Details

analyze3.7s (15.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

Compiler

Compiled 35 to 24 computations (31.4% saved)

sample4.8s (19.7%)

Results

2.9s	14301×	body	128	invalid
1.8s	8256×	body	128	valid

Compiler

Compiled 104 to 71 computations (31.7% saved)

simplify49.0ms (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

33.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	33.5b	(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))))))))
	36.7b	(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

▶

33.5b

(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))))))))

36.7b

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

Compiler

Compiled 189 to 119 computations (37% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.6b	(*.f64 n (/.f64 l Om))
✓	6.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	11.0b	(.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)))))))
✓	21.2b	(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))))))))

series2.0s (8.3%)

Counts

4 → 216

Calls

4 calls:

1.6s	(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))))))))
422.0ms	(.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)))))))
35.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
13.0ms	(*.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:

7.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
7.0ms	(.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)))))))
6.0ms	(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))

simplify255.0ms (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 → 286

Iterations

Useful iterations: 1 (0.0ms)

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

prune453.0ms (1.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	271	15	286
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	272	16	288

Error

16.2b

Counts

288 → 16

Alt Table

Status	Error	Program
✓	33.5b	(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))))))))
	47.0b	(sqrt.f64 (/.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (.f64 t t) (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))) (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))))))) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	59.8b	(.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))
	61.1b	(.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)))
	57.9b	(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)))))))))
	57.9b	(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)))
	40.4b	(cbrt.f64 (pow.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))) 3))
	61.4b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	48.1b	(.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))))))))
	56.1b	(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)))
	33.6b	(.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))))))))))
	41.7b	(sqrt.f64 (.f64 U (fma.f64 2 (fma.f64 n t (/.f64 (.f64 (.f64 (.f64 l l) U) (.f64 n n)) (.f64 Om Om))) (.f64 -4 (/.f64 (.f64 n (.f64 l l)) Om)))))
	60.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	41.4b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
▶	32.8b	(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)))))))))
	38.3b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))

Compiler

Compiled 22820 to 11757 computations (48.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.2b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))))))
	6.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	6.2b	(.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))))))))
✓	21.2b	(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)))))))))

series2.1s (8.7%)

Counts

3 → 192

Calls

3 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)))))))))

402.0ms

(*.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))))))))

226.0ms

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

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
17×	`pow-prod-down_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
10×	`associate-*r/_binary64`

Counts

3 → 72

Calls

3 calls:

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))))))))

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)))))))))

5.0ms

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

simplify281.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-def_binary64`
435×	`*-commutative_binary64`
225×	`associate-r_binary64`
161×	`+-commutative_binary64`
146×	`cancel-sign-sub-inv_binary64`

Counts

264 → 250

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	980	22532
1	3366	21795
2	4974	21795

prune475.0ms (1.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	302	4	306
Fresh	4	10	14
Picked	1	0	1
Done	0	1	1
Total	307	15	322

Error

12.4b

Counts

322 → 15

Alt Table

Status	Error	Program
	61.4b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	53.7b	(/.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)))))
	59.8b	(.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))
	61.1b	(.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)))
	57.9b	(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)))
	37.6b	(cbrt.f64 (pow.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)))) 3))
✓	33.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	44.3b	(.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))))
	48.1b	(.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))))))))
▶	33.0b	(.f64 (sqrt.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))))) (sqrt.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))))))
	56.1b	(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)))
	41.7b	(sqrt.f64 (.f64 U (fma.f64 2 (fma.f64 n t (/.f64 (.f64 (.f64 (.f64 l l) U) (.f64 n n)) (.f64 Om Om))) (.f64 -4 (/.f64 (.f64 n (.f64 l l)) Om)))))
	60.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	41.4b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	38.3b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))

Compiler

Compiled 23555 to 12040 computations (48.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.2b	(.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t))
	6.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	6.2b	(.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)))
✓	21.2b	(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))))

series2.0s (8.3%)

Counts

3 → 192

Calls

3 calls:

1.5s

(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))))

366.0ms

(*.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)))

188.0ms

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

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
17×	`pow-prod-down_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
9×	`cbrt-unprod_binary64`

Counts

3 → 66

Calls

3 calls:

6.0ms

(*.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)))

4.0ms

(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))))

3.0ms

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

simplify257.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
430×	`*-commutative_binary64`
221×	`associate-r_binary64`
158×	`+-commutative_binary64`
144×	`associate-/l*_binary64`

Counts

258 → 213

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	963	22003
1	3269	20593
2	4970	20593

prune880.0ms (3.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	538	0	538
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	538	15	553

