Details

analyze3.1s (12.1%)

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 (18.8%)

Results

2.9s	14301×	body	128	invalid
1.8s	8256×	body	128	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify56.0ms (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

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

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))))))))

series1.9s (7.5%)

Counts

4 → 216

Calls

4 calls:

1.4s	(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))))))))
401.0ms	(.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)))))))
33.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
11.0ms	(*.f64 n (/.f64 l Om))

rewrite261.0ms (1%)

Algorithm

4×	egg-rewrite

Rules

55×	`egg`
46×	`egg`
30×	`egg`
27×	`egg`

Counts

4 → 158

Calls

4 calls:

79.0ms	(.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)))))))
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))))))))
61.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
46.0ms	(*.f64 n (/.f64 l Om))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	37
1	440	35
2	4849	35
3	5137	35
0	19	35
1	420	33
2	4864	33
3	5863	33
0	10	13
1	217	13
2	2949	13
3	4990	13
0	6	7
1	125	7
2	1628	7
3	5106	7

simplify240.0ms (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

374 → 283

Iterations

Useful iterations: 1 (0.0ms)

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

prune466.0ms (1.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	267	16	283
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	269	16	285

Error

12.6b

Counts

285 → 16

Alt Table

Status	Error	Program
	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))))
	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))))
▶	32.8b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	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)))))))))
	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)))
	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))))
	41.7b	(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))))
	60.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	38.3b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	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)))))))))
	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))))))))
	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)
	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)))
	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)))
	41.4b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))

Compiler

Compiled 21438 to 11473 computations (46.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.2b	(.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))
	6.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	6.2b	(.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))
✓	21.2b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))

series2.0s (8%)

Counts

3 → 192

Calls

3 calls:

1.4s

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

402.0ms

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

187.0ms

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

rewrite200.0ms (0.8%)

Algorithm

3×	egg-rewrite

Rules

43×	`egg`
33×	`egg`
28×	`egg`

Counts

3 → 104

Calls

3 calls:

86.0ms

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

72.0ms

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

38.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	35
1	403	35
2	4999	35
0	18	33
1	383	33
2	4904	33
3	6260	33
0	15	27
1	319	27
2	4127	27
3	5428	27

simplify387.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-def_binary64`
403×	`*-commutative_binary64`
197×	`associate-r_binary64`
154×	`+-commutative_binary64`
144×	`associate-/l*_binary64`

Counts

296 → 247

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	872	19502
1	3075	18506
2	5006	18506

prune477.0ms (1.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	310	4	314
Fresh	4	11	15
Picked	0	1	1
Done	0	0	0
Total	314	16	330

Error

12.2b

Counts

330 → 16

Alt Table

Status	Error	Program
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	59.5b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
✓	32.8b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	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)))
	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)))
	62.1b	(sqrt.f64 (.f64 (.f64 2 n) (log.f64 (pow.f64 (exp.f64 U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 (/.f64 l Om) n))) t)))))
	61.1b	(.f64 (.f64 n (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))))))
	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))))
	41.7b	(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))))
	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)))))))))
▶	33.1b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))
	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))))))))
	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)
	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)))
	41.4b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	38.3b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))

Compiler

Compiled 21950 to 11580 computations (47.2% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	6.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
	6.2b	(.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))
✓	21.2b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))
✓	22.3b	(cbrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))

series2.7s (10.6%)

Counts

2 → 120

Calls

2 calls:

1.4s

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

1.3s

(sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 n) (*.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))

rewrite125.0ms (0.5%)

Algorithm

2×	egg-rewrite

Rules

36×	`egg`
26×	`egg`

Counts

2 → 62

Calls

2 calls:

82.0ms

(sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 2 n) (*.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))

39.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	35
1	401	35
2	4986	35
0	22	35
1	448	35
2	4828	35
3	5217	35

simplify379.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

368×	`fma-def_binary64`
327×	`associate-/l*_binary64`
282×	`associate-*r/_binary64`
237×	`associate-/r*_binary64`
221×	`times-frac_binary64`

Counts

182 → 280

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2174	36299
1	5294	36299

prune1.1s (4.3%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	409	10	419
Fresh	1	13	14
Picked	0	1	1
Done	0	1	1
Total	410	25	435

