Details

analyze3.0s (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%	92.5%	7.5%	13
0%	91.4%	8.6%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample8.2s (5.6%)

Results

3.5s	13358×	body	128	invalid
2.4s	8256×	body	128	valid
2.2s	1265×	body	8192	exit

Compiler

Compiled 69 to 47 computations (31.9% saved)

simplify66.0ms (0%)

Algorithm

1×	egg-herbie

Rules

415×	`fma-def_binary64`
378×	`*-commutative_binary64`
322×	`distribute-rgt-in_binary64`
321×	`distribute-lft-in_binary64`
303×	`associate-*r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	42
1	58	40
2	223	40
3	1076	38
4	5088	38

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

27.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	33.4b	(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)))))
▶	31.3b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))

Status

Error

Program

33.4b

(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*)))))

▶

31.3b

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

Compiler

Compiled 192 to 122 computations (36.5% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.5b	(fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))
✓	6.8b	(.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))
✓	10.2b	(.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U))
✓	19.0b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))

series2.9s (2%)

Counts

4 → 240

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
454.0ms	(.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))
201.0ms	(fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))
135.0ms	(.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U))

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`

Counts

4 → 127

Calls

4 calls:

9.0ms	(.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U))
6.0ms	(.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))
6.0ms	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
0.0ms	(fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))

simplify36.6s (25%)

Algorithm

1×	egg-herbie

Rules

762×	`fma-def_binary64`
527×	`*-commutative_binary64`
230×	`associate-r_binary64`
162×	`+-commutative_binary64`
142×	`associate-/l*_binary64`

Counts

367 → 328

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1118	23837
1	3901	23077

prune761.0ms (0.5%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	305	23	328
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	306	24	330

Error

13.7b

Counts

330 → 24

Alt Table

Status	Error	Program
	31.7b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (+.f64 t (.f64 -2 (*.f64 l (/.f64 l Om))))))))
	40.3b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
▶	29.3b	(sqrt.f64 (.f64 1 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))))
	57.4b	(sqrt.f64 (.f64 2 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) (.f64 (.f64 l l) U))) (fma.f64 2 (.f64 l (/.f64 l Om)) (/.f64 n (/.f64 (.f64 Om Om) (.f64 (*.f64 l l) U)))))))))
	44.1b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U t)))) (/.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 t U))) (.f64 (.f64 l l) (sqrt.f64 2))) Om))
	63.0b	(-.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))))))
	31.5b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 U) (cbrt.f64 U)) (.f64 (cbrt.f64 U) (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))))
	60.7b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	33.4b	(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)))))
	29.5b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (.f64 l (/.f64 l Om)) -2 t)))))) (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	37.9b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 n (/.f64 Om (.f64 (*.f64 l l) U))))))
	60.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (-.f64 (.f64 (.f64 l l) U) (.f64 (*.f64 l l) U)))))) (/.f64 (sqrt.f64 2) Om))
	42.6b	(.f64 (sqrt.f64 U) (sqrt.f64 (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
	60.2b	(.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)))))))
	31.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (sqrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	55.7b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (pow.f64 l 2) (.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)))))
	56.6b	(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)))))
	31.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (cbrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (.f64 l (/.f64 l Om)) -2 t)))))))) (cbrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	55.5b	(.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))))) (.f64 l (sqrt.f64 2)))
	33.4b	(exp.f64 (log.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	56.0b	(+.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))))
	30.0b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
	55.7b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (.f64 l (sqrt.f64 2)))
	60.4b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (/.f64 n (/.f64 (.f64 Om Om) (.f64 (.f64 l l) U*)))))))

Compiler

Compiled 25421 to 13470 computations (47% saved)

localize125.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.7b	(*.f64 n (pow.f64 (/.f64 l Om) 2))
✓	4.8b	(fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))
✓	6.8b	(.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))
✓	19.0b	(sqrt.f64 (.f64 1 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))))

series2.8s (1.9%)

Counts

4 → 228

Calls

4 calls:

2.0s	(sqrt.f64 (.f64 1 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))))
490.0ms	(.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))
190.0ms	(fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))
67.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2))

rewrite35.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`pow1_binary64`
23×	`add-sqr-sqrt_binary64`
21×	`add-exp-log_binary64`
19×	`associate-r_binary64`
16×	`pow-prod-down_binary64`

Counts

4 → 98

Calls

4 calls:

13.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2))
8.0ms	(sqrt.f64 (.f64 1 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))))
6.0ms	(.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))
0.0ms	(fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))

simplify38.3s (26.1%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary64`
481×	`*-commutative_binary64`
226×	`associate-r_binary64`
204×	`unswap-sqr_binary64`
161×	`+-commutative_binary64`

Counts

326 → 276

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1047	22199
1	3759	21719

prune513.0ms (0.4%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	275	1	276
Fresh	2	21	23
Picked	0	1	1
Done	0	0	0
Total	277	23	300

