Details

analyze2.7s (10.2%)

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
2.5%	90%	7.5%	13
2.7%	88.7%	8.6%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample3.8s (14.1%)

Results

2.2s	11721×	body	128	invalid
1.5s	8256×	body	128	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify50.0ms (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

prune5.0ms (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

26.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	32.2b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
▶	26.2b	(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))))))))

Status

Error

Program

32.2b

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

▶

26.2b

(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))))))))

Compiler

Compiled 189 to 119 computations (37% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.0b	(*.f64 n (/.f64 l Om))
✓	5.5b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	11.1b	(.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)))))))
✓	15.3b	(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 (7.5%)

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))))))))
411.0ms	(.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)))))))
37.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
12.0ms	(*.f64 n (/.f64 l Om))

rewrite35.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-cbrt-cube_binary64`
27×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
17×	`associate-r_binary64`

Counts

4 → 107

Calls

4 calls:

7.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
7.0ms	(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))))))))
7.0ms	(.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)))))))
5.0ms	(*.f64 n (/.f64 l Om))

simplify267.0ms (1%)

Algorithm

1×	egg-herbie

Rules

787×	`fma-def_binary64`
459×	`*-commutative_binary64`
231×	`associate-r_binary64`
165×	`+-commutative_binary64`
153×	`cancel-sign-sub-inv_binary64`

Counts

323 → 286

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1061	19930
1	3567	19396
2	5115	19396

prune551.0ms (2.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	273	13	286
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	274	14	288

Error

13.1b

Counts

288 → 14

Alt Table

Status	Error	Program
	32.2b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
	27.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (.f64 n l) Om))) t)) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (.f64 n l) Om))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))
	39.8b	(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 -4 (/.f64 (.f64 n (.f64 l l)) Om)))))
▶	26.3b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))
	39.4b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	62.0b	(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))))))))
	27.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 (.f64 n l) (/.f64 1 Om))))))))
	43.6b	(-.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)))
	41.6b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	56.3b	(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)))
	57.8b	(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)))
	36.0b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))
	26.7b	(.f64 (.f64 (cbrt.f64 (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))))))))) (cbrt.f64 (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)))))))))) (cbrt.f64 (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))))))))))
	38.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om)))))))

Compiler

Compiled 22791 to 11732 computations (48.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.3b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))
	5.5b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	7.4b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
✓	15.3b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))

series2.2s (8.1%)

Counts

3 → 192

Calls

3 calls:

1.5s

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

413.0ms

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

240.0ms

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

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
17×	`pow-prod-down_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
10×	`associate-*r/_binary64`

Counts

3 → 72

Calls

3 calls:

7.0ms

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

6.0ms

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

4.0ms

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

simplify289.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-def_binary64`
435×	`*-commutative_binary64`
225×	`associate-r_binary64`
161×	`+-commutative_binary64`
146×	`cancel-sign-sub-inv_binary64`

Counts

264 → 250

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	980	22532
1	3366	21795
2	4974	21795

prune567.0ms (2.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	299	7	306
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	304	16	320

Error

10.5b

Counts

320 → 16

Alt Table

Status	Error	Program
	39.4b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	62.0b	(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))))))))
	27.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 (.f64 n l) (/.f64 1 Om))))))))
	44.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t))) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))
	40.8b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	35.8b	(sqrt.f64 (.f64 (.f64 2 n) (fma.f64 U t (.f64 -2 (/.f64 (.f64 (*.f64 l l) U) Om)))))
	26.6b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (.f64 (cbrt.f64 U) (cbrt.f64 U)) (.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t) (cbrt.f64 U)))))
	27.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (.f64 n l) Om))) t)) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (.f64 n l) Om))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))
	39.8b	(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 -4 (/.f64 (.f64 n (.f64 l l)) Om)))))
	43.6b	(-.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)))
	41.6b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	56.3b	(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)))
	52.6b	(/.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (+.f64 (pow.f64 t 3) (pow.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))) 3))))) (sqrt.f64 (fma.f64 t t (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))) (-.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) t)))))
	57.8b	(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)))
▶	26.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t))))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))
	36.8b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om))))))))

Compiler

Compiled 23792 to 12143 computations (49% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.5b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	6.8b	(sqrt.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))))
✓	7.4b	(.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))
✓	15.3b	(sqrt.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))

series3.4s (12.7%)

Counts

3 → 184

Calls

3 calls:

1.6s

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

1.4s

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

389.0ms

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

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64`
24×	`pow-prod-down_binary64`
17×	`sqrt-pow1_binary64`
15×	`add-cbrt-cube_binary64`
15×	`add-exp-log_binary64`

Counts

3 → 66

Calls

3 calls:

5.0ms

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

4.0ms

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

4.0ms

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

simplify427.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

361×	`fma-def_binary64`
311×	`associate-/l*_binary64`
194×	`associate-/r*_binary64`
194×	`times-frac_binary64`
167×	`associate-*l/_binary64`

Counts

250 → 293

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2225	40254
1	5077	40254

prune2.1s (8.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	698	0	698
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	698	16	714

