Details

Time bar (total: 17.3s)

sample136.0ms

Algorithm
intervals
Results
45.0ms226×body80nan
30.0ms123×body160valid
17.0ms133×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01619
12919
25118
310818
429218
5158518
done500018

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
9.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
28×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 112
Calls
4 calls:
12.0ms
(pow (/ t l) 2.0)
7.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
40.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series578.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(pow (/ t l) 2.0)
98.0ms
(pow (/ Om Omc) 2.0)
13.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
374.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.2s

Counts
124 → 124
Iterations

Useful iterations: 2 (615.0ms)

IterNodesCost
03192298
17402196
218492088
done50002088

prune821.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
9.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
28×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 112
Calls
4 calls:
7.0ms
(pow (/ t l) 2.0)
12.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
45.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series666.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(pow (/ t l) 2.0)
98.0ms
(pow (/ Om Omc) 2.0)
19.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
444.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.0s

Counts
124 → 124
Iterations

Useful iterations: 2 (462.0ms)

IterNodesCost
03192298
17402196
218492088
done50002088

prune911.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.4b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
0.7b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
9.1b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt
95×sqrt-prod
82×times-frac
65×*-un-lft-identity
51×add-cube-cbrt
28×difference-of-squares
27×unpow-prod-down
11×associate-/l*
9×add-exp-log
8×sqr-pow
7×distribute-lft-out--
6×pow1 associate-/r* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×sqrt-div div-exp pow-exp div-inv associate-/l/
1×cbrt-undiv pow-to-exp rem-sqrt-square asin-acos sqrt-undiv flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 clear-num flip--
Counts
4 → 155
Calls
4 calls:
8.0ms
(pow (/ Om Omc) 2.0)
96.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
1.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
4.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series742.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(pow (/ Om Omc) 2.0)
449.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
17.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))
176.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.2s

Counts
167 → 167
Iterations

Useful iterations: 2 (481.0ms)

IterNodesCost
03124370
16194044
217483928
done50003928

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.1b

localize30.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
8.3b
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
9.1b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
9.1b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 72
Calls
4 calls:
3.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
3.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
2.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
2.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

series688.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
178.0ms
(sqrt (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
180.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
135.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))

simplify1.4s

Counts
84 → 84
Iterations

Useful iterations: done (1.4s)

IterNodesCost
0751116
1129960
2263922
3647922
42374886
done5002870

prune506.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.1b

regimes770.0ms

Accuracy

0% (0.1b remaining)

Error of 10.0b against oracle of 9.9b and baseline of 10.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01720
done1720

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.1s7960×body80nan
908.0ms3780×body160valid
786.0ms4220×body80valid