Details

analyze2.4s (6.7%)

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)

sample109.0ms (0.3%)

Algorithm

1×

intervals

Results

43.0ms	443×	body	128	nan
25.0ms	256×	body	128	valid
8.0ms	42×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify422.0ms (1.2%)

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: 31.6b

Counts

2 → 2

Compiler

Compiled 134 to 106 computations (20.9% saved)

localize17.0ms (0%)

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)))))
8.1b	(.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)))))))
11.3b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
22.3b	(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))))))))

rewrite63.0ms (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:

14.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
13.0ms	(.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)))))))
11.0ms	(.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))))))))

series4.8s (13.5%)

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))))))))
797.0ms	(.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)))))))
333.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
202.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify106.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5017	4107

prune439.0ms (1.2%)

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: 23.4b

Counts

145 → 10

Compiler

Compiled 11026 to 5865 computations (46.8% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

5.4b	(*.f64 n (/.f64 l Om))
6.5b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
8.1b	(.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))))))
22.3b	(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)))))))

rewrite53.0ms (0.1%)

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:

14.0ms	(.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)))))))

series4.7s (13.2%)

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)))))))
820.0ms	(.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))))))
208.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
37.0ms	(*.f64 n (/.f64 l Om))

simplify59.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5297	2813

prune257.0ms (0.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	119	10	129

Merged error: 22.4b

Counts

129 → 10

Compiler

Compiled 6658 to 3440 computations (48.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.1b	(.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))))))
8.1b	(.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))))))
22.3b	(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)))))))
22.3b	(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)))))))

rewrite55.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`pow1_binary64_484`
24×	`pow-prod-down_binary64_494`
22×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
12×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
8×	`associate-*r/_binary64_365` `sqrt-pow1_binary64_441`
6×	`-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445` `associate-r*_binary64_363`
4×	`sqrt-div_binary64_440` `flip-+_binary64_397` `flip3-+_binary64_426` `add-log-exp_binary64_462`
2×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372` `associate-l_binary64_364` `sqrt-prod_binary64_439` `*-commutative_binary64_354` `pow1/2_binary64_503`

Counts

4 → 80

Calls

4 calls:

11.0ms	(.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))))))
11.0ms	(.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))))))
10.0ms	(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)))))))
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)))))))

series8.6s (24%)

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)))))))
3.5s	(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)))))))
771.0ms	(.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))))))
764.0ms	(.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))))))

simplify66.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5865	3652

prune281.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	91	11	102

Merged error: 22.4b

Counts

102 → 11

Compiler

Compiled 8086 to 3827 computations (52.7% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

11.2b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))
11.2b	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))
22.3b	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U)))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))))
22.3b	(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)))))))

rewrite72.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`cbrt-div_binary64_455`
44×	`pow1_binary64_484`
34×	`associate-*r/_binary64_365`
30×	`flip-+_binary64_397` `flip3-+_binary64_426`
28×	`sqrt-div_binary64_440` `pow-prod-down_binary64_494` `frac-times_binary64_433`
14×	`associate-*l/_binary64_366`
12×	`sqrt-pow1_binary64_441`
6×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445` `cbrt-prod_binary64_454`
4×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459` `add-log-exp_binary64_462`
2×	`sqrt-prod_binary64_439` `pow1/3_binary64_505` `pow1/2_binary64_503`

Counts

4 → 84

Calls

4 calls:

26.0ms	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U)))))))) (cbrt.f64 (+.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 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
4.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))
3.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))

series8.7s (24.5%)

Counts

4 → 12

Calls

4 calls:

3.6s	(sqrt.f64 (.f64 (.f64 (.f64 (.f64 2 n) U) (.f64 (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U)))))))) (cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))))
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)))))))
778.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))
776.0ms	(cbrt.f64 (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))))))

simplify110.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5004	8423

prune423.0ms (1.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	96	11	107

Merged error: 22.4b

Counts

107 → 11

Compiler

Compiled 11818 to 4638 computations (60.8% saved)

regimes404.0ms (1.1%)

Compiler: Compiled 4378 to 2808 computations (35.9% saved)

bsearch2.0ms (0%)

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

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	426	125
1	426	125

end0.0ms (0%)

sample3.4s (9.5%)

Algorithm

1×

intervals

Results

1.3s	12845×	body	128	nan
808.0ms	8000×	body	128	valid
114.0ms	1141×	body	128	invalid

Compiler

Compiled 623 to 391 computations (37.2% saved)

Details

analyze2.4s (6.7%)

sample109.0ms (0.3%)

simplify422.0ms (1.2%)

prune8.0ms (0%)

localize17.0ms (0%)

rewrite63.0ms (0.2%)

series4.8s (13.5%)

simplify106.0ms (0.3%)

prune439.0ms (1.2%)

localize17.0ms (0%)

rewrite53.0ms (0.1%)

series4.7s (13.2%)

simplify59.0ms (0.2%)

prune257.0ms (0.7%)

localize21.0ms (0.1%)

rewrite55.0ms (0.2%)

series8.6s (24%)

simplify66.0ms (0.2%)

prune281.0ms (0.8%)

localize35.0ms (0.1%)

rewrite72.0ms (0.2%)

series8.7s (24.5%)

simplify110.0ms (0.3%)

prune423.0ms (1.2%)

regimes404.0ms (1.1%)

bsearch2.0ms (0%)

simplify22.0ms (0.1%)

end0.0ms (0%)

sample3.4s (9.5%)

Profiling