Details

Time bar (total: 21.2s)

sample97.0ms

Algorithm
intervals
Results
28.0ms135×body80valid
20.0ms121×body160valid
18.0ms225×body80nan

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

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

localize27.0ms

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)))))

rewrite198.0ms

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:
11.0ms
(pow (/ t l) 2.0)
98.0ms
(/ (- 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))))))
76.0ms
(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:
69.0ms
(pow (/ t l) 2.0)
376.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
34.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
570.0ms
(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

prune909.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.6b

localize35.0ms

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)))))

rewrite121.0ms

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:
115.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms
(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))))))
2.0ms
(sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

series994.0ms

Counts
4 → 12
Calls
4 calls:
289.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
251.0ms
(expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))
15.0ms
(asin (sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))))
440.0ms
(sqrt (log1p (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))))

simplify1.6s

Counts
100 → 100
Iterations

Useful iterations: 2 (152.0ms)

IterNodesCost
01702462
13292320
27522162
322452162
done50002162

prune643.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.6b

localize34.0ms

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))))

rewrite7.0ms

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))))))))
2.0ms
(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)))))))
1.0ms
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
2.0ms
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
27.0ms
(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))))))))
432.0ms
(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)))))))
437.0ms
(sqrt (expm1 (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
399.0ms
(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 (39.0ms)

IterNodesCost
0742059
11121293
21611143
32831143
45891143
514781143
done50001143

prune382.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.8b
(asin (sqrt (log1p (expm1 (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
10.3b
(sqrt (log1p (expm1 (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 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))
10.5b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

rewrite13.0ms

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 (expm1 (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
3.0ms
(sqrt (log1p (expm1 (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 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))
3.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

series740.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(asin (sqrt (log1p (expm1 (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))))))))
405.0ms
(sqrt (log1p (expm1 (* (/ 1 (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (fma (pow (/ t l) 2.0) 2.0 1.0)))))))
136.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
179.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))

simplify2.0s

Counts
67 → 67
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01051590
11711397
23071237
3787951
42045930
done5000922

prune332.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 11.6b

regimes624.0ms

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

sample3.8s

Algorithm
intervals
Results
1.1s7895×body80nan
919.0ms4233×body80valid
865.0ms3767×body160valid