Details

analyze3.1s (18.6%)

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 (28.4%)

Results

2.9s	14506×	body	128	invalid
1.8s	8256×	body	128	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify49.0ms (0.3%)

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

29.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	29.3b	(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))))))))
	32.9b	(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)))))

Status

Error

Program

▶

29.3b

(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))))))))

32.9b

(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*)))))

Compiler

Compiled 189 to 119 computations (37% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.9b	(*.f64 n (/.f64 l Om))
✓	7.0b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	9.4b	(.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)))))))
✓	18.5b	(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))))))))

series1.3s (7.5%)

Counts

4 → 216

Calls

4 calls:

911.0ms	(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))))))))
299.0ms	(.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)))
12.0ms	(*.f64 n (/.f64 l Om))

rewrite80.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

223×	`add-sqr-sqrt_binary64`
211×	`log1p-expm1-u_binary64`
211×	`expm1-log1p-u_binary64`
207×	`add-log-exp_binary64`
206×	`add-cube-cbrt_binary64`

Counts

4 → 88

Calls

4 calls:

77.0ms	(*.f64 n (/.f64 l Om))
77.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
77.0ms	(.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)))))))
77.0ms	(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))))))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	92
1	440	88
2	4849	88
3	5137	88

simplify212.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

734×	`fma-def_binary64`
405×	`*-commutative_binary64`
195×	`associate-r_binary64`
150×	`+-commutative_binary64`
147×	`associate-/l*_binary64`

Counts

304 → 215

Iterations

Useful iterations: 1 (0.0ms)

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

prune419.0ms (2.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	197	18	215
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	198	19	217

Error

12.2b

Counts

217 → 19

Alt Table

Status	Error	Program
	43.5b	(-.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)))
	35.6b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))
	62.7b	(-.f64 (+.f64 (.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))) (.f64 1/2 (.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)) (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)))))))) (.f64 (/.f64 (.f64 (pow.f64 l 2) (sqrt.f64 2)) Om) (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)) (/.f64 (*.f64 (pow.f64 l 2) U) (pow.f64 Om 2)))))))
	32.9b	(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)))))
	29.4b	(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)
	57.4b	(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)))
	29.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (pow.f64 (cbrt.f64 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) 3))))))
	59.0b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))
	39.4b	(.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))))
	39.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	29.6b	(.f64 (cbrt.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))) (cbrt.f64 (sqrt.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)))))
	57.9b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.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))))))))
	62.2b	(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))))
	32.8b	(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)))))))
	61.6b	(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))))))))
	60.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	40.6b	(.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)))
▶	29.2b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 (.f64 (.f64 2 n) U) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	35.6b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))

Compiler

Compiled 19482 to 10795 computations (44.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.9b	(*.f64 n (/.f64 l Om))
	7.0b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	12.1b	(.f64 (.f64 (.f64 2 n) U) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))
✓	18.5b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 (.f64 (.f64 2 n) U) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))

series833.0ms (4.9%)

Counts

2 → 108

Calls

2 calls:

631.0ms

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

201.0ms

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

rewrite69.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

262×	`prod-diff_binary64`
215×	`add-sqr-sqrt_binary64`
201×	`log1p-expm1-u_binary64`
201×	`expm1-log1p-u_binary64`
199×	`add-log-exp_binary64`

Counts

2 → 42

Calls

2 calls:

67.0ms

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

67.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	76
1	426	69
2	4871	69
3	5389	69

simplify251.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
704×	`associate-/l*_binary64`
274×	`*-commutative_binary64`
138×	`cancel-sign-sub-inv_binary64`
121×	`+-commutative_binary64`

Counts

150 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	663	15528
1	2292	14472
2	4872	14354
3	5094	14354

prune461.0ms (2.7%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	193	10	203
Fresh	4	14	18
Picked	1	0	1
Done	0	0	0
Total	198	24	222

