Details

analyze3.0s (10.5%)

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)

sample124.0ms (0.4%)

Algorithm

1×

intervals

Results

48.0ms	401×	body	128	nan
33.0ms	256×	body	128	valid
5.0ms	47×	body	128	invalid

Compiler

Compiled 75 to 53 computations (29.3% saved)

simplify53.0ms (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

28.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	31.6b	(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)))))
▶	28.9b	(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))))))))

Status

Error

Program

31.6b

(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*)))))

▶

28.9b

(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))))))))

Compiler

Compiled 189 to 119 computations (37% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.2b	(*.f64 n (/.f64 l Om))
✓	6.9b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	7.7b	(.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)))))))
✓	19.4b	(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))))))))

rewrite33.0ms (0.1%)

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:

8.0ms	(.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)))))))
7.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
5.0ms	(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))))))))
5.0ms	(*.f64 n (/.f64 l Om))

series2.1s (7.4%)

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))))))))
518.0ms	(.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)))))))
114.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
50.0ms	(*.f64 n (/.f64 l Om))

simplify298.0ms (1%)

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 → 585

Iterations

Useful iterations: 1 (0.0ms)

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

prune552.0ms (1.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	570	15	585
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	571	16	587

Error

14.0b

Counts

587 → 16

Alt Table

Status	Error	Program
	30.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (*.f64 n l) Om))) t))))
	35.0b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om))))
	31.6b	(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)))))
	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 (.f64 n (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 (cbrt.f64 l) Om))))))))
	59.5b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))) (/.f64 (.f64 (sqrt.f64 2) t) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	41.0b	(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 -4 (/.f64 (.f64 n (.f64 l l)) Om)))))
▶	29.1b	(.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))))))))))
	61.7b	(.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)))
	58.9b	(.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))) (.f64 l (sqrt.f64 2)))
	43.5b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	38.3b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	35.1b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))
	62.8b	(neg.f64 (.f64 U (sqrt.f64 (.f64 -2 (/.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 Om Om))))))
	29.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))
	58.4b	(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))))
	61.1b	(.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))

Compiler

Compiled 22839 to 11792 computations (48.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	7.7b	(.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)))))))
	7.7b	(.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)))))))
	19.4b	(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))))))))
	19.4b	(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))))))))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune852.0ms (2.9%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	965	1	966
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	965	17	982

Error

14.0b

Counts

982 → 17

Alt Table

Status	Error	Program
	30.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (*.f64 n l) Om))) t))))
	35.0b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om))))
	61.7b	(.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 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (.f64 (sqrt.f64 2) l))))
	62.8b	(neg.f64 (.f64 U (sqrt.f64 (.f64 -2 (/.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 Om Om))))))
	31.6b	(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)))))
	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 (.f64 n (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 (cbrt.f64 l) Om))))))))
	59.5b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))) (/.f64 (.f64 (sqrt.f64 2) t) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	41.0b	(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 -4 (/.f64 (.f64 n (.f64 l l)) Om)))))
✓	29.1b	(.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))))))))))
	61.7b	(.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)))
	58.9b	(.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))) (.f64 l (sqrt.f64 2)))
	43.5b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	38.3b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	35.1b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))
▶	29.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))
	58.4b	(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))))
	61.1b	(.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))

Compiler

Compiled 48147 to 24524 computations (49.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.2b	(*.f64 n (/.f64 l Om))
✓	5.3b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	6.9b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	19.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`pow1_binary64`
16×	`pow-prod-down_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
8×	`cbrt-unprod_binary64`

Counts

2 → 48

Calls

2 calls:

8.0ms

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

6.0ms

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

series2.1s (7.1%)

Counts

2 → 120

Calls

2 calls:

1.5s

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

540.0ms

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

simplify336.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

764×	`fma-def_binary64`
419×	`*-commutative_binary64`
218×	`associate-r_binary64`
168×	`neg-mul-1_binary64`
157×	`+-commutative_binary64`

