Details

analyze3.2s (11.4%)

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)

sample5.1s (18.2%)

Results

3.2s	14683×	body	128	invalid
1.8s	8256×	body	128	valid

Compiler

Compiled 104 to 71 computations (31.7% 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

prune4.0ms (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

31.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	31.4b	(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))))))))
	34.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))

Status

Error

Program

▶

31.4b

(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))))))))

34.4b

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

Compiler

Compiled 189 to 119 computations (37% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.4b	(*.f64 n (/.f64 l Om))
✓	7.8b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	8.5b	(.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)))))))
✓	21.9b	(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 (7.1%)

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))))))))
409.0ms	(.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)))
15.0ms	(*.f64 n (/.f64 l Om))

rewrite34.0ms (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)))
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))

simplify292.0ms (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

prune562.0ms (2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

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

Error

14.3b

Counts

288 → 17

Alt Table

Status	Error	Program
▶	31.4b	(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)))))))))
	46.2b	(-.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)))
	31.4b	(sqrt.f64 (+.f64 (.f64 t (.f64 (.f64 2 n) U)) (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))) (.f64 (*.f64 2 n) U))))
	39.3b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om))))
	39.4b	(.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))))))))
	57.5b	(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))))
	62.5b	(-.f64 (.f64 2 (/.f64 (.f64 (.f64 l l) U) (.f64 Om (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))))))))) (fma.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)))))) (/.f64 (.f64 U t) (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)))))))))
	59.4b	(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)))
	32.0b	(.f64 (.f64 (cbrt.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))))))))) (cbrt.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)))))))))) (cbrt.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)))
	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)))))
	42.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	34.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
	37.4b	(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)))))))
	60.4b	(.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))
	56.8b	(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)))
	32.5b	(sqrt.f64 (.f64 (.f64 (cbrt.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))) (cbrt.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)))) (cbrt.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)))))

Compiler

Compiled 23211 to 11924 computations (48.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.4b	(*.f64 n (/.f64 l Om))
✓	5.7b	(.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))))))))
	7.8b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	21.9b	(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 (7%)

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)))))))))

434.0ms

(*.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))))))))

rewrite19.0ms (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:

7.0ms

(*.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)))))))))

simplify299.0ms (1.1%)

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

prune521.0ms (1.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	277	6	283
Fresh	6	10	16
Picked	1	0	1
Done	0	0	0
Total	284	16	300

Error

10.5b

Counts

300 → 16

Alt Table

Status	Error	Program
	36.9b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om))))))))
	53.0b	(/.f64 (sqrt.f64 (.f64 (.f64 2 n) (.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 (+.f64 (.f64 t t) (-.f64 (.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))))))))))
	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)))
	31.6b	(.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))))))
▶	31.4b	(sqrt.f64 (+.f64 (.f64 t (.f64 (.f64 2 n) U)) (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))) (.f64 (*.f64 2 n) U))))
	39.3b	(sqrt.f64 (fma.f64 2 (.f64 n (.f64 U t)) (.f64 -4 (/.f64 (.f64 n (.f64 (.f64 l l) U)) Om))))
	39.4b	(.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))))))))
	62.5b	(-.f64 (.f64 2 (/.f64 (.f64 (.f64 l l) U) (.f64 Om (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))))))))) (fma.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)))))) (/.f64 (.f64 U t) (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)))))))))
	41.5b	(.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))))
	56.8b	(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)))
	55.4b	(/.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))))))))
	59.4b	(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)))
	42.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
	34.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
	46.2b	(-.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)))
	60.4b	(.f64 (sqrt.f64 (.f64 n (.f64 U (.f64 n (.f64 (.f64 l l) (-.f64 U* U)))))) (/.f64 (sqrt.f64 2) Om))

Compiler

Compiled 22409 to 11670 computations (47.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.4b	(*.f64 n (/.f64 l Om))
	7.8b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	8.6b	(.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om))))) (.f64 (*.f64 2 n) U))
✓	21.9b	(sqrt.f64 (+.f64 (.f64 t (.f64 (.f64 2 n) U)) (.f64 (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om))))) (.f64 (*.f64 2 n) U))))

series1.6s (5.7%)

Counts

2 → 108

Calls

2 calls:

1.3s

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

281.0ms

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

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-cbrt-cube_binary64`
38×	`add-exp-log_binary64`
24×	`cbrt-unprod_binary64`
24×	`prod-exp_binary64`
24×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

8.0ms

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

6.0ms

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

simplify230.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

721×	`associate-/l*_binary64`
583×	`fma-def_binary64`
302×	`*-commutative_binary64`
160×	`cancel-sign-sub-inv_binary64`
145×	`associate-r_binary64`

Counts

163 → 185

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	780	17956
1	2597	16591
2	5408	16591

prune590.0ms (2.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	280	10	290
Fresh	6	9	15
Picked	1	0	1
Done	0	0	0
Total	287	19	306

