Details

analyze2.2s (7%)

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)

sample97.0ms (0.3%)

Algorithm

1×

intervals

Results

38.0ms	424×	body	128	nan
23.0ms	256×	body	128	valid
4.0ms	41×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify215.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4990	39
1	4990	39

prune8.0ms (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: 32.7b

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)))))
9.0b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
9.2b	(.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)))))))
22.8b	(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))))))))

rewrite64.0ms (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:

16.0ms	(.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))))))))

series5.1s (16.3%)

Counts

4 → 12

Calls

4 calls:

3.8s	(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))))))))
780.0ms	(.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)))))))
315.0ms	(.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)))

simplify104.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5017	4107

prune440.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	134	9	143
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	135	10	145

Merged error: 23.6b

Counts

145 → 10

Compiler

Compiled 10872 to 5956 computations (45.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.8b	(*.f64 n (/.f64 l Om))
7.4b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.2b	(.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))))))
22.8b	(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)))))))

rewrite52.0ms (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))
8.0ms	(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 (14.6%)

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)))))))
796.0ms	(.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))))))
201.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
34.0ms	(*.f64 n (/.f64 l Om))

simplify62.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5297	2813

prune204.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	119	10	129

Merged error: 22.9b

Counts

129 → 10

Compiler

Compiled 5450 to 2640 computations (51.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.8b	(*.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)))))))
7.4b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
22.8b	(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))))))))

rewrite53.0ms (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:

12.0ms	(.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 (15.1%)

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))))))))
842.0ms	(.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)))))))
220.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
34.0ms	(*.f64 n (/.f64 l Om))

simplify62.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5160	2911

prune318.0ms (1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	121	12	133

Merged error: 18.8b

Counts

133 → 12

Compiler

Compiled 8099 to 4355 computations (46.2% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

22.8b	(sqrt.f64 (.f64 (.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))
23.7b	(cbrt.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))))))))
23.7b	(cbrt.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))))))))
23.7b	(cbrt.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))))))))

rewrite71.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`associate-*r/_binary64_365`
60×	`cbrt-div_binary64_455`
30×	`flip-+_binary64_397` `flip3-+_binary64_426`
28×	`frac-times_binary64_433`
26×	`sqrt-div_binary64_440`
24×	`pow1_binary64_484`
15×	`sqrt-pow1_binary64_441`
14×	`associate-*l/_binary64_366`
12×	`pow1/3_binary64_505`
9×	`pow-prod-up_binary64_493`
6×	`pow-plus_binary64_486`
5×	`pow-prod-down_binary64_494`
4×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459` `add-log-exp_binary64_462`
3×	`pow-sqr_binary64_396` `cbrt-prod_binary64_454`
2×	`pow2_binary64_504`
1×	`sqrt-prod_binary64_439` `pow3_binary64_506` `pow1/2_binary64_503`

Counts

4 → 83

Calls

4 calls:

15.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))
8.0ms	(cbrt.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))))))))
8.0ms	(cbrt.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))))))))
8.0ms	(cbrt.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))))))))

series8.8s (28%)

Counts

4 → 12

Calls

4 calls:

3.5s	(sqrt.f64 (.f64 (.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))
1.8s	(cbrt.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))))))))
1.8s	(cbrt.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))))))))
1.8s	(cbrt.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))))))))

simplify110.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5226	8657

prune349.0ms (1.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	94	13	107

Merged error: 18.8b

Counts

107 → 13

Compiler

Compiled 10333 to 4464 computations (56.8% saved)

regimes475.0ms (1.5%)

Compiler: Compiled 4754 to 3128 computations (34.2% saved)

bsearch2.0ms (0%)

Compiler: Compiled 28 to 23 computations (17.9% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	192	215
1	192	215

end0.0ms (0%)

sample3.2s (10.2%)

Algorithm

1×

intervals

Results

1.2s	12756×	body	128	nan
749.0ms	8000×	body	128	valid
113.0ms	1201×	body	128	invalid

Compiler

Compiled 729 to 459 computations (37% saved)

Details

analyze2.2s (7%)

sample97.0ms (0.3%)

simplify215.0ms (0.7%)

prune8.0ms (0%)

localize17.0ms (0.1%)

rewrite64.0ms (0.2%)

series5.1s (16.3%)

simplify104.0ms (0.3%)

prune440.0ms (1.4%)

localize20.0ms (0.1%)

rewrite52.0ms (0.2%)

series4.6s (14.6%)

simplify62.0ms (0.2%)

prune204.0ms (0.6%)

localize20.0ms (0.1%)

rewrite53.0ms (0.2%)

series4.8s (15.1%)

simplify62.0ms (0.2%)

prune318.0ms (1%)

localize22.0ms (0.1%)

rewrite71.0ms (0.2%)

series8.8s (28%)

simplify110.0ms (0.3%)

prune349.0ms (1.1%)

regimes475.0ms (1.5%)

bsearch2.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample3.2s (10.2%)

Profiling