Details

analyze2.3s (10.9%)

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)

sample102.0ms (0.5%)

Algorithm

1×

intervals

Results

43.0ms	433×	body	128	nan
24.0ms	256×	body	128	valid
4.0ms	47×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify140.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5178	39

prune5.0ms (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: 27.5b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.8b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
7.6b	(.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)))))))
9.2b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
18.5b	(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))))))))

rewrite55.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
29×	`add-sqr-sqrt_binary64_441`
27×	`associate-l_binary64_360`
24×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
19×	`times-frac_binary64_425`
18×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
16×	`pow-prod-down_binary64_490`
14×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
12×	`associate-*r/_binary64_361` `cancel-sign-sub-inv_binary64_385`
7×	`associate-r_binary64_359`
4×	`flip3-+_binary64_422` `sub-neg_binary64_412` `add-log-exp_binary64_458` `frac-times_binary64_429` `flip-+_binary64_393` `sqrt-pow1_binary64_437`
3×	`*-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`associate-*l/_binary64_362` `sqrt-div_binary64_436` `div-inv_binary64_416` `unswap-sqr_binary64_387` `flip3--_binary64_423` `flip--_binary64_394`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435`

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)))))
9.0ms	(.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)))))))
7.0ms	(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))))))))

series2.7s (13.2%)

Counts

4 → 12

Calls

4 calls:

2.1s	(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))))))))
428.0ms	(.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)))))))
150.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
92.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify89.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5099	4107

prune209.0ms (1%)

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: 20.1b

Counts

145 → 13

Compiler

Compiled 5423 to 2266 computations (58.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(*.f64 n (/.f64 l Om))
5.9b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
7.6b	(.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))))))
18.5b	(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_480`
27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
23×	`add-sqr-sqrt_binary64_441`
21×	`associate-r_binary64_359`
18×	`*-un-lft-identity_binary64_419`
16×	`pow-prod-down_binary64_490` `add-cube-cbrt_binary64_454`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
10×	`times-frac_binary64_425` `associate-*r/_binary64_361`
6×	`cancel-sign-sub-inv_binary64_385`
5×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437`
3×	`*-commutative_binary64_350`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `frac-times_binary64_429` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`associate-*l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435`

Counts

4 → 107

Calls

4 calls:

11.0ms	(.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)))))))

series2.6s (12.4%)

Counts

4 → 12

Calls

4 calls:

2.0s	(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)))))))
429.0ms	(.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))))))
103.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
18.0ms	(*.f64 n (/.f64 l Om))

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5059	2829

prune157.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	121	11	132

Merged error: 19.4b

Counts

132 → 11

Compiler

Compiled 4336 to 1894 computations (56.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(*.f64 n (/.f64 l Om))
5.9b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
7.2b	(.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)))))))
18.5b	(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_480`
30×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
22×	`add-sqr-sqrt_binary64_441`
20×	`pow-prod-down_binary64_490`
19×	`associate-r_binary64_359`
17×	`*-un-lft-identity_binary64_419`
15×	`add-cube-cbrt_binary64_454` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
14×	`associate-*r/_binary64_361`
10×	`times-frac_binary64_425`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
6×	`cancel-sign-sub-inv_binary64_385`
5×	`associate-l_binary64_360` `sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458`
3×	`*-commutative_binary64_350`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `frac-times_binary64_429` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`associate-*l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435`

Counts

4 → 111

Calls

4 calls:

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

series2.6s (12.7%)

Counts

4 → 12

Calls

4 calls:

2.1s	(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))))))))
438.0ms	(.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)))))))
100.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
18.0ms	(*.f64 n (/.f64 l Om))

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5016	2927

prune163.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	122	12	134

Merged error: 16.3b

Counts

134 → 12

Compiler

Compiled 4468 to 1941 computations (56.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.2b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
9.2b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
18.5b	(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))))))))
18.5b	(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))))))))

rewrite67.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64_480`
32×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
28×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
26×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `associate-l*_binary64_360`
24×	`cancel-sign-sub-inv_binary64_385`
18×	`pow-prod-down_binary64_490` `times-frac_binary64_425`
16×	`associate-*r/_binary64_361`
12×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`sub-neg_binary64_412` `sqrt-pow1_binary64_437`
4×	`sqrt-div_binary64_436` `add-log-exp_binary64_458` `frac-times_binary64_429` `flip3--_binary64_423` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`flip3-+_binary64_422` `associate-l/_binary64_362` `pow1/2_binary64_499` `div-inv_binary64_416` `associate-r_binary64_359` `-commutative_binary64_350` `flip-+_binary64_393` `sqrt-prod_binary64_435`

Counts

4 → 136

Calls

4 calls:

13.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
13.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
7.0ms	(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))))))))
7.0ms	(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))))))))

series4.3s (20.8%)

Counts

4 → 12

Calls

4 calls:

2.1s	(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))))))))
2.1s	(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))))))))
95.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
92.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify57.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5874	3336

prune311.0ms (1.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	148	12	160

Merged error: 16.3b

Counts

160 → 12

Compiler

Compiled 9170 to 3815 computations (58.4% saved)

regimes875.0ms (4.2%)

Compiler: Compiled 10994 to 7208 computations (34.4% saved)

bsearch54.0ms (0.3%)

Steps

Iters	Range		Point
7	4.0112291610860414e-300	7.5665373907247155e-298	4.1003121033902976e-300

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	50	86
1	50	86

end0.0ms (0%)

sample3.6s (17.5%)

Algorithm

1×

intervals

Results

1.2s	12826×	body	128	nan
751.0ms	8000×	body	128	valid
115.0ms	1200×	body	128	invalid

Compiler

Compiled 1424 to 926 computations (35% saved)

Details

analyze2.3s (10.9%)

sample102.0ms (0.5%)

simplify140.0ms (0.7%)

prune5.0ms (0%)

localize21.0ms (0.1%)

rewrite55.0ms (0.3%)

series2.7s (13.2%)

simplify89.0ms (0.4%)

prune209.0ms (1%)

localize17.0ms (0.1%)

rewrite50.0ms (0.2%)

series2.6s (12.4%)

simplify76.0ms (0.4%)

prune157.0ms (0.8%)

localize17.0ms (0.1%)

rewrite50.0ms (0.2%)

series2.6s (12.7%)

simplify77.0ms (0.4%)

prune163.0ms (0.8%)

localize21.0ms (0.1%)

rewrite67.0ms (0.3%)

series4.3s (20.8%)

simplify57.0ms (0.3%)

prune311.0ms (1.5%)

regimes875.0ms (4.2%)

bsearch54.0ms (0.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.6s (17.5%)

Profiling