Details

analyze5.1s (22.2%)

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)

sample131.0ms (0.6%)

Algorithm

1×

intervals

Results

53.0ms	399×	body	128	nan
32.0ms	256×	body	128	valid
4.0ms	32×	body	128	invalid

Compiler

Compiled 75 to 53 computations (29.3% saved)

simplify54.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

716×	`neg-sub0_binary64`
716×	`neg-mul-1_binary64`
377×	`distribute-rgt-neg-out_binary64`
358×	`cancel-sign-sub-inv_binary64`
354×	`distribute-lft-neg-out_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	42
1	58	42
2	180	42
3	719	39
4	2459	39
5	3995	39
6	5181	39

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

28.5b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	30.2b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
	31.3b	(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

▶

30.2b

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

31.3b

(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 164 to 106 computations (35.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
11.4b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
13.0b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
16.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

rewrite291.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

21.5b

Rules

30×	`add-cbrt-cube_binary64`
30×	`add-exp-log_binary64`
30×	`pow1_binary64`
29×	`add-sqr-sqrt_binary64`
27×	`associate-l_binary64`

Counts

4 → 131

Calls

4 calls:

9.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
8.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
7.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
6.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

Compiler

Compiled 4890 to 1897 computations (61.2% saved)

series1.1s (4.8%)

Error

16.5b

Counts

4 → 112

Calls

4 calls:

426.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
354.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
161.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
60.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 11311 to 7996 computations (29.3% saved)

simplify245.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

576×	`*-commutative_binary64`
268×	`distribute-rgt-in_binary64`
253×	`associate-/l*_binary64`
251×	`associate-*l/_binary64`
248×	`distribute-lft-in_binary64`

Counts

243 → 219

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	540	8858
1	1649	8476
2	4678	8476
3	4928	8476
4	5071	8476

prune186.0ms (0.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	201	18	219
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	203	18	221

Error

13.2b

Counts

221 → 18

Alt Table

Status	Error	Program
	59.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	29.9b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))))
	56.4b	(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)))
	57.6b	(+.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)) (.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 t (sqrt.f64 2)) l))))
	40.0b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 t U)))) (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (*.f64 n U) t))))
	60.7b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 2 (.f64 n U))) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U U)) (/.f64 l Om)) (*.f64 l -2)))))))
▶	28.2b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
	56.6b	(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)))))))))
	44.4b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
	36.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (*.f64 t U))))
	37.5b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))) 3))
	32.2b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))))
	42.8b	(sqrt.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 n n) (.f64 U (.f64 (.f64 l l) U))) (.f64 Om Om)) (.f64 n (.f64 t U)))) (+.f64 (.f64 4 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om)) (.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U U))) (*.f64 Om Om))))))
	55.2b	(/.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (-.f64 (.f64 t t) (.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (.f64 l -2))) (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (.f64 l -2))))))) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
	60.3b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	30.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))
	34.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 -2 (/.f64 (*.f64 l l) Om)))))
	33.1b	(sqrt.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 U (*.f64 l l))) Om))))

Compiler

Compiled 5966 to 2548 computations (57.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.2b	(*.f64 n (/.f64 l Om))
7.8b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
11.4b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
16.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

rewrite159.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

13.2b

Rules

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

Counts

4 → 107

Calls

4 calls:

8.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
8.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
6.0ms	(*.f64 n (/.f64 l Om))
5.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

Compiler

Compiled 3765 to 1527 computations (59.4% saved)

series898.0ms (3.9%)

Error

13.2b

Counts

4 → 94

Calls

4 calls:

428.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
346.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
55.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
24.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 9981 to 7064 computations (29.2% saved)

simplify124.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

734×	`associate-l_binary64`
679×	`associate-r_binary64`
228×	`associate-/l*_binary64`
194×	`*-commutative_binary64`
157×	`associate-*r/_binary64`

Counts

201 → 165

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	460	7009
1	1318	6495
2	5236	6495

prune125.0ms (0.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	2	15	17
Picked	0	1	1
Done	0	0	0
Total	164	19	183

