Details

Time bar (total: 1.1m)

sample107.0ms

Algorithm
intervals
Results
24.0ms252×body80nan
20.0ms117×body160valid
13.0ms139×body80valid

simplify6.1s

Counts
1 → 1
Iterations
IterNodes
done5000
62611
5774
4250
3102
251
129
016

prune53.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize94.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
0.5b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
8.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

rewrite273.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
65×times-frac
51×*-un-lft-identity
37×add-cube-cbrt
28×sqrt-prod 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 insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square div-exp pow-exp associate-/l/
1×pow-to-exp cbrt-undiv asin-acos clear-num pow-pow frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub flip--
Counts
4 → 138
Calls
4 calls:
9.0ms
(pow (/ Om Omc) 2.0)
181.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
69.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

series1.9s

Counts
4 → 12
Calls
4 calls:
191.0ms
(pow (/ Om Omc) 2.0)
662.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))
47.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0))))
1.0s
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma (pow (/ t l) 2.0) 2.0 1.0)))

simplify7.8s

Counts
150 → 150
Iterations
IterNodes
done5002
34209
21307
1599
0280

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.6b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma (pow (/ t l) 2.0) 2.0 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))
0.5b
(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma (pow (/ t l) 2.0) 2.0 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))))
8.8b
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma (pow (/ t l) 2.0) 2.0 1.0) (+ 1.0 (pow (/ Om Omc) 2.0)))))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt times-frac
16×*-un-lft-identity add-cube-cbrt
13×unpow-prod-down
12×add-exp-log
10×sqrt-prod
9×add-cbrt-cube
6×pow1
4×expm1-log1p-u associate-*r/ associate-/r/ insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×pow-unpow div-exp div-inv difference-of-squares
2×cbrt-undiv flip3-+ pow-exp flip-+ associate-/l/
1×pow-to-exp rem-sqrt-square asin-acos clear-num associate-/r* pow-pow frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub prod-exp cbrt-unprod flip-- sqr-pow
Counts
4 → 97
Calls
4 calls:
9.0ms
(pow (/ Om Omc) 2.0)
69.0ms
(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma (pow (/ t l) 2.0) 2.0 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))
1.0ms
(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma (pow (/ t l) 2.0) 2.0 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))))
41.0ms
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma (pow (/ t l) 2.0) 2.0 1.0) (+ 1.0 (pow (/ Om Omc) 2.0)))))

series4.8s

Counts
4 → 12
Calls
4 calls:
183.0ms
(pow (/ Om Omc) 2.0)
2.0s
(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma (pow (/ t l) 2.0) 2.0 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))
128.0ms
(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma (pow (/ t l) 2.0) 2.0 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))))
2.6s
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma (pow (/ t l) 2.0) 2.0 1.0) (+ 1.0 (pow (/ Om Omc) 2.0)))))

simplify5.4s

Counts
109 → 109
Iterations
IterNodes
done5000
22309
1665
0255

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.6b

localize118.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
8.9b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
19.9b
(sqrt (pow (/ Om Omc) 2.0))
19.9b
(sqrt (pow (/ Om Omc) 2.0))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
32×add-sqr-sqrt
30×unpow-prod-down
22×*-un-lft-identity add-cube-cbrt
20×times-frac
10×rem-sqrt-square
6×pow1
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u add-log-exp sqr-pow
2×div-inv
Counts
4 → 98
Calls
4 calls:
5.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
5.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
30.0ms
(sqrt (pow (/ Om Omc) 2.0))
28.0ms
(sqrt (pow (/ Om Omc) 2.0))

series2.7s

Counts
4 → 12
Calls
4 calls:
319.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
330.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.1s
(sqrt (pow (/ Om Omc) 2.0))
1.0s
(sqrt (pow (/ Om Omc) 2.0))

simplify7.5s

Counts
110 → 110
Iterations
IterNodes
done5001
43340
31335
2608
1324
0173

prune2.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.6b

localize175.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (fma (pow (/ (/ -1 l) (/ -1 t)) 2.0) 2.0 1.0))
8.9b
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
19.9b
(sqrt (pow (/ Om Omc) 2.0))
19.9b
(sqrt (pow (/ Om Omc) 2.0))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
40×sqrt-prod
32×add-sqr-sqrt
30×unpow-prod-down
22×*-un-lft-identity add-cube-cbrt
20×times-frac
10×rem-sqrt-square
6×pow1
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u add-log-exp sqr-pow
2×div-inv
Counts
4 → 98
Calls
4 calls:
3.0ms
(sqrt (fma (pow (/ (/ -1 l) (/ -1 t)) 2.0) 2.0 1.0))
3.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
15.0ms
(sqrt (pow (/ Om Omc) 2.0))
18.0ms
(sqrt (pow (/ Om Omc) 2.0))

series2.7s

Counts
4 → 12
Calls
4 calls:
294.0ms
(sqrt (fma (pow (/ (/ -1 l) (/ -1 t)) 2.0) 2.0 1.0))
291.0ms
(sqrt (fma (pow (/ t l) 2.0) 2.0 1.0))
1.0s
(sqrt (pow (/ Om Omc) 2.0))
1.1s
(sqrt (pow (/ Om Omc) 2.0))

simplify8.1s

Counts
110 → 110
Iterations
IterNodes
done5024
43535
31443
2661
1353
0191

prune2.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.6b

regimes2.7s

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.0b and baseline of 10.1b

bsearch0.0ms

simplify14.0ms

Iterations
IterNodes
done21
121
019

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.4s7980×body80nan
1.0s3824×body160valid
498.0ms4176×body80valid