Details

analyze2.9s (13.2%)

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)

sample4.4s (19.8%)

Results

2.7s	14408×	body	128	invalid
1.6s	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

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

29.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	29.2b	(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))))))))
	32.5b	(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)))))

Status

Error

Program

▶

29.2b

(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))))))))

32.5b

(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*)))))

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))
✓	8.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	10.8b	(.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)))))))
✓	17.6b	(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))))))))

series1.8s (8.3%)

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))))))))
387.0ms	(.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))

rewrite78.0ms (0.4%)

Algorithm

2×	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 → 84

Calls

4 calls:

76.0ms	(*.f64 n (/.f64 l Om))
76.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
76.0ms	(.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)))))))
76.0ms	(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: 0 (0.0ms)

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

simplify199.0ms (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

300 → 211

Iterations

Useful iterations: 1 (0.0ms)

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

prune415.0ms (1.9%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	191	20	211
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	192	21	213

Error

10.8b

Counts

213 → 21

Alt Table

Status	Error	Program
	31.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n (-.f64 U* U)) Om) l))))))
	42.9b	(sqrt.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U* U))) (.f64 Om Om)) (.f64 n (.f64 U t)))) (fma.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U U))) (.f64 Om Om)) (.f64 4 (/.f64 (.f64 n (.f64 (*.f64 l l) U)) 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))))
	56.3b	(.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))
	61.1b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	34.4b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	38.0b	(.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)))))
	60.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	30.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U*)) 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))))))))
	31.8b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 (-.f64 U* U) l)) Om))))))
	58.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	57.2b	(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)))
	63.1b	(-.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)))))))
	33.5b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))
✓	29.2b	(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))))))))
	44.2b	(.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)))
	42.8b	(.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))))
	42.1b	(-.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)))
	38.7b	(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))))

Compiler

Compiled 19551 to 10848 computations (44.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	8.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	10.8b	(.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))
✓	17.6b	(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)))
✓	18.7b	(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)))

series3.2s (14.4%)

Counts

3 → 192

Calls

3 calls:

1.4s

(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)))

1.4s

(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)))

445.0ms

(*.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))

rewrite87.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

378×	`prod-diff_binary64`
211×	`add-sqr-sqrt_binary64`
197×	`log1p-expm1-u_binary64`
197×	`expm1-log1p-u_binary64`
195×	`add-cube-cbrt_binary64`

Counts

3 → 66

Calls

3 calls:

85.0ms

(*.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))

84.0ms

(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)))

84.0ms

(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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	103
1	421	103
2	4943	103
3	5694	103
0	0	0
1	0	0

simplify369.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

408×	`fma-def_binary64`
375×	`associate-/l*_binary64`
243×	`associate-/r*_binary64`
243×	`times-frac_binary64`
101×	`sub-neg_binary64`

Counts

258 → 314

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2399	41513
1	5173	41513

prune1.0s (4.5%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	423	0	423
Fresh	0	19	19
Picked	0	1	1
Done	0	1	1
Total	423	21	444

Error

10.8b

Counts

444 → 21

Alt Table

Status	Error	Program
	31.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n (-.f64 U* U)) Om) l))))))
	42.9b	(sqrt.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U* U))) (.f64 Om Om)) (.f64 n (.f64 U t)))) (fma.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U U))) (.f64 Om Om)) (.f64 4 (/.f64 (.f64 n (.f64 (*.f64 l l) U)) 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))))
	56.3b	(.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))
	61.1b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	34.4b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	38.0b	(.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)))))
	60.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
▶	30.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U*)) 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))))))))
	31.8b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (.f64 (-.f64 U* U) l)) Om))))))
	58.7b	(neg.f64 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	57.2b	(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)))
	63.1b	(-.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)))))))
	33.5b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))
✓	29.2b	(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))))))))
	44.2b	(.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)))
	42.8b	(.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))))
	42.1b	(-.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)))
	38.7b	(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))))

Compiler

Compiled 66394 to 35569 computations (46.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.4b	(.f64 (.f64 n l) (-.f64 U U*))
✓	6.7b	(/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om)
✓	10.8b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om))))))
✓	17.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om)))))))

series1.8s (8.3%)

Counts

4 → 228

Calls

4 calls:

1.4s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om)))))))
400.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om))))))
32.0ms	(/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om)
13.0ms	(.f64 (.f64 n l) (-.f64 U U*))

rewrite76.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

247×	`add-sqr-sqrt_binary64`
233×	`log1p-expm1-u_binary64`
233×	`expm1-log1p-u_binary64`
228×	`add-cbrt-cube_binary64`
228×	`add-exp-log_binary64`

Counts

4 → 74

Calls

4 calls:

74.0ms	(.f64 (.f64 n l) (-.f64 U U*))
74.0ms	(/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om)
74.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om))))))
74.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U*)) Om)))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	99
1	488	95
2	4867	95
3	4990	95
0	0	0
1	0	0

simplify210.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Counts

302 → 209

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	872	17255
1	3084	16361
2	5016	16361

prune362.0ms (1.6%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	205	4	209
Fresh	3	15	18
Picked	1	0	1
Done	0	2	2
Total	209	21	230

Error

10.8b

Counts

230 → 21

Alt Table

Status	Error	Program
	31.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n (-.f64 U* U)) Om) l))))))
	42.9b	(sqrt.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U* U))) (.f64 Om Om)) (.f64 n (.f64 U t)))) (fma.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U U))) (.f64 Om Om)) (.f64 4 (/.f64 (.f64 n (.f64 (*.f64 l l) U)) 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))))
	56.3b	(.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))
	61.1b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	34.4b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	38.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	42.1b	(-.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)))
▶	30.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (.f64 (.f64 (.f64 n l) (-.f64 U U)) (/.f64 1 Om))))))))
✓	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)))))
	60.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) 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))))))))
	61.4b	(.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))))))
	33.5b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))
✓	29.2b	(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))))))))
	44.2b	(.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)))
	39.1b	(pow.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U)) Om))) t)) 3/2) 1/3)
	43.8b	(.f64 (sqrt.f64 (.f64 2 n)) (pow.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U)) Om))) t)) 1/2))
	58.7b	(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)))
	38.7b	(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))))
	57.2b	(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)))

Compiler

Compiled 19177 to 10624 computations (44.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	6.4b	(.f64 (.f64 n l) (-.f64 U U*))
✓	6.8b	(.f64 (.f64 (.f64 n l) (-.f64 U U)) (/.f64 1 Om))
✓	10.8b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (.f64 (.f64 (.f64 n l) (-.f64 U U)) (/.f64 1 Om)))))))
✓	17.6b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (.f64 (.f64 (.f64 n l) (-.f64 U U)) (/.f64 1 Om))))))))

series1.8s (8.2%)

Counts

3 → 180

Calls

3 calls:

1.4s

(sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (*.f64 (*.f64 (*.f64 n l) (-.f64 U U*)) (/.f64 1 Om))))))))

398.0ms

(*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (*.f64 (*.f64 (*.f64 n l) (-.f64 U U*)) (/.f64 1 Om)))))))

32.0ms

(*.f64 (*.f64 (*.f64 n l) (-.f64 U U*)) (/.f64 1 Om))

rewrite38.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

260×	`add-sqr-sqrt_binary64`
245×	`log1p-expm1-u_binary64`
245×	`expm1-log1p-u_binary64`
241×	`add-log-exp_binary64`
240×	`add-cbrt-cube_binary64`

Counts

3 → 59

Calls

3 calls:

36.0ms

(*.f64 (*.f64 (*.f64 n l) (-.f64 U U*)) (/.f64 1 Om))

36.0ms

(*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (*.f64 (*.f64 (*.f64 n l) (-.f64 U U*)) (/.f64 1 Om)))))))

35.0ms

(sqrt.f64 (*.f64 (*.f64 (*.f64 2 n) U) (+.f64 t (*.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (*.f64 (*.f64 (*.f64 n l) (-.f64 U U*)) (/.f64 1 Om))))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	89
1	525	85
2	4997	85
0	0	0
1	0	0

simplify196.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

734×	`fma-def_binary64`
403×	`*-commutative_binary64`
194×	`associate-r_binary64`
150×	`+-commutative_binary64`
145×	`associate-/l*_binary64`

Counts

239 → 186

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	871	16787
1	3082	15893
2	5016	15893

prune319.0ms (1.4%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	207	1	208
Fresh	1	17	18
Picked	1	0	1
Done	0	2	2
Total	209	20	229