Error

10.5b

Counts

714 → 16

Alt Table

Status	Error	Program
	39.4b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	62.0b	(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))))))))
	27.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 (.f64 n l) (/.f64 1 Om))))))))
	44.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t))) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))
	40.8b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	35.8b	(sqrt.f64 (.f64 (.f64 2 n) (fma.f64 U t (.f64 -2 (/.f64 (.f64 (*.f64 l l) U) Om)))))
▶	26.6b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (.f64 (cbrt.f64 U) (cbrt.f64 U)) (.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t) (cbrt.f64 U)))))
	27.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (.f64 n l) Om))) t)) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (.f64 n l) Om))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))
	39.8b	(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 -4 (/.f64 (.f64 n (.f64 l l)) Om)))))
	43.6b	(-.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)))
	41.6b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	56.3b	(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)))
	52.6b	(/.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (+.f64 (pow.f64 t 3) (pow.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))) 3))))) (sqrt.f64 (fma.f64 t t (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))) (-.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) t)))))
	57.8b	(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)))
✓	26.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t))))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))
	36.8b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om))))))))

Compiler

Compiled 115905 to 62223 computations (46.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.0b	(*.f64 n (/.f64 l Om))
	5.5b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	7.4b	(.f64 (.f64 2 n) (.f64 (.f64 (cbrt.f64 U) (cbrt.f64 U)) (.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t) (cbrt.f64 U))))
✓	15.3b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (.f64 (cbrt.f64 U) (cbrt.f64 U)) (.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t) (cbrt.f64 U)))))

series2.1s (7.9%)

Counts

2 → 120

Calls

2 calls:

1.7s

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

423.0ms

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

rewrite37.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

85×	`pow1_binary64`
62×	`pow-prod-down_binary64`
43×	`add-exp-log_binary64`
31×	`cbrt-unprod_binary64`
31×	`prod-exp_binary64`

Counts

2 → 64

Calls

2 calls:

11.0ms

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

10.0ms

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

simplify446.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
353×	`*-commutative_binary64`
191×	`associate-r_binary64`
155×	`+-commutative_binary64`
128×	`associate-+r+_binary64`

Counts

184 → 177

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	849	20145
1	3026	18777
2	4926	18744
3	4980	18744
4	4977	18744

prune490.0ms (1.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	281	1	282
Fresh	2	12	14
Picked	0	1	1
Done	0	1	1
Total	283	15	298

Error

10.5b

Counts

298 → 15

Alt Table

Status	Error	Program
	39.4b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	62.0b	(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))))))))
	27.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 (.f64 n l) (/.f64 1 Om))))))))
	44.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t))) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))
	36.5b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))
	41.6b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
✓	26.6b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (.f64 (cbrt.f64 U) (cbrt.f64 U)) (.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t) (cbrt.f64 U)))))
	27.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 (.f64 n U)) (.f64 (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (.f64 n l) Om))) t)) (cbrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (.f64 n l) Om))) t)))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))
	40.8b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	43.6b	(-.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)))
	56.3b	(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)))
	52.6b	(/.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (+.f64 (pow.f64 t 3) (pow.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))) 3))))) (sqrt.f64 (fma.f64 t t (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))) (-.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) t)))))
	57.8b	(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)))
✓	26.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t))))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))
	36.8b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om))))))))

Compiler

Compiled 23898 to 11937 computations (50.1% saved)

regimes4.8s (17.9%)

Accuracy

Total 13.0b remaining (54%)

Threshold costs 0b (0%)

Counts

254 → 3

Compiler

Compiled 86138 to 51226 computations (40.5% saved)

bsearch16.0ms (0.1%)

Compiler: Compiled 33 to 22 computations (33.3% saved)

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	211
1	78	211
2	106	211
3	129	211
4	155	211
5	172	211
6	179	211
7	189	211
8	195	211
9	198	211
10	199	211
11	194	211

end320.0ms (1.2%)

Compiler: Compiled 919 to 496 computations (46% saved)

Iter	Nodes	Cost
0	49	211
1	78	211
2	106	211
3	129	211
4	155	211
5	172	211
6	179	211
7	189	211
8	195	211
9	198	211
10	199	211
11	194	211

Iter	Nodes	Cost
0	49	211
1	78	211
2	106	211
3	129	211
4	155	211
5	172	211
6	179	211
7	189	211
8	195	211
9	198	211
10	199	211
11	194	211

Details

analyze2.7s (10.2%)

sample3.8s (14.1%)

simplify50.0ms (0.2%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series2.0s (7.5%)

rewrite35.0ms (0.1%)

simplify267.0ms (1%)

prune551.0ms (2.1%)

localize15.0ms (0.1%)

series2.2s (8.1%)

rewrite27.0ms (0.1%)

simplify289.0ms (1.1%)

prune567.0ms (2.1%)

localize17.0ms (0.1%)

series3.4s (12.7%)

rewrite22.0ms (0.1%)

simplify427.0ms (1.6%)

prune2.1s (8.1%)

localize20.0ms (0.1%)

series2.1s (7.9%)

rewrite37.0ms (0.1%)

simplify446.0ms (1.7%)

prune490.0ms (1.8%)

regimes4.8s (17.9%)

bsearch16.0ms (0.1%)

simplify12.0ms (0%)

end320.0ms (1.2%)

Profiling

Iter	Nodes	Cost
0	49	211
1	78	211
2	106	211
3	129	211
4	155	211
5	172	211
6	179	211
7	189	211
8	195	211
9	198	211
10	199	211
11	194	211