Details

Time bar (total: 29.1s)

sample129.0ms

Algorithm
intervals
Results
48.0ms122×body160valid
37.0ms236×body80nan
20.0ms134×body80valid

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
63283
5883
4308
3120
257
130
016

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.7b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
8.4b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
21×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×prod-exp associate-/r/ cbrt-unprod insert-posit16 add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square flip3-+ flip-+ 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 → 152
Calls
4 calls:
17.0ms
(* (/ Om Omc) (/ Om Omc))
30.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
22.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (/ Om Omc) (/ Om Omc))
96.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
19.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
144.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify1.1s

Counts
164 → 164
Iterations
IterNodes
22110
1708
0267

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ Om Omc) (/ Om Omc))
0.4b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.7b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
8.7b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite62.0ms

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* sqrt-div
5×cbrt-undiv div-exp div-inv
4×prod-exp cbrt-unprod insert-posit16 add-log-exp unswap-sqr
2×flip3-+ associate-/r/ flip-+ 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 → 173
Calls
4 calls:
18.0ms
(* (/ Om Omc) (/ Om Omc))
32.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
2.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
7.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series339.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (/ Om Omc) (/ Om Omc))
179.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
11.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
102.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify2.9s

Counts
185 → 185
Iterations
IterNodes
36232
21862
1677
0281

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.2b

localize68.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (/ (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fabs (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (sqrt (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
1.7b
(sqrt (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
16.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
16.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-div sqrt-prod
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×flip3-+ pow1/3 flip-+
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×asin-acos pow1/2
Counts
4 → 58
Calls
4 calls:
1.0ms
(asin (/ (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fabs (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (sqrt (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
4.0ms
(sqrt (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
2.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
2.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series636.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(asin (/ (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (fabs (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))) (sqrt (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
183.0ms
(sqrt (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
202.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
216.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify6.7s

Counts
70 → 70
Iterations
IterNodes
48133
31880
2598
1249
0123

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.2b

localize83.0ms

Local error

Found 4 expressions with local error:

16.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
16.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
16.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
16.4b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt cbrt-div *-un-lft-identity add-cube-cbrt
4×pow1 flip3-+ add-cbrt-cube pow1/3 add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 56
Calls
4 calls:
2.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
2.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
2.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
2.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series717.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
183.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
172.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
177.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify2.6s

Counts
68 → 68
Iterations
IterNodes
44384
31291
2363
1133
059

prune1.4s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.2b

regimes552.0ms

Accuracy

98.9% (0.1b remaining)

Error of 5.6b against oracle of 5.6b and baseline of 10.4b

bsearch2.0ms

simplify5.0ms

Iterations
IterNodes
228
128
025

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.7s7849×body80nan
1.7s3836×body160valid
1.1s4164×body80valid