Details

analyze1.4s (13.8%)

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)

sample57.0ms (0.5%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
13.0ms	139×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify217.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4908	29
1	4908	29

prune6.0ms (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: 10.4b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.2b	(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))))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite65.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`add-sqr-sqrt_binary64_98`
108×	`times-frac_binary64_83`
98×	`*-un-lft-identity_binary64_77`
70×	`difference-of-squares_binary64_46`
49×	`add-cube-cbrt_binary64_109`
48×	`sqrt-prod_binary64_92`
41×	`unpow-prod-down_binary64_153`
15×	`sqr-pow_binary64_49` `unpow2_binary64_139`
14×	`associate-/l*_binary64_24`
9×	`add-exp-log_binary64_112`
7×	`distribute-lft-out--_binary64_31`
6×	`add-cbrt-cube_binary64_110` `pow1_binary64_135`
4×	`add-log-exp_binary64_113` `associate-/r/_binary64_25`
3×	`associate-/r*_binary64_23` `pow-unpow_binary64_151` `div-inv_binary64_74`
2×	`rem-sqrt-square_binary64_90` `flip-+_binary64_51` `flip3-+_binary64_80` `pow-exp_binary64_142` `div-exp_binary64_125` `associate-/l/_binary64_26`
1×	`pow-to-exp_binary64_143` `sqrt-pow1_binary64_94` `cbrt-undiv_binary64_108` `sqrt-div_binary64_93` `div-sub_binary64_82` `flip--_binary64_52` `asin-acos_binary64_254` `pow1/2_binary64_154` `clear-num_binary64_76` `flip3--_binary64_81` `frac-2neg_binary64_88` `pow-pow_binary64_146`

Counts

4 → 173

Calls

4 calls:

18.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
17.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
5.0ms	(pow.f64 (/.f64 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))))))

series568.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

333.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
157.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
53.0ms	(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)

simplify105.0ms (1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4936	6663
1	4936	6663

prune352.0ms (3.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	179	6	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	179	7	186

Merged error: 10.3b

Counts

186 → 7

Compiler

Compiled 5853 to 3988 computations (31.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.4b	(/.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))))))
9.6b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite60.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`sqrt-prod_binary64_92` `add-sqr-sqrt_binary64_98`
125×	`times-frac_binary64_83`
112×	`*-un-lft-identity_binary64_77`
70×	`difference-of-squares_binary64_46`
63×	`add-cube-cbrt_binary64_109`
41×	`unpow-prod-down_binary64_153`
17×	`associate-/l*_binary64_24`
15×	`sqr-pow_binary64_49` `unpow2_binary64_139`
9×	`add-exp-log_binary64_112`
7×	`distribute-lft-out--_binary64_31`
6×	`associate-/r*_binary64_23` `add-cbrt-cube_binary64_110` `sqrt-div_binary64_93` `pow1_binary64_135`
4×	`add-log-exp_binary64_113`
3×	`pow-unpow_binary64_151`
2×	`flip-+_binary64_51` `flip3-+_binary64_80` `pow-exp_binary64_142` `div-exp_binary64_125` `associate-/r/_binary64_25` `associate-/l/_binary64_26` `div-inv_binary64_74`
1×	`pow-to-exp_binary64_143` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-undiv_binary64_108` `flip--_binary64_52` `sqrt-undiv_binary64_97` `asin-acos_binary64_254` `pow1/2_binary64_154` `clear-num_binary64_76` `flip3--_binary64_81` `frac-2neg_binary64_88` `pow-pow_binary64_146`

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)
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))))))

series499.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

327.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
78.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
57.0ms	(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))))))
35.0ms	(pow.f64 (/.f64 Om Omc) 2)

simplify120.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5070	8052

prune447.0ms (4.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	205	8	213

Merged error: 5.2b

Counts

213 → 8

Compiler

Compiled 6821 to 4774 computations (30% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
2.0b	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
15.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
15.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64_105` `add-sqr-sqrt_binary64_98`
8×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
6×	`sqrt-prod_binary64_92` `cbrt-div_binary64_106`
5×	`pow1_binary64_135`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113`
3×	`flip-+_binary64_51` `flip3-+_binary64_80` `pow1/3_binary64_156`
2×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `sqrt-div_binary64_93`
1×	`asin-acos_binary64_254` `pow1/2_binary64_154`

Counts

4 → 54

Calls

4 calls:

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

series677.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
185.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
179.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
126.0ms	(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

simplify95.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4861	1747
1	4861	1747

prune143.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	66	8	74

Merged error: 5.2b

Counts

74 → 8

Compiler

Compiled 2781 to 2082 computations (25.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

7.5b	(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)))))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite108.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

185×	`add-sqr-sqrt_binary64_98`
147×	`times-frac_binary64_83`
144×	`sqrt-prod_binary64_92`
122×	`*-un-lft-identity_binary64_77`
90×	`difference-of-squares_binary64_46`
59×	`add-cube-cbrt_binary64_109`
36×	`unpow-prod-down_binary64_153`
18×	`sqr-pow_binary64_49` `unpow2_binary64_139`
9×	`distribute-lft-out--_binary64_31`
7×	`pow1_binary64_135`
6×	`rem-sqrt-square_binary64_90` `associate-/r/_binary64_25`
4×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `add-log-exp_binary64_113`
3×	`sqrt-pow1_binary64_94` `flip-+_binary64_51` `sqrt-div_binary64_93` `flip3-+_binary64_80` `cbrt-prod_binary64_105` `pow1/2_binary64_154` `div-inv_binary64_74`
1×	`pow1/3_binary64_156`

Counts

4 → 191

Calls

4 calls:

22.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
19.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
19.0ms	(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)))))))

series1.2s (11.9%)

Counts

4 → 12

Calls

4 calls:

331.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
326.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
312.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
280.0ms	(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)))))))

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4923	8775
1	4923	8775

prune1.1s (10.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	198	5	203
Fresh	1	3	4
Picked	1	0	1
Done	0	3	3
Total	200	11	211

Merged error: 5.2b

Counts

211 → 11

Compiler

Compiled 15224 to 10746 computations (29.4% saved)

regimes736.0ms (7%)

Compiler: Compiled 10212 to 8605 computations (15.7% saved)

bsearch53.0ms (0.5%)

Steps

Iters	Range		Point
9	1.523018861538269e+74	3.492756617328103e+79	1.4817959701473245e+75

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%)

sample2.2s (20.7%)

Algorithm

1×

intervals

Results

787.0ms	8000×	body	128	valid
478.0ms	4868×	body	128	nan

Compiler

Compiled 601 to 506 computations (15.8% saved)

Details

analyze1.4s (13.8%)

sample57.0ms (0.5%)

simplify217.0ms (2.1%)

prune6.0ms (0.1%)

localize15.0ms (0.1%)

rewrite65.0ms (0.6%)

series568.0ms (5.4%)

simplify105.0ms (1%)

prune352.0ms (3.4%)

localize15.0ms (0.1%)

rewrite60.0ms (0.6%)

series499.0ms (4.8%)

simplify120.0ms (1.1%)

prune447.0ms (4.3%)

localize19.0ms (0.2%)

rewrite18.0ms (0.2%)

series677.0ms (6.5%)

simplify95.0ms (0.9%)

prune143.0ms (1.4%)

localize21.0ms (0.2%)

rewrite108.0ms (1%)

series1.2s (11.9%)

simplify102.0ms (1%)

prune1.1s (10.5%)

regimes736.0ms (7%)

bsearch53.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (20.7%)

Profiling