Details

Time bar (total: 9.0s)

analyze1.5s

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
18.7%76.4%4.9%9
18.7%76.4%4.9%10
21.8%72.5%5.7%11
21.8%69.8%8.4%12
32.7%46.6%20.7%13
32.7%46.6%20.7%14

sample65.0ms

Algorithm
intervals
Results
21.0ms114×body160valid
15.0ms122×body80nan
13.0ms142×body80valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
0474519
1474519

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.0b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.3b
(pow (/ Om Omc) 2.0)
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
11.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
104×add-sqr-sqrt
74×times-frac
59×*-un-lft-identity
45×add-cube-cbrt
40×unpow-prod-down
30×sqrt-prod
28×difference-of-squares
12×add-exp-log
9×sqr-pow
8×associate-/l*
7×pow1 distribute-lft-out--
6×pow-unpow add-cbrt-cube
4×pow-exp associate-/r/ div-inv add-log-exp
3×div-exp associate-/r*
2×pow-to-exp rem-sqrt-square pow-pow flip3-+ flip-+ associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub clear-num flip--
Counts
4 → 150
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
4.0ms
(pow (/ Om Omc) 2.0)
12.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series247.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(pow (/ t l) 2.0)
12.0ms
(pow (/ Om Omc) 2.0)
92.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
130.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
049503385
149503385

prune457.0ms

Filtered
125 candidates to 162 candidates (-29.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1557162
Fresh000
Picked011
Done000
Total1558163

Merged error: 11.9b

Counts
163 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.3b
(pow (/ Om Omc) 2.0)
0.4b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.4b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
116×add-sqr-sqrt
95×sqrt-prod
91×times-frac
73×*-un-lft-identity
59×add-cube-cbrt
40×unpow-prod-down
28×difference-of-squares
12×add-exp-log
11×associate-/l*
9×sqr-pow
7×pow1 distribute-lft-out--
6×pow-unpow sqrt-div associate-/r* add-cbrt-cube
4×pow-exp add-log-exp
3×div-exp div-inv
2×pow-to-exp pow-pow flip3-+ associate-/r/ flip-+ associate-/l/
1×cbrt-undiv rem-sqrt-square sqrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 clear-num flip--
Counts
4 → 171
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
4.0ms
(pow (/ Om Omc) 2.0)
18.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series204.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(pow (/ t l) 2.0)
13.0ms
(pow (/ Om Omc) 2.0)
133.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
46.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify71.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049734153
149734153

prune425.0ms

Filtered
117 candidates to 183 candidates (-56.4%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1821183
Fresh156
Picked011
Done011
Total1838191

Merged error: 11.9b

Counts
191 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

11.0b
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
17.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
126×sqrt-prod
117×add-sqr-sqrt
80×cbrt-div
72×*-un-lft-identity
71×cbrt-prod
60×add-cube-cbrt
50×associate-/r/
40×flip3-+ flip-+
24×frac-times difference-of-squares
12×unpow-prod-down associate-*r/ associate-*l/
7×div-inv
6×distribute-lft-out-- sqr-pow
5×pow1 rem-sqrt-square
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 180
Calls
4 calls:
29.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
5.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series322.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(sqrt (/ (/ (- 1.0 (pow (/ Om Omc) 2.0)) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
61.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
63.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
66.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify94.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
0536110323

prune1.2s

Filtered
160 candidates to 192 candidates (-20.0%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1911192
Fresh145
Picked011
Done022
Total1928200

Merged error: 11.9b

Counts
200 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.1b
(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
11.4b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.6b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
103×add-sqr-sqrt
73×times-frac
62×sqrt-prod
60×*-un-lft-identity
46×add-cube-cbrt
45×cbrt-prod
28×difference-of-squares
14×unpow-prod-down
11×associate-/l*
7×distribute-lft-out-- sqr-pow
6×add-exp-log cbrt-div sqrt-div associate-/r*
5×pow1 add-cbrt-cube
4×flip3-+ flip-+ add-log-exp
2×pow1/3 associate-/r/ associate-/l/
1×cbrt-undiv rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-exp clear-num flip-- div-inv
Counts
4 → 143
Calls
4 calls:
17.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
4.0ms
(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
63.0ms
(cbrt (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
49.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
62.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify67.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
049714378
149714378

prune629.0ms

Filtered
122 candidates to 155 candidates (-27.0%)
Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New1550155
Fresh044
Picked011
Done033
Total1558163

Merged error: 11.9b

Counts
163 → 8

regimes1.2s

Accuracy

0% (0.1b remaining)

Error of 10.6b against oracle of 10.5b and baseline of 10.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02819
12819

end0.0ms

sample1.9s

Algorithm
intervals
Results
715.0ms3787×body160valid
444.0ms4560×body80nan
397.0ms4213×body80valid

Profiling

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