Error

9.3b

Counts

222 → 24

Alt Table

Status	Error	Program
	60.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	61.5b	(.f64 (sqrt.f64 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) (.f64 U U)) (*.f64 Om Om))))) n)
	62.7b	(-.f64 (+.f64 (.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))) (.f64 1/2 (.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)) (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)))))))) (.f64 (/.f64 (.f64 (pow.f64 l 2) (sqrt.f64 2)) Om) (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)) (/.f64 (*.f64 (pow.f64 l 2) U) (pow.f64 Om 2)))))))
	36.0b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 (.f64 n (.f64 (pow.f64 l 2) (.f64 (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (*.f64 n U) Om))) U))) Om))))
	29.4b	(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)
	57.4b	(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)))
▶	26.7b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (+.f64 (.f64 (.f64 l -2) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))) (.f64 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))))))
	39.3b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 (fma.f64 (/.f64 (.f64 n n) Om) (.f64 (.f64 l l) U) (.f64 (.f64 (.f64 l l) n) -2)) (/.f64 Om U)))))
	29.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (pow.f64 (cbrt.f64 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) 3))))))
	38.5b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 (.f64 (-.f64 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) U)) Om) (.f64 2 (*.f64 n (pow.f64 l 2)))) U) Om))))
	40.6b	(.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)))
	59.0b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))
	39.4b	(.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))))
	39.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	29.6b	(.f64 (cbrt.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))) (cbrt.f64 (sqrt.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)))))
	57.9b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.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))))))))
	62.2b	(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))))
	58.9b	(.f64 l (sqrt.f64 (fma.f64 2 (-.f64 (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 Om Om)) (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 Om Om))) (.f64 -4 (/.f64 (.f64 U n) Om)))))
	35.6b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	30.9b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 -2 (/.f64 (.f64 (.f64 n (.f64 l U)) (fma.f64 2 l (/.f64 (.f64 n (.f64 l U)) Om))) Om))))
	61.6b	(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))))))))
	34.6b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 -4 (/.f64 (.f64 n (*.f64 (pow.f64 l 2) U)) Om))))
	61.5b	(.f64 (/.f64 1 Om) (sqrt.f64 (-.f64 (.f64 2 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U)))) (.f64 2 (.f64 (pow.f64 n 2) (*.f64 (pow.f64 l 2) (pow.f64 U 2)))))))
	58.9b	(.f64 (sqrt.f64 (fma.f64 2 (-.f64 (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 Om Om)) (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 Om Om))) (.f64 -4 (/.f64 (.f64 U n) Om)))) (neg.f64 l))

Compiler

Compiled 21001 to 11508 computations (45.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.9b	(*.f64 n (/.f64 l Om))
	7.0b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	9.7b	(.f64 (.f64 (*.f64 2 n) U) (/.f64 l Om))
✓	18.5b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (+.f64 (.f64 (.f64 l -2) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))) (.f64 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))))))

series663.0ms (3.9%)

Counts

2 → 96

Calls

2 calls:

637.0ms

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

26.0ms

(*.f64 (*.f64 (*.f64 2 n) U) (/.f64 l Om))

rewrite63.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

244×	`add-sqr-sqrt_binary64`
230×	`log1p-expm1-u_binary64`
230×	`expm1-log1p-u_binary64`
226×	`add-log-exp_binary64`
225×	`add-cube-cbrt_binary64`

Counts

2 → 36

Calls

2 calls:

61.0ms

(*.f64 (*.f64 (*.f64 2 n) U) (/.f64 l Om))

61.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	59
1	484	57
2	4894	57
3	4961	57

simplify158.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

652×	`associate-/l*_binary64`
565×	`associate-/r*_binary64`
539×	`fma-def_binary64`
243×	`*-commutative_binary64`
123×	`cancel-sign-sub-inv_binary64`

Counts

132 → 123

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	604	12907
1	2112	11801
2	5350	11801

prune441.0ms (2.6%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	186	4	190
Fresh	2	21	23
Picked	0	1	1
Done	0	0	0
Total	188	26	214

