Details

analyze1.4s (15.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	76.4%	4.9%	9
18.7%	76.4%	4.9%	10
21.8%	72.5%	5.7%	11
21.8%	69.8%	8.4%	12
32.7%	46.6%	20.7%	13
32.7%	46.6%	20.7%	14

Compiler

Compiled 20 to 20 computations (0% saved)

sample52.0ms (0.6%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
12.0ms	131×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify223.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4908	29
1	4908	29

prune3.0ms (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: 8.1b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.3b	(pow.f64 (/.f64 Om Omc) 2)
0.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
7.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite71.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`add-sqr-sqrt_binary64_435`
108×	`times-frac_binary64_420`
98×	`*-un-lft-identity_binary64_414`
70×	`difference-of-squares_binary64_383`
49×	`add-cube-cbrt_binary64_446`
48×	`sqrt-prod_binary64_429`
41×	`unpow-prod-down_binary64_490`
15×	`sqr-pow_binary64_386` `unpow2_binary64_476`
14×	`associate-/l*_binary64_361`
9×	`add-exp-log_binary64_449`
7×	`distribute-lft-out--_binary64_368`
6×	`pow1_binary64_472` `add-cbrt-cube_binary64_447`
4×	`associate-/r/_binary64_362` `add-log-exp_binary64_450`
3×	`div-inv_binary64_411` `pow-unpow_binary64_488` `associate-/r*_binary64_360`
2×	`flip3-+_binary64_417` `pow-exp_binary64_479` `flip-+_binary64_388` `associate-/l/_binary64_363` `div-exp_binary64_462` `rem-sqrt-square_binary64_427`
1×	`flip3--_binary64_418` `clear-num_binary64_413` `sqrt-div_binary64_430` `sqrt-pow1_binary64_431` `cbrt-undiv_binary64_445` `pow-pow_binary64_483` `pow-to-exp_binary64_480` `frac-2neg_binary64_425` `pow1/2_binary64_491` `flip--_binary64_389` `div-sub_binary64_419` `asin-acos_binary64_591`

Counts

4 → 173

Calls

4 calls:

20.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
18.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.0ms	(pow.f64 (/.f64 Om Omc) 2)
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

series561.0ms (6%)

Counts

4 → 12

Calls

4 calls:

326.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
152.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
56.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
26.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4936	6663
1	4936	6663

prune327.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	180	5	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	180	6	186

Merged error: 8.0b

Counts

186 → 6

Compiler

Compiled 5846 to 3975 computations (32% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 Om Omc) 2)
0.3b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
0.5b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
7.3b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`sqrt-prod_binary64_429` `add-sqr-sqrt_binary64_435`
125×	`times-frac_binary64_420`
112×	`*-un-lft-identity_binary64_414`
70×	`difference-of-squares_binary64_383`
63×	`add-cube-cbrt_binary64_446`
41×	`unpow-prod-down_binary64_490`
17×	`associate-/l*_binary64_361`
15×	`sqr-pow_binary64_386` `unpow2_binary64_476`
9×	`add-exp-log_binary64_449`
7×	`distribute-lft-out--_binary64_368`
6×	`sqrt-div_binary64_430` `pow1_binary64_472` `add-cbrt-cube_binary64_447` `associate-/r*_binary64_360`
4×	`add-log-exp_binary64_450`
3×	`pow-unpow_binary64_488`
2×	`associate-/r/_binary64_362` `flip3-+_binary64_417` `div-inv_binary64_411` `pow-exp_binary64_479` `flip-+_binary64_388` `associate-/l/_binary64_363` `div-exp_binary64_462`
1×	`flip3--_binary64_418` `clear-num_binary64_413` `sqrt-pow1_binary64_431` `cbrt-undiv_binary64_445` `pow-pow_binary64_483` `pow-to-exp_binary64_480` `sqrt-undiv_binary64_434` `frac-2neg_binary64_425` `pow1/2_binary64_491` `flip--_binary64_389` `asin-acos_binary64_591` `rem-sqrt-square_binary64_427`