Counts

168 → 330

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	940	18125
1	3260	16803
2	4884	16803
3	5048	16803

prune548.0ms (1.9%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	587	6	593
Fresh	2	13	15
Picked	1	0	1
Done	0	1	1
Total	590	20	610

Error

11.2b

Counts

610 → 20

Alt Table

Status	Error	Program
▶	29.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 (.f64 (cbrt.f64 (.f64 n (/.f64 l Om))) (cbrt.f64 (.f64 n (/.f64 l Om)))) (cbrt.f64 (*.f64 n (/.f64 l Om)))))))))))
	35.0b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om))))
	61.7b	(.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 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (.f64 (sqrt.f64 2) l))))
	62.8b	(neg.f64 (.f64 U (sqrt.f64 (.f64 -2 (/.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 Om Om))))))
	29.8b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 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 n 2) (.f64 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 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))
	58.4b	(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))))
	30.6b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (-.f64 U U)) (/.f64 Om l))))))))
	31.6b	(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)))))
	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 (.f64 n (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 (cbrt.f64 l) Om))))))))
	59.5b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))) (/.f64 (.f64 (sqrt.f64 2) t) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	41.0b	(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 -4 (/.f64 (.f64 n (.f64 l l)) Om)))))
✓	29.1b	(.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))))))))))
	61.7b	(.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)))
	58.9b	(.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))) (.f64 l (sqrt.f64 2)))
	43.5b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	38.3b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	35.1b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))
	61.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	41.7b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	62.8b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 (sqrt.f64 2) t)) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))

Compiler

Compiled 22612 to 11847 computations (47.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	17.4b	(cbrt.f64 (*.f64 n (/.f64 l Om)))
	17.4b	(cbrt.f64 (*.f64 n (/.f64 l Om)))
✓	17.4b	(cbrt.f64 (*.f64 n (/.f64 l Om)))
✓	19.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 (.f64 (cbrt.f64 (.f64 n (/.f64 l Om))) (cbrt.f64 (.f64 n (/.f64 l Om)))) (cbrt.f64 (*.f64 n (/.f64 l Om)))))))))))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`pow1_binary64`
8×	`pow-prod-down_binary64`
5×	`associate-*r/_binary64`
5×	`sqrt-pow1_binary64`
2×	`*-un-lft-identity_binary64`

Counts

2 → 30

Calls

2 calls:

6.0ms

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

2.0ms

(cbrt.f64 (*.f64 n (/.f64 l Om)))

series3.5s (12.2%)

Counts

2 → 84

Calls

2 calls:

1.8s

(cbrt.f64 (*.f64 n (/.f64 l Om)))

1.7s

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

simplify460.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

922×	`fma-def_binary64`
417×	`*-commutative_binary64`
198×	`associate-r_binary64`
168×	`+-commutative_binary64`
143×	`associate-/l*_binary64`

Counts

114 → 194

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	970	13118
1	3329	12928
2	4975	12928
3	5075	12928

prune769.0ms (2.7%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	389	0	389
Fresh	0	18	18
Picked	0	1	1
Done	0	1	1
Total	389	20	409

Error

11.2b

Counts

409 → 20

Alt Table

Status	Error	Program
✓	29.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 (.f64 (cbrt.f64 (.f64 n (/.f64 l Om))) (cbrt.f64 (.f64 n (/.f64 l Om)))) (cbrt.f64 (*.f64 n (/.f64 l Om)))))))))))
	35.0b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om))))
	61.7b	(.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 (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (.f64 (sqrt.f64 2) l))))
	62.8b	(neg.f64 (.f64 U (sqrt.f64 (.f64 -2 (/.f64 (.f64 (.f64 l l) (.f64 n n)) (.f64 Om Om))))))
	29.8b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 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 n 2) (.f64 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 n 2) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))) t))))))
	58.4b	(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))))
	30.6b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (/.f64 (.f64 n (-.f64 U U)) (/.f64 Om l))))))))
	31.6b	(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)))))
	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 (.f64 n (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 (cbrt.f64 l) Om))))))))
	59.5b	(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))) (/.f64 (.f64 (sqrt.f64 2) t) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l)))
	41.0b	(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 -4 (/.f64 (.f64 n (.f64 l l)) Om)))))
✓	29.1b	(.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))))))))))
	61.7b	(.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)))
	58.9b	(.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))) (.f64 l (sqrt.f64 2)))
	43.5b	(.f64 (sqrt.f64 (.f64 (.f64 2 n) U)) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	38.3b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	35.1b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))
	61.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	41.7b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))))
	62.8b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 (sqrt.f64 2) t)) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))

