Details

Time bar (total: 1.4m)

sample190.0ms

Algorithm
intervals
Results
62.0ms118×body160valid
58.0ms253×body80nan
32.0ms138×body80valid

simplify453.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
453.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.3b

localize59.0ms

Local error

Found 4 expressions with local error:

10.7b
(sqrt (/ (- 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
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ t l) (/ t l))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
96×times-frac
72×*-un-lft-identity
69×add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
21×sqrt-prod
19×pow1
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
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 → 179
Calls
4 calls:
Slowest
25.0ms
(* (/ t l) (/ t l))
25.0ms
(* (/ Om Omc) (/ Om Omc))
15.0ms
(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)))))))

series248.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
171.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
33.0ms
(* (/ Om Omc) (/ Om Omc))
31.0ms
(* (/ t l) (/ t l))
12.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify10.4s

Counts
187 → 191
Calls
187 calls:
Slowest
419.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
410.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
321.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
297.0ms
(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))))))))
284.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))

prune2.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.2b

localize51.0ms

Local error

Found 4 expressions with local error:

10.7b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
0.5b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))
0.3b
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ l t) (/ l t))

rewrite60.0ms

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
26.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
16.0ms
(* (/ l t) (/ l t))
13.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

series207.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
33.0ms
(* (/ l t) (/ l t))
27.0ms
(* (/ Om Omc) (/ Om Omc))
14.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

simplify10.3s

Counts
192 → 196
Calls
192 calls:
Slowest
412.0ms
(* (/ (* (cbrt l) (cbrt l)) (* (cbrt t) (cbrt t))) (/ (* (cbrt l) (cbrt l)) (* (cbrt t) (cbrt t))))
346.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
336.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (- (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (* 1 1))))
308.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))
261.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (+ (* 2 (/ (pow t 2) (pow l 2))) 1))))

prune3.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.2b

localize64.0ms

Local error

Found 4 expressions with local error:

10.5b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.5b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b
(* (/ Om Omc) (/ Om Omc))
0.2b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))

rewrite63.0ms

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))))))
24.0ms
(* (/ Om Omc) (/ Om Omc))
7.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
2.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series347.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))
114.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
45.0ms
(* (/ Om Omc) (/ Om Omc))
20.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify26.9s

Counts
210 → 185
Calls
210 calls:
Slowest
517.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
483.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
413.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
366.0ms
(/ (* (* (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)))))))
315.0ms
(/ (sqrt (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))))) (* (cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (sqrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune2.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.4b

localize67.0ms

Local error

Found 4 expressions with local error:

16.3b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
16.3b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
16.3b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
9.9b
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))

rewrite129.0ms

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
37.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))
36.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
27.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
26.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
274.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
267.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))
260.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))))
257.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1)))

simplify16.7s

Counts
107 → 143
Calls
107 calls:
Slowest
483.0ms
(cbrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) 1))
366.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (- (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (* 1 1))))
327.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (- (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (* 1 1))))
320.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (- (* (/ 2 (* (/ l t) (/ l t))) (/ 2 (* (/ l t) (/ l t)))) (* 1 1))))
313.0ms
(* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ (/ 2 (* (/ l t) (/ l t))) 1))))

prune2.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.4b

regimes477.0ms

Accuracy

97.9% (0.1b remaining)

Error of 5.7b against oracle of 5.6b and baseline of 10.6b

bsearch8.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.8s7907×body80nan
1.7s3851×body160valid
1.3s4149×body80valid