Error

9.0b

Counts

214 → 26

Alt Table

Status	Error	Program
▶	26.9b	(pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))) 2)
	30.9b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 -2 (/.f64 (.f64 (.f64 n (.f64 l U)) (fma.f64 2 l (/.f64 (.f64 n (.f64 l U)) Om))) Om))))
	60.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	61.5b	(.f64 (sqrt.f64 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) (.f64 U U)) (*.f64 Om Om))))) n)
	27.0b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (+.f64 (.f64 (.f64 l -2) (.f64 2 (/.f64 (.f64 n (.f64 l U)) Om))) (.f64 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))))))
	62.7b	(-.f64 (+.f64 (.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))) (.f64 1/2 (.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)) (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)))))))) (.f64 (/.f64 (.f64 (pow.f64 l 2) (sqrt.f64 2)) Om) (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)) (/.f64 (*.f64 (pow.f64 l 2) U) (pow.f64 Om 2)))))))
	36.0b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 (.f64 n (.f64 (pow.f64 l 2) (.f64 (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (*.f64 n U) Om))) U))) Om))))
	57.4b	(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)))
✓	26.7b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (+.f64 (.f64 (.f64 l -2) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))) (.f64 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))))))
	39.3b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 (fma.f64 (/.f64 (.f64 n n) Om) (.f64 (.f64 l l) U) (.f64 (.f64 (.f64 l l) n) -2)) (/.f64 Om U)))))
	38.5b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 (.f64 (-.f64 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) U)) Om) (.f64 2 (*.f64 n (pow.f64 l 2)))) U) Om))))
	40.6b	(.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)))
	59.0b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))
	39.4b	(.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))))
	39.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	29.6b	(.f64 (cbrt.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))) (cbrt.f64 (sqrt.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)))))
	61.5b	(.f64 (/.f64 1 Om) (sqrt.f64 (-.f64 (.f64 2 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U)))) (.f64 2 (.f64 (pow.f64 n 2) (*.f64 (pow.f64 l 2) (pow.f64 U 2)))))))
	31.5b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (+.f64 (.f64 (.f64 l -2) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))) (.f64 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om)) (.f64 (.f64 (*.f64 2 n) U) (/.f64 l Om))))))
	57.9b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.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))))))))
	62.2b	(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))))
	30.0b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (+.f64 (.f64 (.f64 l -2) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))) (.f64 (/.f64 (.f64 n (.f64 l (-.f64 U* U))) Om) (.f64 (.f64 (*.f64 2 n) U) (/.f64 l Om))))))
	58.9b	(.f64 l (sqrt.f64 (fma.f64 2 (-.f64 (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 Om Om)) (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 Om Om))) (.f64 -4 (/.f64 (.f64 U n) Om)))))
	35.6b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	61.6b	(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))))))))
	34.6b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 -4 (/.f64 (.f64 n (*.f64 (pow.f64 l 2) U)) Om))))
	58.9b	(.f64 (sqrt.f64 (fma.f64 2 (-.f64 (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 Om Om)) (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 Om Om))) (.f64 -4 (/.f64 (.f64 U n) Om)))) (neg.f64 l))

Compiler

Compiled 21775 to 11978 computations (45% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.9b	(*.f64 n (/.f64 l Om))
	7.0b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
	9.7b	(.f64 (.f64 (*.f64 2 n) U) (/.f64 l Om))
✓	18.5b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))

series618.0ms (3.7%)

Counts

1 → 48

Calls

1 calls:

617.0ms

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

rewrite63.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

255×	`prod-diff_binary64`
215×	`add-sqr-sqrt_binary64`
201×	`log1p-expm1-u_binary64`
201×	`expm1-log1p-u_binary64`
199×	`add-log-exp_binary64`

Counts

1 → 22

Calls

1 calls:

62.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	44
1	426	37
2	4865	37
3	5361	37

simplify154.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

648×	`associate-/l*_binary64`
563×	`associate-/r*_binary64`
536×	`fma-def_binary64`
240×	`*-commutative_binary64`
126×	`cancel-sign-sub-inv_binary64`

Counts

70 → 108

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	601	12283
1	2101	11179
2	5335	11179

prune397.0ms (2.4%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	1	23	24
Picked	1	0	1
Done	0	1	1
Total	176	25	201

