Details

Time bar (total: 20.5s)

sample162.0ms

Algorithm
intervals
Results
42.0ms133×body80valid
35.0ms123×body160valid
32.0ms226×body80nan

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01619
12919
24919
310119
427719
5156119
done500119

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize32.0ms

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)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.3b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
30×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×pow-exp add-cbrt-cube add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp associate-/r/
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 106
Calls
4 calls:
10.0ms
(pow (/ t l) 2.0)
12.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
54.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series649.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(pow (/ t l) 2.0)
86.0ms
(pow (/ Om Omc) 2.0)
30.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
440.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify1.5s

Counts
118 → 118
Iterations

Useful iterations: 2 (644.0ms)

IterNodesCost
03522388
18582272
223722160
done50022160

prune764.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.1b

localize21.0ms

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 (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
0.7b
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))))
9.1b
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

rewrite154.0ms

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:
6.0ms
(pow (/ Om Omc) 2.0)
117.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
1.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))))
18.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

series849.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(pow (/ Om Omc) 2.0)
509.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
23.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))))
231.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

simplify1.3s

Counts
163 → 163
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03254597
17004260
222224132
done50004128

prune889.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.1b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt *-un-lft-identity sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
Counts
4 → 72
Calls
4 calls:
18.0ms
(sqrt (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
24.0ms
(sqrt (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
34.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
22.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
335.0ms
(sqrt (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
332.0ms
(sqrt (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
303.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
266.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))

simplify2.0s

Counts
84 → 84
Iterations

Useful iterations: 3 (740.0ms)

IterNodesCost
0931458
12071304
26671234
336061218
done50021218

prune562.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.1b

localize38.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
9.1b
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
9.1b
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
16.1b
(cbrt (pow (sqrt (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))) 3))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
34×sqrt-prod
24×cbrt-prod
19×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
12×sqrt-div
9×unpow-prod-down cube-prod
8×pow1
6×sqrt-pow1
4×add-exp-log rem-sqrt-square flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
2×cube-div cbrt-div
1×cube-mult pow1/3 unpow3 rem-cbrt-cube sqr-pow
Counts
4 → 86
Calls
4 calls:
36.0ms
(sqrt (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
36.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
34.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
40.0ms
(cbrt (pow (sqrt (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))) 3))

series1.3s

Counts
4 → 12
Calls
4 calls:
317.0ms
(sqrt (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0)))
251.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
303.0ms
(sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))
384.0ms
(cbrt (pow (sqrt (sqrt (+ (* 2.0 (pow (/ t l) 2.0)) 1.0))) 3))

simplify2.2s

Counts
98 → 98
Iterations

Useful iterations: 2 (324.0ms)

IterNodesCost
01382084
13551632
218621580
done50001580

prune706.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.1b

regimes907.0ms

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
01619
11819
done1819

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.3s7960×body80nan
957.0ms3780×body160valid
493.0ms4220×body80valid