Error

13.0b

Counts

183 → 19

Alt Table

Status	Error	Program
	59.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
▶	29.9b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))))
	56.4b	(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)))
	57.6b	(+.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)) (.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 t (sqrt.f64 2)) l))))
	40.0b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 t U)))) (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (*.f64 n U) t))))
	60.7b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 2 (.f64 n U))) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U U)) (/.f64 l Om)) (*.f64 l -2)))))))
✓	28.2b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
	56.6b	(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)))))))))
	37.5b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))) 3))
	32.2b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))))
	42.8b	(sqrt.f64 (-.f64 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 n n) (.f64 U (.f64 (.f64 l l) U))) (.f64 Om Om)) (.f64 n (.f64 t U)))) (+.f64 (.f64 4 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om)) (.f64 2 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (.f64 U U))) (*.f64 Om Om))))))
	54.9b	(/.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (-.f64 (.f64 t t) (.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2))) (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2))))))) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
	59.4b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (-.f64 U* U))) Om) (/.f64 U Om))))
	60.3b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	30.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))
	36.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (*.f64 t U))))
	43.4b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
	34.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 -2 (/.f64 (*.f64 l l) Om)))))
	33.1b	(sqrt.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 U (*.f64 l l))) Om))))

Compiler

Compiled 4750 to 2139 computations (55% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.8b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))
6.4b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
13.0b	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
16.3b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))))

rewrite867.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

11.3b

Rules

36×	`pow1_binary64`
30×	`add-cbrt-cube_binary64`
30×	`add-exp-log_binary64`
20×	`pow-prod-down_binary64`
17×	`associate-r_binary64`

Counts

4 → 103

Calls

4 calls:

9.0ms	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
7.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
5.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))))
4.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))

Compiler

Compiled 3827 to 1512 computations (60.5% saved)

series1.5s (6.4%)

Error

13.0b

Counts

4 → 124

Calls

4 calls:

632.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))))
421.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
288.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))
69.0ms	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))

Compiler

Compiled 12253 to 8718 computations (28.9% saved)

simplify167.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

718×	`associate-r_binary64`
655×	`associate-l_binary64`
224×	`associate-/l*_binary64`
199×	`*-commutative_binary64`
169×	`distribute-rgt-in_binary64`

Counts

227 → 198

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	464	9277
1	1322	8580
2	5286	8580

prune144.0ms (0.6%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	190	8	198
Fresh	3	14	17
Picked	1	0	1
Done	0	1	1
Total	194	23	217

Error

10.8b

Counts

217 → 23

Alt Table

Status	Error	Program
	41.5b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 (.f64 U U) (.f64 U U)))) (+.f64 U* U)) (*.f64 l -2)))))))
▶	30.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))
	47.5b	(sqrt.f64 (.f64 (.f64 2 n) (/.f64 (.f64 U (-.f64 (.f64 t t) (.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2))) (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2)))))) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))))
	44.2b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))))
	43.6b	(sqrt.f64 (.f64 (.f64 2 n) (cbrt.f64 (pow.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))) 3))))
	53.8b	(/.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (+.f64 (pow.f64 t 3) (pow.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2))) 3))))) (sqrt.f64 (+.f64 (.f64 t t) (.f64 (/.f64 l Om) (.f64 (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2)) (-.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))) t))))))
	59.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	56.4b	(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)))
	57.6b	(+.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)) (.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 t (sqrt.f64 2)) l))))
	40.0b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 t U)))) (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (*.f64 n U) t))))
	60.7b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 2 (.f64 n U))) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U U)) (/.f64 l Om)) (*.f64 l -2)))))))
	59.4b	(sqrt.f64 (.f64 (.f64 2 n) (/.f64 (.f64 n (.f64 U (.f64 (.f64 l l) U))) (.f64 Om Om))))
✓	28.2b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
	56.6b	(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)))))))))
	37.5b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))) 3))
	32.2b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))))
	61.4b	(sqrt.f64 (.f64 (.f64 2 n) (neg.f64 (/.f64 (.f64 n (.f64 U (.f64 U (.f64 l l)))) (*.f64 Om Om)))))
	33.1b	(sqrt.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 U (*.f64 l l))) Om))))
	35.3b	(sqrt.f64 (.f64 (.f64 2 n) (-.f64 (+.f64 (.f64 t U) (/.f64 (.f64 n (.f64 U (.f64 (.f64 l l) U))) (.f64 Om Om))) (+.f64 (/.f64 (.f64 n (.f64 U (.f64 U (.f64 l l)))) (.f64 Om Om)) (.f64 2 (.f64 (/.f64 (*.f64 l l) Om) U))))))
	59.4b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (-.f64 U* U))) Om) (/.f64 U Om))))
	36.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (*.f64 t U))))
	43.4b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
	34.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 -2 (/.f64 (*.f64 l l) Om)))))

