Details

analyze3.1s (16.8%)

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)

sample128.0ms (0.7%)

Algorithm

1×

intervals

Results

53.0ms	451×	body	128	nan
34.0ms	256×	body	128	valid
3.0ms	24×	body	128	invalid

Compiler

Compiled 75 to 53 computations (29.3% saved)

simplify52.0ms (0.3%)

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 → 1

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

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

26.9b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	26.9b	(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))))))))
	31.7b	(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

▶

26.9b

(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))))))))

31.7b

(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 161 to 103 computations (36% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.5b	(*.f64 n (/.f64 l Om))
8.2b	(.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)))))))
10.1b	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
18.1b	(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))))))))

rewrite222.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

20.3b

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:

10.0ms	(*.f64 n (/.f64 l Om))
8.0ms	(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))))))))
8.0ms	(.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)))))))

Compiler

Compiled 3547 to 1377 computations (61.2% saved)

series806.0ms (4.4%)

Error

16.4b

Counts

4 → 96

Calls

4 calls:

355.0ms	(.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)))))))
304.0ms	(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))))))))
61.0ms	(.f64 (-.f64 U U) (*.f64 n (/.f64 l Om)))
22.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 9765 to 6898 computations (29.4% saved)

simplify132.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

669×	`associate-l_binary64`
664×	`associate-r_binary64`
230×	`associate-/l*_binary64`
205×	`*-commutative_binary64`
186×	`fma-def_binary64`

Counts

203 → 171

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	511	7592
1	1326	6954
2	5308	6954

prune133.0ms (0.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	152	19	171
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	153	20	173

Error

12.2b

Counts

173 → 20

Alt Table

Status	Error	Program
	45.6b	(sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) 3)))
	60.1b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (-.f64 U* U))) Om) (/.f64 U Om))))
	63.1b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 t (sqrt.f64 2))) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))
	58.1b	(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 t (sqrt.f64 2)) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (+.f64 (/.f64 2 Om) (/.f64 (.f64 n U) (.f64 Om Om))))))) (*.f64 (sqrt.f64 2) l))))
	61.1b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 2 (.f64 n U))) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t))))
	56.2b	(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)))))))))
▶	27.9b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))))
	40.5b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))))))))) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))
✓	26.9b	(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))))))))
	60.2b	(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))))))))
	38.4b	(sqrt.f64 (.f64 U (fma.f64 2 (fma.f64 n t (/.f64 (.f64 n (.f64 n (.f64 (.f64 l l) U))) (.f64 Om Om))) (.f64 (/.f64 (.f64 n (.f64 l l)) Om) -4))))
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 n (.f64 (.f64 (.f64 l l) (-.f64 U* U)) U)))) (/.f64 (sqrt.f64 2) Om))
	35.0b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))
	56.6b	(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 t (sqrt.f64 2)) 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)))
	43.3b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
	55.5b	(.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))
	35.3b	(sqrt.f64 (fma.f64 t (.f64 2 (.f64 n U)) (.f64 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om) -4)))
	51.3b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))))))))) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))))))))
	42.9b	(-.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))))
	39.1b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (*.f64 t U))))

Compiler

Compiled 4728 to 2031 computations (57% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.8b	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
6.0b	(.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
8.1b	(.f64 (-.f64 U U) (/.f64 l Om))
18.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))))

rewrite190.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

9.8b

Rules

36×	`pow1_binary64`
30×	`add-cbrt-cube_binary64`
30×	`add-exp-log_binary64`
20×	`pow-prod-down_binary64`
20×	`add-sqr-sqrt_binary64`

Counts

4 → 111

Calls

4 calls:

11.0ms	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
8.0ms	(.f64 (-.f64 U U) (/.f64 l Om))
6.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))))
5.0ms	(.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))

Compiler

Compiled 3359 to 1256 computations (62.6% saved)

series812.0ms (4.4%)

Error

12.2b

Counts

4 → 105

Calls

4 calls:

355.0ms	(.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
296.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t))))
59.0ms	(.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))
41.0ms	(.f64 (-.f64 U U) (/.f64 l Om))

Compiler

Compiled 10243 to 7147 computations (30.2% saved)

simplify179.0ms (1%)

Algorithm

1×	egg-herbie

Rules

681×	`fma-def_binary64`
586×	`associate-r_binary64`
523×	`associate-l_binary64`
418×	`*-commutative_binary64`
250×	`fma-neg_binary64`

Counts

216 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	538	7784
1	1293	7220
2	4572	7160
3	5270	7160

prune149.0ms (0.8%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	190	3	193
Fresh	2	16	18
Picked	1	0	1
Done	0	1	1
Total	193	20	213

Error

9.8b

Counts

213 → 20

Alt Table

Status	Error	Program
	45.6b	(sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) 3)))
	60.1b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (-.f64 U* U))) Om) (/.f64 U Om))))
	63.1b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 t (sqrt.f64 2))) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))
	44.9b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))) t))))
	61.1b	(sqrt.f64 (log.f64 (pow.f64 (exp.f64 (.f64 2 (.f64 n U))) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t))))
	40.5b	(sqrt.f64 (/.f64 (.f64 n (.f64 2 (.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))))))))) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 (-.f64 U* U) (*.f64 n (/.f64 l Om))))))))
✓	26.9b	(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))))))))
	58.1b	(neg.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om))))) (/.f64 (.f64 t (sqrt.f64 2)) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om)))))) (*.f64 (sqrt.f64 2) l))))
	42.9b	(-.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))))
	60.2b	(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))))))))
	38.4b	(sqrt.f64 (.f64 U (fma.f64 2 (fma.f64 n t (/.f64 (.f64 n (.f64 n (.f64 (.f64 l l) U))) (.f64 Om Om))) (.f64 (/.f64 (.f64 n (.f64 l l)) Om) -4))))
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 n (.f64 (.f64 (.f64 l l) (-.f64 U* U)) U)))) (/.f64 (sqrt.f64 2) Om))
▶	35.0b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))
	56.6b	(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 t (sqrt.f64 2)) 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)))
	43.3b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
	55.5b	(.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))
	35.3b	(sqrt.f64 (fma.f64 t (.f64 2 (.f64 n U)) (.f64 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om) -4)))
	56.2b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (.f64 l l) (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om))))))))
	51.3b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))))))))) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))))))))
	39.1b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (*.f64 t U))))

Compiler

Compiled 4670 to 2058 computations (55.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.9b	(.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4)))
7.3b	(.f64 (/.f64 (.f64 l l) Om) U)
7.7b	(/.f64 (*.f64 l l) Om)
13.7b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))

rewrite134.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

8.5b

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
17×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 88

Calls

4 calls:

7.0ms	(.f64 (/.f64 (.f64 l l) Om) U)
4.0ms	(/.f64 (*.f64 l l) Om)
3.0ms	(.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4)))
2.0ms	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))

Compiler

Compiled 2066 to 827 computations (60% saved)

series234.0ms (1.3%)

Error

8.8b

Counts

4 → 59

Calls

4 calls:

93.0ms	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4))))
90.0ms	(.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 (*.f64 l l) Om) U) -4)))
25.0ms	(.f64 (/.f64 (.f64 l l) Om) U)
13.0ms	(/.f64 (*.f64 l l) Om)

Compiler

Compiled 3374 to 2443 computations (27.6% saved)

simplify109.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-def_binary64`
539×	`associate-/l*_binary64`
436×	`times-frac_binary64`
202×	`associate-l_binary64`
201×	`associate-/r*_binary64`

Counts

147 → 115

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	211	3072
1	477	2613
2	1618	2613
3	4606	2613
4	5080	2613

prune91.0ms (0.5%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	108	7	115
Fresh	3	15	18
Picked	1	0	1
Done	0	1	1
Total	112	23	135

