Details

analyze3.0s (19.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample4.5s (29.3%)

Results

2.8s	14323×	body	128	invalid
1.7s	8256×	body	128	valid

Compiler

Compiled 70 to 48 computations (31.4% saved)

preprocess39.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

661×	`distribute-rgt-in_binary64`
501×	`fma-def_binary64`
356×	`cancel-sign-sub-inv_binary64`
251×	`distribute-rgt-neg-in_binary64`
235×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	170	672
1	563	640
2	2197	640
0	6	6

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 34 to 23 computations (32.4% saved)

simplify28.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

515×	`fma-neg_binary64`
395×	`fma-def_binary64`
280×	`distribute-rgt-in_binary64`
276×	`distribute-lft-in_binary64`
245×	`associate-*r/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	42
1	58	40
2	192	40
3	983	38
4	4416	37

Stop Event

1×	node limit

Counts

1 → 2

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

27.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	27.9b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	32.6b	(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

▶

27.9b

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

32.6b

(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
✓	4.8b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	5.0b	(*.f64 n (/.f64 l Om))
✓	8.9b	(.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))
✓	18.4b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))

series1.1s (7%)

Counts

4 → 216

Calls

60 calls:

154.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))	U	0
96.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))	n	0
88.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))	U	inf
49.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))	U*	inf
48.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))	t	-inf

rewrite43.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

223×	`add-sqr-sqrt_binary64`
211×	`log1p-expm1-u_binary64`
211×	`expm1-log1p-u_binary64`
210×	`add-cbrt-cube_binary64`
207×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	92
1	441	88

Stop Event

1×	node limit

Counts

4 → 85

simplify189.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	876	17039
1	3328	16151

Stop Event

1×	node limit

Counts

301 → 214

prune404.0ms (2.6%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	194	20	214
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	196	20	216

Error

13.5b

Counts

216 → 20

Alt Table

Status	Error	Program
	39.7b	(.f64 (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) t)) (sqrt.f64 (.f64 (*.f64 2 n) U)))
	55.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om)))))) (neg.f64 (*.f64 (sqrt.f64 2) l)))
	40.5b	(sqrt.f64 (.f64 2 (.f64 n (*.f64 t U))))
	58.2b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om)))))) (*.f64 (sqrt.f64 2) l))
▶	27.9b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l))))))))
	37.9b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 (/.f64 (.f64 l l) (/.f64 Om U)) -4))))
	61.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	62.4b	(.f64 U (neg.f64 (sqrt.f64 (.f64 -2 (/.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 Om Om))))))
	60.3b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (/.f64 (sqrt.f64 2) Om))
	61.7b	(.f64 (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)))))) (neg.f64 n))
	36.9b	(cbrt.f64 (pow.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 3/2))
	60.4b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (.f64 n (.f64 (pow.f64 l 2) U))) U))) (/.f64 (sqrt.f64 2) Om))
	61.1b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (*.f64 Om Om)))
	60.1b	(fma.f64 (.f64 1/8 (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om))) 3) U)))) (/.f64 (.f64 t t) (/.f64 (pow.f64 l 3) (sqrt.f64 2))) (-.f64 (.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) -1/2) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om)))))) (*.f64 (sqrt.f64 2) l))))
	60.7b	(.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)))
	28.1b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	57.3b	(-.f64 (.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) -1/2) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om)))))) (.f64 (sqrt.f64 2) l)))
	41.2b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	38.9b	(sqrt.f64 (fma.f64 2 (.f64 (.f64 n t) U) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))
	44.4b	(-.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)))

Compiler

Compiled 19455 to 10694 computations (45% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.8b	(.f64 (-.f64 U U) (/.f64 n (/.f64 Om l)))
✓	5.1b	(/.f64 n (/.f64 Om l))
✓	8.9b	(.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l)))))))
✓	18.4b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l))))))))

series1.1s (6.8%)

Counts

4 → 216

Calls

60 calls:

149.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l))))))))	U	0
100.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l))))))))	n	0
81.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l))))))))	U	inf
46.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l))))))))	U*	-inf
44.0ms	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l))))))))	t	-inf

rewrite42.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

236×	`add-sqr-sqrt_binary64`
223×	`log1p-expm1-u_binary64`
223×	`expm1-log1p-u_binary64`
222×	`add-cbrt-cube_binary64`
219×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	92
1	468	88

Stop Event

1×	node limit

Counts

4 → 96

simplify178.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	876	17039
1	3328	16151

Stop Event

1×	node limit

Counts

312 → 226

prune362.0ms (2.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	2	17	19
Picked	0	1	1
Done	0	0	0
Total	227	19	246