Error

7.7b

Counts

306 → 19

Alt Table

Status	Error	Program
	36.9b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om))))))))
	39.4b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))
	53.0b	(/.f64 (sqrt.f64 (.f64 (.f64 2 n) (.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 (+.f64 (.f64 t t) (-.f64 (.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))))))))))
	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)))
	31.6b	(.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))))))
	38.9b	(sqrt.f64 (+.f64 (.f64 t (.f64 (.f64 2 n) U)) (.f64 -4 (/.f64 (.f64 n (.f64 (pow.f64 l 2) U)) Om))))
	42.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
▶	31.2b	(sqrt.f64 (+.f64 (.f64 t (.f64 (.f64 2 n) U)) (.f64 (/.f64 l Om) (.f64 (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) (.f64 (*.f64 2 n) U)))))
	62.0b	(-.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 (.f64 n n) (.f64 l l)) (-.f64 (.f64 U U) (.f64 U U))))) Om) (.f64 2 (.f64 (.f64 n (.f64 (.f64 l l) U)) (sqrt.f64 (/.f64 1 (.f64 2 (.f64 (.f64 (.f64 n n) (.f64 l l)) (-.f64 (.f64 U U) (*.f64 U U)))))))))
	36.3b	(sqrt.f64 (+.f64 (.f64 t (.f64 (.f64 2 n) U)) (.f64 -2 (/.f64 (.f64 (.f64 n (.f64 l U)) (fma.f64 2 l (/.f64 (.f64 n (*.f64 l U)) Om))) Om))))
	56.8b	(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)))
	55.4b	(/.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))))))))
	59.4b	(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)))
	61.7b	(-.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)))))) (/.f64 (.f64 (.f64 l l) U) Om))) (fma.f64 n (sqrt.f64 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om))))) (.f64 (.f64 U t) (sqrt.f64 (/.f64 1 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)))))))))
	38.2b	(sqrt.f64 (+.f64 (.f64 t (.f64 (.f64 2 n) U)) (.f64 2 (/.f64 (.f64 n (.f64 (pow.f64 l 2) (.f64 (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))) U))) Om))))
	60.9b	(.f64 (sqrt.f64 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) (.f64 U U)) (*.f64 Om Om))))) (neg.f64 n))
	41.5b	(.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))))
	58.5b	(.f64 (sqrt.f64 (+.f64 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 Om Om)))) (.f64 -4 (/.f64 (*.f64 n U) Om)))) (neg.f64 l))
	59.9b	(.f64 l (sqrt.f64 (+.f64 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 Om Om)))) (.f64 -4 (/.f64 (*.f64 n U) Om)))))

Compiler

Compiled 25488 to 13184 computations (48.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.4b	(.f64 (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) (.f64 (*.f64 2 n) U))
✓	6.4b	(.f64 (/.f64 l Om) (.f64 (fma.f64 l -2 (.f64 (-.f64 U U) (.f64 n (/.f64 l Om)))) (.f64 (*.f64 2 n) U)))
	7.8b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
✓	21.9b	(sqrt.f64 (+.f64 (.f64 t (.f64 (.f64 2 n) U)) (.f64 (/.f64 l Om) (.f64 (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) (.f64 (*.f64 2 n) U)))))

series1.7s (5.8%)

Counts

3 → 168

Calls

3 calls:

1.2s

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

264.0ms

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

143.0ms

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

rewrite35.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-cbrt-cube_binary64`
44×	`add-exp-log_binary64`
27×	`pow1_binary64`
26×	`cbrt-unprod_binary64`
26×	`prod-exp_binary64`

Counts

3 → 85

Calls

3 calls:

10.0ms

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

6.0ms

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

5.0ms

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

simplify278.0ms (1%)

Algorithm

1×	egg-herbie

Rules

768×	`associate-/l*_binary64`
592×	`fma-def_binary64`
352×	`*-commutative_binary64`
182×	`associate-r_binary64`
170×	`cancel-sign-sub-inv_binary64`

Counts

253 → 257

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	862	21462
1	2822	19905
2	5869	19905

prune607.0ms (2.1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	312	1	313
Fresh	1	17	18
Picked	0	1	1
Done	0	0	0
Total	313	19	332

