Details

Time bar (total: 20.7s)

sample83.0ms

Algorithm
intervals
Results
25.0ms121×body160valid
16.0ms225×body80nan
10.0ms135×body80valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01619
12919
25118
310818
427918
583518
6311618
done500018

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
65×times-frac
51×*-un-lft-identity
37×add-cube-cbrt
30×sqrt-prod
28×difference-of-squares
27×unpow-prod-down
9×add-exp-log
8×associate-/l* sqr-pow
7×distribute-lft-out--
6×pow1 add-cbrt-cube
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square flip3-+ div-exp pow-exp flip-+ associate-/l/
1×cbrt-undiv pow-to-exp asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub clear-num flip--
Counts
4 → 138
Calls
4 calls:
8.0ms
(pow (/ t l) 2.0)
110.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
68.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
92.0ms
(pow (/ t l) 2.0)
371.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
39.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
498.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.4s

Counts
150 → 150
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03253783
16633655
215663335
done50003331

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.5b
(expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))
0.8b
(asin (sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))
10.3b
(sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
28×times-frac
26×*-un-lft-identity
18×add-cube-cbrt
16×difference-of-squares
8×unpow-prod-down associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 log1p-expm1-u
4×expm1-log1p-u distribute-lft-out-- add-log-exp sqr-pow
3×associate-/r* sqrt-prod
2×associate-/l/
1×cbrt-undiv rem-sqrt-square asin-acos expm1-log1p flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num flip-- div-inv expm1-udef
Counts
4 → 88
Calls
4 calls:
119.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.0ms
(expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))
1.0ms
(asin (sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))
1.0ms
(sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
301.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
270.0ms
(expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))
26.0ms
(asin (sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))
418.0ms
(sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

simplify1.8s

Counts
100 → 100
Iterations

Useful iterations: 2 (273.0ms)

IterNodesCost
01702462
13292320
27522162
322452162
done50002162

prune551.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (sqrt (log1p (* (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))) (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
10.3b
(sqrt (log1p (* (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))) (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
10.3b
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
10.3b
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×asin-acos
Counts
4 → 55
Calls
4 calls:
1.0ms
(asin (sqrt (log1p (* (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))) (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
3.0ms
(sqrt (log1p (* (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))) (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
3.0ms
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
3.0ms
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
29.0ms
(asin (sqrt (log1p (* (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))) (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
428.0ms
(sqrt (log1p (* (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))) (sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
402.0ms
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
380.0ms
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))

simplify1.8s

Counts
67 → 67
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0742059
11121293
21611143
32831143
45891143
514781143
done50001143

prune318.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.5b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
0.8b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
10.5b
(sqrt (fma (pow (/ t l) 2.0) 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:
6.0ms
(pow (/ t l) 2.0)
92.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
1.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
3.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series587.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(pow (/ t l) 2.0)
363.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))
19.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))
128.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify1.6s

Counts
167 → 167
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03004354
15044027
29413908
321533908
done50003902

prune702.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.6b

regimes361.0ms

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01940
done1940

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.2s7895×body80nan
841.0ms3767×body160valid
482.0ms4233×body80valid