Error

7.6b

Counts

135 → 23

Alt Table

Status	Error	Program
	45.6b	(sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) 3)))
	60.1b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (-.f64 U* U))) Om) (/.f64 U Om))))
	63.1b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 t (sqrt.f64 2))) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))
▶	30.4b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 l 1) (*.f64 U (/.f64 l Om))) -4))))
	56.9b	(sqrt.f64 (.f64 -4 (.f64 n (/.f64 (.f64 U (.f64 l l)) Om))))
	58.1b	(neg.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om))))) (/.f64 (.f64 t (sqrt.f64 2)) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om)))))) (*.f64 (sqrt.f64 2) l))))
	42.9b	(-.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))))
	60.2b	(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))))))))
	35.1b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 n (.f64 U (fma.f64 -4 (/.f64 (.f64 l l) Om) (.f64 2 t)))))) (sqrt.f64 (sqrt.f64 (.f64 n (.f64 U (fma.f64 -4 (/.f64 (.f64 l l) Om) (*.f64 2 t)))))))
	38.4b	(sqrt.f64 (.f64 U (fma.f64 2 (fma.f64 n t (/.f64 (.f64 n (.f64 n (.f64 (.f64 l l) U))) (.f64 Om Om))) (.f64 (/.f64 (.f64 n (.f64 l l)) Om) -4))))
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 n (.f64 (.f64 (.f64 l l) (-.f64 U* U)) U)))) (/.f64 (sqrt.f64 2) Om))
	35.9b	(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 n (.f64 U (fma.f64 -4 (/.f64 (.f64 l l) Om) (.f64 2 t)))))))
	39.1b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (*.f64 t U))))
	57.1b	(neg.f64 (.f64 l (sqrt.f64 (.f64 -4 (/.f64 (*.f64 n U) Om)))))
	56.6b	(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 t (sqrt.f64 2)) 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)))
	43.3b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
	56.6b	(.f64 l (sqrt.f64 (.f64 -4 (/.f64 (*.f64 n U) Om))))
	44.9b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))) t))))
	35.3b	(sqrt.f64 (fma.f64 t (.f64 2 (.f64 n U)) (.f64 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om) -4)))
	56.2b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (.f64 l l) (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om))))))))
	51.3b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))))))))) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))))))))
✓	26.9b	(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))))))))
	48.8b	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 U (fma.f64 -4 (/.f64 (.f64 l l) Om) (.f64 2 t)))))

Compiler

Compiled 2746 to 1484 computations (46% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (/.f64 l 1) (.f64 U (/.f64 l Om)))
6.2b	(*.f64 U (/.f64 l Om))
6.9b	(.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 l 1) (*.f64 U (/.f64 l Om))) -4)))
13.7b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 l 1) (*.f64 U (/.f64 l Om))) -4))))

rewrite144.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

7.6b

Rules

41×	`add-exp-log_binary64`
32×	`add-cbrt-cube_binary64`
28×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`

Counts

4 → 113

Calls

4 calls:

8.0ms	(.f64 (/.f64 l 1) (.f64 U (/.f64 l Om)))
5.0ms	(*.f64 U (/.f64 l Om))
3.0ms	(.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 l 1) (*.f64 U (/.f64 l Om))) -4)))
2.0ms	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 l 1) (*.f64 U (/.f64 l Om))) -4))))

Compiler

Compiled 2920 to 1436 computations (50.8% saved)

series237.0ms (1.3%)

Error

7.6b

Counts

4 → 62

Calls

4 calls:

92.0ms	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 l 1) (*.f64 U (/.f64 l Om))) -4))))
89.0ms	(.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 l 1) (*.f64 U (/.f64 l Om))) -4)))
23.0ms	(.f64 (/.f64 l 1) (.f64 U (/.f64 l Om)))
22.0ms	(*.f64 U (/.f64 l Om))