Error

12.4b

Counts

553 → 15

Alt Table

Status	Error	Program
	61.4b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	53.7b	(/.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)))))
	59.8b	(.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))
	61.1b	(.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)))
	57.9b	(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)))
▶	37.6b	(cbrt.f64 (pow.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)))) 3))
✓	33.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	44.3b	(.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))))
	48.1b	(.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))))))))
✓	33.0b	(.f64 (sqrt.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))))) (sqrt.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))))))
	56.1b	(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)))
	41.7b	(sqrt.f64 (.f64 U (fma.f64 2 (fma.f64 n t (/.f64 (.f64 (.f64 (.f64 l l) U) (.f64 n n)) (.f64 Om Om))) (.f64 -4 (/.f64 (.f64 n (.f64 l l)) Om)))))
	60.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	41.4b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	38.3b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))

Compiler

Compiled 55622 to 27334 computations (50.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	6.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
	6.2b	(.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)))
	21.2b	(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))))
✓	31.0b	(cbrt.f64 (pow.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)))) 3))

series1.6s (6.5%)

Counts

1 → 48

Calls

1 calls:

1.6s	(cbrt.f64 (pow.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)))) 3))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`cbrt-prod_binary64`
4×	`cube-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`unpow-prod-down_binary64`

Counts

1 → 25

Calls

1 calls:

3.0ms

(cbrt.f64 (pow.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)))) 3))

simplify206.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

901×	`associate-/r*_binary64`
695×	`fma-def_binary64`
370×	`*-commutative_binary64`
176×	`associate-r_binary64`
146×	`+-commutative_binary64`

Counts

73 → 118

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	846	12618
1	2941	11752
2	6344	11752

prune703.0ms (2.9%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	332	1	333
Fresh	1	11	12
Picked	0	1	1
Done	0	2	2
Total	333	15	348

Error

12.4b

Counts

348 → 15

Alt Table

Status	Error	Program
	61.4b	(neg.f64 (.f64 n (sqrt.f64 (.f64 -2 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om))))))))
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))
	53.7b	(/.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)))))
	57.9b	(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)))
✓	37.6b	(cbrt.f64 (pow.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)))) 3))
✓	33.5b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (*.f64 n (/.f64 l Om))))))))
	44.3b	(.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))))
	48.1b	(.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))))))))
	61.1b	(.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)))
✓	33.0b	(.f64 (sqrt.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))))) (sqrt.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))))))
	56.1b	(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)))
	41.7b	(sqrt.f64 (.f64 U (fma.f64 2 (fma.f64 n t (/.f64 (.f64 (.f64 (.f64 l l) U) (.f64 n n)) (.f64 Om Om))) (.f64 -4 (/.f64 (.f64 n (.f64 l l)) Om)))))
	60.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 (pow.f64 n 2) (.f64 (pow.f64 l 2) (.f64 U U*))) (pow.f64 Om 2))))
	41.4b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	38.3b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 U t) (.f64 -4 (/.f64 (.f64 (*.f64 l l) U) Om)))))

Compiler

Compiled 35187 to 19556 computations (44.4% saved)

regimes3.9s (16.1%)

Accuracy

Total 15.9b remaining (56.1%)

Threshold costs 0b (0%)

Counts

206 → 3

Compiler

Compiled 63818 to 39602 computations (37.9% saved)

bsearch199.0ms (0.8%)

Steps

Iters	Range		Point
6	6.269049858487873e+231	5.34514105965542e+232	6.715360645371229e+231
7	-1.8771206579959645e+118	-3.759688069887087e+116	-1.140102103818506e+118

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
15×	`+-commutative_binary64`
13×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	139
1	72	139
2	96	139
3	119	139
4	138	139
5	146	139
6	149	139
7	150	139
8	148	139

end281.0ms (1.2%)

Compiler: Compiled 748 to 435 computations (41.8% saved)

Iter	Nodes	Cost
0	44	139
1	72	139
2	96	139
3	119	139
4	138	139
5	146	139
6	149	139
7	150	139
8	148	139

Iter	Nodes	Cost
0	44	139
1	72	139
2	96	139
3	119	139
4	138	139
5	146	139
6	149	139
7	150	139
8	148	139

Details

analyze3.7s (15.1%)

sample4.8s (19.7%)

simplify49.0ms (0.2%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series2.0s (8.3%)

rewrite35.0ms (0.1%)

simplify255.0ms (1%)

prune453.0ms (1.9%)

localize17.0ms (0.1%)

series2.1s (8.7%)

rewrite24.0ms (0.1%)

simplify281.0ms (1.2%)

prune475.0ms (1.9%)

localize17.0ms (0.1%)

series2.0s (8.3%)

rewrite19.0ms (0.1%)

simplify257.0ms (1.1%)

prune880.0ms (3.6%)

localize18.0ms (0.1%)

series1.6s (6.5%)

rewrite8.0ms (0%)

simplify206.0ms (0.8%)

prune703.0ms (2.9%)

regimes3.9s (16.1%)

bsearch199.0ms (0.8%)

simplify13.0ms (0.1%)

end281.0ms (1.2%)

Profiling

Iter	Nodes	Cost
0	44	139
1	72	139
2	96	139
3	119	139
4	138	139
5	146	139
6	149	139
7	150	139
8	148	139