Details

analyze1.4s (0.4%)

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%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
17.0ms	197×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify159.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4895	29
1	4895	29

prune2.0ms (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

10.8b

Counts

2 → 1

Compiler

Compiled 19 to 19 computations (0% saved)

localize14.0ms (0%)

Local error

Found 8 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)
0.2b	(pow.f64 (/.f64 t l) 2)
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
9.3b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite67.0ms (0%)

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

8 calls:

22.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
18.0ms	(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))))))
0.0ms	(*.f64 2 (pow.f64 (/.f64 t l) 2))

series1.4s (0.4%)

Counts

4 → 57

Calls

4 calls:

683.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
539.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
122.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
75.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 3639 to 3375 computations (7.3% saved)

simplify122.0ms (0%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4982	7735
1	4982	7735

prune1.3s (0.4%)

Pruning

86 alts after pruning (85 fresh and 1 done)

	Pruned	Kept	Total
New	145	85	230
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	145	86	231

Error

1.6b

Counts

231 → 86

Compiler

Compiled 6052 to 4641 computations (23.3% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(pow.f64 (/.f64 t l) 2)
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.2b	(/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.3b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
3.2b	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
9.3b	(sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite62.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64_419`
60×	`add-sqr-sqrt_binary64_441`
52×	`times-frac_binary64_425`
36×	`add-cube-cbrt_binary64_454`
27×	`sqrt-prod_binary64_435`
26×	`log-pow_binary64_508`
18×	`exp-prod_binary64_471`
14×	`difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371`
13×	`unpow-prod-down_binary64_498` `pow1_binary64_480`
7×	`associate-/l*_binary64_364`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
4×	`add-log-exp_binary64_458` `associate-/r/_binary64_365`
3×	`div-inv_binary64_416` `log-prod_binary64_505` `associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `flip-+_binary64_393` `rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`
1×	`sqrt-div_binary64_436` `clear-num_binary64_418` `rem-log-exp_binary64_460` `pow1/2_binary64_499` `sqr-pow_binary64_391` `flip3--_binary64_423` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `flip--_binary64_394` `unpow2_binary64_484` `asin-acos_binary64_599` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-sub_binary64_424`

Counts

4 → 125

Calls

8 calls:

22.0ms	(/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
7.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
0.0ms	(*.f64 2 (pow.f64 (/.f64 t l) 2))

series1.9s (0.6%)

Counts

4 → 54

Calls

4 calls:

806.0ms	(sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
766.0ms	(/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
214.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
123.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Compiler

Compiled 3590 to 3356 computations (6.5% saved)

simplify98.0ms (0%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5065	5353

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

0.6b	(asin.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))
0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.0b	(sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))
0.0b	(sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))
0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.6b	(asin.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))

rewrite25.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_441`
19×	`*-un-lft-identity_binary64_419`
17×	`unpow-prod-down_binary64_498`
14×	`sqrt-prod_binary64_435`
12×	`add-cube-cbrt_binary64_454`
11×	`times-frac_binary64_425`
10×	`difference-of-squares_binary64_388`
6×	`add-exp-log_binary64_457`
5×	`pow1_binary64_480`
3×	`add-log-exp_binary64_458` `sqr-pow_binary64_391` `add-cbrt-cube_binary64_455` `pow-unpow_binary64_496` `unpow2_binary64_484`
2×	`sqrt-div_binary64_436` `pow-exp_binary64_487`
1×	`pow1/2_binary64_499` `div-inv_binary64_416` `flip3--_binary64_423` `distribute-lft-out--_binary64_371` `pow-to-exp_binary64_488` `pow-pow_binary64_491` `sqrt-pow1_binary64_437` `flip--_binary64_394` `asin-acos_binary64_599` `rem-sqrt-square_binary64_432` `div-exp_binary64_470`

Counts

3 → 63

Calls

6 calls:

14.0ms	(sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))
5.0ms	(pow.f64 (/.f64 Om Omc) 2)
1.0ms	(asin.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))
0.0ms	(sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))
0.0ms	(pow.f64 (/.f64 Om Omc) 2)

series182.0ms (0.1%)

