Details

Time bar (total: 1.2m)

sample132.0ms

Algorithm
intervals
Results
34.0ms123×body160valid
33.0ms256×body80nan
17.0ms133×body80valid

simplify681.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
681.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize32.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.8b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.5b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b
(* (/ t l) (/ t l))

rewrite67.0ms

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
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
24.0ms
(* (/ t l) (/ t l))
7.0ms
(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)))))))

series291.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
86.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))
35.0ms
(* (/ t l) (/ t l))
15.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify15.9s

Counts
156 → 164
Calls
156 calls:
Slowest
460.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
451.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
309.0ms
(/ (* (* (- 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))))))
307.0ms
(/ (* (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)))))))
301.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))

prune2.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.2b

localize65.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.5b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.4b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.3b
(* (/ t l) (/ t l))

rewrite33.0ms

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
13.0ms
(* (/ t l) (/ t l))
12.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
3.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
194.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
112.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
49.0ms
(* (/ t l) (/ t l))
21.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify26.3s

Counts
210 → 185
Calls
210 calls:
Slowest
567.0ms
(/ (sqrt (- (sqrt 1) (/ Om Omc))) (cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
481.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
475.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
435.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
419.0ms
(/ (* (* (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)))))))

prune2.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

localize44.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
9.4b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
6.2b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
6.2b
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite29.0ms

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
7.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
7.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
7.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
6.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series582.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
205.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
189.0ms
(sqrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
95.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
93.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify7.2s

Counts
52 → 88
Calls
52 calls:
Slowest
534.0ms
(sqrt (sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l)))))))
432.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
425.0ms
(sqrt (sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l)))))))
421.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
206.0ms
(sqrt (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

prune1.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.7b

localize68.0ms

Local error

Found 4 expressions with local error:

9.4b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
9.4b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
9.4b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
6.4b
(cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×sqrt-div
7×pow1
6×cbrt-prod
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 65
Calls
4 calls:
Slowest
7.0ms
(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)))))
2.0ms
(cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

series468.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
210.0ms
(cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
102.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
80.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
77.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify5.1s

Counts
41 → 77
Calls
41 calls:
Slowest
463.0ms
(cbrt (sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l)))))))
423.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
385.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
376.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
216.0ms
(exp (* 1/6 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))

prune1.3s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 5.7b

regimes530.0ms

Accuracy

98.1% (0.1b remaining)

Error of 5.5b against oracle of 5.4b and baseline of 10.3b

bsearch7.0ms

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.5s8166×body80nan
1.8s3800×body160valid
912.0ms4200×body80valid