Error

13.5b

Counts

246 → 19

Alt Table

Status	Error	Program
	39.7b	(.f64 (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) t)) (sqrt.f64 (.f64 (*.f64 2 n) U)))
	55.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om)))))) (neg.f64 (*.f64 (sqrt.f64 2) l)))
	40.5b	(sqrt.f64 (.f64 2 (.f64 n (*.f64 t U))))
	58.2b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om)))))) (*.f64 (sqrt.f64 2) l))
✓	27.9b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l))))))))
	37.9b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 (/.f64 (.f64 l l) (/.f64 Om U)) -4))))
	36.9b	(cbrt.f64 (pow.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 3/2))
	60.4b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (.f64 n (.f64 (pow.f64 l 2) U))) U))) (/.f64 (sqrt.f64 2) Om))
	61.1b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (*.f64 Om Om)))
	60.1b	(fma.f64 (.f64 1/8 (sqrt.f64 (/.f64 n (/.f64 (pow.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om))) 3) U)))) (/.f64 (.f64 t t) (/.f64 (pow.f64 l 3) (sqrt.f64 2))) (-.f64 (.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) -1/2) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om)))))) (*.f64 (sqrt.f64 2) l))))
	60.7b	(.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)))
	62.1b	(sqrt.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 n) U) 2) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))
▶	28.1b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	57.3b	(-.f64 (.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) -1/2) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om)))))) (.f64 (sqrt.f64 2) l)))
	41.2b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	61.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	38.9b	(sqrt.f64 (fma.f64 2 (.f64 (.f64 n t) U) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))
	44.4b	(-.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)))
	61.7b	(.f64 (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)))))) (neg.f64 n))

Compiler

Compiled 19610 to 10694 computations (45.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.8b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
	5.0b	(*.f64 n (/.f64 l Om))
✓	8.9b	(.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))
✓	18.4b	(sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t)))

series731.0ms (4.7%)

Counts

2 → 120

Calls

36 calls:

109.0ms	(sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t)))	U	0
64.0ms	(sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t)))	n	0
55.0ms	(sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t)))	U	-inf
53.0ms	(sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t)))	U	inf
33.0ms	(sqrt.f64 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t)))	U*	inf

rewrite61.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

639×	`prod-diff_binary64`
184×	`add-sqr-sqrt_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`
171×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	62
1	362	62
2	4856	62

Stop Event

1×	node limit

Counts

2 → 45

simplify156.0ms (1%)

Algorithm

1×	egg-herbie

Rules

800×	`associate-/l*_binary64`
671×	`fma-def_binary64`
285×	`*-commutative_binary64`
153×	`+-commutative_binary64`
120×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	709	15123
1	2682	14256

Stop Event

1×	node limit

Counts

165 → 160

prune363.0ms (2.3%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	202	9	211
Fresh	6	11	17
Picked	1	0	1
Done	0	1	1
Total	209	21	230

Error

10.8b

Counts

230 → 21

Alt Table

Status	Error	Program
	60.2b	(.f64 (sqrt.f64 2) (-.f64 (.f64 (.f64 1/8 (sqrt.f64 (.f64 (/.f64 n (pow.f64 (-.f64 (/.f64 n (/.f64 Om (/.f64 U* Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om))))) 3)) U))) (/.f64 (.f64 t t) (pow.f64 l 3))) (fma.f64 l (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 Om (/.f64 U Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om)))))))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 n (/.f64 Om (/.f64 U Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om))))))) (/.f64 t l))))))
	58.2b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om)))))) (*.f64 (sqrt.f64 2) l))
	55.8b	(.f64 (sqrt.f64 2) (.f64 -1 (.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n U) (pow.f64 Om 2)) (+.f64 (.f64 2 (/.f64 1 Om)) (/.f64 (*.f64 n U) (pow.f64 Om 2)))) U))) l)))
	41.2b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	43.2b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U U) (/.f64 l Om)) n)) t)))))
	58.1b	(.f64 (sqrt.f64 2) (.f64 l (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 Om (/.f64 U* Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om))))))))))
▶	34.6b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (fma.f64 U t (.f64 (.f64 (/.f64 l (/.f64 Om l)) U) -2)))))
	36.9b	(cbrt.f64 (pow.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 3/2))
	60.4b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (.f64 n (.f64 (pow.f64 l 2) U))) U))) (/.f64 (sqrt.f64 2) Om))
	38.2b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (-.f64 (.f64 t U) (.f64 2 (/.f64 (*.f64 (pow.f64 l 2) U) Om))))))
	60.6b	(.f64 (sqrt.f64 2) (.f64 n (sqrt.f64 (.f64 U (-.f64 (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) U) (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) U))))))
	61.1b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (*.f64 Om Om)))
	62.1b	(sqrt.f64 (log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 n) U) 2) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))
	57.3b	(-.f64 (.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) -1/2) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om)))))) (.f64 (sqrt.f64 2) l)))
	39.7b	(.f64 (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) t)) (sqrt.f64 (.f64 (*.f64 2 n) U)))
✓	27.9b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l))))))))
	40.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U* U) (/.f64 l Om)) n)) t)) (sqrt.f64 (*.f64 n U))))
	61.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	38.9b	(sqrt.f64 (fma.f64 2 (.f64 (.f64 n t) U) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))
	61.7b	(.f64 (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)))))) (neg.f64 n))
	44.2b	(.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 (.f64 n (.f64 U t))) (.f64 (/.f64 l (/.f64 Om l)) (sqrt.f64 (*.f64 (/.f64 n t) U)))))