Counts

3 → 21

Calls

3 calls:

74.0ms	(pow.f64 (/.f64 Om Omc) 2)
70.0ms	(sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))
38.0ms	(asin.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))

Compiler

Compiled 469 to 541 computations (-15.4% saved)

simplify47.0ms (0%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4930	1112
1	4930	1112

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(pow.f64 (/.f64 t l) 2)
0.0b	(sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
9.3b	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite30.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_441`
29×	`times-frac_binary64_425`
28×	`*-un-lft-identity_binary64_419`
27×	`add-cube-cbrt_binary64_454`
15×	`sqrt-prod_binary64_435`
13×	`unpow-prod-down_binary64_498`
11×	`add-exp-log_binary64_457`
8×	`pow1_binary64_480`
6×	`add-cbrt-cube_binary64_455`
4×	`add-log-exp_binary64_458` `associate-/r/_binary64_365`
3×	`div-inv_binary64_416` `pow-unpow_binary64_496` `sqrt-pow1_binary64_437` `associate-/r_binary64_363` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `associate-/l_binary64_364`
2×	`flip3-+_binary64_422` `inv-pow_binary64_504` `pow-exp_binary64_487` `pow-flip_binary64_493` `flip-+_binary64_393`
1×	`sqrt-div_binary64_436` `clear-num_binary64_418` `1-exp_binary64_463` `pow1/2_binary64_499` `sqr-pow_binary64_391` `rec-exp_binary64_469` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `pow-pow_binary64_491` `unpow2_binary64_484` `asin-acos_binary64_599` `cbrt-undiv_binary64_453`

Counts

4 → 100

Calls

8 calls:

8.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
5.0ms	(/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
5.0ms	(pow.f64 (/.f64 Om Omc) 2)
1.0ms	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
0.0ms	(*.f64 2 (pow.f64 (/.f64 t l) 2))

series368.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

123.0ms	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
89.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
79.0ms	(pow.f64 (/.f64 Om Omc) 2)
77.0ms	(/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 1502 to 1490 computations (0.8% saved)

simplify89.0ms (0%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4966	2631
1	4966	2631

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(pow.f64 (/.f64 t l) 2)
0.0b	(/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc))))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.3b	(/.f64 (+.f64 (sqrt.f64 1) (sqrt.f64 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))
1.3b	(asin.f64 (sqrt.f64 (/.f64 (+.f64 (sqrt.f64 1) (sqrt.f64 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))))
9.3b	(sqrt.f64 (/.f64 (+.f64 (sqrt.f64 1) (sqrt.f64 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc))))))
21.1b	(sqrt.f64 (pow.f64 (/.f64 Om Omc) 2))

rewrite137.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

467×	`*-un-lft-identity_binary64_419`
451×	`times-frac_binary64_425`
281×	`add-sqr-sqrt_binary64_441`
241×	`sqrt-prod_binary64_435`
172×	`add-cube-cbrt_binary64_454`
98×	`distribute-lft-out_binary64_370`
66×	`difference-of-squares_binary64_388`
33×	`distribute-lft-out--_binary64_371`
24×	`associate-/r/_binary64_365` `associate-/r*_binary64_363`
15×	`unpow-prod-down_binary64_498`
14×	`div-inv_binary64_416`
11×	`flip3--_binary64_423` `flip--_binary64_394`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`rem-sqrt-square_binary64_432`
5×	`pow1_binary64_480` `associate-/l*_binary64_364`
4×	`add-log-exp_binary64_458`
3×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`pow1/2_binary64_499` `sqr-pow_binary64_391` `sqrt-pow1_binary64_437` `unpow2_binary64_484` `associate-/l/_binary64_366`
1×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `clear-num_binary64_418` `frac-2neg_binary64_430` `flip-+_binary64_393` `asin-acos_binary64_599`

Counts

4 → 344

Calls

8 calls:

