Details

analyze2.4s (7.3%)

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)

sample101.0ms (0.3%)

Algorithm

1×

intervals

Results

39.0ms	408×	body	128	nan
24.0ms	256×	body	128	valid
3.0ms	33×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify414.0ms (1.3%)

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: 33.0b

Counts

2 → 2

Compiler

Compiled 134 to 106 computations (20.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.6b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
11.1b	(.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)))))))
11.8b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
20.4b	(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:

17.0ms	(.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 (15.3%)

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 l Om) (.f64 n (-.f64 U U))))))))
789.0ms	(.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)))))
196.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify104.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5017	4107

prune540.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	132	11	143
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	132	13	145

Merged error: 23.9b

Counts

145 → 13

Compiler

Compiled 14107 to 7758 computations (45% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(*.f64 n (/.f64 l Om))
8.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
11.1b	(.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))))))
20.4b	(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)))))))

series4.8s (14.9%)

Counts

4 → 12

Calls

4 calls:

3.7s	(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)))))))
844.0ms	(.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))))))
224.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
37.0ms	(*.f64 n (/.f64 l Om))

simplify60.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5297	2813

prune329.0ms (1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	5	6	11
Picked	1	0	1
Done	0	1	1
Total	120	12	132

Merged error: 22.7b

Counts

132 → 12

Compiler

Compiled 8673 to 4698 computations (45.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.2b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
5.9b	(.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)))))))
8.1b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
20.4b	(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))))))))

rewrite49.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 101

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	(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))))))))
7.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))

series5.4s (16.9%)

Counts

4 → 12

Calls

4 calls:

3.8s	(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))))))))
793.0ms	(.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)))))))
623.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
219.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))

simplify62.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5054	3449

prune410.0ms (1.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	110	15	125

Merged error: 18.9b

Counts

125 → 15

Compiler

Compiled 10930 to 6113 computations (44.1% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

16.7b	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
16.7b	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
16.7b	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
20.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (.f64 (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))) (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))) (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))))

rewrite61.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`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` `pow1_binary64_484`
15×	`pow-prod-down_binary64_494`
14×	`associate-*l/_binary64_366`
7×	`sqrt-pow1_binary64_441`
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×	`pow1/3_binary64_505` `cbrt-prod_binary64_454`
1×	`sqrt-prod_binary64_439` `pow1/2_binary64_503`

Counts

4 → 75

Calls

4 calls:

20.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (.f64 (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))) (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))) (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))))
5.0ms	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
5.0ms	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
5.0ms	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

series7.7s (24.1%)

Counts

4 → 12

Calls

4 calls:

4.3s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 (.f64 (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))) (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))) (cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))))
1.1s	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
1.1s	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
1.1s	(cbrt.f64 (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

simplify92.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5069	8114

prune388.0ms (1.2%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	85	17	102

Merged error: 18.8b

Counts

102 → 17

Compiler

Compiled 12157 to 5298 computations (56.4% saved)

regimes547.0ms (1.7%)

Compiler: Compiled 7018 to 4272 computations (39.1% saved)

bsearch48.0ms (0.2%)

Steps

Iters	Range		Point
6	-4.437370271988686e-305	-7.368626793695857e-306	-7.486729739335176e-306

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%)

sample3.5s (10.8%)

Algorithm

1×

intervals

Results

1.2s	12905×	body	128	nan
780.0ms	8000×	body	128	valid
117.0ms	1169×	body	128	invalid

Compiler

Compiled 927 to 559 computations (39.7% saved)

Details

analyze2.4s (7.3%)

sample101.0ms (0.3%)

simplify414.0ms (1.3%)

prune8.0ms (0%)

localize17.0ms (0.1%)

rewrite64.0ms (0.2%)

series4.9s (15.3%)

simplify104.0ms (0.3%)

prune540.0ms (1.7%)

localize17.0ms (0.1%)

rewrite52.0ms (0.2%)

series4.8s (14.9%)

simplify60.0ms (0.2%)

prune329.0ms (1%)

localize20.0ms (0.1%)

rewrite49.0ms (0.2%)

series5.4s (16.9%)

simplify62.0ms (0.2%)

prune410.0ms (1.3%)

localize26.0ms (0.1%)

rewrite61.0ms (0.2%)

series7.7s (24.1%)

simplify92.0ms (0.3%)

prune388.0ms (1.2%)

regimes547.0ms (1.7%)

bsearch48.0ms (0.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.5s (10.8%)

Profiling