Details

Time bar (total: 22.8s)

sample187.0ms

Algorithm
intervals
Results
49.0ms117×body160valid
42.0ms219×body80nan
28.0ms139×body80valid

simplify863.0ms

Counts
1 → 1

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.6b

localize57.0ms

Local error

Found 4 expressions with local error:

7.5b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.5b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.5b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite33.0ms

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:
Slowest
13.0ms
(* (/ Om Omc) (/ Om Omc))
12.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
5.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

series319.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
94.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
50.0ms
(* (/ Om Omc) (/ Om Omc))
9.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify917.0ms

Counts
168 → 168

prune2.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 8.6b

localize49.0ms

Local error

Found 4 expressions with local error:

8.0b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
0.5b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
0.2b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite38.0ms

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:
Slowest
22.0ms
(* (/ Om Omc) (/ Om Omc))
10.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
110.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
48.0ms
(* (/ Om Omc) (/ Om Omc))
12.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

simplify781.0ms

Counts
189 → 189

prune3.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.0b

localize50.0ms

Local error

Found 4 expressions with local error:

9.8b
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
9.8b
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
8.0b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
8.0b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
10×pow1 *-un-lft-identity sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 76
Calls
4 calls:
Slowest
7.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
2.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series478.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
169.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
162.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
82.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
65.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify750.0ms

Counts
88 → 88

prune1.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.0b

localize72.0ms

Local error

Found 4 expressions with local error:

10.0b
(cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
10.0b
(cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
9.8b
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
8.0b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
19×sqrt-prod
14×add-sqr-sqrt
12×cbrt-prod
11×*-un-lft-identity add-cube-cbrt
7×pow1
5×sqrt-pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square pow1/2
2×pow1/3
Counts
4 → 72
Calls
4 calls:
Slowest
3.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
2.0ms
(cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
2.0ms
(cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
2.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series580.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
171.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
169.0ms
(cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
149.0ms
(cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
91.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify1.1s

Counts
84 → 84

prune2.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.0b

regimes690.0ms

Accuracy

98.9% (0.1b remaining)

Error of 5.6b against oracle of 5.5b and baseline of 10.0b

bsearch9.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.0s8151×body80nan
1.6s3875×body160valid
974.0ms4125×body80valid