32.0ms	(sqrt.f64 (/.f64 (+.f64 (sqrt.f64 1) (sqrt.f64 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc))))))
26.0ms	(/.f64 (+.f64 (sqrt.f64 1) (sqrt.f64 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))
8.0ms	(sqrt.f64 (pow.f64 (/.f64 Om Omc) 2))
1.0ms	(asin.f64 (sqrt.f64 (/.f64 (+.f64 (sqrt.f64 1) (sqrt.f64 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))))
0.0ms	(*.f64 2 (pow.f64 (/.f64 t l) 2))

series2.3s (0.7%)

Counts

4 → 58

Calls

4 calls:

1.4s	(sqrt.f64 (/.f64 (+.f64 (sqrt.f64 1) (sqrt.f64 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc))))))
761.0ms	(/.f64 (+.f64 (sqrt.f64 1) (sqrt.f64 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))
137.0ms	(asin.f64 (sqrt.f64 (/.f64 (+.f64 (sqrt.f64 1) (sqrt.f64 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))))
56.0ms	(sqrt.f64 (pow.f64 (/.f64 Om Omc) 2))

Compiler

Compiled 7705 to 5620 computations (27.1% saved)

simplify223.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

402 → 402

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5036	22530

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.2b	(.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)))))))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
1.3b	(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))))))))
1.7b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
14.7b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.7b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite93.0ms (0%)

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

8 calls:

22.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
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))))))
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))))))))
0.0ms	(*.f64 2 (pow.f64 (/.f64 t l) 2))

series3.8s (1.2%)

Counts

4 → 69

Calls

4 calls:

1.2s	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.2s	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
1.2s	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
287.0ms	(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))))))))

Compiler

Compiled 10439 to 9140 computations (12.4% saved)

simplify137.0ms (0%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5619	12289

prune22.9s (7%)

Pruning

393 alts after pruning (387 fresh and 6 done)

	Pruned	Kept	Total
New	734	323	1057
Fresh	16	64	80
Picked	0	0	0
Done	0	6	6
Total	750	393	1143

Error

1.6b

Counts

1143 → 393

Compiler

Compiled 39514 to 28291 computations (28.4% saved)

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(pow.f64 (/.f64 t l) 2)
0.0b	(sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.2b	(pow.f64 (/.f64 t l) 2)
0.2b	(pow.f64 (/.f64 Om Omc) 2)
1.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (pow.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) -1/2)))
9.5b	(pow.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) -1/2)

rewrite23.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`unpow-prod-down_binary64_498`
22×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
18×	`times-frac_binary64_425`
11×	`add-exp-log_binary64_457`
9×	`pow-unpow_binary64_496`
7×	`pow1_binary64_480`
5×	`pow-exp_binary64_487`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455`
3×	`sqr-pow_binary64_391` `pow-to-exp_binary64_488` `pow-pow_binary64_491`
2×	`div-inv_binary64_416` `unpow2_binary64_484` `div-exp_binary64_470`
1×	`asin-acos_binary64_599`

Counts

4 → 83

Calls

8 calls:

5.0ms	(pow.f64 (/.f64 t l) 2)
5.0ms	(pow.f64 (/.f64 Om Omc) 2)
5.0ms	(pow.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) -1/2)
1.0ms	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (pow.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) -1/2)))
0.0ms	(*.f64 2 (pow.f64 (/.f64 t l) 2))

series451.0ms (0.1%)

Counts

4 → 35

Calls

4 calls:

175.0ms	(pow.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) -1/2)
120.0ms	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (pow.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) -1/2)))
80.0ms	(pow.f64 (/.f64 Om Omc) 2)
76.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 1666 to 1635 computations (1.9% saved)

simplify67.0ms (0%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4933	1906
1	4933	1906