Compiler

Compiled 20953 to 10993 computations (47.5% saved)

regimes6.7s (23.2%)

Accuracy

Total 14.3b remaining (52%)

Threshold costs 0b (0%)

Compiler

Compiled 70874 to 42682 computations (39.8% saved)

bsearch34.0ms (0.1%)

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

simplify70.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

162×	`distribute-rgt-neg-in_binary64`
112×	`cancel-sign-sub-inv_binary64`
108×	`distribute-lft-neg-in_binary64`
97×	`distribute-lft-neg-out_binary64`
93×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	295
1	89	295
2	123	295
3	157	295
4	194	295
5	219	295
6	233	295
7	261	295
8	288	295
9	332	295
10	392	295
11	467	295
12	522	295
13	572	295
14	630	295
15	693	295
16	735	295
17	759	295
18	770	295
19	772	295
20	766	295

end5.0ms (0%)

Compiler: Compiled 203 to 105 computations (48.3% saved)

sample7.2s (24.9%)

Algorithm

1×

intervals

Results

2.7s	12758×	body	128	nan
1.7s	8000×	body	128	valid
259.0ms	1193×	body	128	invalid

Compiler

Compiled 1086 to 624 computations (42.5% saved)

Iter	Nodes	Cost
0	57	295
1	89	295
2	123	295
3	157	295
4	194	295
5	219	295
6	233	295
7	261	295
8	288	295
9	332	295
10	392	295
11	467	295
12	522	295
13	572	295
14	630	295
15	693	295
16	735	295
17	759	295
18	770	295
19	772	295
20	766	295

Iter	Nodes	Cost
0	57	295
1	89	295
2	123	295
3	157	295
4	194	295
5	219	295
6	233	295
7	261	295
8	288	295
9	332	295
10	392	295
11	467	295
12	522	295
13	572	295
14	630	295
15	693	295
16	735	295
17	759	295
18	770	295
19	772	295
20	766	295

Details

analyze3.0s (10.5%)

sample124.0ms (0.4%)

simplify53.0ms (0.2%)

prune5.0ms (0%)

localize15.0ms (0.1%)

rewrite33.0ms (0.1%)

series2.1s (7.4%)

simplify298.0ms (1%)

prune552.0ms (1.9%)

localize20.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify22.0ms (0.1%)

prune852.0ms (2.9%)

localize18.0ms (0.1%)

rewrite18.0ms (0.1%)

series2.1s (7.1%)

simplify336.0ms (1.2%)

prune548.0ms (1.9%)

localize20.0ms (0.1%)

rewrite11.0ms (0%)

series3.5s (12.2%)

simplify460.0ms (1.6%)

prune769.0ms (2.7%)

regimes6.7s (23.2%)

bsearch34.0ms (0.1%)

simplify70.0ms (0.2%)

end5.0ms (0%)

sample7.2s (24.9%)

Profiling

Iter	Nodes	Cost
0	57	295
1	89	295
2	123	295
3	157	295
4	194	295
5	219	295
6	233	295
7	261	295
8	288	295
9	332	295
10	392	295
11	467	295
12	522	295
13	572	295
14	630	295
15	693	295
16	735	295
17	759	295
18	770	295
19	772	295
20	766	295