Error

9.0b

Counts

201 → 25

Alt Table

Status	Error	Program
	60.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	61.5b	(.f64 (sqrt.f64 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) (.f64 U U)) (*.f64 Om Om))))) n)
	27.0b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (+.f64 (.f64 (.f64 l -2) (.f64 2 (/.f64 (.f64 n (.f64 l U)) Om))) (.f64 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))))))
	62.7b	(-.f64 (+.f64 (.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))) (.f64 1/2 (.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)) (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)))))))) (.f64 (/.f64 (.f64 (pow.f64 l 2) (sqrt.f64 2)) Om) (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (pow.f64 l 2) U) (pow.f64 Om 2)) (/.f64 (*.f64 (pow.f64 l 2) U) (pow.f64 Om 2)))))))
	31.7b	(pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om)) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om))))))) 2)
	36.0b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 (.f64 n (.f64 (pow.f64 l 2) (.f64 (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (*.f64 n U) Om))) U))) Om))))
	57.4b	(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)))
✓	26.7b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (+.f64 (.f64 (.f64 l -2) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))) (.f64 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))))))
	39.3b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 (fma.f64 (/.f64 (.f64 n n) Om) (.f64 (.f64 l l) U) (.f64 (.f64 (.f64 l l) n) -2)) (/.f64 Om U)))))
	38.5b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 2 (/.f64 (.f64 (-.f64 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) U)) Om) (.f64 2 (*.f64 n (pow.f64 l 2)))) U) Om))))
	40.6b	(.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)))
	59.0b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))
	39.4b	(.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))))
	39.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	29.6b	(.f64 (cbrt.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))) (cbrt.f64 (sqrt.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)))))
	57.9b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 U (-.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))))))))
	62.2b	(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))))
	30.0b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (+.f64 (.f64 (.f64 l -2) (.f64 (.f64 (.f64 2 n) U) (/.f64 l Om))) (.f64 (/.f64 (.f64 n (.f64 l (-.f64 U* U))) Om) (.f64 (.f64 (*.f64 2 n) U) (/.f64 l Om))))))
	58.9b	(.f64 l (sqrt.f64 (fma.f64 2 (-.f64 (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 Om Om)) (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 Om Om))) (.f64 -4 (/.f64 (.f64 U n) Om)))))
	35.6b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	30.9b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 -2 (/.f64 (.f64 (.f64 n (.f64 l U)) (fma.f64 2 l (/.f64 (.f64 n (.f64 l U)) Om))) Om))))
	61.6b	(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))))))))
	34.6b	(sqrt.f64 (fma.f64 (.f64 (.f64 2 n) U) t (.f64 -4 (/.f64 (.f64 n (*.f64 (pow.f64 l 2) U)) Om))))
	61.5b	(.f64 (/.f64 1 Om) (sqrt.f64 (-.f64 (.f64 2 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U)))) (.f64 2 (.f64 (pow.f64 n 2) (*.f64 (pow.f64 l 2) (pow.f64 U 2)))))))
	58.9b	(.f64 (sqrt.f64 (fma.f64 2 (-.f64 (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 Om Om)) (/.f64 (.f64 (.f64 U U) (.f64 n n)) (.f64 Om Om))) (.f64 -4 (/.f64 (.f64 U n) Om)))) (neg.f64 l))

Compiler

Compiled 19775 to 11074 computations (44% saved)

regimes2.2s (12.9%)

Accuracy

Total 16.5b remaining (62.6%)

Threshold costs 0b (0%)

Counts

161 → 2

Compiler

Compiled 47394 to 31018 computations (34.6% saved)

bsearch77.0ms (0.5%)

Steps

Iters	Range		Point
9	-3.2121946617569775e-306	4.773887678510666e-304	2.998073525591517e-309

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	87
1	43	87
2	47	87
3	49	87
4	50	87
5	49	87

end435.0ms (2.6%)

Compiler: Compiled 1096 to 682 computations (37.8% saved)

Details

analyze3.1s (18.6%)

sample4.8s (28.4%)

simplify49.0ms (0.3%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series1.3s (7.5%)

rewrite80.0ms (0.5%)

simplify212.0ms (1.3%)

prune419.0ms (2.5%)

localize17.0ms (0.1%)

series833.0ms (4.9%)

rewrite69.0ms (0.4%)

simplify251.0ms (1.5%)

prune461.0ms (2.7%)

localize18.0ms (0.1%)

series663.0ms (3.9%)

rewrite63.0ms (0.4%)

simplify158.0ms (0.9%)

prune441.0ms (2.6%)

localize18.0ms (0.1%)

series618.0ms (3.7%)

rewrite63.0ms (0.4%)

simplify154.0ms (0.9%)

prune397.0ms (2.4%)

regimes2.2s (12.9%)

bsearch77.0ms (0.5%)

simplify4.0ms (0%)

end435.0ms (2.6%)

Profiling