Compiler

Compiled 3550 to 2564 computations (27.8% saved)

simplify116.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

714×	`fma-def_binary64`
358×	`associate-/r*_binary64`
299×	`associate-/l/_binary64`
281×	`associate-r_binary64`
278×	`associate-l_binary64`

Counts

175 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	3472
1	549	3150
2	2025	2943
3	4476	2943
4	5077	2943

prune92.0ms (0.5%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	1	20	21
Picked	0	1	1
Done	0	1	1
Total	147	24	171

Error

7.6b

Counts

171 → 24

Alt Table

Status	Error	Program
	45.6b	(sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 2 (.f64 n U)) (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)) 3)))
	60.1b	(sqrt.f64 (.f64 2 (.f64 (/.f64 (.f64 (.f64 n n) (.f64 (.f64 l l) (-.f64 U* U))) Om) (/.f64 U Om))))
	63.1b	(fma.f64 n (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om)))))) (.f64 (sqrt.f64 (/.f64 U (-.f64 (/.f64 (.f64 (.f64 l l) U) (.f64 Om Om)) (/.f64 (.f64 U (.f64 l l)) (.f64 Om Om))))) (-.f64 (.f64 1/2 (.f64 t (sqrt.f64 2))) (/.f64 (.f64 (sqrt.f64 2) (*.f64 l l)) Om))))
✓	30.4b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 l 1) (*.f64 U (/.f64 l Om))) -4))))
	56.9b	(sqrt.f64 (.f64 -4 (.f64 n (/.f64 (.f64 U (.f64 l l)) Om))))
	56.2b	(sqrt.f64 (.f64 2 (.f64 n (.f64 (.f64 l l) (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om))))))))
	40.6b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 l 1) (log.f64 (exp.f64 (/.f64 (*.f64 U l) Om)))) -4))))
	58.1b	(neg.f64 (fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 (.f64 n U) (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om))))) (/.f64 (.f64 t (sqrt.f64 2)) l)) (.f64 (sqrt.f64 (.f64 n (.f64 U (-.f64 (/.f64 (.f64 n U) (.f64 Om Om)) (fma.f64 (/.f64 U Om) (/.f64 n Om) (/.f64 2 Om)))))) (*.f64 (sqrt.f64 2) l))))
	42.9b	(-.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))))
	60.2b	(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))))))))
	38.4b	(sqrt.f64 (.f64 U (fma.f64 2 (fma.f64 n t (/.f64 (.f64 n (.f64 n (.f64 (.f64 l l) U))) (.f64 Om Om))) (.f64 (/.f64 (.f64 n (.f64 l l)) Om) -4))))
	59.8b	(.f64 (sqrt.f64 (.f64 n (.f64 n (.f64 (.f64 (.f64 l l) (-.f64 U* U)) U)))) (/.f64 (sqrt.f64 2) Om))
	35.9b	(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 n (.f64 U (fma.f64 -4 (/.f64 (.f64 l l) Om) (.f64 2 t)))))))
	39.1b	(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (*.f64 t U))))
	57.1b	(neg.f64 (.f64 l (sqrt.f64 (.f64 -4 (/.f64 (*.f64 n U) Om)))))
	56.6b	(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 t (sqrt.f64 2)) 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)))
	43.3b	(.f64 (sqrt.f64 (.f64 2 (.f64 n U))) (sqrt.f64 (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))) t)))
	56.6b	(.f64 l (sqrt.f64 (.f64 -4 (/.f64 (*.f64 n U) Om))))
	44.9b	(.f64 (sqrt.f64 (.f64 n 2)) (sqrt.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))) t))))
	35.3b	(sqrt.f64 (fma.f64 t (.f64 2 (.f64 n U)) (.f64 (/.f64 (.f64 n (.f64 U (.f64 l l))) Om) -4)))
	32.8b	(sqrt.f64 (.f64 n (fma.f64 2 (.f64 t U) (.f64 (.f64 (/.f64 l 1) (expm1.f64 (log1p.f64 (/.f64 (*.f64 U l) Om)))) -4))))
	51.3b	(/.f64 (sqrt.f64 (.f64 n (.f64 2 (.f64 (.f64 U (fma.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U* U) (/.f64 l Om)))) t)) (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om)))))))))) (sqrt.f64 (-.f64 t (.f64 (/.f64 l Om) (fma.f64 l -2 (.f64 n (.f64 (-.f64 U U) (/.f64 l Om))))))))
✓	26.9b	(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))))))))
	48.8b	(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 U (fma.f64 -4 (/.f64 (.f64 l l) Om) (.f64 2 t)))))

