Details

analyze1.5s (15.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4997	203
1	4997	203
0	4	4
1	4	4

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)

sample55.0ms (0.6%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
15.0ms	174×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify55.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4895	29
1	4895	29

prune7.0ms (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

Error

10.9b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.3b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.9b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
9.7b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite64.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`add-sqr-sqrt_binary64_441`
108×	`times-frac_binary64_425`
98×	`*-un-lft-identity_binary64_419`
70×	`difference-of-squares_binary64_388`
49×	`add-cube-cbrt_binary64_454`
48×	`sqrt-prod_binary64_435`
41×	`unpow-prod-down_binary64_498`
15×	`sqr-pow_binary64_391` `unpow2_binary64_484`
14×	`associate-/l*_binary64_364`
9×	`add-exp-log_binary64_457`
7×	`distribute-lft-out--_binary64_371`
6×	`add-cbrt-cube_binary64_455` `pow1_binary64_480`
4×	`add-log-exp_binary64_458` `associate-/r/_binary64_365`
3×	`div-inv_binary64_416` `pow-unpow_binary64_496` `associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `pow-exp_binary64_487` `flip-+_binary64_393` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `associate-/l/_binary64_366`
1×	`sqrt-div_binary64_436` `clear-num_binary64_418` `pow1/2_binary64_499` `flip3--_binary64_423` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `pow-pow_binary64_491` `sqrt-pow1_binary64_437` `flip--_binary64_394` `asin-acos_binary64_599` `cbrt-undiv_binary64_453` `div-sub_binary64_424`

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))))
5.0ms	(pow.f64 (/.f64 t l) 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))))))

series321.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
93.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
33.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
14.0ms	(pow.f64 (/.f64 t l) 2)

simplify105.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4950	6453
1	4950	6453

prune544.0ms (5.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	177	8	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	8	186

Error

10.9b

Counts

186 → 8

Compiler

Compiled 5803 to 3985 computations (31.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 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)))))
0.9b	(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))))))
9.9b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite56.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`add-sqr-sqrt_binary64_441` `sqrt-prod_binary64_435`
125×	`times-frac_binary64_425`
112×	`*-un-lft-identity_binary64_419`
70×	`difference-of-squares_binary64_388`
63×	`add-cube-cbrt_binary64_454`
41×	`unpow-prod-down_binary64_498`
17×	`associate-/l*_binary64_364`
15×	`sqr-pow_binary64_391` `unpow2_binary64_484`
9×	`add-exp-log_binary64_457`
7×	`distribute-lft-out--_binary64_371`
6×	`sqrt-div_binary64_436` `add-cbrt-cube_binary64_455` `associate-/r*_binary64_363` `pow1_binary64_480`
4×	`add-log-exp_binary64_458`
3×	`pow-unpow_binary64_496`
2×	`flip3-+_binary64_422` `div-inv_binary64_416` `pow-exp_binary64_487` `associate-/r/_binary64_365` `flip-+_binary64_393` `div-exp_binary64_470` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `sqrt-undiv_binary64_440` `pow1/2_binary64_499` `flip3--_binary64_423` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `pow-pow_binary64_491` `sqrt-pow1_binary64_437` `flip--_binary64_394` `asin-acos_binary64_599` `rem-sqrt-square_binary64_432` `cbrt-undiv_binary64_453`

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 t l) 2)
3.0ms	(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))))))

series261.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
36.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
31.0ms	(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))))))
14.0ms	(pow.f64 (/.f64 t l) 2)

simplify127.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4985	7842
1	4985	7842

prune382.0ms (3.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	205	9	214

Error

5.8b

Counts

214 → 9

Compiler

Compiled 6773 to 4773 computations (29.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.9b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
9.9b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64_435`
16×	`add-sqr-sqrt_binary64_441`
12×	`sqrt-div_binary64_436`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `sqrt-pow1_binary64_437` `pow1_binary64_480`
6×	`pow1/2_binary64_499` `rem-sqrt-square_binary64_432`
4×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `flip-+_binary64_393` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`

Counts

4 → 72

Calls

4 calls:

4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
4.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series283.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
101.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
40.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
35.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4920	1536
1	4920	1536

prune178.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	84	9	93

Error

5.8b

Counts

93 → 9

Compiler

Compiled 3448 to 2576 computations (25.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.9b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
2.6b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
15.4b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
15.4b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite90.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`add-sqr-sqrt_binary64_441`
146×	`cbrt-prod_binary64_450`
145×	`times-frac_binary64_425`
122×	`*-un-lft-identity_binary64_419`
90×	`difference-of-squares_binary64_388`
59×	`add-cube-cbrt_binary64_454`
51×	`sqrt-prod_binary64_435`
36×	`unpow-prod-down_binary64_498`
18×	`sqr-pow_binary64_391` `unpow2_binary64_484`
9×	`distribute-lft-out--_binary64_371`
6×	`associate-/r/_binary64_365`
5×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`flip3-+_binary64_422` `pow1/3_binary64_501` `cbrt-div_binary64_451` `div-inv_binary64_416` `flip-+_binary64_393` `rem-sqrt-square_binary64_432`
2×	`sqrt-pow1_binary64_437`
1×	`sqrt-div_binary64_436` `pow1/2_binary64_499` `asin-acos_binary64_599`

Counts

4 → 187

Calls

4 calls:

23.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
16.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
16.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

series918.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

285.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
277.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
274.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
81.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

simplify119.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5129	9753

prune652.0ms (6.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	198	10	208

Error

5.8b

Counts

208 → 10

Compiler

Compiled 10935 to 7647 computations (30.1% saved)

regimes1.3s (13.1%)

Accuracy

Total 0.1b remaining (1.4%)

Threshold costs 0.1b (1.4%)

Compiler

Compiled 17717 to 15806 computations (10.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 3 to 5 computations (-66.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	63
1	39	63

end0.0ms (0%)

sample2.6s (26.6%)

Algorithm

1×

intervals

Results

769.0ms	8000×	body	128	valid
470.0ms	5001×	body	128	nan

Compiler

Compiled 1077 to 956 computations (11.2% saved)

Details

analyze1.5s (15.6%)

sample55.0ms (0.6%)

simplify55.0ms (0.6%)

prune7.0ms (0.1%)

localize14.0ms (0.1%)

rewrite64.0ms (0.7%)

series321.0ms (3.3%)

simplify105.0ms (1.1%)

prune544.0ms (5.5%)

localize15.0ms (0.2%)

rewrite56.0ms (0.6%)

series261.0ms (2.7%)

simplify127.0ms (1.3%)

prune382.0ms (3.9%)

localize17.0ms (0.2%)

rewrite23.0ms (0.2%)

series283.0ms (2.9%)

simplify77.0ms (0.8%)

prune178.0ms (1.8%)

localize18.0ms (0.2%)

rewrite90.0ms (0.9%)

series918.0ms (9.4%)

simplify119.0ms (1.2%)

prune652.0ms (6.6%)

regimes1.3s (13.1%)

bsearch2.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.6s (26.6%)

Profiling