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(pow.f64 (/.f64 t l) 2)
0.0b	(sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.6b	(pow.f64 (asin.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))) 3)
1.3b	(asin.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))
9.3b	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
13.6b	(cbrt.f64 (pow.f64 (asin.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))) 3))

rewrite21.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_441`
18×	`*-un-lft-identity_binary64_419`
17×	`add-cube-cbrt_binary64_454`
15×	`sqrt-prod_binary64_435`
12×	`cbrt-prod_binary64_450`
11×	`times-frac_binary64_425`
7×	`pow1_binary64_480`
6×	`unpow-prod-down_binary64_498` `cube-prod_binary64_447`
5×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
4×	`add-log-exp_binary64_458`
3×	`pow-unpow_binary64_496` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
2×	`unpow3_binary64_485` `cube-mult_binary64_449` `sqr-pow_binary64_391` `associate-/r/_binary64_365`
1×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `pow1/3_binary64_501` `inv-pow_binary64_504` `pow1/2_binary64_499` `div-inv_binary64_416` `rem-cube-cbrt_binary64_442` `pow-exp_binary64_487` `rem-cbrt-cube_binary64_443` `pow-to-exp_binary64_488` `pow-flip_binary64_493` `flip-+_binary64_393` `pow-pow_binary64_491` `asin-acos_binary64_599`

Counts

4 → 82

Calls

8 calls:

6.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
2.0ms	(cbrt.f64 (pow.f64 (asin.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))) 3))
2.0ms	(pow.f64 (asin.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))) 3)
1.0ms	(asin.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))
0.0ms	(*.f64 2 (pow.f64 (/.f64 t l) 2))

series874.0ms (0.3%)

Counts

4 → 45

Calls

4 calls:

539.0ms	(pow.f64 (asin.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))) 3)
123.0ms	(cbrt.f64 (pow.f64 (asin.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))))) 3))
120.0ms	(asin.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))) (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))))
92.0ms	(sqrt.f64 (/.f64 1 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

Compiler

Compiled 2159 to 2153 computations (0.3% saved)

simplify75.0ms (0%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4894	4182
1	4894	4182

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.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 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
0.0b	(cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
1.3b	(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 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
1.7b	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
14.7b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.8b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite65.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

124×	`add-sqr-sqrt_binary64_441`
101×	`cbrt-prod_binary64_450`
97×	`times-frac_binary64_425`
84×	`*-un-lft-identity_binary64_419`
60×	`difference-of-squares_binary64_388`
51×	`sqrt-prod_binary64_435`
42×	`add-cube-cbrt_binary64_454`
24×	`unpow-prod-down_binary64_498`
12×	`sqr-pow_binary64_391` `unpow2_binary64_484`
6×	`distribute-lft-out--_binary64_371`
5×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `cbrt-div_binary64_451` `associate-/r/_binary64_365` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`flip3-+_binary64_422` `pow1/3_binary64_501` `flip-+_binary64_393` `rem-sqrt-square_binary64_432`
2×	`div-inv_binary64_416` `sqrt-pow1_binary64_437`
1×	`sqrt-div_binary64_436` `pow1/2_binary64_499` `asin-acos_binary64_599`

Counts

4 → 143

Calls

8 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)))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.0ms	(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 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
0.0ms	(.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 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

series2.8s (0.9%)

Counts

4 → 62

Calls

4 calls:

1.2s	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.2s	(sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
286.0ms	(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 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
215.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 8435 to 7408 computations (12.2% saved)

simplify128.0ms (0%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4957	9366
1	4957	9366

localize33.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 5)
0.0b	(*.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 5)) 1/6))
0.0b	(/.f64 1 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 5))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
6.2b	(.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 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 1/6) (.f64 (.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 5)) 1/6)) (-.f64 (*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2)) (pow.f64 (/.f64 t l) 2)))))
6.5b	(-.f64 (*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2)) (pow.f64 (/.f64 t l) 2))
13.3b	(*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2))
14.7b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite117.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

