Details

Time bar (total: 14.9s)

analyze3.5s (23.4%)

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)

sample116.0ms (0.8%)

Algorithm
intervals
Results
59.0ms256×body128valid
28.0ms134×body128nan
Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify62.0ms (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

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
11.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
11.0b
(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)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(pow.f64 (/.f64 Om Omc) 2)
0.4b
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
0.5b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
10.0b
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))

series1.2s (7.8%)

Counts
4 → 168
Calls

4 calls:

685.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
427.0ms
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
35.0ms
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))
23.0ms
(pow.f64 (/.f64 Om Omc) 2)

rewrite101.0ms (0.7%)

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:

27.0ms
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
23.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
6.0ms
(pow.f64 (/.f64 Om Omc) 2)
1.0ms
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))

simplify706.0ms (4.7%)

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

prune1.2s (7.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3027309
Fresh000
Picked101
Done000
Total3037310
Error
0.6b
Counts
310 → 7
Alt Table
StatusErrorProgram
11.0b
(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
44.6b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
23.3b
(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
44.3b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
12.2b
(*.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))))))
23.4b
(asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1))))
11.1b
(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))))
Compiler

Compiled 18214 to 13434 computations (26.2% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(pow.f64 (/.f64 Om Omc) 2)
0.4b
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
0.5b
(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
10.0b
(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

series755.0ms (5.1%)

Counts
2 → 96
Calls

2 calls:

715.0ms
(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
38.0ms
(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

rewrite5.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
sqrt-prod_binary64
add-cube-cbrt_binary64
pow1_binary64
Counts
2 → 25
Calls

2 calls:

2.0ms
(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
1.0ms
(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))

simplify296.0ms (2%)

Algorithm
egg-herbie
Rules
516×fma-def_binary64
396×times-frac_binary64
338×associate-/r*_binary64
333×associate-*l*_binary64
255×associate-/l*_binary64
Counts
121 → 108
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
047111719
114459757
252249757

prune979.0ms (6.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2691270
Fresh066
Picked101
Done000
Total2707277
Error
0.6b
Counts
277 → 7
Alt Table
StatusErrorProgram
11.0b
(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
23.4b
(asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1))))
23.3b
(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
44.3b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
44.6b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
12.2b
(*.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))))))
11.1b
(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))))
Compiler

Compiled 17118 to 12889 computations (24.7% saved)

localize51.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(pow.f64 (/.f64 Om Omc) 2)
0.4b
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
0.5b
(asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
10.0b
(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))

prune726.0ms (4.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2700270
Fresh066
Picked011
Done000
Total2707277
Error
0.6b
Counts
277 → 7
Alt Table
StatusErrorProgram
11.0b
(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
23.4b
(asin.f64 (sqrt.f64 (/.f64 1 (+.f64 (*.f64 2 (/.f64 (pow.f64 t 2) (pow.f64 l 2))) 1))))
23.3b
(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))))
44.3b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
44.6b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
12.2b
(*.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))))))
11.1b
(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))))
Compiler

Compiled 17632 to 13407 computations (24% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(pow.f64 (/.f64 Om Omc) 2)
0.5b
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
0.5b
(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))))
10.1b
(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))

series428.0ms (2.9%)

Counts
3 → 120
Calls

3 calls:

388.0ms
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))
20.0ms
(sqrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))
19.0ms
(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))))

rewrite43.0ms (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:

14.0ms
(/.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))))

simplify321.0ms (2.1%)

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

prune524.0ms (3.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2986304
Fresh235
Picked101
Done011
Total30110311
Error
0.5b
Counts
311 → 10
Alt Table
StatusErrorProgram
44.9b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (sqrt.f64 1/2) (/.f64 t l)))))
44.6b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
12.2b
(*.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))))))
45.0b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
11.1b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (pow.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1) 1/2)))
44.3b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (sqrt.f64 1/2) (/.f64 t l))))
47.6b
(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)))))
11.0b
(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))))
44.3b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
11.2b
(asin.f64 (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
Compiler

Compiled 17813 to 13257 computations (25.6% saved)

regimes1.6s (10.7%)

Accuracy

Total 0.4b remaining (43.7%)

Threshold costs 0.4b (43.7%)

Counts
79 → 3
Compiler

Compiled 35741 to 29006 computations (18.8% saved)

bsearch4.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify7.0ms (0%)

Algorithm
egg-herbie
Rules
15×*-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
036118
157118
281118
3103118
4117118
5123118
6124118
7122118

end1.0ms (0%)

Compiler

Compiled 81 to 58 computations (28.4% saved)

sample2.3s (15.4%)

Algorithm
intervals
Results
979.0ms8000×body128valid
531.0ms4556×body128nan
Compiler

Compiled 404 to 318 computations (21.3% saved)

Profiling

Loading profile data...