Error

13.7b

Counts

300 → 23

Alt Table

Status	Error	Program
	31.7b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (+.f64 t (.f64 -2 (*.f64 l (/.f64 l Om))))))))
	40.3b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	44.1b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U t)))) (/.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 t U))) (.f64 (.f64 l l) (sqrt.f64 2))) Om))
	55.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 (.f64 Om Om) U)))))))) (*.f64 l (sqrt.f64 2)))
✓	29.3b	(sqrt.f64 (.f64 1 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))))
	63.0b	(-.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))))))
	31.5b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 U) (cbrt.f64 U)) (.f64 (cbrt.f64 U) (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))))
	60.7b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	33.4b	(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)))))
▶	29.5b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (.f64 l (/.f64 l Om)) -2 t)))))) (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	37.9b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 n (/.f64 Om (.f64 (*.f64 l l) U))))))
	60.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (-.f64 (.f64 (.f64 l l) U) (.f64 (*.f64 l l) U)))))) (/.f64 (sqrt.f64 2) Om))
	42.6b	(.f64 (sqrt.f64 U) (sqrt.f64 (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
	60.2b	(.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)))))))
	31.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (sqrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	55.7b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (pow.f64 l 2) (.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)))))
	56.6b	(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)))))
	33.4b	(exp.f64 (log.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	56.0b	(+.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))))
	31.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (cbrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (.f64 l (/.f64 l Om)) -2 t)))))))) (cbrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	30.0b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
	55.7b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (.f64 l (sqrt.f64 2)))
	60.4b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (/.f64 n (/.f64 (.f64 Om Om) (.f64 (.f64 l l) U*)))))))

Compiler

Compiled 23504 to 12931 computations (45% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.8b	(fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))
	6.8b	(.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))
✓	19.0b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (.f64 l (/.f64 l Om)) -2 t)))))) (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
✓	21.0b	(cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))

series2.5s (1.7%)

Counts

2 → 120

Calls

2 calls:

1.4s

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

1.1s

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

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64`
15×	`sqrt-pow1_binary64`
10×	`pow1/3_binary64`
9×	`pow-prod-up_binary64`
6×	`pow-plus_binary64`

Counts

2 → 37

Calls

2 calls:

7.0ms

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

4.0ms

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

simplify18.4s (12.6%)

Algorithm

1×	egg-herbie

Rules

369×	`fma-def_binary64`
328×	`associate-/l*_binary64`
284×	`associate-*r/_binary64`
238×	`associate-/r*_binary64`
222×	`times-frac_binary64`

Counts

157 → 261

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2236	37327

prune2.9s (2%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	891	1	892
Fresh	1	20	21
Picked	0	1	1
Done	0	1	1
Total	892	23	915

Error

13.7b

Counts

915 → 23

Alt Table

Status	Error	Program
	31.7b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (+.f64 t (.f64 -2 (*.f64 l (/.f64 l Om))))))))
	40.3b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	44.1b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U t)))) (/.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 t U))) (.f64 (.f64 l l) (sqrt.f64 2))) Om))
	55.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 (.f64 Om Om) U)))))))) (*.f64 l (sqrt.f64 2)))
✓	29.3b	(sqrt.f64 (.f64 1 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))))
	63.0b	(-.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))))))
	31.5b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 U) (cbrt.f64 U)) (.f64 (cbrt.f64 U) (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))))
	60.7b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	33.4b	(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)))))
✓	29.5b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (.f64 l (/.f64 l Om)) -2 t)))))) (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	37.9b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 n (/.f64 Om (.f64 (*.f64 l l) U))))))
	60.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (-.f64 (.f64 (.f64 l l) U) (.f64 (*.f64 l l) U)))))) (/.f64 (sqrt.f64 2) Om))
	42.6b	(.f64 (sqrt.f64 U) (sqrt.f64 (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
	60.2b	(.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)))))))
	31.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (sqrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	55.7b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (pow.f64 l 2) (.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)))))
	56.6b	(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)))))
	31.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (cbrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (.f64 l (/.f64 l Om)) -2 t)))))))) (cbrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	56.0b	(+.f64 (.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 t (.f64 l (sqrt.f64 2)))) (.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))))
▶	30.0b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
	33.4b	(exp.f64 (log.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	55.7b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (.f64 l (sqrt.f64 2)))
	60.4b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (/.f64 n (/.f64 (.f64 Om Om) (.f64 (.f64 l l) U*)))))))

Compiler

Compiled 172949 to 93821 computations (45.8% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.0b	(.f64 (/.f64 l Om) (-.f64 U U))
✓	6.5b	(fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U* U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))
✓	6.8b	(.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))
✓	19.0b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))

series2.1s (1.4%)

Counts

4 → 240

Calls

4 calls:

1.4s	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
443.0ms	(.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))
195.0ms	(fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U* U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))
18.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`

Counts

4 → 122

Calls

4 calls:

8.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
6.0ms	(.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))
5.0ms	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
0.0ms	(fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U* U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))

simplify21.8s (14.9%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-def_binary64`
529×	`*-commutative_binary64`
232×	`associate-r_binary64`
164×	`+-commutative_binary64`
145×	`associate-/l*_binary64`

