Details

analyze2.3s (7.6%)

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 29 to 24 computations (17.2% saved)

sample296.0ms (1%)

Algorithm

1×

intervals

Results

223.0ms	256×	body	128	valid
40.0ms	428×	body	128	nan
4.0ms	39×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify209.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4990	39
1	4990	39

prune12.0ms (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

Merged error: 30.5b

Counts

2 → 2

Compiler

Compiled 134 to 106 computations (20.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.3b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.0b	(.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)))))))
10.7b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
19.3b	(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))))))))

rewrite58.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_484` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
29×	`add-sqr-sqrt_binary64_445`
27×	`associate-l_binary64_364`
24×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
19×	`times-frac_binary64_429`
18×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372`
16×	`pow-prod-down_binary64_494`
14×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
12×	`cancel-sign-sub-inv_binary64_389` `associate-*r/_binary64_365`
7×	`associate-r_binary64_363`
4×	`sub-neg_binary64_416` `frac-times_binary64_433` `flip-+_binary64_397` `flip3-+_binary64_426` `add-log-exp_binary64_462` `sqrt-pow1_binary64_441`
3×	`*-commutative_binary64_354` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
2×	`sqrt-div_binary64_440` `flip3--_binary64_427` `associate-*l/_binary64_366` `flip--_binary64_398` `div-inv_binary64_420` `unswap-sqr_binary64_391`
1×	`sqrt-prod_binary64_439` `pow1/2_binary64_503`

Counts

4 → 131

Calls

4 calls:

13.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
11.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.0ms	(.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)))))))
8.0ms	(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))))))))

series4.9s (15.8%)

Counts

4 → 12

Calls

4 calls:

3.5s	(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))))))))
798.0ms	(.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)))))))
317.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
210.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify105.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5017	4107

prune536.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	131	12	143
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	132	13	145

Merged error: 22.3b

Counts

145 → 13

Compiler

Compiled 13459 to 7331 computations (45.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.2b	(*.f64 n (/.f64 l Om))
7.3b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.0b	(.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))))))
19.3b	(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)))))))

rewrite50.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_484`
27×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
23×	`add-sqr-sqrt_binary64_445`
21×	`associate-r_binary64_363`
18×	`*-un-lft-identity_binary64_423`
16×	`pow-prod-down_binary64_494` `add-cube-cbrt_binary64_458`
13×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
10×	`times-frac_binary64_429` `associate-*r/_binary64_365`
6×	`cancel-sign-sub-inv_binary64_389`
5×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372` `associate-l_binary64_364`
4×	`add-log-exp_binary64_462` `sqrt-pow1_binary64_441`
3×	`*-commutative_binary64_354`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `frac-times_binary64_433` `flip-+_binary64_397` `flip3--_binary64_427` `flip3-+_binary64_426` `flip--_binary64_398` `unswap-sqr_binary64_391` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
1×	`sqrt-prod_binary64_439` `associate-*l/_binary64_366` `distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392` `pow1/2_binary64_503` `div-inv_binary64_420`

Counts

4 → 107

Calls

4 calls:

12.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.0ms	(.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))))))
8.0ms	(*.f64 n (/.f64 l Om))
7.0ms	(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)))))))

series4.6s (15.1%)

Counts

4 → 12

Calls

4 calls:

3.6s	(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)))))))
789.0ms	(.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))))))
213.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
33.0ms	(*.f64 n (/.f64 l Om))

simplify59.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5297	2813

prune255.0ms (0.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	119	13	132

Merged error: 21.6b

Counts

132 → 13

Compiler

Compiled 6792 to 3375 computations (50.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.2b	(*.f64 n (/.f64 l Om))
6.4b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
7.3b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
19.3b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))

rewrite50.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64_484`
30×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
22×	`add-sqr-sqrt_binary64_445`
20×	`pow-prod-down_binary64_494`
19×	`associate-r_binary64_363`
17×	`*-un-lft-identity_binary64_423`
15×	`add-cube-cbrt_binary64_458` `prod-exp_binary64_472` `cbrt-unprod_binary64_456`
14×	`associate-*r/_binary64_365`
10×	`times-frac_binary64_429`
8×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372`
6×	`cancel-sign-sub-inv_binary64_389`
5×	`associate-l_binary64_364` `sqrt-pow1_binary64_441`
4×	`add-log-exp_binary64_462`
3×	`*-commutative_binary64_354`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `frac-times_binary64_433` `flip-+_binary64_397` `flip3--_binary64_427` `flip3-+_binary64_426` `flip--_binary64_398` `unswap-sqr_binary64_391` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
1×	`sqrt-prod_binary64_439` `associate-*l/_binary64_366` `distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392` `pow1/2_binary64_503` `div-inv_binary64_420`

