Details

Time bar (total: 13.8s)

analyze1.9s (13.5%)

Algorithm
search
Search
TrueOtherFalseIter
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 24 to 20 computations (16.7% saved)

sample125.0ms (0.9%)

Algorithm
intervals
Results
33.0ms256×body128valid
18.0ms160×body128nan
Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify53.0ms (0.4%)

Algorithm
egg-herbie
Rules
564×fma-def_binary64
527×associate-/r/_binary64
522×fma-neg_binary64
484×unswap-sqr_binary64
458×associate-/l/_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01729
13327
26327
316527
449227
5167927
6365527
7495027
8504327

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
7.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
7.7b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
Compiler

Compiled 85 to 67 computations (21.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(pow.f64 (/.f64 Om Omc) 2)
0.2b
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
0.6b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
6.9b
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series635.0ms (4.6%)

Counts
4 → 168
Calls

4 calls:

378.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
225.0ms
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
20.0ms
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
12.0ms
(pow.f64 (/.f64 Om Omc) 2)

rewrite51.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
143×add-sqr-sqrt_binary64
108×times-frac_binary64
98×*-un-lft-identity_binary64
70×difference-of-squares_binary64
49×add-cube-cbrt_binary64
Counts
4 → 177
Calls

4 calls:

15.0ms
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
11.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
3.0ms
(pow.f64 (/.f64 Om Omc) 2)
0.0ms
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

simplify938.0ms (6.8%)

Algorithm
egg-herbie
Rules
968×fma-def_binary64
483×times-frac_binary64
368×associate-/l*_binary64
208×*-commutative_binary64
144×+-commutative_binary64
Counts
345 → 309
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
077521028
1209117483
2484917362
3517517362

prune562.0ms (4.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New3018309
Fresh000
Picked101
Done000
Total3028310
Error
0.6b
Counts
310 → 8
Alt Table
StatusErrorProgram
7.8b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
7.7b
(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
9.0b
(*.f64 (*.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
12.1b
(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
7.9b
(asin.f64 (*.f64 (fabs.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
46.1b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
47.0b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
16.4b
(asin.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3))))
Compiler

Compiled 18312 to 13508 computations (26.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(pow.f64 (/.f64 Om Omc) 2)
0.2b
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
0.6b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
6.9b
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

prune543.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3081309
Fresh167
Picked101
Done000
Total3107317
Error
0.6b
Counts
317 → 7
Alt Table
StatusErrorProgram
9.0b
(*.f64 (*.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
12.1b
(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
7.8b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
46.1b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
47.0b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
16.4b
(asin.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3))))
8.0b
(expm1.f64 (log1p.f64 (asin.f64 (*.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
Compiler

Compiled 18852 to 14062 computations (25.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(pow.f64 (/.f64 Om Omc) 2)
0.4b
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
0.6b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
6.8b
(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series414.0ms (3%)

Counts
3 → 120
Calls

3 calls:

373.0ms
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
24.0ms
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
17.0ms
(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

rewrite40.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
155×sqrt-prod_binary64
148×add-sqr-sqrt_binary64
116×times-frac_binary64
103×*-un-lft-identity_binary64
70×difference-of-squares_binary64
Counts
3 → 168
Calls

3 calls:

13.0ms
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
1.0ms
(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
0.0ms
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

simplify311.0ms (2.2%)

Algorithm
egg-herbie
Rules
818×fma-def_binary64
433×times-frac_binary64
377×associate-/r*_binary64
291×associate-/l*_binary64
202×associate-*l/_binary64
Counts
288 → 263
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
064519365
1176116645
2492316520
3518816520

prune553.0ms (4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3013304
Fresh066
Picked101
Done000
Total3029311
Error
0.6b
Counts
311 → 9
Alt Table
StatusErrorProgram
46.2b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
12.1b
(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
8.0b
(expm1.f64 (log1p.f64 (asin.f64 (*.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
47.2b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
9.0b
(*.f64 (*.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
49.7b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fma.f64 1/2 (/.f64 l (*.f64 t (sqrt.f64 2))) (fma.f64 (/.f64 t l) (sqrt.f64 2) (*.f64 (/.f64 (pow.f64 l 3) (*.f64 (pow.f64 t 3) (*.f64 2 (sqrt.f64 2)))) -1/8)))))
46.1b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
47.0b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
16.4b
(asin.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3))))
Compiler

Compiled 18050 to 13443 computations (25.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(pow.f64 (/.f64 t l) 2)
0.3b
(/.f64 (-.f64 1 (/.f64 Om Omc)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
0.6b
(asin.f64 (*.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
6.9b
(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series466.0ms (3.4%)

Counts
4 → 156
Calls

4 calls:

280.0ms
(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
161.0ms
(/.f64 (-.f64 1 (/.f64 Om Omc)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
14.0ms
(asin.f64 (*.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
10.0ms
(pow.f64 (/.f64 t l) 2)

rewrite38.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt_binary64
72×times-frac_binary64
65×*-un-lft-identity_binary64
37×add-cube-cbrt_binary64
28×difference-of-squares_binary64
Counts
4 → 135
Calls

4 calls:

11.0ms
(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
10.0ms
(/.f64 (-.f64 1 (/.f64 Om Omc)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
3.0ms
(pow.f64 (/.f64 t l) 2)
1.0ms
(asin.f64 (*.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

simplify205.0ms (1.5%)

Algorithm
egg-herbie
Rules
592×fma-def_binary64
451×times-frac_binary64
356×associate-/r*_binary64
337×associate-/l*_binary64
252×associate-*l/_binary64
Counts
291 → 231
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
067315447
1184613671
2508213671

prune437.0ms (3.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2310231
Fresh088
Picked011
Done000
Total2319240
Error
0.6b
Counts
240 → 9
Alt Table
StatusErrorProgram
46.2b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
12.1b
(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 3))
8.0b
(expm1.f64 (log1p.f64 (asin.f64 (*.f64 (sqrt.f64 (+.f64 1 (/.f64 Om Omc))) (sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))))
47.2b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
9.0b
(*.f64 (*.f64 (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))) (cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
49.7b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (fma.f64 1/2 (/.f64 l (*.f64 t (sqrt.f64 2))) (fma.f64 (/.f64 t l) (sqrt.f64 2) (*.f64 (/.f64 (pow.f64 l 3) (*.f64 (pow.f64 t 3) (*.f64 2 (sqrt.f64 2)))) -1/8)))))
46.1b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
47.0b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
16.4b
(asin.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 3))))
Compiler

Compiled 14482 to 9891 computations (31.7% saved)

regimes4.2s (30.6%)

Accuracy

Total 0.1b remaining (15.7%)

Threshold costs 0.1b (15.7%)

Counts
187 → 3
Compiler

Compiled 99874 to 80257 computations (19.6% saved)

bsearch8.0ms (0.1%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Rules
13×*-commutative_binary64
12×+-commutative_binary64
12×sub-neg_binary64
10×neg-sub0_binary64
10×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
037104
155104
280104
399104
4112104
5116104
6115104

end1.0ms (0%)

Compiler

Compiled 71 to 48 computations (32.4% saved)

sample2.3s (16.6%)

Algorithm
intervals
Results
1.0s8000×body128valid
531.0ms4733×body128nan
Compiler

Compiled 365 to 283 computations (22.5% saved)

Profiling

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