Counts

362 → 322

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1114	22922
1	4024	22420

prune647.0ms (0.4%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	320	2	322
Fresh	0	20	20
Picked	1	0	1
Done	1	1	2
Total	322	23	345

Error

13.4b

Counts

345 → 23

Alt Table

Status	Error	Program
	31.7b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (+.f64 t (.f64 -2 (*.f64 l (/.f64 l Om))))))))
	40.3b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	44.1b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U t)))) (/.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 t U))) (.f64 (.f64 l l) (sqrt.f64 2))) Om))
	55.4b	(.f64 (neg.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 (.f64 Om Om) U)))))))) (*.f64 l (sqrt.f64 2)))
	63.0b	(-.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))))))
	31.5b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 U) (cbrt.f64 U)) (.f64 (cbrt.f64 U) (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t)))))))
	60.7b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	33.4b	(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)))))
✓	29.5b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (.f64 l (/.f64 l Om)) -2 t)))))) (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (cbrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	37.9b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 n (/.f64 Om (.f64 (*.f64 l l) U))))))
	60.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (-.f64 (.f64 (.f64 l l) U) (.f64 (*.f64 l l) U)))))) (/.f64 (sqrt.f64 2) Om))
	42.6b	(.f64 (sqrt.f64 U) (sqrt.f64 (.f64 2 (.f64 n (fma.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U* U) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
	60.2b	(.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)))))))
	31.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (sqrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	55.7b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (pow.f64 l 2) (.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)))))
	56.6b	(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)))))
	31.9b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (.f64 l (/.f64 l Om)) -2 t))))))) (cbrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (.f64 l (/.f64 l Om)) -2 t)))))))) (cbrt.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	28.3b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (+.f64 (.f64 (.f64 n (/.f64 l Om)) (.f64 (-.f64 U* U) (/.f64 l Om))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
	56.0b	(+.f64 (.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 t (.f64 l (sqrt.f64 2)))) (.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))))
	43.0b	(.f64 (sqrt.f64 U) (sqrt.f64 (.f64 2 (.f64 n (fma.f64 n (.f64 (/.f64 l Om) (.f64 (/.f64 l Om) (-.f64 U U))) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))
	33.4b	(exp.f64 (log.f64 (sqrt.f64 (.f64 U (.f64 2 (.f64 n (fma.f64 n (.f64 (pow.f64 (/.f64 l Om) 2) (-.f64 U* U)) (fma.f64 (*.f64 l (/.f64 l Om)) -2 t))))))))
	55.7b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 (.f64 Om Om) U)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (.f64 l (sqrt.f64 2)))
	60.4b	(sqrt.f64 (.f64 U (.f64 2 (.f64 n (/.f64 n (/.f64 (.f64 Om Om) (.f64 (.f64 l l) U*)))))))

Compiler

Compiled 24422 to 12077 computations (50.5% saved)

regimes3.6s (2.5%)

Accuracy

Total 15.6b remaining (52.1%)

Threshold costs 0b (0%)

Counts

194 → 5

Compiler

Compiled 73322 to 42970 computations (41.4% saved)

bsearch445.0ms (0.3%)

Steps

Iters	Range		Point
7	9.496350780870478e+111	9.66092118612539e+113	9.502321434313212e+113
9	3.4687362466646802e-276	5.080427070018269e-268	1.1867004569328641e-275
10	-3.1109564863368068e-263	-4.1540946133195447e-274	-4.194893587798726e-274
7	-7.284133016237404e+135	-2.8797926050653026e+134	-1.169333522807784e+135

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify14.0ms (0%)

Algorithm

1×	egg-herbie

Rules

36×	`*-commutative_binary64`
17×	`+-commutative_binary64`
14×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	297
1	108	297
2	125	297
3	155	297
4	182	297
5	196	297
6	202	297
7	203	297

soundness128.0ms (0.1%)

Compiler: Compiled 6760 to 4492 computations (33.6% saved)

end481.0ms (0.3%)

Compiler: Compiled 1408 to 863 computations (38.7% saved)

Details

analyze3.0s (2%)

sample8.2s (5.6%)

simplify66.0ms (0%)

prune9.0ms (0%)

localize18.0ms (0%)

series2.9s (2%)

rewrite33.0ms (0%)

simplify36.6s (25%)

prune761.0ms (0.5%)

localize125.0ms (0.1%)

series2.8s (1.9%)

rewrite35.0ms (0%)

simplify38.3s (26.1%)

prune513.0ms (0.4%)

localize20.0ms (0%)

series2.5s (1.7%)

rewrite16.0ms (0%)

simplify18.4s (12.6%)

prune2.9s (2%)

localize16.0ms (0%)

series2.1s (1.4%)

rewrite29.0ms (0%)

simplify21.8s (14.9%)

prune647.0ms (0.4%)

regimes3.6s (2.5%)

bsearch445.0ms (0.3%)

simplify14.0ms (0%)

soundness128.0ms (0.1%)

end481.0ms (0.3%)

Profiling