Details

Time bar (total: 7.5s)

sample79.0ms

Algorithm
intervals
Results
26.0ms270×body80nan
19.0ms113×body160valid
12.0ms143×body80valid

simplify134.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5438410
6500210

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 10.3b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.2b
(pow (/ t l) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
9.5b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite28.0ms

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:
7.0ms
(pow (/ Om Omc) 2.0)
4.0ms
(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))))))
12.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series447.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ Om Omc) 2.0)
61.0ms
(pow (/ t l) 2.0)
16.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
310.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
06951235
120431164
250021152

prune406.0ms

Filtered
118 candidates to 92 candidates (78.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1135118
Fresh000
Picked101
Done000
Total1145119

Merged error: 10.2b

Counts
119 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.7b
(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
3.2b
(log (exp (pow (/ Om Omc) 2.0)))
9.5b
(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt *-un-lft-identity
37×times-frac
31×add-cube-cbrt
26×unpow-prod-down
24×sqrt-prod
21×log-pow
17×exp-prod
10×pow1
7×add-exp-log
6×distribute-lft-out--
4×add-cbrt-cube add-log-exp
3×pow-unpow log-prod div-inv difference-of-squares
2×rem-sqrt-square pow-exp associate-/r/ sqr-pow
1×pow-to-exp asin-acos pow-pow sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp rem-log-exp flip-+
Counts
4 → 101
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
6.0ms
(log (exp (pow (/ Om Omc) 2.0)))
14.0ms
(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series443.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(pow (/ t l) 2.0)
16.0ms
(asin (sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
60.0ms
(log (exp (pow (/ Om Omc) 2.0)))
306.0ms
(sqrt (/ (- 1.0 (log (exp (pow (/ Om Omc) 2.0)))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify55.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
06241169
118631079
250021061

prune387.0ms

Filtered
113 candidates to 88 candidates (77.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1121113
Fresh044
Picked011
Done000
Total1126118

Merged error: 10.2b

Counts
118 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.3b
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.7b
(asin (/ (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))))

rewrite31.0ms

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:
4.0ms
(pow (/ t l) 2.0)
14.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
1.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(pow (/ t l) 2.0)
303.0ms
(/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
16.0ms
(asin (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
174.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify68.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
06192493
119832321
250012311

prune476.0ms

Filtered
163 candidates to 107 candidates (65.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1621163
Fresh134
Picked101
Done011
Total1645169

Merged error: 10.2b

Counts
169 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (* (fabs (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
2.3b
(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
14.4b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
14.4b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
98×add-sqr-sqrt
91×cbrt-prod
76×times-frac
72×sqrt-prod
53×*-un-lft-identity
41×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
6×cbrt-div distribute-lft-out-- sqr-pow
5×pow1 rem-sqrt-square
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ flip-+
2×pow1/3 associate-/r/
1×asin-acos sqrt-pow1 pow1/2 sqrt-div div-inv
Counts
4 → 121
Calls
4 calls:
1.0ms
(asin (* (fabs (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
17.0ms
(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series834.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(asin (* (fabs (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
329.0ms
(sqrt (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
236.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
232.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify63.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
05842691
114692588
250012576

prune694.0ms

Filtered
133 candidates to 120 candidates (90.2%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1330133
Fresh033
Picked011
Done011
Total1335138

Merged error: 10.2b

Counts
138 → 5

regimes492.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02012
12012

end0.0ms

sample2.1s

Algorithm
intervals
Results
689.0ms8002×body80nan
644.0ms3779×body160valid
360.0ms4221×body80valid

Profiling

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