Details

analyze3.1s (15.4%)

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)

sample4.8s (23.5%)

Results

2.9s	14455×	body	128	invalid
1.8s	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

prune7.0ms (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

30.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	34.5b	(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)))))
▶	30.6b	(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

34.5b

(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*)))))

▶

30.6b

(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)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.9b	(*.f64 n (/.f64 l Om))
✓	6.3b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	10.4b	(.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)))))))
✓	18.8b	(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))))))))

series1.9s (9.5%)

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))))))))
393.0ms	(.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)))))))
35.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
13.0ms	(*.f64 n (/.f64 l Om))

rewrite33.0ms (0.2%)

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)))
6.0ms	(.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)))))))
6.0ms	(*.f64 n (/.f64 l Om))
5.0ms	(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))))))))

simplify256.0ms (1.3%)

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

prune591.0ms (2.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	272	14	286
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	273	15	288

Error

13.7b

Counts

288 → 15

Alt Table

Status	Error	Program
	42.7b	(.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))))))))
	59.4b	(.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))
▶	29.2b	(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)))))))))
	55.0b	(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)))
	60.1b	(.f64 (.f64 n (sqrt.f64 2)) (sqrt.f64 (.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)))
	47.7b	(sqrt.f64 (/.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (.f64 t t) (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	31.8b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 l U*)) Om))))))
	56.9b	(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)))
	32.0b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (.f64 n l) Om))) t))) (cbrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (.f64 n l) Om))) t)))) (cbrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))) t)))))
	39.2b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	35.9b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om))))
	38.8b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.f64 t (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om))))))))
	34.5b	(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)))))
	32.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (-.f64 U U)) (/.f64 Om l)))))))
	30.8b	(.f64 (sqrt.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))))))))) (sqrt.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))))))))))

Compiler

Compiled 22887 to 11772 computations (48.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.9b	(*.f64 n (/.f64 l Om))
	6.3b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	6.8b	(.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))))))))
✓	18.8b	(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)))))))))

series1.9s (9.4%)

Counts

2 → 120

Calls

2 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)))))))))

408.0ms

(*.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))))))))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`pow1_binary64`
16×	`pow-prod-down_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
8×	`cbrt-unprod_binary64`

Counts

2 → 48

Calls

2 calls:

6.0ms

(*.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)))))))))

simplify292.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

764×	`fma-def_binary64`
419×	`*-commutative_binary64`
218×	`associate-r_binary64`
168×	`neg-mul-1_binary64`
157×	`+-commutative_binary64`

Counts

168 → 178

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	940	18125
1	3260	16803
2	4884	16803
3	5048	16803

prune539.0ms (2.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	278	5	283
Fresh	3	11	14
Picked	0	1	1
Done	0	0	0
Total	281	17	298

Error

9.8b

Counts

298 → 17

Alt Table

Status	Error	Program
▶	30.6b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 l U*)) Om)))))))
	38.8b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.f64 t (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om))))))))
	34.5b	(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)))))
	62.6b	(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))))
✓	29.2b	(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)))))))))
	55.0b	(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)))
	60.1b	(.f64 (.f64 n (sqrt.f64 2)) (sqrt.f64 (.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)))
	47.7b	(sqrt.f64 (/.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (.f64 t t) (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	56.9b	(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)))
	50.9b	(/.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)))))
	30.8b	(.f64 (sqrt.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))))))))) (sqrt.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))))))))))
	32.0b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (.f64 n l) Om))) t))) (cbrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (.f64 n l) Om))) t)))) (cbrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))) t)))))
	39.2b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	35.9b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om))))
	59.4b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	42.7b	(.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))))))))
	42.9b	(.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))))

Compiler

Compiled 22452 to 11705 computations (47.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.5b	(.f64 n (.f64 l U*))
✓	6.3b	(/.f64 (.f64 n (.f64 l U*)) Om)
✓	6.8b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 l U*)) Om))))))
✓	18.8b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 l U*)) Om)))))))

series1.5s (7.4%)

Counts

4 → 112

Calls

4 calls:

1.2s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 l U*)) Om)))))))
270.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 l U*)) Om))))))
25.0ms	(/.f64 (.f64 n (.f64 l U*)) Om)
9.0ms	(.f64 n (.f64 l U*))

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64`
30×	`add-cbrt-cube_binary64`
30×	`add-exp-log_binary64`
19×	`pow-prod-down_binary64`
14×	`cbrt-unprod_binary64`

Counts

4 → 93

Calls

4 calls:

8.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 l U*)) Om))))))
6.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 l U*)) Om)))))))
5.0ms	(/.f64 (.f64 n (.f64 l U*)) Om)
4.0ms	(.f64 n (.f64 l U*))

simplify157.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

415×	`associate-/l*_binary64`
407×	`times-frac_binary64`
380×	`fma-def_binary64`
263×	`associate-/r*_binary64`
200×	`*-commutative_binary64`

Counts

205 → 212

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	552	9960
1	1734	9324
2	5054	9324

prune339.0ms (1.7%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	207	5	212
Fresh	1	14	15
Picked	0	1	1
Done	0	1	1
Total	208	21	229

