Details

analyze2.8s (6.8%)

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
2.5%	90%	7.5%	13
2.7%	88.7%	8.6%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample6.1s (14.7%)

Results

3.5s	11617×	body	128	invalid
2.5s	8256×	body	128	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify69.0ms (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

prune9.0ms (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

22.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	22.9b	(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))))))))
	29.4b	(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

▶

22.9b

(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))))))))

29.4b

(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)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.5b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	5.7b	(*.f64 n (/.f64 l Om))
✓	6.9b	(.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)))))))
✓	16.0b	(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))))))))

series3.7s (9%)

Counts

4 → 216

Calls

4 calls:

2.6s	(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))))))))
983.0ms	(.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)))))))
84.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
29.0ms	(*.f64 n (/.f64 l Om))

rewrite73.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-cbrt-cube_binary64`
27×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
17×	`associate-r_binary64`

Counts

4 → 107

Calls

4 calls:

22.0ms	(*.f64 n (/.f64 l Om))
14.0ms	(.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)))))))
11.0ms	(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))))))))
7.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))

simplify492.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

787×	`fma-def_binary64`
459×	`*-commutative_binary64`
231×	`associate-r_binary64`
165×	`+-commutative_binary64`
153×	`cancel-sign-sub-inv_binary64`

Counts

323 → 286

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1061	19930
1	3567	19396
2	5115	19396

prune1.0s (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	275	11	286
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	277	11	288

Error

11.3b

Counts

288 → 11

Alt Table

Status	Error	Program
	23.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om)))))))
	58.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (-.f64 (.f64 (.f64 l l) U) (.f64 (*.f64 l l) U)))))) (/.f64 (sqrt.f64 2) Om))
	36.2b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))
	44.3b	(-.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)))
	41.3b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	56.0b	(neg.f64 (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))))
	55.1b	(.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))
	55.8b	(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)))
	23.5b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n l) Om) (-.f64 U U))) t))))
▶	23.0b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))))))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))))
	41.2b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n l) Om) (-.f64 U U))) t)))

Compiler

Compiled 22517 to 11581 computations (48.6% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.7b	(*.f64 n (/.f64 l Om))
	6.9b	(.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)))))))
✓	9.5b	(sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))
	16.0b	(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))))))))

series2.6s (6.2%)

Counts

1 → 64

Calls

1 calls:

2.6s	(sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1_binary64`
10×	`sqrt-pow1_binary64`
6×	`pow-prod-down_binary64`
5×	`sqrt-prod_binary64`
4×	`sqrt-div_binary64`

Counts

1 → 23

Calls

1 calls:

21.0ms

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

simplify527.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

763×	`*-commutative_binary64`
412×	`associate-r_binary64`
229×	`fma-def_binary64`
185×	`associate-/l*_binary64`
170×	`associate-+r+_binary64`

Counts

87 → 150

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1453	22712
1	4955	22712
2	4985	22712

prune4.3s (10.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	759	1	760
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	759	12	771

Error

11.3b

Counts

771 → 12

Alt Table

Status	Error	Program
▶	23.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om)))))))
	58.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (-.f64 (.f64 (.f64 l l) U) (.f64 (*.f64 l l) U)))))) (/.f64 (sqrt.f64 2) Om))
	36.2b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))
	44.3b	(-.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)))
	41.3b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	56.0b	(neg.f64 (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))))
	55.1b	(.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))
	55.8b	(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)))
	23.5b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n l) Om) (-.f64 U U))) t))))
	23.2b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))))))) (.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))))))
✓	23.0b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))))))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))))
	41.2b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n l) Om) (-.f64 U U))) t)))

Compiler

Compiled 120675 to 64612 computations (46.5% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(/.f64 (*.f64 n l) Om)
✓	4.5b	(.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))
✓	6.9b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))))))
✓	16.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om)))))))

series3.8s (9.1%)

Counts

4 → 180

Calls

4 calls:

2.9s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om)))))))
768.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))))))
79.0ms	(.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))
28.0ms	(/.f64 (*.f64 n l) Om)

rewrite66.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-cbrt-cube_binary64`
27×	`add-exp-log_binary64`
25×	`pow1_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`pow-prod-down_binary64`

Counts

4 → 102

Calls

4 calls:

17.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))))))
15.0ms	(.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))
11.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om)))))))
7.0ms	(/.f64 (*.f64 n l) Om)

simplify470.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

787×	`fma-def_binary64`
446×	`*-commutative_binary64`
223×	`associate-r_binary64`
164×	`+-commutative_binary64`
154×	`cancel-sign-sub-inv_binary64`