Error

12.2b

Counts

435 → 25

Alt Table

Status	Error	Program
✓	33.1b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))
	60.6b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U* U))) (*.f64 Om Om)))) 3))
	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))))))))
	53.7b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 2) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (*.f64 n U)) (log.f64 (/.f64 1 t)))))) 3))
	35.1b	(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))) 3/2))
	59.5b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	59.6b	(sqrt.f64 (pow.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))) U))) (.f64 2 (log.f64 (/.f64 -1 l)))))) (cbrt.f64 2)) 3))
✓	32.8b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	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)))
	41.7b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 n (*.f64 t U))) (cbrt.f64 2)) 3))
	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)
	44.5b	(.f64 (pow.f64 (cbrt.f64 (.f64 2 n)) 3/2) (pow.f64 (cbrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 3/2))
	43.0b	(sqrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 n (*.f64 t U)) 1/3) (cbrt.f64 2)) 3))
	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)))
	52.9b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 2) (exp.f64 (.f64 1/3 (+.f64 (log.f64 (-.f64 (.f64 t U) (.f64 2 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))) (log.f64 n))))) 3))
	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)))
	62.1b	(sqrt.f64 (.f64 (.f64 2 n) (log.f64 (pow.f64 (exp.f64 U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 (/.f64 l Om) n))) t)))))
	61.1b	(.f64 (.f64 n (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))))))
	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))))
	41.7b	(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))))
	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)))))))))
	46.3b	(sqrt.f64 (pow.f64 (-.f64 (.f64 (cbrt.f64 (.f64 n (.f64 t U))) (cbrt.f64 2)) (.f64 2/3 (.f64 (cbrt.f64 (/.f64 (.f64 n U) (.f64 t t))) (/.f64 (.f64 (*.f64 l l) (cbrt.f64 2)) Om)))) 3))
▶	33.2b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (cbrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))
	38.3b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))

Compiler

Compiled 55572 to 31765 computations (42.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.2b	(.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))
	6.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	19.7b	(cbrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))
✓	21.2b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (cbrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))

series2.7s (10.8%)

Counts

2 → 120

Calls

2 calls:

1.5s

(sqrt.f64 (pow.f64 (*.f64 (cbrt.f64 (*.f64 2 n)) (cbrt.f64 (*.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))

1.2s

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

rewrite141.0ms (0.6%)

Algorithm

2×	egg-rewrite

Rules

32×	`egg`
25×	`egg`

Counts

2 → 57

Calls

2 calls:

70.0ms

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

68.0ms

(sqrt.f64 (pow.f64 (*.f64 (cbrt.f64 (*.f64 2 n)) (cbrt.f64 (*.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (*.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	38
1	480	35
2	4856	35
3	4899	35
0	16	29
1	337	29
2	4322	29
3	5606	29

simplify331.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

357×	`associate-r_binary64`
341×	`fma-def_binary64`
269×	`associate-/l*_binary64`
240×	`associate-*r/_binary64`
206×	`associate-/r*_binary64`

Counts

177 → 274

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1887	31948
1	5195	31948

prune967.0ms (3.8%)

Pruning

29 alts after pruning (27 fresh and 2 done)

	Pruned	Kept	Total
New	395	7	402
Fresh	2	20	22
Picked	1	0	1
Done	0	2	2
Total	398	29	427

