Details

analyze1.5s (7.6%)

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)

sample52.0ms (0.3%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
10.0ms	122×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify54.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4895	29
1	4895	29

prune4.0ms (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

Error

9.4b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.3b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 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))))))
8.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite412.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

9.3b

Rules

143×	`add-sqr-sqrt_binary64_100`
108×	`times-frac_binary64_84`
98×	`*-un-lft-identity_binary64_78`
70×	`difference-of-squares_binary64_47`
49×	`add-cube-cbrt_binary64_113`
48×	`sqrt-prod_binary64_94`
41×	`unpow-prod-down_binary64_157`
15×	`unpow2_binary64_143` `sqr-pow_binary64_50`
14×	`associate-/l*_binary64_23`
9×	`add-exp-log_binary64_116`
7×	`distribute-lft-out--_binary64_30`
6×	`pow1_binary64_139` `add-cbrt-cube_binary64_114`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`div-inv_binary64_75` `associate-/r*_binary64_22` `pow-unpow_binary64_155`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `div-exp_binary64_129` `associate-/l/_binary64_25` `pow-exp_binary64_146`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `asin-acos_binary64_258` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `div-sub_binary64_83` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53` `pow-pow_binary64_150` `pow-to-exp_binary64_147`

Counts

4 → 173

Calls

4 calls:

17.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
5.0ms	(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))))))

Compiler

Compiled 6194 to 4303 computations (30.5% saved)

series1.5s (7.5%)

Error

2.2b

Counts

4 → 63

Calls

4 calls:

604.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
600.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
116.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
79.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 5815 to 5190 computations (10.7% saved)

simplify116.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4955	8166
1	4955	8166

prune437.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	228	8	236
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	228	9	237

Error

0.6b

Counts

237 → 9

Compiler

Compiled 7029 to 4819 computations (31.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
0.2b	(pow.f64 (/.f64 Om Omc) 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))))))
8.7b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite507.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

155×	`add-sqr-sqrt_binary64_100` `sqrt-prod_binary64_94`
125×	`times-frac_binary64_84`
112×	`*-un-lft-identity_binary64_78`
70×	`difference-of-squares_binary64_47`
63×	`add-cube-cbrt_binary64_113`
41×	`unpow-prod-down_binary64_157`
17×	`associate-/l*_binary64_23`
15×	`unpow2_binary64_143` `sqr-pow_binary64_50`
9×	`add-exp-log_binary64_116`
7×	`distribute-lft-out--_binary64_30`
6×	`pow1_binary64_139` `add-cbrt-cube_binary64_114` `sqrt-div_binary64_95` `associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117`
3×	`pow-unpow_binary64_155`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `div-inv_binary64_75` `div-exp_binary64_129` `pow-exp_binary64_146` `associate-/l/_binary64_25` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `asin-acos_binary64_258` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `sqrt-undiv_binary64_99` `frac-2neg_binary64_89` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53`

Counts

4 → 194

Calls

4 calls:

20.0ms	(/.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)
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))))))

Compiler

Compiled 7390 to 5274 computations (28.6% saved)

series1.0s (5.1%)

Error

0.5b

Counts

4 → 57

Calls

4 calls:

589.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
150.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
112.0ms	(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))))))
81.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 5101 to 4528 computations (11.2% saved)

simplify137.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4950	9305
1	4950	9305

prune498.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	249	2	251
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	250	10	260

Error

0.5b

Counts

260 → 10

Compiler

Compiled 7880 to 5544 computations (29.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

8.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.5b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.8b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.8b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

rewrite630.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

128×	`add-sqr-sqrt_binary64_100`
102×	`sqrt-prod_binary64_94`
98×	`times-frac_binary64_84`
84×	`*-un-lft-identity_binary64_78`
60×	`difference-of-squares_binary64_47`
42×	`add-cube-cbrt_binary64_113`
24×	`unpow-prod-down_binary64_157`
12×	`unpow2_binary64_143` `sqr-pow_binary64_50`
8×	`pow1_binary64_139`
6×	`rem-sqrt-square_binary64_91` `distribute-lft-out--_binary64_30`
4×	`pow1/2_binary64_158` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `sqrt-pow1_binary64_96` `associate-/r/_binary64_24`
2×	`sqrt-div_binary64_95` `div-inv_binary64_75` `flip3-+_binary64_81` `flip-+_binary64_52`

Counts

4 → 146

Calls

4 calls:

17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.0ms	(sqrt.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	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

Compiler

Compiled 8808 to 6286 computations (28.6% saved)

series1.9s (9.5%)

Error

0.5b

Counts

4 → 72

Calls

4 calls:

611.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
603.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
240.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
226.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

Compiler

Compiled 11654 to 9920 computations (14.9% saved)

simplify121.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5583	8976

prune805.0ms (4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	214	4	218
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	217	11	228

Error

0.5b

Counts

228 → 11

Compiler

Compiled 11715 to 8320 computations (29% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.8b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
8.8b	(sqrt.f64 (asin.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))))
13.6b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
13.6b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite227.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

10×	`add-sqr-sqrt_binary64_100`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`pow1_binary64_139` `cbrt-prod_binary64_109` `sqrt-prod_binary64_94`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `cbrt-div_binary64_110`
2×	`pow1/3_binary64_160` `flip3-+_binary64_81` `flip-+_binary64_52` `pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91`

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.0ms	(sqrt.f64 (asin.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))))
1.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

Compiler

Compiled 4232 to 3080 computations (27.2% saved)

series1.4s (6.8%)

Error

0.5b

Counts

4 → 48

Calls

4 calls:

498.0ms	(sqrt.f64 (asin.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))))
254.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
226.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
220.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 9606 to 7921 computations (17.5% saved)

simplify117.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5024	3427

prune407.0ms (2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	8	8
Picked	1	0	1
Done	1	1	2
Total	100	11	111

Error

0.5b

Counts

111 → 11

Compiler

Compiled 6973 to 5019 computations (28% saved)

regimes3.4s (17.2%)

Accuracy

Total 0.6b remaining (53%)

Threshold costs 0.6b (53%)

Compiler

Compiled 52240 to 44467 computations (14.9% saved)

bsearch4.0ms (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	80	99
1	80	99

end0.0ms (0%)

sample4.6s (23.2%)

Algorithm

1×

intervals

Results

767.0ms	8000×	body	128	valid
633.0ms	4741×	body	128	nan

Compiler

Compiled 2945 to 2509 computations (14.8% saved)

Details

analyze1.5s (7.6%)

sample52.0ms (0.3%)

simplify54.0ms (0.3%)

prune4.0ms (0%)

localize18.0ms (0.1%)

rewrite412.0ms (2.1%)

series1.5s (7.5%)

simplify116.0ms (0.6%)

prune437.0ms (2.2%)

localize15.0ms (0.1%)

rewrite507.0ms (2.5%)

series1.0s (5.1%)

simplify137.0ms (0.7%)

prune498.0ms (2.5%)

localize19.0ms (0.1%)

rewrite630.0ms (3.1%)

series1.9s (9.5%)

simplify121.0ms (0.6%)

prune805.0ms (4%)

localize31.0ms (0.2%)

rewrite227.0ms (1.1%)

series1.4s (6.8%)

simplify117.0ms (0.6%)

prune407.0ms (2%)

regimes3.4s (17.2%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.6s (23.2%)

Profiling