Counts

4 → 194

Calls

4 calls:

22.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
5.0ms	(pow.f64 (/.f64 Om Omc) 2)
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

series474.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

323.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
69.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
56.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
26.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify122.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5070	8052

prune418.0ms (4.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	206	6	212

Merged error: 3.6b

Counts

212 → 6

Compiler

Compiled 6778 to 4731 computations (30.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.3b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
7.3b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
7.6b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
7.6b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64_429`
16×	`add-sqr-sqrt_binary64_435`
12×	`sqrt-div_binary64_430`
10×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `sqrt-pow1_binary64_431` `*-un-lft-identity_binary64_414`
6×	`pow1/2_binary64_491` `rem-sqrt-square_binary64_427`
4×	`flip3-+_binary64_417` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450` `flip-+_binary64_388`

Counts

4 → 72

Calls

4 calls:

5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series519.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
183.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
72.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
70.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4901	1536
1	4901	1536

prune174.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	84	6	90

Merged error: 3.6b

Counts

90 → 6

Compiler

Compiled 3333 to 2472 computations (25.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.1b	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.1b	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.1b	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64_435`
49×	`times-frac_binary64_420`
48×	`sqrt-prod_binary64_429`
46×	`*-un-lft-identity_binary64_414`
30×	`difference-of-squares_binary64_383`
25×	`add-cube-cbrt_binary64_446`
12×	`unpow-prod-down_binary64_490`
9×	`cbrt-prod_binary64_442`
6×	`sqr-pow_binary64_386` `unpow2_binary64_476`
5×	`pow1_binary64_472`
4×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450`
3×	`distribute-lft-out--_binary64_368` `pow1/3_binary64_493`
2×	`associate-/r/_binary64_362` `rem-sqrt-square_binary64_427`
1×	`sqrt-div_binary64_430` `flip3-+_binary64_417` `div-inv_binary64_411` `sqrt-pow1_binary64_431` `flip-+_binary64_388` `pow1/2_binary64_491`

Counts

4 → 93

Calls

4 calls:

20.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
1.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
1.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

series1.1s (12.3%)

Counts

4 → 12

Calls

4 calls:

301.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
292.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
276.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
276.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

simplify61.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4923	4317
1	4923	4317

prune464.0ms (5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	101	4	105
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	102	9	111

Merged error: 3.6b

Counts

111 → 9

Compiler

Compiled 7728 to 5488 computations (29% saved)

regimes622.0ms (6.7%)

Compiler: Compiled 8450 to 7098 computations (16% saved)

bsearch21.0ms (0.2%)

Steps

Iters	Range		Point
4	5.828892761156686e+58	9.44574430147431e+58	6.394025814331313e+58

Compiler

Compiled 3 to 5 computations (-66.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	65
1	39	65

end0.0ms (0%)

sample2.3s (24.3%)

Algorithm

1×

intervals

Results

788.0ms	8000×	body	128	valid
649.0ms	4697×	body	128	nan

Compiler

Compiled 502 to 422 computations (15.9% saved)

Details

analyze1.4s (15.5%)

sample52.0ms (0.6%)

simplify223.0ms (2.4%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite71.0ms (0.8%)

series561.0ms (6%)

simplify100.0ms (1.1%)

prune327.0ms (3.5%)

localize15.0ms (0.2%)

rewrite63.0ms (0.7%)

series474.0ms (5.1%)

simplify122.0ms (1.3%)

prune418.0ms (4.5%)

localize17.0ms (0.2%)

rewrite27.0ms (0.3%)

series519.0ms (5.6%)

simplify54.0ms (0.6%)

prune174.0ms (1.9%)

localize20.0ms (0.2%)

rewrite44.0ms (0.5%)

series1.1s (12.3%)

simplify61.0ms (0.7%)

prune464.0ms (5%)

regimes622.0ms (6.7%)

bsearch21.0ms (0.2%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (24.3%)

Profiling