Counts

282 → 267

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1046	19642
1	3532	19126
2	5107	19126

prune922.0ms (2.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	267	12	279

Error

11.3b

Counts

279 → 12

Alt Table

Status	Error	Program
✓	23.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om)))))))
	58.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (-.f64 (.f64 (.f64 l l) U) (.f64 (*.f64 l l) U)))))) (/.f64 (sqrt.f64 2) Om))
	36.2b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))
	44.3b	(-.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)))
	41.3b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	56.0b	(neg.f64 (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))))
	55.1b	(.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))
	55.8b	(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)))
	23.5b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n l) Om) (-.f64 U U))) t))))
▶	23.2b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))))))) (.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))))))
✓	23.0b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))))))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))))
	41.2b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n l) Om) (-.f64 U U))) t)))

Compiler

Compiled 21987 to 11380 computations (48.2% saved)

localize57.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	9.5b	(sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))
✓	11.7b	(cbrt.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))
✓	16.0b	(sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	16.0b	(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))))))))

series5.6s (13.4%)

Counts

2 → 120

Calls

2 calls:

2.9s

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

2.7s

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

rewrite19.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1_binary64`
6×	`pow-prod-down_binary64`
4×	`cbrt-prod_binary64`
4×	`sqrt-div_binary64`
4×	`associate-*r/_binary64`

Counts

2 → 33

Calls

2 calls:

7.0ms

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

6.0ms

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

simplify585.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

405×	`fma-def_binary64`
344×	`associate-/l*_binary64`
232×	`associate-/r*_binary64`
232×	`times-frac_binary64`
99×	`sub-neg_binary64`

Counts

153 → 253

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2437	41002
1	5121	41002

prune5.3s (12.7%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	766	0	766
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	766	12	778

Error

11.3b

Counts

778 → 12

Alt Table

Status	Error	Program
✓	23.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om)))))))
	58.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (-.f64 (.f64 (.f64 l l) U) (.f64 (*.f64 l l) U)))))) (/.f64 (sqrt.f64 2) Om))
	36.2b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))
	44.3b	(-.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)))
	41.3b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	56.0b	(neg.f64 (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))))
	55.1b	(.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))
	55.8b	(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)))
	23.5b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n l) Om) (-.f64 U U))) t))))
✓	23.2b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))))))) (.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 U (.f64 2 n)) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))))))
✓	23.0b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))))))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))))
	41.2b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (/.f64 (.f64 n l) Om) (-.f64 U U))) t)))

Compiler

Compiled 194643 to 106908 computations (45.1% saved)

regimes2.7s (6.4%)

Accuracy

Total 10.6b remaining (43.8%)

Threshold costs 0b (0%)

Counts

125 → 3

Compiler

Compiled 44994 to 27290 computations (39.3% saved)

bsearch9.0ms (0%)

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

simplify16.0ms (0%)

Algorithm

1×	egg-herbie

Rules

36×	`*-commutative_binary64`
23×	`+-commutative_binary64`
21×	`sub-neg_binary64`
20×	`neg-sub0_binary64`
20×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	199
1	83	199
2	110	199
3	133	199
4	159	199
5	180	199
6	191	199
7	207	199
8	222	199
9	228	199
10	230	199
11	225	199

end313.0ms (0.8%)

Compiler: Compiled 789 to 440 computations (44.2% saved)

Iter	Nodes	Cost
0	52	199
1	83	199
2	110	199
3	133	199
4	159	199
5	180	199
6	191	199
7	207	199
8	222	199
9	228	199
10	230	199
11	225	199

Iter	Nodes	Cost
0	52	199
1	83	199
2	110	199
3	133	199
4	159	199
5	180	199
6	191	199
7	207	199
8	222	199
9	228	199
10	230	199
11	225	199

Details

analyze2.8s (6.8%)

sample6.1s (14.7%)

simplify69.0ms (0.2%)

prune9.0ms (0%)

localize33.0ms (0.1%)

series3.7s (9%)

rewrite73.0ms (0.2%)

simplify492.0ms (1.2%)

prune1.0s (2.4%)

localize39.0ms (0.1%)

series2.6s (6.2%)

rewrite26.0ms (0.1%)

simplify527.0ms (1.3%)

prune4.3s (10.3%)

localize27.0ms (0.1%)

series3.8s (9.1%)

rewrite66.0ms (0.2%)

simplify470.0ms (1.1%)

prune922.0ms (2.2%)

localize57.0ms (0.1%)

series5.6s (13.4%)

rewrite19.0ms (0%)

simplify585.0ms (1.4%)

prune5.3s (12.7%)

regimes2.7s (6.4%)

bsearch9.0ms (0%)

simplify16.0ms (0%)

end313.0ms (0.8%)

Profiling

Iter	Nodes	Cost
0	52	199
1	83	199
2	110	199
3	133	199
4	159	199
5	180	199
6	191	199
7	207	199
8	222	199
9	228	199
10	230	199
11	225	199