Compiler

Compiled 19208 to 10034 computations (47.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(fma.f64 U t (.f64 (.f64 (/.f64 l (/.f64 Om l)) U) -2))
✓	7.1b	(*.f64 (/.f64 l (/.f64 Om l)) U)
✓	7.4b	(.f64 n (fma.f64 U t (.f64 (*.f64 (/.f64 l (/.f64 Om l)) U) -2)))
✓	13.7b	(sqrt.f64 (.f64 n (fma.f64 U t (.f64 (*.f64 (/.f64 l (/.f64 Om l)) U) -2))))

series303.0ms (2%)

Counts

4 → 168

Calls

51 calls:

26.0ms	(sqrt.f64 (.f64 n (fma.f64 U t (.f64 (*.f64 (/.f64 l (/.f64 Om l)) U) -2))))	n	0
26.0ms	(sqrt.f64 (.f64 n (fma.f64 U t (.f64 (*.f64 (/.f64 l (/.f64 Om l)) U) -2))))	n	-inf
24.0ms	(sqrt.f64 (.f64 n (fma.f64 U t (.f64 (*.f64 (/.f64 l (/.f64 Om l)) U) -2))))	n	inf
22.0ms	(sqrt.f64 (.f64 n (fma.f64 U t (.f64 (*.f64 (/.f64 l (/.f64 Om l)) U) -2))))	U	0
21.0ms	(sqrt.f64 (.f64 n (fma.f64 U t (.f64 (*.f64 (/.f64 l (/.f64 Om l)) U) -2))))	U	inf

rewrite61.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

263×	`expm1-udef_binary64`
263×	`log1p-udef_binary64`
258×	`prod-diff_binary64`
147×	`add-sqr-sqrt_binary64`
136×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	69
1	294	69
2	3870	69

Stop Event

1×	node limit

Counts

4 → 92

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

782×	`associate-/r*_binary64`
332×	`associate-*l/_binary64`
272×	`associate-/r/_binary64`
268×	`fma-def_binary64`
162×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	3650
1	409	3554
2	1618	3334

Stop Event

1×	node limit

Counts

260 → 146

prune151.0ms (1%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	2	17	19
Picked	1	0	1
Done	0	1	1
Total	143	24	167

