Details

Time bar (total: 30.0s)

sample148.0ms

Algorithm
intervals
Results
54.0ms286×body80nan
32.0ms129×body160valid
16.0ms127×body80valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01619
12919
24919
310019
426519
579819
6301619
done500119

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.3b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite167.0ms

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×associate-/r/ 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 → 130
Calls
4 calls:
9.0ms
(pow (/ Om Omc) 2.0)
102.0ms
(/ (- 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))))))
49.0ms
(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:
116.0ms
(pow (/ Om Omc) 2.0)
337.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
36.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
534.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify3.0s

Counts
142 → 142
Iterations

Useful iterations: done (3.0s)

IterNodesCost
03083657
16333542
214833367
344673355
done50013352

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
0.5b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
9.4b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite137.0ms

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 sqrt-div associate-/r* add-cbrt-cube
4×add-log-exp
3×pow-unpow
2×flip3-+ div-exp pow-exp associate-/r/ flip-+ 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 → 151
Calls
4 calls:
11.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
102.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
10.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series885.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(pow (/ Om Omc) 2.0)
25.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
482.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
302.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify2.3s

Counts
163 → 163
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03254597
16034254
213114128
337464122
done50004119

prune924.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 10.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))))
9.4b
(sqrt (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))))
18.8b
(sqrt (pow (/ Om Omc) 2.0))
18.8b
(sqrt (pow (/ Om Omc) 2.0))

rewrite488.0ms

Algorithm
rewrite-expression-head
Rules
1094×times-frac
1007×add-sqr-sqrt
995×sqrt-prod
877×*-un-lft-identity
333×add-cube-cbrt
330×difference-of-squares
206×distribute-lft-out
162×unpow-prod-down
70×sqr-pow
66×distribute-lft-out--
51×associate-/r*
24×associate-/r/
15×div-inv
11×rem-sqrt-square flip3-- flip--
9×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×add-log-exp
3×cbrt-undiv sqrt-pow1 pow1/2 div-exp
2×associate-/l/
1×frac-2neg flip3-+ sqrt-div clear-num flip-+
Counts
4 → 661
Calls
4 calls:
184.0ms
(/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))))
195.0ms
(sqrt (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))))
9.0ms
(sqrt (pow (/ Om Omc) 2.0))
9.0ms
(sqrt (pow (/ Om Omc) 2.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
592.0ms
(/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0)))))
859.0ms
(sqrt (/ (+ (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))) (/ (+ 1.0 (* 2.0 (pow (/ t l) 2.0))) (- (sqrt 1.0) (sqrt (pow (/ Om Omc) 2.0))))))
327.0ms
(sqrt (pow (/ Om Omc) 2.0))
395.0ms
(sqrt (pow (/ Om Omc) 2.0))

simplify2.1s

Counts
673 → 673
Iterations

Useful iterations: done (2.0s)

IterNodesCost
069335695
1126734189
2381432564
done500032332

prune2.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
1.5b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
15.3b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.3b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
82×add-sqr-sqrt
56×times-frac
54×sqrt-prod
41×*-un-lft-identity
31×cbrt-prod
29×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
6×cbrt-div distribute-lft-out-- sqr-pow
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square flip3-+ flip-+
2×pow1/3 associate-/r/
1×asin-acos sqrt-pow1 pow1/2 sqrt-div div-inv
Counts
4 → 101
Calls
4 calls:
1.0ms
(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
54.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
45.0ms
(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
408.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
325.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
313.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify1.9s

Counts
113 → 113
Iterations

Useful iterations: 3 (988.0ms)

IterNodesCost
02973717
15483588
211733410
333913400
done50013400

prune845.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 10.1b

regimes1.0s

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01720
11920
done1920

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.7s8023×body80nan
1.2s3861×body160valid
569.0ms4139×body80valid