Compiler

Compiled 5582 to 2491 computations (55.4% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

16.1b	(cbrt.f64 (/.f64 l Om))
16.1b	(cbrt.f64 (/.f64 l Om))
16.1b	(cbrt.f64 (/.f64 l Om))
16.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))

rewrite119.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

10.8b

Rules

39×	`cbrt-prod_binary64`
27×	`times-frac_binary64`
25×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`

Counts

4 → 81

Calls

4 calls:

5.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))
2.0ms	(cbrt.f64 (/.f64 l Om))
2.0ms	(cbrt.f64 (/.f64 l Om))
2.0ms	(cbrt.f64 (/.f64 l Om))

Compiler

Compiled 3721 to 1183 computations (68.2% saved)

series679.0ms (3%)

Error

10.8b

Counts

4 → 46

Calls

4 calls:

518.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))
43.0ms	(cbrt.f64 (/.f64 l Om))
41.0ms	(cbrt.f64 (/.f64 l Om))
39.0ms	(cbrt.f64 (/.f64 l Om))

Compiler

Compiled 7461 to 5160 computations (30.8% saved)

simplify128.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

719×	`times-frac_binary64`
268×	`associate-r_binary64`
242×	`cancel-sign-sub-inv_binary64`
225×	`*-commutative_binary64`
210×	`associate-l_binary64`

Counts

127 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	324	3838
1	844	3459
2	2710	3405
3	4800	3264
4	5008	3264

prune71.0ms (0.3%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	20	21
Picked	0	1	1
Done	0	1	1
Total	74	23	97

Error

10.6b

Counts

97 → 23

Alt Table

Status	Error	Program
	41.5b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 (/.f64 l Om) (.f64 n (-.f64 (.f64 U U) (.f64 U U)))) (+.f64 U* U)) (*.f64 l -2)))))))
	30.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (.f64 (cbrt.f64 (/.f64 l Om)) (cbrt.f64 (/.f64 l Om))) (.f64 (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)) (cbrt.f64 (/.f64 l Om)))))))
	47.5b	(sqrt.f64 (.f64 (.f64 2 n) (/.f64 (.f64 U (-.f64 (.f64 t t) (.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2))) (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2)))))) (-.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))))
	44.2b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2)))))))
	43.6b	(sqrt.f64 (.f64 (.f64 2 n) (cbrt.f64 (pow.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))) 3))))
	53.8b	(/.f64 (sqrt.f64 (.f64 (.f64 n 2) (.f64 U (+.f64 (pow.f64 t 3) (pow.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2))) 3))))) (sqrt.f64 (+.f64 (.f64 t t) (.f64 (/.f64 l Om) (.f64 (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (.f64 l -2)) (-.f64 (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))) t))))))
	59.1b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	56.4b	(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)))
	57.6b	(+.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)) (.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 t (sqrt.f64 2)) l))))
	40.0b	(-.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (.f64 t U)))) (.f64 (/.f64 (.f64 (sqrt.f64 2) (.f64 l l)) Om) (sqrt.f64 (/.f64 (*.f64 n U) t))))
	60.7b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 2 (.f64 n U))) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U U)) (/.f64 l Om)) (*.f64 l -2)))))))
	59.4b	(sqrt.f64 (.f64 (.f64 2 n) (/.f64 (.f64 n (.f64 U (.f64 (.f64 l l) U))) (.f64 Om Om))))
	28.2b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
	56.6b	(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)))))))))
	37.5b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))) 3))
	32.2b	(exp.f64 (log.f64 (sqrt.f64 (.f64 (.f64 2 (.f64 n U)) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))))
	35.3b	(sqrt.f64 (.f64 (.f64 2 n) (-.f64 (+.f64 (.f64 t U) (/.f64 (.f64 n (.f64 U (.f64 (.f64 l l) U))) (.f64 Om Om))) (+.f64 (/.f64 (.f64 n (.f64 U (.f64 U (.f64 l l)))) (.f64 Om Om)) (.f64 2 (.f64 (/.f64 (*.f64 l l) Om) U))))))
	59.4b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (-.f64 U* U))) Om) (/.f64 U Om))))
	59.1b	(.f64 (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 l Om)) 6) U) (.f64 (pow.f64 (cbrt.f64 (/.f64 l Om)) 6) U))))) (neg.f64 n))
	36.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (*.f64 t U))))
	43.4b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om))) (*.f64 l -2))))))
	34.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 -2 (/.f64 (*.f64 l l) Om)))))
	33.1b	(sqrt.f64 (-.f64 (.f64 2 (.f64 n (.f64 t U))) (.f64 4 (/.f64 (.f64 n (.f64 U (*.f64 l l))) Om))))