129×	`add-sqr-sqrt_binary64_441`
86×	`times-frac_binary64_425`
73×	`*-un-lft-identity_binary64_419` `unpow-prod-down_binary64_498`
48×	`add-cube-cbrt_binary64_454` `cbrt-prod_binary64_450`
38×	`add-exp-log_binary64_457`
30×	`difference-of-squares_binary64_388`
26×	`unswap-sqr_binary64_387`
21×	`associate-r_binary64_359` `associate-l_binary64_360`
19×	`sqr-pow_binary64_391` `unpow2_binary64_484`
18×	`cancel-sign-sub-inv_binary64_385`
17×	`prod-exp_binary64_468`
16×	`pow-exp_binary64_487`
8×	`pow-to-exp_binary64_488` `add-cbrt-cube_binary64_455` `div-exp_binary64_470`
6×	`add-log-exp_binary64_458` `pow1_binary64_480`
4×	`div-inv_binary64_416`
3×	`distribute-rgt-out--_binary64_373` `distribute-lft-out--_binary64_371`
2×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `cbrt-unprod_binary64_452` `associate-r/_binary64_361` `associate-/r/_binary64_365` `-commutative_binary64_350` `flip-+_binary64_393`
1×	`pow1/3_binary64_501` `sub-neg_binary64_412` `cbrt-div_binary64_451` `distribute-rgt-in_binary64_369` `flip3--_binary64_423` `distribute-lft-in_binary64_368` `diff-log_binary64_511` `flip--_binary64_394`

Counts

4 → 198

Calls

8 calls:

23.0ms	(.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 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 1/6) (.f64 (.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 5)) 1/6)) (-.f64 (*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2)) (pow.f64 (/.f64 t l) 2)))))
17.0ms	(*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2))
17.0ms	(-.f64 (*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 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)))))
0.0ms	(*.f64 2 (pow.f64 (/.f64 t l) 2))

series6.6s (2%)

Counts

4 → 66

Calls

4 calls:

4.6s	(.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 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 1/6) (.f64 (.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 5)) 1/6)) (-.f64 (*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2)) (pow.f64 (/.f64 t l) 2)))))
1.0s	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
557.0ms	(-.f64 (*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2)) (pow.f64 (/.f64 t l) 2))
417.0ms	(*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2))

Compiler

Compiled 10753 to 9023 computations (16.1% saved)

simplify159.0ms (0%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4961	10971
1	4961	10971

prune29.1s (8.9%)

Pruning

650 alts after pruning (639 fresh and 11 done)

	Pruned	Kept	Total
New	445	269	714
Fresh	12	370	382
Picked	0	0	0
Done	0	11	11
Total	457	650	1107

Error

1.6b

Counts

1107 → 650

Compiler

Compiled 53117 to 40170 computations (24.4% saved)

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(pow.f64 (/.f64 t l) 2)
0.0b	(sqrt.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.2b	(pow.f64 (/.f64 Om Omc) 2)
1.3b	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2))))) (pow.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) -1/2)))
3.2b	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
9.5b	(pow.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) -1/2)

rewrite26.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`unpow-prod-down_binary64_498`
23×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
19×	`log-pow_binary64_508`
18×	`times-frac_binary64_425` `exp-prod_binary64_471`
8×	`add-exp-log_binary64_457`
7×	`pow1_binary64_480`
6×	`pow-unpow_binary64_496`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455`
3×	`log-prod_binary64_505` `pow-exp_binary64_487` `sqr-pow_binary64_391`
2×	`div-inv_binary64_416` `pow-to-exp_binary64_488` `pow-pow_binary64_491` `unpow2_binary64_484`
1×	`rem-log-exp_binary64_460` `asin-acos_binary64_599` `div-exp_binary64_470`

Counts

4 → 84

Calls

8 calls:

7.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
5.0ms	(pow.f64 (/.f64 Om Omc) 2)
4.0ms	(pow.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) -1/2)
1.0ms	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2))))) (pow.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) -1/2)))
0.0ms	(*.f64 2 (pow.f64 (/.f64 t l) 2))

series606.0ms (0.2%)

Counts

4 → 35

Calls

4 calls:

222.0ms	(log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2)))
183.0ms	(pow.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) -1/2)
121.0ms	(asin.f64 (.f64 (sqrt.f64 (-.f64 1 (log.f64 (exp.f64 (pow.f64 (/.f64 Om Omc) 2))))) (pow.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))) -1/2)))
80.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 1724 to 1693 computations (1.8% saved)

simplify74.0ms (0%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5064	1847

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

25.0b	(sqrt.f64 (neg.f64 (*.f64 Om Om)))
25.0b	(sqrt.f64 (neg.f64 (*.f64 Om Om)))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`sqrt-prod_binary64_435`
3×	`add-sqr-sqrt_binary64_441`
2×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `pow1_binary64_480`
1×	`distribute-lft-neg-in_binary64_376` `add-log-exp_binary64_458` `neg-mul-1_binary64_415` `pow1/2_binary64_499` `distribute-rgt-neg-in_binary64_377` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`

Counts

1 → 16

Calls

2 calls:

2.0ms	(sqrt.f64 (neg.f64 (*.f64 Om Om)))
0.0ms	(sqrt.f64 (neg.f64 (*.f64 Om Om)))

series32.0ms (0%)

Counts

1 → 3

Calls

1 calls:

31.0ms

(sqrt.f64 (neg.f64 (*.f64 Om Om)))

Compiler

Compiled 46 to 58 computations (-26.1% saved)

simplify104.0ms (0%)

Algorithm

1×	egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4671	175
1	4671	175

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))
0.0b	(cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))
0.0b	(.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2))))))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.2b	(/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.3b	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
9.3b	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite81.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`add-sqr-sqrt_binary64_441`
127×	`times-frac_binary64_425`
111×	`*-un-lft-identity_binary64_419`
99×	`cbrt-prod_binary64_450`
70×	`difference-of-squares_binary64_388`
62×	`add-cube-cbrt_binary64_454`
57×	`sqrt-prod_binary64_435`
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×	`pow1_binary64_480`
5×	`add-cbrt-cube_binary64_455`
4×	`add-log-exp_binary64_458` `associate-/r/_binary64_365`
3×	`div-inv_binary64_416` `pow-unpow_binary64_496` `associate-/r*_binary64_363` `rem-sqrt-square_binary64_432`
2×	`flip3-+_binary64_422` `cbrt-div_binary64_451` `pow-exp_binary64_487` `flip-+_binary64_393` `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`

Counts

4 → 194

Calls

8 calls:

19.0ms	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
18.0ms	(/.f64 (cbrt.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 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
0.0ms	(*.f64 2 (pow.f64 (/.f64 t l) 2))

series1.5s (0.5%)

Counts

4 → 54

Calls

4 calls:

617.0ms	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
589.0ms	(/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
237.0ms	(asin.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))
81.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 4250 to 3924 computations (7.7% saved)

simplify150.0ms (0%)

Algorithm

1×	egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4955	9633
1	4955	9633

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc))))
0.0b	(/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc))))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
6.9b	(sqrt.f64 (sqrt.f64 (/.f64 (+.f64 (fabs.f64 (/.f64 Om Omc)) 1) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))))
6.9b	(sqrt.f64 (sqrt.f64 (/.f64 (+.f64 (fabs.f64 (/.f64 Om Omc)) 1) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))))
9.3b	(sqrt.f64 (/.f64 (+.f64 (fabs.f64 (/.f64 Om Omc)) 1) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc))))))
9.3b	(sqrt.f64 (/.f64 (+.f64 (fabs.f64 (/.f64 Om Omc)) 1) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc))))))

rewrite228.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

684×	`times-frac_binary64_425`
618×	`sqrt-prod_binary64_435`
602×	`*-un-lft-identity_binary64_419`
436×	`add-sqr-sqrt_binary64_441`
266×	`add-cube-cbrt_binary64_454`
96×	`difference-of-squares_binary64_388` `distribute-lft-out_binary64_370`
48×	`distribute-lft-out--_binary64_371`
36×	`associate-/r/_binary64_365`
20×	`div-inv_binary64_416`
16×	`flip3--_binary64_423` `flip--_binary64_394`
14×	`rem-sqrt-square_binary64_432`
10×	`sqrt-pow1_binary64_437` `pow1_binary64_480`
6×	`sqrt-div_binary64_436` `pow1/2_binary64_499`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`

Counts

4 → 468

Calls

8 calls:

25.0ms	(sqrt.f64 (/.f64 (+.f64 (fabs.f64 (/.f64 Om Omc)) 1) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc))))))
24.0ms	(sqrt.f64 (sqrt.f64 (/.f64 (+.f64 (fabs.f64 (/.f64 Om Omc)) 1) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))))
24.0ms	(sqrt.f64 (sqrt.f64 (/.f64 (+.f64 (fabs.f64 (/.f64 Om Omc)) 1) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))))
20.0ms	(sqrt.f64 (/.f64 (+.f64 (fabs.f64 (/.f64 Om Omc)) 1) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc))))))
0.0ms	(*.f64 2 (pow.f64 (/.f64 t l) 2))

series6.0s (1.8%)

Counts

4 → 64

Calls

4 calls:

2.2s	(sqrt.f64 (sqrt.f64 (/.f64 (+.f64 (fabs.f64 (/.f64 Om Omc)) 1) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))))
2.2s	(sqrt.f64 (sqrt.f64 (/.f64 (+.f64 (fabs.f64 (/.f64 Om Omc)) 1) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc)))))))
813.0ms	(sqrt.f64 (/.f64 (+.f64 (fabs.f64 (/.f64 Om Omc)) 1) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc))))))
807.0ms	(sqrt.f64 (/.f64 (+.f64 (fabs.f64 (/.f64 Om Omc)) 1) (/.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))) (-.f64 1 (fabs.f64 (/.f64 Om Omc))))))

Compiler

Compiled 11958 to 8092 computations (32.3% saved)

simplify322.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

532 → 532

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5018	34832

localize41.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 5)) 1/6))
0.0b	(/.f64 1 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 5))
0.0b	(exp.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
0.0b	(*.f64 2 (pow.f64 (/.f64 t l) 2))
6.5b	(-.f64 (*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2)) (pow.f64 (/.f64 t l) 2))
13.3b	(*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2))
14.7b	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
17.3b	(.f64 (fabs.f64 (log.f64 (exp.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))) (+.f64 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 1/6) (.f64 (.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 5)) 1/6)) (-.f64 (*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2)) (pow.f64 (/.f64 t l) 2)))))

rewrite129.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

129×	`add-sqr-sqrt_binary64_441`
86×	`times-frac_binary64_425`
73×	`*-un-lft-identity_binary64_419` `unpow-prod-down_binary64_498`
48×	`add-cube-cbrt_binary64_454` `cbrt-prod_binary64_450`
38×	`add-exp-log_binary64_457`
30×	`difference-of-squares_binary64_388`
26×	`unswap-sqr_binary64_387`
21×	`associate-r_binary64_359` `associate-l_binary64_360`
19×	`sqr-pow_binary64_391` `unpow2_binary64_484`
18×	`cancel-sign-sub-inv_binary64_385`
17×	`prod-exp_binary64_468`
16×	`pow-exp_binary64_487`
8×	`pow-to-exp_binary64_488` `add-cbrt-cube_binary64_455` `div-exp_binary64_470`
6×	`add-log-exp_binary64_458` `pow1_binary64_480`
4×	`div-inv_binary64_416`
3×	`distribute-rgt-out--_binary64_373` `distribute-lft-out--_binary64_371`
2×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `cbrt-unprod_binary64_452` `associate-r/_binary64_361` `associate-/r/_binary64_365` `-commutative_binary64_350` `flip-+_binary64_393`
1×	`pow1/3_binary64_501` `sub-neg_binary64_412` `cbrt-div_binary64_451` `distribute-rgt-in_binary64_369` `flip3--_binary64_423` `distribute-lft-in_binary64_368` `diff-log_binary64_511` `flip--_binary64_394`

Counts

4 → 198

Calls

8 calls:

23.0ms	(.f64 (fabs.f64 (log.f64 (exp.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))) (+.f64 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 1/6) (.f64 (.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 5)) 1/6)) (-.f64 (*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2)) (pow.f64 (/.f64 t l) 2)))))
21.0ms	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
18.0ms	(*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2))
17.0ms	(-.f64 (*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2)) (pow.f64 (/.f64 t l) 2))
0.0ms	(*.f64 2 (pow.f64 (/.f64 t l) 2))

series6.7s (2%)

