Details

Time bar (total: 19.3s)

sample166.0ms

Algorithm
intervals
Results
59.0ms122×body160valid
50.0ms276×body80nan
23.0ms134×body80valid

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
done2050
62050
51097
4396
3153
263
132
016

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.9b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
0.2b
(* (/ Om Omc) (/ Om Omc))
0.2b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
7.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
19×sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
6×div-inv
5×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 sqrt-div div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 156
Calls
4 calls:
27.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
26.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
11.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

series396.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))
47.0ms
(* (/ Om Omc) (/ Om Omc))
19.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1))))
230.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) 2) (/ t l) 1)))

simplify1.5s

Counts
168 → 168
Iterations
IterNodes
done2000
32000
21959
1648
0255

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.2b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
0.3b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
7.5b
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
85×add-sqr-sqrt
72×*-un-lft-identity
65×add-cube-cbrt sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
8×associate-/l*
6×associate-/r*
5×cbrt-undiv div-exp div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×sqrt-div associate-/l/
1×pow2 frac-times rem-sqrt-square asin-acos sqrt-undiv clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 177
Calls
4 calls:
16.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
11.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
1.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

series312.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (/ Om Omc) (/ Om Omc))
13.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1))))
168.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) 2) (/ t l) 1)))
95.0ms
(sqrt (fma (* (/ t l) 2) (/ t l) 1))

simplify1.4s

Counts
189 → 189
Iterations
IterNodes
done2001
32001
21844
1636
0269

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.6b

localize61.0ms

Local error

Found 4 expressions with local error:

7.6b
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (cbrt (fma (* (/ t l) 2) (/ t l) 1)) (cbrt (fma (* (/ t l) 2) (/ t l) 1)))) (cbrt (fma (* (/ t l) 2) (/ t l) 1))))
14.3b
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
14.3b
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
14.3b
(cbrt (fma (* (/ t l) 2) (/ t l) 1))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
58×sqrt-prod
53×add-sqr-sqrt
44×*-un-lft-identity
38×cbrt-prod add-cube-cbrt
12×difference-of-squares
7×div-inv
5×pow1 rem-sqrt-square
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 118
Calls
4 calls:
16.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (cbrt (fma (* (/ t l) 2) (/ t l) 1)) (cbrt (fma (* (/ t l) 2) (/ t l) 1)))) (cbrt (fma (* (/ t l) 2) (/ t l) 1))))
1.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
1.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
1.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))

series708.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (cbrt (fma (* (/ t l) 2) (/ t l) 1)) (cbrt (fma (* (/ t l) 2) (/ t l) 1)))) (cbrt (fma (* (/ t l) 2) (/ t l) 1))))
177.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
161.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
200.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))

simplify1.3s

Counts
130 → 130
Iterations
IterNodes
done2000
32000
2888
1433
0261

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.6b

localize89.0ms

Local error

Found 4 expressions with local error:

14.3b
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
14.3b
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
14.3b
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
14.3b
(cbrt (fma (* (/ t l) 2) (/ t l) 1))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 56
Calls
4 calls:
1.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
1.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
1.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
1.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))

series660.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
158.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
163.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))
171.0ms
(cbrt (fma (* (/ t l) 2) (/ t l) 1))

simplify1.0s

Counts
68 → 68
Iterations
IterNodes
done2001
52001
4995
3404
2176
182
045

prune817.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 4.6b

regimes483.0ms

Accuracy

98.6% (0.1b remaining)

Error of 5.8b against oracle of 5.7b and baseline of 10.1b

bsearch2.0ms

simplify5.0ms

Iterations
IterNodes
done28
128
024

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.0s3797×body160valid
1.9s8081×body80nan
862.0ms4203×body80valid