Details

analyze1.5s (14.1%)

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)

sample50.0ms (0.5%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
12.0ms	150×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify54.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4895	29
1	4895	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: 11.3b

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 Om Omc) 2)
0.4b	(/.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))))))
10.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite63.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

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×	`add-cbrt-cube_binary64_114` `pow1_binary64_139`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`div-inv_binary64_75` `associate-/r*_binary64_22` `pow-unpow_binary64_155`
2×	`pow-exp_binary64_146` `div-exp_binary64_129` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `associate-/l/_binary64_25` `flip3-+_binary64_81`
1×	`pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `flip3--_binary64_82` `frac-2neg_binary64_89` `pow-pow_binary64_150` `flip--_binary64_53` `sqrt-div_binary64_95` `clear-num_binary64_77` `asin-acos_binary64_258` `div-sub_binary64_83` `pow1/2_binary64_158`

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)))))
17.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(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))))))

series327.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

182.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
94.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
36.0ms	(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 Om Omc) 2)

simplify106.0ms (1%)

Algorithm

1×	egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5043	6451

prune330.0ms (3.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	178	7	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	178	8	186

Merged error: 11.3b

Counts

186 → 8

Compiler

Compiled 5772 to 3959 computations (31.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(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))))))))
2.1b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
15.8b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
15.8b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite88.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`add-sqr-sqrt_binary64_100`
146×	`cbrt-prod_binary64_109`
145×	`times-frac_binary64_84`
122×	`*-un-lft-identity_binary64_78`
90×	`difference-of-squares_binary64_47`
59×	`add-cube-cbrt_binary64_113`
51×	`sqrt-prod_binary64_94`
36×	`unpow-prod-down_binary64_157`
18×	`unpow2_binary64_143` `sqr-pow_binary64_50`
9×	`distribute-lft-out--_binary64_30`
6×	`associate-/r/_binary64_24`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
3×	`cbrt-div_binary64_110` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `pow1/3_binary64_160` `div-inv_binary64_75` `flip3-+_binary64_81`
2×	`sqrt-pow1_binary64_96`
1×	`sqrt-div_binary64_95` `asin-acos_binary64_258` `pow1/2_binary64_158`

Counts

4 → 187

Calls

4 calls:

19.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
15.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
15.0ms	(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))))))))

series932.0ms (8.9%)

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)))))
282.0ms	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
275.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
89.0ms	(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))))))))

simplify126.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5129	9753

prune701.0ms (6.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	197	2	199
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	199	8	207

Merged error: 11.3b

Counts

207 → 8

Compiler

Compiled 11220 to 7893 computations (29.7% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(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)))))) (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
2.5b	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
15.8b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
16.1b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64_100`
55×	`cbrt-prod_binary64_109`
48×	`times-frac_binary64_84`
46×	`*-un-lft-identity_binary64_78`
30×	`difference-of-squares_binary64_47`
25×	`add-cube-cbrt_binary64_113`
12×	`unpow-prod-down_binary64_157`
6×	`sqrt-prod_binary64_94` `unpow2_binary64_143` `sqr-pow_binary64_50`
5×	`cbrt-div_binary64_110` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
3×	`flip-+_binary64_52` `distribute-lft-out--_binary64_30` `pow1/3_binary64_160` `flip3-+_binary64_81`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `sqrt-div_binary64_95` `associate-/r/_binary64_24`
1×	`div-inv_binary64_75` `asin-acos_binary64_258` `pow1/2_binary64_158`

Counts

4 → 98

Calls

4 calls:

15.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
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))))
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)))))) (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

series555.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

275.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
100.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
100.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
79.0ms	(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)))))) (/.f64 (sqrt.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4988	4311
1	4988	4311

prune344.0ms (3.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	110	8	118

Merged error: 11.3b

Counts

118 → 8

Compiler

Compiled 6054 to 4384 computations (27.6% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

15.8b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
16.1b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
16.1b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
16.1b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-sqr-sqrt_binary64_100`
57×	`cbrt-prod_binary64_109`
48×	`times-frac_binary64_84`
46×	`*-un-lft-identity_binary64_78`
30×	`difference-of-squares_binary64_47`
25×	`add-cube-cbrt_binary64_113`
12×	`unpow-prod-down_binary64_157`
7×	`cbrt-div_binary64_110`
6×	`unpow2_binary64_143` `sqr-pow_binary64_50`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `flip-+_binary64_52` `pow1/3_binary64_160` `add-exp-log_binary64_116` `pow1_binary64_139` `flip3-+_binary64_81`
3×	`distribute-lft-out--_binary64_30`
2×	`associate-/r/_binary64_24`
1×	`div-inv_binary64_75`

Counts

4 → 96

Calls

4 calls:

15.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.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))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

series591.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

277.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
109.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
107.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
97.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

simplify110.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5183	3992

prune525.0ms (5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	108	8	116

Merged error: 11.3b

Counts

116 → 8

Compiler

Compiled 8421 to 6099 computations (27.6% saved)

regimes1.2s (11.5%)

Compiler: Compiled 17204 to 14736 computations (14.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	29
1	29	29

end0.0ms (0%)

sample2.6s (25.2%)

Algorithm

1×

intervals

Results

742.0ms	8000×	body	128	valid
404.0ms	4742×	body	128	nan

Compiler

Compiled 1254 to 1078 computations (14% saved)

Details

analyze1.5s (14.1%)

sample50.0ms (0.5%)

simplify54.0ms (0.5%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite63.0ms (0.6%)

series327.0ms (3.1%)

simplify106.0ms (1%)

prune330.0ms (3.1%)

localize21.0ms (0.2%)

rewrite88.0ms (0.8%)

series932.0ms (8.9%)

simplify126.0ms (1.2%)

prune701.0ms (6.7%)

localize26.0ms (0.3%)

rewrite38.0ms (0.4%)

series555.0ms (5.3%)

simplify83.0ms (0.8%)

prune344.0ms (3.3%)

localize31.0ms (0.3%)

rewrite44.0ms (0.4%)

series591.0ms (5.6%)

simplify110.0ms (1.1%)

prune525.0ms (5%)

regimes1.2s (11.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (25.2%)

Profiling