Compiler

Compiled 2986 to 1379 computations (53.8% saved)

regimes4.4s (19.1%)

Accuracy

Total 17.0b remaining (59.8%)

Threshold costs 0b (0%)

Compiler

Compiled 76938 to 46106 computations (40.1% saved)

bsearch515.0ms (2.2%)

Steps

Iters	Range		Point
7	3.424089032930542e+140	1.0379577541746275e+142	1.0262748173296868e+142
5	5.029549784728504e-221	1.0773965678871626e-220	5.253788384023585e-221
9	-1.2733500548676322e-117	-2.924844580852531e-123	-2.6334565220071494e-122
3	-1.1966335559533627e+125	-8.17959796760297e+124	-1.171204455798095e+125
9	-3.8541133264885623e+177	-7.1294178792345836e+171	-2.3600349946707946e+176
8	-7.075390275171441e+211	-1.3680012492149799e+209	-3.223783303575266e+210

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify48.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

186×	`distribute-rgt-neg-in_binary64`
130×	`cancel-sign-sub-inv_binary64`
126×	`distribute-lft-neg-in_binary64`
104×	`neg-sub0_binary64`
104×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	331
1	116	331
2	163	331
3	206	331
4	247	331
5	271	331
6	287	331
7	314	331
8	340	331
9	383	331
10	441	331
11	517	331
12	587	331
13	656	331
14	720	331
15	793	331
16	852	331
17	875	331
18	881	331
19	875	331

end3.0ms (0%)

Compiler: Compiled 225 to 114 computations (49.3% saved)

sample5.9s (25.6%)

Algorithm

1×

intervals

Results

2.3s	12660×	body	128	nan
1.5s	8000×	body	128	valid
219.0ms	1174×	body	128	invalid

Compiler

Compiled 1129 to 663 computations (41.3% saved)

Iter	Nodes	Cost
0	69	331
1	116	331
2	163	331
3	206	331
4	247	331
5	271	331
6	287	331
7	314	331
8	340	331
9	383	331
10	441	331
11	517	331
12	587	331
13	656	331
14	720	331
15	793	331
16	852	331
17	875	331
18	881	331
19	875	331

Iter	Nodes	Cost
0	69	331
1	116	331
2	163	331
3	206	331
4	247	331
5	271	331
6	287	331
7	314	331
8	340	331
9	383	331
10	441	331
11	517	331
12	587	331
13	656	331
14	720	331
15	793	331
16	852	331
17	875	331
18	881	331
19	875	331

Details

analyze5.1s (22.2%)

sample131.0ms (0.6%)

simplify54.0ms (0.2%)

prune4.0ms (0%)

localize17.0ms (0.1%)

rewrite291.0ms (1.3%)

series1.1s (4.8%)

simplify245.0ms (1.1%)

prune186.0ms (0.8%)

localize20.0ms (0.1%)

rewrite159.0ms (0.7%)

series898.0ms (3.9%)

simplify124.0ms (0.5%)

prune125.0ms (0.5%)

localize20.0ms (0.1%)

rewrite867.0ms (3.8%)

series1.5s (6.4%)

simplify167.0ms (0.7%)

prune144.0ms (0.6%)

localize23.0ms (0.1%)

rewrite119.0ms (0.5%)

series679.0ms (3%)

simplify128.0ms (0.6%)

prune71.0ms (0.3%)

regimes4.4s (19.1%)

bsearch515.0ms (2.2%)

simplify48.0ms (0.2%)

end3.0ms (0%)

sample5.9s (25.6%)

Profiling

Iter	Nodes	Cost
0	69	331
1	116	331
2	163	331
3	206	331
4	247	331
5	271	331
6	287	331
7	314	331
8	340	331
9	383	331
10	441	331
11	517	331
12	587	331
13	656	331
14	720	331
15	793	331
16	852	331
17	875	331
18	881	331
19	875	331