Details

analyze2.4s (18.3%)

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)

sample95.0ms (0.7%)

Algorithm

1×

intervals

Results

38.0ms	386×	body	80	nan
24.0ms	256×	body	80	valid
4.0ms	38×	body	80	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify81.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4939	39
1	4939	39

prune12.0ms (0.1%)

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: 31.5b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.6b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
7.3b	(.f64 (/.f64 l Om) (-.f64 U U))
10.5b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
20.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
21×	`add-sqr-sqrt_binary64`
17×	`associate-l_binary64`
16×	`pow-prod-down_binary64` `*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`cbrt-unprod_binary64` `associate-*r/_binary64` `prod-exp_binary64`
10×	`times-frac_binary64`
9×	`associate-r_binary64`
6×	`sub-neg_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `flip--_binary64` `frac-times_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `flip-+_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

13.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
11.0ms	(.f64 n (.f64 (/.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 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series938.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

747.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
152.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
24.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
14.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify106.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5106	2913

prune149.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	112	9	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	114	9	123

Merged error: 23.3b

Counts

123 → 9

Compiler

Compiled 4379 to 1909 computations (56.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.3b	(*.f64 n (/.f64 l Om))
7.7b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.5b	(.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))))))
20.1b	(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)))))))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
21×	`associate-r_binary64` `add-sqr-sqrt_binary64`
16×	`pow-prod-down_binary64` `*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
10×	`associate-*r/_binary64` `times-frac_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `sqrt-pow1_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `sqrt-prod_binary64` `associate-*l/_binary64`

Counts

4 → 101

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	(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)))))))
7.0ms	(*.f64 n (/.f64 l Om))

series933.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

759.0ms	(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)))))))
146.0ms	(.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))))))
23.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
5.0ms	(*.f64 n (/.f64 l Om))

simplify89.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4992	2691
1	4992	2691

prune114.0ms (0.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	113	9	122

Merged error: 23.1b

Counts

122 → 9

Compiler

Compiled 4051 to 1764 computations (56.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

20.1b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))))
21.2b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
21.2b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
21.2b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`associate-*r/_binary64`
60×	`cbrt-div_binary64`
30×	`flip3-+_binary64` `flip-+_binary64`
28×	`frac-times_binary64`
26×	`sqrt-div_binary64`
24×	`pow1_binary64`
15×	`sqrt-pow1_binary64`
14×	`associate-*l/_binary64`
12×	`pow1/3_binary64`
9×	`pow-prod-up_binary64`
6×	`pow-plus_binary64`
5×	`pow-prod-down_binary64`
4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`pow-sqr_binary64` `cbrt-prod_binary64`
2×	`pow2_binary64`
1×	`pow1/2_binary64` `pow3_binary64` `sqrt-prod_binary64`

Counts

4 → 83

Calls

4 calls:

16.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))))
8.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
7.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
7.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series1.7s (12.8%)

Counts

4 → 12

Calls

4 calls:

656.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))) (cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))))
348.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
328.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
322.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

simplify125.0ms (1%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5435	8681

prune222.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	95	9	104

Merged error: 23.1b

Counts

104 → 9

Compiler

Compiled 9520 to 3952 computations (58.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

10.5b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
10.5b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
21.2b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
21.2b	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite37.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
8×	`associate-*r/_binary64`
6×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`cbrt-div_binary64` `flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
2×	`pow1/3_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `cbrt-prod_binary64` `*-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.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 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
7.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
7.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series936.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

326.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
322.0ms	(cbrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
146.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
142.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	6353	3642

prune113.0ms (0.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	84	9	93

Merged error: 23.1b

Counts

93 → 9

Compiler

Compiled 5582 to 2380 computations (57.4% saved)

regimes522.0ms (4%)

Compiler: Compiled 2550 to 1632 computations (36% saved)

bsearch192.0ms (1.5%)

Steps

Iters	Range		Point
8	4.533160254158414e+45	8.550423935753303e+49	7.326913697535261e+45
11	-2.0520796202499384e+136	-1.4618702769811048e+114	-1.6871124400902934e+125

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	92
1	55	92

end0.0ms (0%)

sample4.0s (30.8%)

Algorithm

1×

intervals

Results

1.2s	13065×	body	80	nan
749.0ms	8000×	body	80	valid
117.0ms	1202×	body	80	invalid

Compiler

Compiled 513 to 327 computations (36.3% saved)

Details

analyze2.4s (18.3%)

sample95.0ms (0.7%)

simplify81.0ms (0.6%)

prune12.0ms (0.1%)

localize17.0ms (0.1%)

rewrite44.0ms (0.3%)

series938.0ms (7.2%)

simplify106.0ms (0.8%)

prune149.0ms (1.2%)

localize17.0ms (0.1%)

rewrite40.0ms (0.3%)

series933.0ms (7.2%)

simplify89.0ms (0.7%)

prune114.0ms (0.9%)

localize23.0ms (0.2%)

rewrite44.0ms (0.3%)

series1.7s (12.8%)

simplify125.0ms (1%)

prune222.0ms (1.7%)

localize20.0ms (0.2%)

rewrite37.0ms (0.3%)

series936.0ms (7.2%)

simplify68.0ms (0.5%)

prune113.0ms (0.9%)

regimes522.0ms (4%)

bsearch192.0ms (1.5%)

simplify5.0ms (0%)

end0.0ms (0%)

sample4.0s (30.8%)

Profiling