Details

Time bar (total: 1.3m)

sample115.0ms

Algorithm
intervals
Results
38.0ms118×body160valid
35.0ms225×body80nan
23.0ms138×body80valid

simplify393.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
393.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize43.0ms

Local error

Found 4 expressions with local error:

10.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.2b
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ t l) (/ t l))
0.2b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

rewrite38.0ms

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*
19×pow1 sqrt-prod
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 185
Calls
4 calls:
Slowest
16.0ms
(* (/ t l) (/ t l))
12.0ms
(* (/ Om Omc) (/ Om Omc))
5.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

series269.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
161.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
48.0ms
(* (/ Om Omc) (/ Om Omc))
45.0ms
(* (/ t l) (/ t l))
15.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify10.2s

Counts
185 → 197
Calls
185 calls:
Slowest
459.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
442.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
277.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
276.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
272.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1))))

prune2.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.5b

localize32.0ms

Local error

Found 4 expressions with local error:

10.1b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
0.3b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
0.2b
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ t l) (/ t l))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
125×add-sqr-sqrt
100×*-un-lft-identity
93×add-cube-cbrt
65×sqrt-prod
30×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1
14×difference-of-squares
9×cbrt-undiv div-exp div-inv
8×prod-exp cbrt-unprod associate-/l* unswap-sqr
6×associate-/r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow2 frac-times pow-plus sqrt-div pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up associate-/l/
1×rem-sqrt-square sqrt-undiv clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 flip--
Counts
4 → 236
Calls
4 calls:
Slowest
24.0ms
(* (/ Om Omc) (/ Om Omc))
24.0ms
(* (/ t l) (/ t l))
10.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series357.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
186.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
99.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
37.0ms
(* (/ Om Omc) (/ Om Omc))
36.0ms
(* (/ t l) (/ t l))

simplify27.4s

Counts
281 → 248
Calls
281 calls:
Slowest
524.0ms
(/ (sqrt 1) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
497.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
441.0ms
(/ (* (* (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (* (sqrt (fma (* (/ t l) (/ t l)) 2 1)) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
423.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
415.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))

prune3.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

localize62.0ms

Local error

Found 4 expressions with local error:

10.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
10.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
10.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
8.1b
(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
57×sqrt-prod
50×add-sqr-sqrt
48×times-frac
41×*-un-lft-identity
32×add-cube-cbrt
18×difference-of-squares
7×pow1
6×rem-sqrt-square
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod sqrt-pow1 pow1/2 sqrt-div div-inv
1×pow1/3
Counts
4 → 116
Calls
4 calls:
Slowest
20.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
11.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
9.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

series556.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
145.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
141.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
104.0ms
(cbrt (asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

simplify12.4s

Counts
84 → 128
Calls
84 calls:
Slowest
365.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1)))) 1/3)
343.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1)))) 1/3)
334.0ms
(pow (asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1)))) 1/3)
289.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
285.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))

prune2.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

localize143.0ms

Local error

Found 4 expressions with local error:

16.2b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
16.2b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
16.2b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
10.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×*-un-lft-identity sqrt-prod
16×times-frac add-cube-cbrt
9×cbrt-prod
6×difference-of-squares
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
2×rem-sqrt-square
1×sqrt-pow1 pow1/2 sqrt-div div-inv
Counts
4 → 76
Calls
4 calls:
Slowest
5.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

series712.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
188.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
181.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
176.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
167.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify5.6s

Counts
44 → 88
Calls
44 calls:
Slowest
297.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
288.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
282.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
244.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
234.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

prune2.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

regimes556.0ms

Accuracy

79.6% (1.3b remaining)

Error of 6.5b against oracle of 5.2b and baseline of 11.5b

bsearch8.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.7s3723×body160valid
1.7s8009×body80nan
1.3s4277×body80valid