Error

8.0b

Counts

229 → 21

Alt Table

Status	Error	Program
	59.4b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	58.7b	(neg.f64 (.f64 (/.f64 (.f64 n (.f64 l (sqrt.f64 2))) Om) (sqrt.f64 (.f64 U U*))))
	34.5b	(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)))))
	62.6b	(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))))
✓	29.2b	(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)))))))))
	55.0b	(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)))
	60.1b	(.f64 (.f64 n (sqrt.f64 2)) (sqrt.f64 (.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)))
	43.4b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 l U)) Om)) t))))
	47.7b	(sqrt.f64 (/.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (.f64 t t) (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	56.9b	(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)))
	50.9b	(/.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)))))
	55.7b	(neg.f64 (.f64 (.f64 l (sqrt.f64 2)) (sqrt.f64 (.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (*.f64 Om Om)) (/.f64 2 Om))))))
▶	30.8b	(.f64 (sqrt.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))))))))) (sqrt.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))))))))))
	32.0b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (.f64 n l) Om))) t))) (cbrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (.f64 n l) Om))) t)))) (cbrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))) t)))))
	39.2b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	35.9b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om))))
✓	30.6b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 l U*)) Om)))))))
	42.7b	(.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))))))))
	42.9b	(.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))))
	59.7b	(-.f64 (.f64 (/.f64 (.f64 n (.f64 l (sqrt.f64 2))) Om) (sqrt.f64 (.f64 U* U))) (.f64 (.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 U U*))))
	58.0b	(fma.f64 (.f64 l (sqrt.f64 2)) (sqrt.f64 (.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)))) (/.f64 t (/.f64 l (sqrt.f64 2))))))

Compiler

Compiled 11597 to 6156 computations (46.9% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.9b	(*.f64 n (/.f64 l Om))
	6.3b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
	10.4b	(.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)))))))
	18.8b	(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))))))))

prune1.2s (6%)

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	572	0	572
Fresh	0	18	18
Picked	0	1	1
Done	0	2	2
Total	572	21	593

Error

8.0b

Counts

593 → 21

Alt Table

Status	Error	Program
	59.4b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	58.7b	(neg.f64 (.f64 (/.f64 (.f64 n (.f64 l (sqrt.f64 2))) Om) (sqrt.f64 (.f64 U U*))))
	34.5b	(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)))))
	62.6b	(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))))
✓	29.2b	(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)))))))))
	55.0b	(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)))
	60.1b	(.f64 (.f64 n (sqrt.f64 2)) (sqrt.f64 (.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)))
	43.4b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 l U)) Om)) t))))
	47.7b	(sqrt.f64 (/.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (.f64 t t) (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	56.9b	(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)))
	50.9b	(/.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)))))
	55.7b	(neg.f64 (.f64 (.f64 l (sqrt.f64 2)) (sqrt.f64 (.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (*.f64 Om Om)) (/.f64 2 Om))))))
✓	30.8b	(.f64 (sqrt.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))))))))) (sqrt.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))))))))))
	32.0b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (.f64 n l) Om))) t))) (cbrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (.f64 n l) Om))) t)))) (cbrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))) t)))))
	39.2b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	35.9b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om))))
✓	30.6b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 l U*)) Om)))))))
	42.7b	(.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))))))))
	42.9b	(.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))))
	59.7b	(-.f64 (.f64 (/.f64 (.f64 n (.f64 l (sqrt.f64 2))) Om) (sqrt.f64 (.f64 U* U))) (.f64 (.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 U U*))))
	58.0b	(fma.f64 (.f64 l (sqrt.f64 2)) (sqrt.f64 (.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)))) (/.f64 t (/.f64 l (sqrt.f64 2))))))

Compiler

Compiled 60232 to 29154 computations (51.6% saved)

regimes2.7s (13.1%)

Accuracy

Total 19.4b remaining (67.2%)

Threshold costs 0b (0%)

Counts

150 → 5

Compiler

Compiled 49738 to 30146 computations (39.4% saved)

bsearch426.0ms (2.1%)

Steps

Iters	Range		Point
7	1.052647418891976e+140	1.7840002875024055e+141	8.190127014100475e+140
9	4.134219806585572e-208	2.0319819745420742e-199	4.2440359176280085e-208
7	9.598235397776866e-250	3.105986861051172e-248	3.070934356675914e-248
9	-8.245618608028308e+187	-3.8830858801320624e+181	-7.803253604088981e+181

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

27×	`*-commutative_binary64`
15×	`+-commutative_binary64`
13×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	223
1	89	223
2	113	223
3	136	223
4	155	223
5	163	223
6	166	223
7	167	223
8	165	223

end405.0ms (2%)

Compiler: Compiled 1182 to 649 computations (45.1% saved)

Iter	Nodes	Cost
0	59	223
1	89	223
2	113	223
3	136	223
4	155	223
5	163	223
6	166	223
7	167	223
8	165	223

Iter	Nodes	Cost
0	59	223
1	89	223
2	113	223
3	136	223
4	155	223
5	163	223
6	166	223
7	167	223
8	165	223

Details

analyze3.1s (15.4%)

sample4.8s (23.5%)

simplify47.0ms (0.2%)

prune7.0ms (0%)

localize16.0ms (0.1%)

series1.9s (9.5%)

rewrite33.0ms (0.2%)

simplify256.0ms (1.3%)

prune591.0ms (2.9%)

localize15.0ms (0.1%)

series1.9s (9.4%)

rewrite19.0ms (0.1%)

simplify292.0ms (1.4%)

prune539.0ms (2.6%)

localize16.0ms (0.1%)

series1.5s (7.4%)

rewrite30.0ms (0.1%)

simplify157.0ms (0.8%)

prune339.0ms (1.7%)

localize23.0ms (0.1%)

prune1.2s (6%)

regimes2.7s (13.1%)

bsearch426.0ms (2.1%)

simplify11.0ms (0.1%)

end405.0ms (2%)

Profiling

Iter	Nodes	Cost
0	59	223
1	89	223
2	113	223
3	136	223
4	155	223
5	163	223
6	166	223
7	167	223
8	165	223