Error

7.7b

Counts

332 → 19

Alt Table

Status	Error	Program
	36.9b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (neg.f64 (/.f64 (.f64 n (.f64 l U)) Om))))))))
	39.4b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om)))) t)))
	53.0b	(/.f64 (sqrt.f64 (.f64 (.f64 2 n) (.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 (+.f64 (.f64 t t) (-.f64 (.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))))))))))
	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)))
	31.6b	(.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))))))
	42.0b	(.f64 (sqrt.f64 (.f64 n (*.f64 t U))) (sqrt.f64 2))
✓	31.2b	(sqrt.f64 (+.f64 (.f64 t (.f64 (.f64 2 n) U)) (.f64 (/.f64 l Om) (.f64 (fma.f64 l -2 (.f64 (-.f64 U* U) (.f64 n (/.f64 l Om)))) (.f64 (*.f64 2 n) U)))))
	62.0b	(-.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (.f64 (.f64 n n) (.f64 l l)) (-.f64 (.f64 U U) (.f64 U U))))) Om) (.f64 2 (.f64 (.f64 n (.f64 (.f64 l l) U)) (sqrt.f64 (/.f64 1 (.f64 2 (.f64 (.f64 (.f64 n n) (.f64 l l)) (-.f64 (.f64 U U) (*.f64 U U)))))))))
	36.3b	(sqrt.f64 (+.f64 (.f64 t (.f64 (.f64 2 n) U)) (.f64 -2 (/.f64 (.f64 (.f64 n (.f64 l U)) (fma.f64 2 l (/.f64 (.f64 n (*.f64 l U)) Om))) Om))))
	56.8b	(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)))
	55.4b	(/.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))))))))
	59.4b	(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)))
	61.7b	(-.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)))))) (/.f64 (.f64 (.f64 l l) U) Om))) (fma.f64 n (sqrt.f64 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om))))) (.f64 (.f64 U t) (sqrt.f64 (/.f64 1 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)))))))))
	38.2b	(sqrt.f64 (+.f64 (.f64 t (.f64 (.f64 2 n) U)) (.f64 2 (/.f64 (.f64 n (.f64 (pow.f64 l 2) (.f64 (-.f64 (/.f64 (.f64 n U) Om) (+.f64 2 (/.f64 (.f64 n U) Om))) U))) Om))))
	60.9b	(.f64 (sqrt.f64 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 l l) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 l l) (.f64 U U)) (*.f64 Om Om))))) (neg.f64 n))
	35.4b	(sqrt.f64 (+.f64 (.f64 t (.f64 (.f64 2 n) U)) (.f64 (/.f64 l Om) (.f64 -4 (.f64 n (*.f64 l U))))))
	41.5b	(.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))))
	58.5b	(.f64 (sqrt.f64 (+.f64 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 Om Om)))) (.f64 -4 (/.f64 (*.f64 n U) Om)))) (neg.f64 l))
	59.9b	(.f64 l (sqrt.f64 (+.f64 (.f64 2 (-.f64 (/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 Om Om)) (/.f64 (.f64 (.f64 n n) (.f64 U U)) (.f64 Om Om)))) (.f64 -4 (/.f64 (*.f64 n U) Om)))))

Compiler

Compiled 25636 to 13074 computations (49% saved)

regimes8.6s (30.5%)

Accuracy

Total 15.9b remaining (63.5%)

Threshold costs 0b (0%)

Counts

346 → 4

Compiler

Compiled 109434 to 67450 computations (38.4% saved)

bsearch23.0ms (0.1%)

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

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

35×	`*-commutative_binary64`
20×	`+-commutative_binary64`
18×	`sub-neg_binary64`
16×	`neg-sub0_binary64`
16×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	298
1	96	298
2	124	298
3	147	298
4	173	298
5	190	298
6	197	298
7	207	298
8	213	298
9	216	298
10	217	298
11	212	298

end396.0ms (1.4%)

Compiler: Compiled 1295 to 681 computations (47.4% saved)

Iter	Nodes	Cost
0	61	298
1	96	298
2	124	298
3	147	298
4	173	298
5	190	298
6	197	298
7	207	298
8	213	298
9	216	298
10	217	298
11	212	298

Iter	Nodes	Cost
0	61	298
1	96	298
2	124	298
3	147	298
4	173	298
5	190	298
6	197	298
7	207	298
8	213	298
9	216	298
10	217	298
11	212	298

Details

analyze3.2s (11.4%)

sample5.1s (18.2%)

simplify53.0ms (0.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series2.0s (7.1%)

rewrite34.0ms (0.1%)

simplify292.0ms (1%)

prune562.0ms (2%)

localize16.0ms (0.1%)

series2.0s (7%)

rewrite19.0ms (0.1%)

simplify299.0ms (1.1%)

prune521.0ms (1.8%)

localize17.0ms (0.1%)

series1.6s (5.7%)

rewrite24.0ms (0.1%)

simplify230.0ms (0.8%)

prune590.0ms (2.1%)

localize17.0ms (0.1%)

series1.7s (5.8%)

rewrite35.0ms (0.1%)

simplify278.0ms (1%)

prune607.0ms (2.1%)

regimes8.6s (30.5%)

bsearch23.0ms (0.1%)

simplify18.0ms (0.1%)

end396.0ms (1.4%)

Profiling

Iter	Nodes	Cost
0	61	298
1	96	298
2	124	298
3	147	298
4	173	298
5	190	298
6	197	298
7	207	298
8	213	298
9	216	298
10	217	298
11	212	298