Details

Time bar (total: 1.3m)

sample185.0ms

Algorithm
intervals
Results
77.0ms128×body160valid
50.0ms225×body80nan
31.0ms128×body80valid

simplify412.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
412.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize38.0ms

Local error

Found 4 expressions with local error:

10.9b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.2b
(* (/ t l) (/ t l))

rewrite72.0ms

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:
Slowest
29.0ms
(* (/ t l) (/ t l))
25.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
13.0ms
(sqrt (/ (- 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)))))))

series330.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
191.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
92.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
27.0ms
(* (/ t l) (/ t l))
21.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify16.3s

Counts
156 → 164
Calls
156 calls:
Slowest
771.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
415.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
360.0ms
(- 1 (* 2 (* (/ t l) (/ t l))))
301.0ms
(/ (* (* (- 1 (* (/ Om Omc) (/ Om Omc))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (* (+ 1 (* 2 (* (/ t l) (/ t l)))) (+ 1 (* 2 (* (/ t l) (/ t l))))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
300.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.1b

localize57.0ms

Local error

Found 4 expressions with local error:

11.1b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.8b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.2b
(* (/ t l) (/ t l))

rewrite71.0ms

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:
Slowest
25.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
25.0ms
(* (/ t l) (/ t l))
9.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
6.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series271.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
80.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
34.0ms
(* (/ t l) (/ t l))
11.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify26.0s

Counts
210 → 185
Calls
210 calls:
Slowest
483.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
444.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
433.0ms
(/ (* (* (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (* (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
420.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
361.0ms
(sqrt (- 1 (* 2 (* (/ t l) (/ t l)))))

prune2.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.2b

localize49.0ms

Local error

Found 4 expressions with local error:

11.1b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
11.1b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
5.2b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
5.2b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
12×sqrt-div
10×pow1 *-un-lft-identity sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
Counts
4 → 76
Calls
4 calls:
Slowest
4.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
4.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
3.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
3.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series907.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
478.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
197.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
153.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
79.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify7.1s

Counts
52 → 88
Calls
52 calls:
Slowest
545.0ms
(sqrt (sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l)))))))
503.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
451.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
444.0ms
(sqrt (sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l)))))))
235.0ms
(exp (* 1/4 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.2b

localize40.0ms

Local error

Found 4 expressions with local error:

10.9b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
10.9b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
5.4b
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
5.4b
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
48×sqrt-prod
38×add-sqr-sqrt
32×times-frac
30×*-un-lft-identity
24×add-cube-cbrt
12×difference-of-squares
8×pow1
6×rem-sqrt-square
4×sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log associate-/r/ insert-posit16 add-log-exp
2×flip3-+ sqrt-div flip-+ div-inv
Counts
4 → 96
Calls
4 calls:
Slowest
23.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
14.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
2.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
1.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

series426.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
161.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
52.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
49.0ms
(sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

simplify12.0s

Counts
72 → 108
Calls
72 calls:
Slowest
347.0ms
(sqrt (sqrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))))
325.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
324.0ms
(sqrt (* (cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))) (cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))))
308.0ms
(sqrt (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1)))))
296.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune2.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.2b

regimes698.0ms

Accuracy

98% (0.1b remaining)

Error of 6.0b against oracle of 5.9b and baseline of 10.6b

bsearch8.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.5s7949×body80nan
1.7s3830×body160valid
901.0ms4170×body80valid