Error

10.8b

Counts

229 → 20

Alt Table

Status	Error	Program
	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))))
	56.3b	(.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))
	61.1b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	34.4b	(sqrt.f64 (.f64 n (-.f64 (.f64 2 (.f64 t U)) (.f64 4 (/.f64 (*.f64 (pow.f64 l 2) U) Om)))))
	38.0b	(.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)))))
	60.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) 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))))))))
	61.4b	(.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))))))
	31.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 l (.f64 n (-.f64 U U*))) Om)))))))
	58.7b	(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)))
	42.9b	(sqrt.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U* U))) (.f64 Om Om)) (.f64 n (.f64 U t)))) (fma.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U U))) (.f64 Om Om)) (.f64 4 (/.f64 (.f64 n (.f64 (*.f64 l l) U)) Om)))))
	33.5b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))
✓	29.2b	(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))))))))
	44.2b	(.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)))
	39.1b	(pow.f64 (pow.f64 (.f64 (.f64 (.f64 2 n) U) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U)) Om))) t)) 3/2) 1/3)
	42.1b	(-.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)))
	43.8b	(.f64 (sqrt.f64 (.f64 2 n)) (pow.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 (.f64 n l) (-.f64 U U)) Om))) t)) 1/2))
	38.7b	(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))))
	57.2b	(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)))

Compiler

Compiled 18509 to 10252 computations (44.6% saved)

regimes2.3s (10.3%)

Accuracy

Total 13.9b remaining (52.1%)

Threshold costs 0b (0%)

Counts

116 → 3

Compiler

Compiled 36674 to 23786 computations (35.1% saved)

bsearch7.0ms (0%)

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

simplify33.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

198×	`distribute-rgt-neg-in_binary64`
135×	`distribute-lft-neg-in_binary64`
135×	`cancel-sign-sub-inv_binary64`
121×	`distribute-lft-neg-out_binary64`
115×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	211
1	105	211
2	147	211
3	191	209
4	232	209
5	258	209
6	271	209
7	298	209
8	325	209
9	374	209
10	449	209
11	541	209
12	612	209
13	694	209
14	791	209
15	860	209
16	906	209
17	923	209
18	925	209
19	919	209

end394.0ms (1.8%)

Compiler: Compiled 983 to 589 computations (40.1% saved)

Iter	Nodes	Cost
0	62	211
1	105	211
2	147	211
3	191	209
4	232	209
5	258	209
6	271	209
7	298	209
8	325	209
9	374	209
10	449	209
11	541	209
12	612	209
13	694	209
14	791	209
15	860	209
16	906	209
17	923	209
18	925	209
19	919	209

Iter	Nodes	Cost
0	62	211
1	105	211
2	147	211
3	191	209
4	232	209
5	258	209
6	271	209
7	298	209
8	325	209
9	374	209
10	449	209
11	541	209
12	612	209
13	694	209
14	791	209
15	860	209
16	906	209
17	923	209
18	925	209
19	919	209

Details

analyze2.9s (13.2%)

sample4.4s (19.8%)

simplify47.0ms (0.2%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series1.8s (8.3%)

rewrite78.0ms (0.4%)

simplify199.0ms (0.9%)

prune415.0ms (1.9%)

localize20.0ms (0.1%)

series3.2s (14.4%)

rewrite87.0ms (0.4%)

simplify369.0ms (1.7%)

prune1.0s (4.5%)

localize18.0ms (0.1%)

series1.8s (8.3%)

rewrite76.0ms (0.3%)

simplify210.0ms (0.9%)

prune362.0ms (1.6%)

localize17.0ms (0.1%)

series1.8s (8.2%)

rewrite38.0ms (0.2%)

simplify196.0ms (0.9%)

prune319.0ms (1.4%)

regimes2.3s (10.3%)

bsearch7.0ms (0%)

simplify33.0ms (0.2%)

end394.0ms (1.8%)

Profiling

Iter	Nodes	Cost
0	62	211
1	105	211
2	147	211
3	191	209
4	232	209
5	258	209
6	271	209
7	298	209
8	325	209
9	374	209
10	449	209
11	541	209
12	612	209
13	694	209
14	791	209
15	860	209
16	906	209
17	923	209
18	925	209
19	919	209