Counts

4 → 111

Calls

4 calls:

11.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
8.0ms	(*.f64 n (/.f64 l Om))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))

series4.8s (15.6%)

Counts

4 → 12

Calls

4 calls:

3.7s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
841.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
207.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
33.0ms	(*.f64 n (/.f64 l Om))

simplify57.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5160	2911

prune395.0ms (1.3%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	118	18	136

Merged error: 18.3b

Counts

136 → 18

Compiler

Compiled 10628 to 5667 computations (46.7% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.3b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
7.3b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
19.3b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
19.3b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))

rewrite58.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`pow1_binary64_484`
22×	`pow-prod-down_binary64_494` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
18×	`associate-*r/_binary64_365`
14×	`*-un-lft-identity_binary64_423` `add-sqr-sqrt_binary64_445`
12×	`cancel-sign-sub-inv_binary64_389`
10×	`add-cube-cbrt_binary64_458` `prod-exp_binary64_472` `associate-r_binary64_363` `sqrt-pow1_binary64_441` `cbrt-unprod_binary64_456`
8×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372`
4×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `frac-times_binary64_433` `flip3--_binary64_427` `add-log-exp_binary64_462` `flip--_binary64_398`
2×	`associate-l_binary64_364` `flip-+_binary64_397` `sqrt-prod_binary64_439` `associate-l/_binary64_366` `-commutative_binary64_354` `distribute-lft-out--_binary64_375` `flip3-+_binary64_426` `difference-of-squares_binary64_392` `pow1/2_binary64_503` `cbrt-undiv_binary64_457` `div-exp_binary64_474`

Counts

4 → 102

Calls

4 calls:

12.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
12.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))

series7.5s (24.6%)

Counts

4 → 12

Calls

4 calls:

3.6s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
3.5s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
217.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
217.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))

simplify52.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4978	2680
1	4978	2680

prune273.0ms (0.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	2	13	15
Picked	1	0	1
Done	0	2	2
Total	116	16	132

Merged error: 18.3b

Counts

132 → 16

Compiler

Compiled 7946 to 3505 computations (55.9% saved)

regimes492.0ms (1.6%)

Compiler: Compiled 6082 to 3808 computations (37.4% saved)

bsearch79.0ms (0.3%)

Steps

Iters	Range		Point
10	-8.017226046718044e-303	1.62488923798826e-300	-5.0296597147651e-310

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	86
1	48	86

end0.0ms (0%)

sample3.4s (11.1%)

Algorithm

1×

intervals

Results

1.3s	13053×	body	128	nan
765.0ms	8000×	body	128	valid
115.0ms	1169×	body	128	invalid

Compiler

Compiled 810 to 501 computations (38.1% saved)

Details

analyze2.3s (7.6%)

sample296.0ms (1%)

simplify209.0ms (0.7%)

prune12.0ms (0%)

localize17.0ms (0.1%)

rewrite58.0ms (0.2%)

series4.9s (15.8%)

simplify105.0ms (0.3%)

prune536.0ms (1.8%)

localize17.0ms (0.1%)

rewrite50.0ms (0.2%)

series4.6s (15.1%)

simplify59.0ms (0.2%)

prune255.0ms (0.8%)

localize18.0ms (0.1%)

rewrite50.0ms (0.2%)

series4.8s (15.6%)

simplify57.0ms (0.2%)

prune395.0ms (1.3%)

localize21.0ms (0.1%)

rewrite58.0ms (0.2%)

series7.5s (24.6%)

simplify52.0ms (0.2%)

prune273.0ms (0.9%)

regimes492.0ms (1.6%)

bsearch79.0ms (0.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (11.1%)

Profiling