Error

11.7b

Counts

427 → 29

Alt Table

Status	Error	Program
✓	33.1b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))) 3))
	60.6b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U* U))) (*.f64 Om Om)))) 3))
	61.3b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))) U)) (.f64 2 (log.f64 (/.f64 -1 l))))))) 3))
	46.3b	(sqrt.f64 (pow.f64 (-.f64 (.f64 (cbrt.f64 (.f64 n (.f64 t U))) (cbrt.f64 2)) (.f64 2/3 (.f64 (cbrt.f64 (/.f64 (.f64 n U) (.f64 t t))) (/.f64 (.f64 (*.f64 l l) (cbrt.f64 2)) Om)))) 3))
	35.1b	(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))) 3/2))
	59.5b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	38.7b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (cbrt.f64 (-.f64 (.f64 t U) (.f64 2 (/.f64 (*.f64 (pow.f64 l 2) U) Om))))) 3))
	57.2b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (exp.f64 (*.f64 1/3 (-.f64 (log.f64 (neg.f64 U)) (log.f64 (/.f64 -1 t)))))) 3))
✓	32.8b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	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)))
	41.7b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 n (*.f64 t U))) (cbrt.f64 2)) 3))
	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)
	62.6b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (pow.f64 (exp.f64 1/3) (-.f64 (log.f64 (.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))) U)) (*.f64 2 (neg.f64 (log.f64 l)))))) 3))
	44.5b	(.f64 (pow.f64 (cbrt.f64 (.f64 2 n)) 3/2) (pow.f64 (cbrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 3/2))
	43.0b	(sqrt.f64 (pow.f64 (.f64 (pow.f64 (.f64 n (*.f64 t U)) 1/3) (cbrt.f64 2)) 3))
	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)))
	62.6b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.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 2 (log.f64 (/.f64 1 l))))))) 3))
	52.9b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 2) (exp.f64 (.f64 1/3 (+.f64 (log.f64 (-.f64 (.f64 t U) (.f64 2 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))) (log.f64 n))))) 3))
	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)))
	62.1b	(sqrt.f64 (.f64 (.f64 2 n) (log.f64 (pow.f64 (exp.f64 U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 (/.f64 l Om) n))) t)))))
	61.1b	(.f64 (.f64 n (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))))))
	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))))
	41.7b	(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))))
	38.3b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	59.2b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (exp.f64 (*.f64 1/3 (-.f64 (log.f64 U) (log.f64 (/.f64 1 t)))))) 3))
	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)))))))))
	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))))))))
	59.7b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 n)) (fma.f64 1/3 (.f64 t (cbrt.f64 (/.f64 U (pow.f64 (-.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)))) 2)))) (cbrt.f64 (.f64 (-.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)))) U)))) 3))

Compiler

Compiled 49845 to 28005 computations (43.8% saved)

regimes2.2s (8.8%)

Accuracy

Total 13.1b remaining (52.4%)

Threshold costs 0b (0%)

Counts

175 → 3

Compiler

Compiled 48034 to 31418 computations (34.6% saved)

bsearch211.0ms (0.8%)

Steps

Iters	Range		Point
6	6.269049858487873e+231	5.34514105965542e+232	7.905522743726848e+231
7	-3.3758483694513526e+228	-6.952471997638566e+226	-8.728822343383789e+226

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
14×	`+-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	46	146
1	70	146
2	94	146
3	117	146
4	136	146
5	144	146
6	147	146
7	148	146
8	147	146

end531.0ms (2.1%)

Compiler: Compiled 1212 to 776 computations (36% saved)

Iter	Nodes	Cost
0	46	146
1	70	146
2	94	146
3	117	146
4	136	146
5	144	146
6	147	146
7	148	146
8	147	146

Iter	Nodes	Cost
0	46	146
1	70	146
2	94	146
3	117	146
4	136	146
5	144	146
6	147	146
7	148	146
8	147	146

Details

analyze3.1s (12.1%)

sample4.8s (18.8%)

simplify56.0ms (0.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series1.9s (7.5%)

rewrite261.0ms (1%)

simplify240.0ms (0.9%)

prune466.0ms (1.8%)

localize16.0ms (0.1%)

series2.0s (8%)

rewrite200.0ms (0.8%)

simplify387.0ms (1.5%)

prune477.0ms (1.9%)

localize22.0ms (0.1%)

series2.7s (10.6%)

rewrite125.0ms (0.5%)

simplify379.0ms (1.5%)

prune1.1s (4.3%)

localize21.0ms (0.1%)

series2.7s (10.8%)

rewrite141.0ms (0.6%)

simplify331.0ms (1.3%)

prune967.0ms (3.8%)

regimes2.2s (8.8%)

bsearch211.0ms (0.8%)

simplify10.0ms (0%)

end531.0ms (2.1%)

Profiling

Iter	Nodes	Cost
0	46	146
1	70	146
2	94	146
3	117	146
4	136	146
5	144	146
6	147	146
7	148	146
8	147	146