Counts

4 → 66

Calls

4 calls:

4.7s	(.f64 (fabs.f64 (log.f64 (exp.f64 (cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))))) (+.f64 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 1/6) (.f64 (.f64 1/3 (pow.f64 (/.f64 1 (pow.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) 5)) 1/6)) (-.f64 (*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2)) (pow.f64 (/.f64 t l) 2)))))
1.0s	(cbrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
592.0ms	(-.f64 (*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2)) (pow.f64 (/.f64 t l) 2))
419.0ms	(*.f64 (pow.f64 (/.f64 Om Omc) 2) (pow.f64 (/.f64 t l) 2))

Compiler

Compiled 11089 to 9359 computations (15.6% saved)

simplify448.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4984	10851
1	4984	10851

prune1.6min (29.2%)

Pruning

897 alts after pruning (882 fresh and 15 done)

	Pruned	Kept	Total
New	877	305	1182
Fresh	57	577	634
Picked	0	0	0
Done	1	15	16
Total	935	897	1832

Error

1.6b

Counts

1832 → 897

Compiler

Compiled 40703 to 25800 computations (36.6% saved)

simplify2.1s (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	6304	131127

regimes2.0min (37.4%)

Compiler: Compiled 1483975 to 1161507 computations (21.7% saved)

bsearch128.0ms (0%)

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

regimes2.3s (0.7%)

Compiler: Compiled 20926 to 21526 computations (-2.9% saved)

bsearch105.0ms (0%)

Steps

Iters	Range		Point
10	9.947907328610289e+143	1.714067951565936e+157	1.0800233055072413e+146
9	-2.4028048080907052e+114	-6.318763473088243e+107	-2.3765008719296084e+114

Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes2.3s (0.7%)

Compiler: Compiled 20029 to 20663 computations (-3.2% saved)

bsearch91.0ms (0%)

Steps

Iters	Range		Point
7	1.5721747939912137e+19	1.0177490757046716e+21	1.4558158866244431e+20
9	-2.4028048080907052e+114	-6.318763473088243e+107	-2.11346151031864e+114

Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes1.2s (0.4%)

Compiler: Compiled 9124 to 9856 computations (-8% saved)

bsearch38.0ms (0%)

Steps

Iters	Range		Point
7	1.5721747939912137e+19	1.0177490757046716e+21	1.4558158866244431e+20

Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes880.0ms (0.3%)

Compiler: Compiled 6902 to 7505 computations (-8.7% saved)

bsearch0.0ms (0%)

regimes514.0ms (0.2%)

Compiler: Compiled 3661 to 4164 computations (-13.7% saved)

bsearch0.0ms (0%)

regimes311.0ms (0.1%)

Compiler: Compiled 1607 to 1967 computations (-22.4% saved)

bsearch45.0ms (0%)

Steps

Iters	Range		Point
8	9.036580378777497e+114	3.010879452694016e+118	5.546388378083076e+115

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes101.0ms (0%)

Compiler: Compiled 272 to 396 computations (-45.6% saved)

bsearch42.0ms (0%)

Steps

Iters	Range		Point
8	9.036580378777497e+114	3.010879452694016e+118	4.167382628070661e+116

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes66.0ms (0%)

Compiler: Compiled 20 to 92 computations (-360% saved)

bsearch105.0ms (0%)

Steps

Iters	Range		Point
10	3.232620470106745e-54	1.815742404979642e-43	2.1941543636572065e-53
7	-6.29313297400155e-104	-8.439768049972154e-106	-2.035219707846875e-104

Compiler

Compiled 314 to 256 computations (18.5% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	173	478
1	173	478

end0.0ms (0%)

sample4.6s (1.4%)

Algorithm

1×

intervals

Results

793.0ms	8000×	body	128	valid
428.0ms	4707×	body	128	nan

Compiler

Compiled 83474 to 65055 computations (22.1% saved)