Details

analyze1.7s (11.6%)

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)

sample65.0ms (0.4%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
20.0ms	172×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

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

10.6b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(pow.f64 (/.f64 t l) 2)
0.3b	(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)))))

rewrite337.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

10.5b

Rules

80×	`add-sqr-sqrt_binary64_100`
67×	`times-frac_binary64_84`
59×	`*-un-lft-identity_binary64_78`
48×	`sqrt-prod_binary64_94`
38×	`add-cube-cbrt_binary64_113` `unpow-prod-down_binary64_157`
30×	`difference-of-squares_binary64_47`
10×	`add-exp-log_binary64_116`
8×	`unpow2_binary64_143` `sqr-pow_binary64_50`
7×	`pow1_binary64_139`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114` `pow-exp_binary64_146`
3×	`distribute-lft-out--_binary64_30` `div-inv_binary64_75`
2×	`associate-/r/_binary64_24` `rem-sqrt-square_binary64_91` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `div-exp_binary64_129`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `flip3-+_binary64_81` `flip-+_binary64_52` `asin-acos_binary64_258`

Counts

4 → 126

Calls

4 calls:

23.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
6.0ms	(pow.f64 (/.f64 Om Omc) 2)
6.0ms	(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))))))

Compiler

Compiled 4135 to 2867 computations (30.7% saved)

series994.0ms (6.9%)

Error

1.3b

Counts

4 → 42

Calls

4 calls:

632.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
126.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
109.0ms	(pow.f64 (/.f64 t l) 2)
72.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 3802 to 3424 computations (9.9% saved)

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4978	4603
1	4978	4603

prune331.0ms (2.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	160	8	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	8	169

Error

0.3b

Counts

169 → 8

Compiler

Compiled 4652 to 3185 computations (31.5% saved)

localize25.0ms (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)))))
0.3b	(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))))))
10.1b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite553.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

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-exp_binary64_129` `div-inv_binary64_75` `associate-/l/_binary64_25` `associate-/r/_binary64_24` `pow-exp_binary64_146`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `asin-acos_binary64_258` `cbrt-undiv_binary64_112` `sqrt-undiv_binary64_99` `frac-2neg_binary64_89` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53` `pow-pow_binary64_150` `pow-to-exp_binary64_147`

Counts

4 → 194

Calls

4 calls:

23.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
6.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
5.0ms	(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 5278 computations (28.6% saved)

series1.0s (7.1%)

Error

0.3b

Counts

4 → 57

Calls

4 calls:

538.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
208.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
142.0ms	(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))))))
72.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 4687 to 4155 computations (11.4% saved)

simplify123.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4953	9047
1	4953	9047

prune483.0ms (3.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	249	2	251
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	250	9	259

Error

0.3b

Counts

259 → 9

Compiler

Compiled 7800 to 5476 computations (29.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
10.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (/.f64 t l) (cbrt.f64 t)) (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) l))))))

rewrite200.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

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

Counts

4 → 93

Calls

4 calls:

22.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (/.f64 t l) (cbrt.f64 t)) (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) l))))))
1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)

Compiler

Compiled 4454 to 1934 computations (56.6% saved)

series895.0ms (6.2%)

Error

0.3b

Counts

4 → 27

Calls

4 calls:

565.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (.f64 (/.f64 t l) (cbrt.f64 t)) (/.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) l))))))
121.0ms	(cbrt.f64 t)
91.0ms	(cbrt.f64 t)
77.0ms	(cbrt.f64 t)

Compiler

Compiled 3086 to 2608 computations (15.5% saved)

simplify91.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4999	3856
1	4999	3856

prune204.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	119	10	129

Error

0.3b

Counts

129 → 10

Compiler

Compiled 4209 to 2219 computations (47.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (cbrt.f64 (/.f64 t l)) 4)
10.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))))))
15.4b	(cbrt.f64 (/.f64 t l))
15.4b	(cbrt.f64 (/.f64 t l))

rewrite383.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

87×	`add-sqr-sqrt_binary64_100`
76×	`times-frac_binary64_84`
66×	`*-un-lft-identity_binary64_78`
48×	`sqrt-prod_binary64_94`
45×	`add-cube-cbrt_binary64_113`
39×	`cbrt-prod_binary64_109`
30×	`difference-of-squares_binary64_47`
28×	`unpow-prod-down_binary64_157`
7×	`sqr-pow_binary64_50`
6×	`pow1_binary64_139` `unpow2_binary64_143`
5×	`add-exp-log_binary64_116`
4×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114` `div-inv_binary64_75`
3×	`pow1/3_binary64_160` `distribute-lft-out--_binary64_30` `pow-unpow_binary64_155`
2×	`cbrt-div_binary64_110` `associate-/r/_binary64_24` `rem-sqrt-square_binary64_91` `pow-pow_binary64_150`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `flip3-+_binary64_81` `flip-+_binary64_52` `pow-to-exp_binary64_147` `pow-exp_binary64_146`

Counts

4 → 135

Calls

4 calls:

23.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))))))
7.0ms	(pow.f64 (cbrt.f64 (/.f64 t l)) 4)
3.0ms	(cbrt.f64 (/.f64 t l))
3.0ms	(cbrt.f64 (/.f64 t l))

Compiler

Compiled 5854 to 3453 computations (41% saved)

series1.5s (10.1%)

Error

0.3b

Counts

4 → 36

Calls

4 calls:

630.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (.f64 (pow.f64 (cbrt.f64 (/.f64 t l)) 4) (pow.f64 (cbrt.f64 (/.f64 t l)) 2))))))
332.0ms	(pow.f64 (cbrt.f64 (/.f64 t l)) 4)
229.0ms	(cbrt.f64 (/.f64 t l))
208.0ms	(cbrt.f64 (/.f64 t l))

Compiler

Compiled 4204 to 3680 computations (12.5% saved)

simplify109.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4956	4735
1	4956	4735

prune299.0ms (2.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	171	10	181

Error

0.3b

Counts

181 → 10

Compiler

Compiled 5535 to 3421 computations (38.2% saved)

regimes1.8s (12.5%)

Accuracy

Total 0.6b remaining (52.9%)

Threshold costs 0.6b (52.9%)

Compiler

Compiled 21040 to 18919 computations (10.1% saved)

bsearch3.0ms (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	91	99
1	91	99

end0.0ms (0%)

sample3.2s (22%)

Algorithm

1×

intervals

Results

783.0ms	8000×	body	128	valid
431.0ms	4658×	body	128	nan

Compiler

Compiled 1310 to 1175 computations (10.3% saved)

Details

analyze1.7s (11.6%)

sample65.0ms (0.4%)

simplify63.0ms (0.4%)

prune4.0ms (0%)

localize19.0ms (0.1%)

rewrite337.0ms (2.3%)

series994.0ms (6.9%)

simplify87.0ms (0.6%)

prune331.0ms (2.3%)

localize25.0ms (0.2%)

rewrite553.0ms (3.8%)

series1.0s (7.1%)

simplify123.0ms (0.8%)

prune483.0ms (3.3%)

localize21.0ms (0.1%)

rewrite200.0ms (1.4%)

series895.0ms (6.2%)

simplify91.0ms (0.6%)

prune204.0ms (1.4%)

localize21.0ms (0.1%)

rewrite383.0ms (2.6%)

series1.5s (10.1%)

simplify109.0ms (0.8%)

prune299.0ms (2.1%)

regimes1.8s (12.5%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (22%)

Profiling