Error

8.8b

Counts

167 → 24

Alt Table

Status	Error	Program
	60.2b	(.f64 (sqrt.f64 2) (-.f64 (.f64 (.f64 1/8 (sqrt.f64 (.f64 (/.f64 n (pow.f64 (-.f64 (/.f64 n (/.f64 Om (/.f64 U* Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om))))) 3)) U))) (/.f64 (.f64 t t) (pow.f64 l 3))) (fma.f64 l (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 Om (/.f64 U Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om)))))))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 n (/.f64 Om (/.f64 U Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om))))))) (/.f64 t l))))))
	58.2b	(.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om)))))) (*.f64 (sqrt.f64 2) l))
	55.8b	(.f64 (sqrt.f64 2) (.f64 -1 (.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n U) (pow.f64 Om 2)) (+.f64 (.f64 2 (/.f64 1 Om)) (/.f64 (*.f64 n U) (pow.f64 Om 2)))) U))) l)))
	41.2b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (*.f64 n t) U)))
	43.2b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 n) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U U) (/.f64 l Om)) n)) t)))))
	58.1b	(.f64 (sqrt.f64 2) (.f64 l (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 n (/.f64 Om (/.f64 U* Om))) (+.f64 (/.f64 2 Om) (/.f64 n (/.f64 Om (/.f64 U Om))))))))))
	39.2b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (fma.f64 U t (.f64 (sqrt.f64 (pow.f64 (.f64 l (*.f64 (/.f64 l Om) U)) 2)) -2)))))
	61.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	34.0b	(.f64 (sqrt.f64 2) (expm1.f64 (log1p.f64 (sqrt.f64 (.f64 n (fma.f64 U t (.f64 (.f64 l (*.f64 (/.f64 l Om) U)) -2)))))))
	61.7b	(.f64 (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)))))) (neg.f64 n))
	36.9b	(cbrt.f64 (pow.f64 (.f64 2 (.f64 (.f64 n U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))) 3/2))
	60.4b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (.f64 n (.f64 (pow.f64 l 2) U)) (.f64 n (.f64 (pow.f64 l 2) U))) U))) (/.f64 (sqrt.f64 2) Om))
	60.6b	(.f64 (sqrt.f64 2) (.f64 n (sqrt.f64 (.f64 U (-.f64 (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) U) (.f64 (/.f64 (.f64 l l) (.f64 Om Om)) U))))))
	61.1b	(sqrt.f64 (/.f64 (.f64 2 (.f64 n (.f64 U (.f64 (.f64 n (.f64 l l)) (-.f64 U* U))))) (*.f64 Om Om)))
	44.2b	(.f64 (sqrt.f64 2) (-.f64 (sqrt.f64 (.f64 n (.f64 U t))) (.f64 (/.f64 l (/.f64 Om l)) (sqrt.f64 (*.f64 (/.f64 n t) U)))))
	57.2b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (.f64 -2 (.f64 (/.f64 n Om) U))) (neg.f64 l)))
	39.7b	(.f64 (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) t)) (sqrt.f64 (.f64 (*.f64 2 n) U)))
	59.0b	(.f64 (sqrt.f64 2) (.f64 l (sqrt.f64 (.f64 -2 (.f64 (/.f64 n Om) U)))))
	45.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 (pow.f64 (.f64 n (fma.f64 U t (.f64 (.f64 l (*.f64 (/.f64 l Om) U)) -2))) 2))))
✓	27.9b	(sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 n (/.f64 Om l))))))))
	40.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (.f64 (-.f64 U* U) (/.f64 l Om)) n)) t)) (sqrt.f64 (*.f64 n U))))
	38.9b	(sqrt.f64 (fma.f64 2 (.f64 (.f64 n t) U) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))
	32.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (fma.f64 U t (.f64 (/.f64 (/.f64 (.f64 U l) Om) (/.f64 1 l)) -2)))))
	57.3b	(-.f64 (.f64 (.f64 (sqrt.f64 (/.f64 n (/.f64 (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om))) U))) (/.f64 t (/.f64 l (sqrt.f64 2)))) -1/2) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (/.f64 2 Om)) (/.f64 (.f64 n U) (.f64 Om Om)))))) (.f64 (sqrt.f64 2) l)))

Compiler

Compiled 4693 to 2578 computations (45.1% saved)

regimes2.2s (14%)

Accuracy

Total 16.8b remaining (62.5%)

Threshold costs 0b (0%)

Counts

146 → 3

Compiler

Compiled 35826 to 24474 computations (31.7% saved)

bsearch7.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms

(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*)))))

0.0ms

(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*)))))

Steps

Iters	Point		Range
3.9311733367951677e+145	∈ [	3.9311733367951677e+145	,	#hash((type . real) (value . +inf))	]
0.0	∈ [	0.0	,	8.750190191364712e-152	]

Compiler

Compiled 34 to 23 computations (32.4% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

34×	`*-commutative_binary64`
18×	`+-commutative_binary64`
17×	`sub-neg_binary64`
15×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	189
1	96	189
2	126	189
3	149	189
4	179	189
5	201	189
6	211	189
7	216	189
8	219	189
9	220	189

Stop Event

1×

saturated

end419.0ms (2.7%)

Stop Event

1×

fuel

Compiler

Compiled 1062 to 669 computations (37% saved)

Iter	Nodes	Cost
0	62	189
1	96	189
2	126	189
3	149	189
4	179	189
5	201	189
6	211	189
7	216	189
8	219	189
9	220	189

Iter	Nodes	Cost
0	62	189
1	96	189
2	126	189
3	149	189
4	179	189
5	201	189
6	211	189
7	216	189
8	219	189
9	220	189

Details

analyze3.0s (19.2%)

sample4.5s (29.3%)

preprocess39.0ms (0.3%)

simplify28.0ms (0.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series1.1s (7%)

rewrite43.0ms (0.3%)

simplify189.0ms (1.2%)

prune404.0ms (2.6%)

localize16.0ms (0.1%)

series1.1s (6.8%)

rewrite42.0ms (0.3%)

simplify178.0ms (1.1%)

prune362.0ms (2.3%)

localize15.0ms (0.1%)

series731.0ms (4.7%)

rewrite61.0ms (0.4%)

simplify156.0ms (1%)

prune363.0ms (2.3%)

localize12.0ms (0.1%)

series303.0ms (2%)

rewrite61.0ms (0.4%)

simplify66.0ms (0.4%)

prune151.0ms (1%)

regimes2.2s (14%)

bsearch7.0ms (0%)

simplify9.0ms (0.1%)

end419.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	62	189
1	96	189
2	126	189
3	149	189
4	179	189
5	201	189
6	211	189
7	216	189
8	219	189
9	220	189