Details

analyze3.0s (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
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample160.0ms (0.4%)

Algorithm

1×

intervals

Results

52.0ms	435×	body	128	nan
29.0ms	256×	body	128	valid
3.0ms	26×	body	128	invalid

Compiler

Compiled 75 to 53 computations (29.3% saved)

simplify42.0ms (0.1%)

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

28.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	28.2b	(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))))))))
	33.0b	(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

▶

28.2b

(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))))))))

33.0b

(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)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.6b	(*.f64 n (/.f64 l Om))
✓	6.4b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	9.2b	(.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)))))))
✓	17.9b	(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))))))))

series2.0s (5.3%)

Counts

4 → 216

Calls

4 calls:

1.5s	(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))))))))
397.0ms	(.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)))))))
36.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
12.0ms	(*.f64 n (/.f64 l Om))

rewrite35.0ms (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 U U) (*.f64 n (/.f64 l Om)))
7.0ms	(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))))))))
6.0ms	(.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)))))))
5.0ms	(*.f64 n (/.f64 l Om))

simplify243.0ms (0.7%)

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

prune519.0ms (1.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	270	16	286
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	271	17	288

Error

13.5b

Counts

288 → 17

Alt Table

Status	Error	Program
	59.5b	(.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))
	56.5b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (.f64 l l) (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))))))))
	56.2b	(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)))
	61.1b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
▶	28.5b	(sqrt.f64 (.f64 (.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))
	35.7b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om)))))))
✓	28.2b	(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))))))))
	57.0b	(sqrt.f64 (.f64 2 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 (.f64 l l) U)) (*.f64 Om Om))))))))
	36.3b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))
	41.3b	(-.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)))
	42.0b	(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)))))
	29.2b	(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)))))))))
	28.7b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (.f64 n l) Om))) t)))) (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (/.f64 (*.f64 n l) Om))) t)))))
	45.0b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (*.f64 n 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))
	57.4b	(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)))
	39.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))

Compiler

Compiled 22924 to 11819 computations (48.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	6.4b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
	9.2b	(.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)))))))
✓	17.9b	(sqrt.f64 (.f64 (.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))
✓	19.3b	(cbrt.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 (6.9%)

Counts

2 → 120

Calls

2 calls:

1.4s

(cbrt.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))))))))

1.1s

(sqrt.f64 (*.f64 (*.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))

rewrite55.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`associate-*r/_binary64`
56×	`cbrt-div_binary64`
28×	`frac-times_binary64`
28×	`flip-+_binary64`
28×	`flip3-+_binary64`

Counts

2 → 65

Calls

2 calls:

10.0ms

(sqrt.f64 (*.f64 (*.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))

6.0ms

(cbrt.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))))))))

simplify427.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

369×	`fma-def_binary64`
327×	`associate-/l*_binary64`
283×	`associate-*r/_binary64`
237×	`associate-/r*_binary64`
221×	`times-frac_binary64`

Counts

185 → 313

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2317	43123
1	5480	43123

prune2.9s (7.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	991	1	992
Fresh	2	13	15
Picked	0	1	1
Done	1	0	1
Total	994	15	1009

Error

13.5b

Counts

1009 → 15

Alt Table

Status	Error	Program
	59.5b	(.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))
	56.2b	(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)))
	61.1b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
✓	28.5b	(sqrt.f64 (.f64 (.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))
	35.2b	(cbrt.f64 (.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 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))))
	57.0b	(sqrt.f64 (.f64 2 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 (.f64 l l) U)) (*.f64 Om Om))))))))
	36.3b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))
	41.3b	(-.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)))
	42.0b	(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)))))
	45.0b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (*.f64 n 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))
	35.7b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om)))))))
	57.4b	(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)))
▶	29.2b	(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)))))))))
	39.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))

Compiler

Compiled 183809 to 93601 computations (49.1% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.6b	(*.f64 n (/.f64 l Om))
	6.4b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	6.7b	(.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))))))))
✓	17.9b	(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)))))))))

series2.0s (5.4%)

Counts

2 → 120

Calls

2 calls:

1.6s

(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)))))))))

406.0ms

(*.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))))))))

rewrite18.0ms (0%)

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

(*.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

(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)))))))))

simplify273.0ms (0.7%)

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 → 178

Iterations

Useful iterations: 1 (0.0ms)

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

prune489.0ms (1.3%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	278	5	283
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	280	18	298

Error

9.3b

Counts

298 → 18

Alt Table

Status	Error	Program
	59.5b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	45.0b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (*.f64 n l) Om))) t)))
	61.1b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
✓	28.5b	(sqrt.f64 (.f64 (.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))
▶	35.2b	(cbrt.f64 (.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 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))))
	42.9b	(.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))))
	57.0b	(sqrt.f64 (.f64 2 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 (.f64 l l) U)) (*.f64 Om Om))))))))
	41.3b	(-.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)))
	55.3b	(/.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))))) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	42.0b	(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)))))
	52.8b	(/.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (+.f64 (pow.f64 t 3) (pow.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))) 3))))) (sqrt.f64 (fma.f64 t t (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))) (-.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) t)))))
✓	29.2b	(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)))))))))
	56.2b	(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)))
	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))
	35.7b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om)))))))
	57.4b	(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)))
	39.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	36.2b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))

Compiler

Compiled 22364 to 11685 computations (47.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	6.4b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
	9.2b	(.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)))))))
	17.9b	(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))))))))
✓	28.5b	(cbrt.f64 (.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 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))))

series13.3s (35.8%)

Counts

1 → 48

Calls

1 calls:

13.3s

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

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`associate-*r/_binary64`
8×	`cbrt-div_binary64`
6×	`flip-+_binary64`
6×	`sqrt-div_binary64`
6×	`flip3-+_binary64`

Counts

1 → 19

Calls

1 calls:

16.0ms

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

simplify492.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

375×	`fma-def_binary64`
322×	`associate-/l*_binary64`
255×	`associate-/r*_binary64`
255×	`times-frac_binary64`
233×	`associate-*r/_binary64`

Counts

67 → 111

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2370	58802
1	5333	58802

prune1.7s (4.6%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	472	3	475
Fresh	2	13	15
Picked	0	1	1
Done	0	2	2
Total	474	19	493

Error

9.3b

Counts

493 → 19

Alt Table

Status	Error	Program
	56.2b	(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)))
	39.3b	(.f64 (sqrt.f64 (.f64 n (.f64 t U))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2)))
	59.5b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	45.0b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (/.f64 (*.f64 n l) Om))) t)))
	61.1b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
✓	28.5b	(sqrt.f64 (.f64 (.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))
✓	35.2b	(cbrt.f64 (.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 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))))
	42.9b	(.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))))
	57.0b	(sqrt.f64 (.f64 2 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) (.f64 Om Om)) (fma.f64 2 (/.f64 (.f64 l l) Om) (/.f64 (.f64 n (.f64 (.f64 l l) U)) (*.f64 Om Om))))))))
	41.3b	(-.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)))
	55.3b	(/.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) t) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))))) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	42.0b	(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)))))
	52.8b	(/.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (+.f64 (pow.f64 t 3) (pow.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))) 3))))) (sqrt.f64 (fma.f64 t t (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))) (-.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))) t)))))
✓	29.2b	(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)))))))))
	35.7b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om)))))))
	57.4b	(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)))
	41.6b	(-.f64 (.f64 (sqrt.f64 (.f64 n (.f64 t U))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2))) (.f64 (sqrt.f64 (/.f64 (.f64 n U) t)) (.f64 (/.f64 (.f64 (*.f64 l l) (cbrt.f64 2)) Om) (cbrt.f64 (sqrt.f64 2)))))
	56.4b	(.f64 (sqrt.f64 (.f64 n (.f64 (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om)))) U))) (.f64 (.f64 l (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
	36.2b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om) -4)))

Compiler

Compiled 111398 to 58651 computations (47.4% saved)

regimes2.7s (7.3%)

Accuracy

Total 13.3b remaining (51.6%)

Threshold costs 0b (0%)

Counts

159 → 4

Compiler

Compiled 52594 to 32330 computations (38.5% saved)

bsearch11.0ms (0%)

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

simplify50.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

195×	`distribute-rgt-neg-in_binary64`
136×	`distribute-lft-neg-in_binary64`
129×	`cancel-sign-sub-inv_binary64`
118×	`neg-sub0_binary64`
118×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	297
1	110	297
2	157	297
3	200	297
4	242	297
5	271	297
6	287	297
7	320	297
8	356	297
9	408	297
10	483	297
11	579	297
12	659	297
13	744	297
14	823	297
15	872	297
16	896	297
17	910	297
18	916	297
19	921	297
20	926	297
21	928	297
22	922	297

end3.0ms (0%)

Compiler: Compiled 204 to 109 computations (46.6% saved)

sample4.0s (10.8%)

Algorithm

1×

intervals

Results

1.5s	12672×	body	128	nan
950.0ms	8000×	body	128	valid
126.0ms	1114×	body	128	invalid

Compiler

Compiled 1038 to 599 computations (42.3% saved)

Iter	Nodes	Cost
0	65	297
1	110	297
2	157	297
3	200	297
4	242	297
5	271	297
6	287	297
7	320	297
8	356	297
9	408	297
10	483	297
11	579	297
12	659	297
13	744	297
14	823	297
15	872	297
16	896	297
17	910	297
18	916	297
19	921	297
20	926	297
21	928	297
22	922	297

Iter	Nodes	Cost
0	65	297
1	110	297
2	157	297
3	200	297
4	242	297
5	271	297
6	287	297
7	320	297
8	356	297
9	408	297
10	483	297
11	579	297
12	659	297
13	744	297
14	823	297
15	872	297
16	896	297
17	910	297
18	916	297
19	921	297
20	926	297
21	928	297
22	922	297

Details

analyze3.0s (8%)

sample160.0ms (0.4%)

simplify42.0ms (0.1%)

prune5.0ms (0%)

localize21.0ms (0.1%)

series2.0s (5.3%)

rewrite35.0ms (0.1%)

simplify243.0ms (0.7%)

prune519.0ms (1.4%)

localize21.0ms (0.1%)

series2.6s (6.9%)

rewrite55.0ms (0.1%)

simplify427.0ms (1.2%)

prune2.9s (7.9%)

localize15.0ms (0%)

series2.0s (5.4%)

rewrite18.0ms (0%)

simplify273.0ms (0.7%)

prune489.0ms (1.3%)

localize22.0ms (0.1%)

series13.3s (35.8%)

rewrite21.0ms (0.1%)

simplify492.0ms (1.3%)

prune1.7s (4.6%)

regimes2.7s (7.3%)

bsearch11.0ms (0%)

simplify50.0ms (0.1%)

end3.0ms (0%)

sample4.0s (10.8%)

Profiling

Iter	Nodes	Cost
0	65	297
1	110	297
2	157	297
3	200	297
4	242	297
5	271	297
6	287	297
7	320	297
8	356	297
9	408	297
10	483	297
11	579	297
12	659	297
13	744	297
14	823	297
15	872	297
16	896	297
17	910	297
18	916	297
19	921	297
20	926	297
21	928	297
22	922	297