Compiler

Compiled 2443 to 1270 computations (48% saved)

regimes7.0s (37.9%)

Accuracy

Total 16.2b remaining (61.1%)

Threshold costs 0b (0%)

Compiler

Compiled 91010 to 56042 computations (38.4% saved)

bsearch22.0ms (0.1%)

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

simplify37.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

181×	`distribute-rgt-neg-in_binary64`
119×	`cancel-sign-sub-inv_binary64`
118×	`distribute-lft-neg-out_binary64`
116×	`distribute-lft-neg-in_binary64`
99×	`distribute-rgt-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	184
1	88	184
2	116	184
3	139	184
4	165	184
5	186	184
6	201	184
7	227	184
8	256	184
9	289	184
10	350	184
11	444	184
12	555	184
13	635	184
14	711	184
15	768	184
16	802	184
17	821	184
18	825	184
19	817	184

end2.0ms (0%)

Compiler: Compiled 130 to 73 computations (43.8% saved)

sample4.3s (23.1%)

Algorithm

1×

intervals

Results

1.5s	12279×	body	128	nan
1.1s	8000×	body	128	valid
144.0ms	1148×	body	128	invalid

Compiler

Compiled 973 to 590 computations (39.4% saved)

Iter	Nodes	Cost
0	54	184
1	88	184
2	116	184
3	139	184
4	165	184
5	186	184
6	201	184
7	227	184
8	256	184
9	289	184
10	350	184
11	444	184
12	555	184
13	635	184
14	711	184
15	768	184
16	802	184
17	821	184
18	825	184
19	817	184

Iter	Nodes	Cost
0	54	184
1	88	184
2	116	184
3	139	184
4	165	184
5	186	184
6	201	184
7	227	184
8	256	184
9	289	184
10	350	184
11	444	184
12	555	184
13	635	184
14	711	184
15	768	184
16	802	184
17	821	184
18	825	184
19	817	184

Details

analyze3.1s (16.8%)

sample128.0ms (0.7%)

simplify52.0ms (0.3%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite222.0ms (1.2%)

series806.0ms (4.4%)

simplify132.0ms (0.7%)

prune133.0ms (0.7%)

localize15.0ms (0.1%)

rewrite190.0ms (1%)

series812.0ms (4.4%)

simplify179.0ms (1%)

prune149.0ms (0.8%)

localize12.0ms (0.1%)

rewrite134.0ms (0.7%)

series234.0ms (1.3%)

simplify109.0ms (0.6%)

prune91.0ms (0.5%)

localize14.0ms (0.1%)

rewrite144.0ms (0.8%)

series237.0ms (1.3%)

simplify116.0ms (0.6%)

prune92.0ms (0.5%)

regimes7.0s (37.9%)

bsearch22.0ms (0.1%)

simplify37.0ms (0.2%)

end2.0ms (0%)

sample4.3s (23.1%)

Profiling

Iter	Nodes	Cost
0	54	184
1	88	184
2	116	184
3	139	184
4	165	184
5	186	184
6	201	184
7	227	184
8	256	184
9	289	184
10	350	184
11	444	184
12	555	184
13	635	184
14	711	184
15	768	184
16	802	184
17	821	184
18	825	184
19	817	184