	`fma-def_binary64`
372×	`cancel-sign-sub-inv_binary64`
212×	`associate-r_binary64`
203×	`distribute-neg-frac_binary64`
168×	`*-commutative_binary64`

Counts

293 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	270	8758
1	846	8464
2	2995	8152
3	5171	8152

prune379.0ms (1.6%)

Pruning

35 alts after pruning (34 fresh and 1 done)

	Pruned	Kept	Total
New	283	6	289
Fresh	3	28	31
Picked	1	0	1
Done	0	1	1
Total	287	35	322

Error

8.7b

Counts

322 → 35

Alt Table

Status	Error	Program
	55.1b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 (log.f64 U) (log.f64 (.f64 n (fma.f64 -4 (/.f64 (.f64 l l) Om) (.f64 2 t))))))) 2)) (sqrt.f64 (cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4))))))
	46.4b	(pow.f64 (pow.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 n n)) (.f64 Om Om)) (.f64 n (.f64 t U)))) (fma.f64 4 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om) (.f64 2 (/.f64 (.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 n n)) (.f64 Om Om))))) 1/4) 2)
	38.6b	(.f64 (sqrt.f64 (pow.f64 (.f64 (cbrt.f64 n) (cbrt.f64 (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (.f64 l l)) Om) -4)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4))))))
	48.7b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (pow.f64 (/.f64 l (sqrt.f64 (/.f64 Om U))) 2)))))
	62.0b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.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 2 (log.f64 (/.f64 -1 n)))))) 2)
	43.4b	(pow.f64 (pow.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4))) 3/2) 1/3)
	58.1b	(neg.f64 (.f64 l (sqrt.f64 (.f64 -4 (/.f64 (*.f64 n U) Om)))))
	44.4b	(pow.f64 (.f64 (pow.f64 (.f64 2 n) 1/4) (pow.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)) 1/4)) 2)
	49.8b	(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)
	55.7b	(.f64 (sqrt.f64 (pow.f64 (-.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 2 (.f64 n U))) (log.f64 (/.f64 1 t))))) (.f64 2/3 (/.f64 (.f64 (pow.f64 l 2) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 2 (.f64 n U))) (log.f64 (/.f64 1 t)))))) (.f64 Om t)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4))))))
	49.9b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (*.f64 n U))) (log.f64 (/.f64 -1 t))))) 2)
	48.1b	(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	(.f64 (sqrt.f64 (.f64 -4 (/.f64 (*.f64 n U) Om))) l)
	51.9b	(pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 2 (.f64 n U))) (neg.f64 (log.f64 t)))) 2)
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	62.5b	(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))))
	38.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (.f64 l l)) Om) -4)))) 2)) (sqrt.f64 (fabs.f64 (cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4)))))))
	61.9b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (log.f64 (.f64 -4 (.f64 n (.f64 U (.f64 l l))))) (log.f64 Om)))) 2)) (sqrt.f64 (cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (.f64 l l)) Om) -4))))))
	57.3b	(pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 2 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))))) (.f64 2 (log.f64 (/.f64 -1 l)))))) 2)
	56.1b	(neg.f64 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	41.5b	(pow.f64 (pow.f64 (.f64 2 (.f64 n (*.f64 t U))) 1/4) 2)
	57.9b	(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)))))))))
	57.9b	(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)))
✓	33.5b	(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))))))))
	47.0b	(sqrt.f64 (sqrt.f64 (pow.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (*.f64 l l)) Om) -4))) 2)))
	46.2b	(.f64 (sqrt.f64 (pow.f64 (fma.f64 (.f64 (/.f64 (.f64 l l) Om) (cbrt.f64 (/.f64 (.f64 2 (.f64 n U)) (.f64 t t)))) -2/3 (cbrt.f64 (.f64 n (.f64 2 (.f64 t U))))) 2)) (sqrt.f64 (cbrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (.f64 l l)) Om) -4))))))
	48.1b	(.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)))
	41.7b	(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))))
	44.3b	(.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))))
	52.7b	(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)
	51.0b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (.f64 (.f64 l (sqrt.f64 U)) (.f64 (.f64 l (sqrt.f64 U)) (/.f64 1 Om)))))))
	63.2b	(pow.f64 (-.f64 (fma.f64 1/2 (/.f64 (.f64 (.f64 l l) (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 2 (log.f64 (/.f64 -1 n))))))) (.f64 (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))) (.f64 n Om))) (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 2 (log.f64 (/.f64 -1 n))))))) (.f64 1/4 (/.f64 (.f64 t (exp.f64 (.f64 1/4 (-.f64 (log.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 2 (log.f64 (/.f64 -1 n))))))) (.f64 n (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))) 2)
	58.8b	(sqrt.f64 (.f64 -4 (/.f64 (.f64 n (*.f64 (pow.f64 l 2) U)) Om)))
	62.7b	(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)
	62.1b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 n) (fma.f64 2 (.f64 t U) (.f64 (/.f64 (.f64 U (.f64 l l)) Om) -4)))))

Compiler

Compiled 17233 to 9491 computations (44.9% saved)

regimes4.7s (20.5%)

Accuracy

Total 18.3b remaining (67.6%)

Threshold costs 0b (0%)

Counts

205 → 4

Compiler

Compiled 59658 to 40938 computations (31.4% saved)

bsearch184.0ms (0.8%)

Steps

Iters

Range

Point

1.870362836452262e-298

1.1697109282845015e-297

1.8895719119205843e-298

-5.579186548188872e-287

-3.928674297873732e-288

-1.1801343746820894e-287

-4.427593118573703e-126

-4.1970724401234504e-134

-7.76442369845317e-134

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	154
1	59	154
2	64	154
3	66	154
4	67	154
5	67	154

end677.0ms (2.9%)

Compiler: Compiled 1623 to 1002 computations (38.3% saved)

Details

analyze2.8s (12.3%)

sample4.5s (19.3%)

simplify47.0ms (0.2%)

prune9.0ms (0%)

localize15.0ms (0.1%)

series2.0s (8.7%)

rewrite73.0ms (0.3%)

simplify205.0ms (0.9%)

prune409.0ms (1.8%)

localize19.0ms (0.1%)

series1.3s (5.6%)

rewrite67.0ms (0.3%)

simplify258.0ms (1.1%)

prune620.0ms (2.7%)

localize14.0ms (0.1%)

series517.0ms (2.2%)

rewrite88.0ms (0.4%)

simplify60.0ms (0.3%)

prune201.0ms (0.9%)

localize17.0ms (0.1%)

series3.6s (15.7%)

rewrite76.0ms (0.3%)

simplify156.0ms (0.7%)

prune379.0ms (1.6%)

regimes4.7s (20.5%)

bsearch184.0ms (0.8%)

simplify6.0ms (0%)

end677.0ms (2.9%)

Profiling