Details

Time bar (total: 24.4s)

sample158.0ms

Algorithm
intervals
Results
52.0ms242×body80nan
46.0ms118×body160valid
25.0ms138×body80valid

simplify1.7s

Counts
1 → 1

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize58.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
0.3b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
0.2b
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ t l) (/ t l))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
101×add-sqr-sqrt times-frac
84×*-un-lft-identity
70×add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l* sqrt-prod
19×pow1
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod difference-of-squares unswap-sqr
5×distribute-lft-out
4×insert-posit16 add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 184
Calls
4 calls:
Slowest
90.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
26.0ms
(* (/ t l) (/ t l))
26.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

series258.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
39.0ms
(* (/ t l) (/ t l))
27.0ms
(* (/ Om Omc) (/ Om Omc))
11.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

simplify1.2s

Counts
196 → 196

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.9b

localize38.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
2.0b
(log (exp (* (/ Om Omc) (/ Om Omc))))
0.3b
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
72×add-sqr-sqrt
69×times-frac
45×add-cube-cbrt
34×sqrt-prod
17×pow1
16×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
8×distribute-lft-out-- difference-of-squares
7×log-pow distribute-lft-out
5×div-inv add-log-exp
4×cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 unswap-sqr
3×log-prod
2×rem-sqrt-square associate-/r/
1×pow2 frac-times asin-acos exp-prod sqrt-pow1 flip3-+ pow-plus exp-to-pow pow1/2 sqrt-div rem-log-exp pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 139
Calls
4 calls:
Slowest
46.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
12.0ms
(* (/ Om Omc) (/ Om Omc))
3.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
1.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

series267.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l))))))
51.0ms
(* (/ Om Omc) (/ Om Omc))
50.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
22.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (+ 1 (+ (* (/ t l) (/ t l)) (* (/ t l) (/ t l)))))))

simplify997.0ms

Counts
151 → 151

prune2.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.9b

localize65.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))
0.9b
(* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))
0.6b
(cbrt t)
0.6b
(cbrt t)

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
39×times-frac
36×add-sqr-sqrt add-exp-log
29×add-cube-cbrt
26×sqrt-prod
22×add-cbrt-cube associate-*r*
18×prod-exp cbrt-unprod
15×cbrt-prod
14×pow1
8×difference-of-squares
6×cbrt-undiv div-exp pow-prod-down
5×distribute-lft-out
4×insert-posit16 add-log-exp
3×associate-*l/ associate-*r/
2×rem-sqrt-square pow1/3 associate-/r/ div-inv
1×frac-times sqrt-pow1 flip3-+ pow1/2 sqrt-div associate-*l* *-commutative flip-+
Counts
4 → 117
Calls
4 calls:
Slowest
100.0ms
(* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))
68.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))
1.0ms
(cbrt t)
1.0ms
(cbrt t)

series713.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
227.0ms
(cbrt t)
221.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))
217.0ms
(cbrt t)
48.0ms
(* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))

simplify918.0ms

Counts
129 → 129

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.9b

localize105.0ms

Local error

Found 4 expressions with local error:

16.5b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))
16.5b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))
16.5b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))
11.5b
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
78×cbrt-prod
76×*-un-lft-identity
60×times-frac
46×add-sqr-sqrt
34×add-cube-cbrt
24×difference-of-squares
15×distribute-lft-out
12×pow1
9×sqrt-pow1 pow1/3
7×cbrt-div
6×associate-/r/
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×flip3-+ sqrt-div flip-+ div-inv
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times rem-sqrt-square pow-plus pow1/2 associate-*l/ associate-*r/ sqrt-prod
Counts
4 → 131
Calls
4 calls:
Slowest
58.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))))
31.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))
28.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))
28.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
301.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))
271.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))
271.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))))
266.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (+ (* (/ t l) (/ t l)) (* (* (cbrt t) (* (/ t l) (cbrt t))) (/ (cbrt t) l))))))

simplify1.9s

Counts
143 → 143

prune2.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 10.9b

regimes425.0ms

Accuracy

0% (0.4b remaining)

Error of 10.6b against oracle of 10.2b and baseline of 10.6b

bsearch5.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s3808×body160valid
1.5s8039×body80nan
795.0ms4192×body80valid