Details

Time bar (total: 3.4m)

sample143.0ms

Algorithm
intervals
Results
44.0ms275×body80nan
39.0ms113×body160valid
33.0ms143×body80valid

simplify470.0ms

Calls
1 calls:
Slowest
470.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.7b

localize31.0ms

Local error

Found 4 expressions with local error:

8.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.5b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.3b
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ t l) (/ t l))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
384×add-sqr-sqrt
223×*-un-lft-identity
198×times-frac
169×add-cube-cbrt
162×frac-times
145×associate-/l*
123×associate-/r*
73×sqrt-prod
72×difference-of-squares
43×clear-num
42×swap-sqr
41×frac-2neg
40×unswap-sqr
31×sqrt-div
30×associate-*l*
28×add-cbrt-cube add-exp-log
26×associate-*r*
19×pow1
18×associate-*l/ associate-*r/
10×*-commutative
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod distribute-lft-out--
4×expm1-log1p-u un-div-inv insert-posit16 log1p-expm1-u add-log-exp
2×pow2 rem-sqrt-square pow-plus pow-prod-down pow-sqr pow-prod-up associate-/l/
1×asin-acos sqrt-pow1 flip3-- pow1/2 flip--
Calls
4 calls:
Slowest
113.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
22.0ms
(* (/ Om Omc) (/ Om Omc))
18.0ms
(* (/ t l) (/ t l))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

series254.0ms

Calls
4 calls:
Slowest
173.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
37.0ms
(* (/ Om Omc) (/ Om Omc))
34.0ms
(* (/ t l) (/ t l))
10.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify29.8s

Calls
623 calls:
Slowest
549.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) 1))
517.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
441.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
420.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
415.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))

prune7.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.6b

localize26.0ms

Local error

Found 4 expressions with local error:

8.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (/ (/ t l) (/ l t)) 2 1)))
0.5b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (/ (/ t l) (/ l t)) 2 1))))
0.3b
(* (/ Om Omc) (/ Om Omc))
0.2b
(/ (/ t l) (/ l t))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
579×times-frac
504×add-sqr-sqrt
354×*-un-lft-identity
301×add-cube-cbrt
103×associate-/l*
82×associate-/r*
81×frac-times
73×sqrt-prod
72×difference-of-squares
36×unswap-sqr
34×div-inv
31×sqrt-div
29×swap-sqr
28×add-cbrt-cube add-exp-log
25×clear-num
24×frac-2neg
17×associate-*l*
13×associate-*r*
12×pow1 cbrt-undiv div-exp
11×associate-/l/
9×associate-*l/ associate-*r/ associate-/r/ *-commutative
8×distribute-lft-out--
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square un-div-inv
1×pow2 asin-acos sqrt-pow1 pow-plus flip3-- pow1/2 pow-prod-down pow-sqr pow-prod-up flip--
Calls
4 calls:
Slowest
144.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (/ (/ t l) (/ l t)) 2 1)))
18.0ms
(* (/ Om Omc) (/ Om Omc))
13.0ms
(/ (/ t l) (/ l t))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (/ (/ t l) (/ l t)) 2 1))))

series282.0ms

Calls
4 calls:
Slowest
205.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (/ (/ t l) (/ l t)) 2 1)))
31.0ms
(* (/ Om Omc) (/ Om Omc))
31.0ms
(/ (/ t l) (/ l t))
15.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (/ (/ t l) (/ l t)) 2 1))))

simplify54.2s

Calls
754 calls:
Slowest
945.0ms
(/ (* (* (/ t l) (/ t l)) (/ t l)) (* (* (/ l t) (/ l t)) (/ l t)))
701.0ms
(/ (/ (* (cbrt t) (cbrt t)) 1) (/ (* (cbrt l) (cbrt l)) 1))
564.0ms
(/ (/ (* (cbrt t) (cbrt t)) 1) (/ (* (cbrt l) (cbrt l)) (* (cbrt t) (cbrt t))))
549.0ms
(/ (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (sqrt l) 1))
529.0ms
(/ (/ 1 (* (cbrt l) (cbrt l))) (/ 1 (* (cbrt t) (cbrt t))))

prune8.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.6b

localize13.0ms

Local error

Found 4 expressions with local error:

8.0b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
0.5b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
0.3b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
0.3b
(* (/ Om Omc) (/ Om Omc))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
483×add-sqr-sqrt
280×times-frac
245×sqrt-prod
233×*-un-lft-identity
141×add-cube-cbrt
126×difference-of-squares
87×associate-/l*
81×frac-times
66×associate-/r*
60×unswap-sqr
41×swap-sqr
22×clear-num
21×frac-2neg
20×associate-*l*
18×add-cbrt-cube add-exp-log
15×*-commutative
14×distribute-lft-out--
13×associate-*r*
12×pow1
9×associate-*l/ associate-*r/
5×cbrt-undiv div-exp div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×sqrt-div un-div-inv associate-/l/
1×pow2 rem-sqrt-square asin-acos sqrt-undiv sqrt-pow1 pow-plus flip3-- pow1/2 pow-prod-down pow-sqr pow-prod-up flip--
Calls
4 calls:
Slowest
116.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
34.0ms
(* (/ Om Omc) (/ Om Omc))
2.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

series292.0ms

Calls
4 calls:
Slowest
158.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
86.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
30.0ms
(* (/ Om Omc) (/ Om Omc))
17.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

simplify1.2m

Calls
617 calls:
Slowest
671.0ms
(/ (sqrt (+ 1 (* (/ (sqrt Om) (sqrt Omc)) (/ (sqrt Om) (sqrt Omc))))) (* (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
597.0ms
(/ (sqrt (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
485.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
459.0ms
(/ (* (* (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))))
442.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))

prune6.7s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.3b

localize29.0ms

Local error

Found 4 expressions with local error:

8.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ (/ t l) (cbrt l)) (/ t (* (cbrt l) (cbrt l)))) 2 1)))
0.6b
(cbrt l)
0.6b
(cbrt l)
0.6b
(cbrt l)

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
227×add-sqr-sqrt
118×times-frac
88×*-un-lft-identity
73×sqrt-prod
72×difference-of-squares
36×add-cube-cbrt
32×unswap-sqr
31×sqrt-div
23×associate-/l*
16×swap-sqr
9×cbrt-prod
8×*-commutative distribute-lft-out--
5×pow1
4×expm1-log1p-u add-cbrt-cube associate-*l* add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* pow1/3
2×rem-sqrt-square associate-/l/
1×clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 div-inv flip--
Calls
4 calls:
Slowest
130.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ (/ t l) (cbrt l)) (/ t (* (cbrt l) (cbrt l)))) 2 1)))
1.0ms
(cbrt l)
1.0ms
(cbrt l)
1.0ms
(cbrt l)

series1.2s

Calls
4 calls:
Slowest
331.0ms
(cbrt l)
296.0ms
(cbrt l)
289.0ms
(cbrt l)
261.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ (/ t l) (cbrt l)) (/ t (* (cbrt l) (cbrt l)))) 2 1)))

simplify17.1s

Calls
128 calls:
Slowest
571.0ms
(sqrt (/ (+ 1 (/ Om Omc)) (* (cbrt (fma (* (/ (/ t l) (cbrt l)) (/ t (* (cbrt l) (cbrt l)))) 2 1)) (cbrt (fma (* (/ (/ t l) (cbrt l)) (/ t (* (cbrt l) (cbrt l)))) 2 1)))))
422.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
359.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ (/ t l) (cbrt l)) (/ t (* (cbrt l) (cbrt l)))) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ (/ t l) (cbrt l)) (/ t (* (cbrt l) (cbrt l)))) 2 1)))))
356.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (* (cbrt (fma (* (/ (/ t l) (cbrt l)) (/ t (* (cbrt l) (cbrt l)))) 2 1)) (cbrt (fma (* (/ (/ t l) (cbrt l)) (/ t (* (cbrt l) (cbrt l)))) 2 1)))))
309.0ms
(sqrt (/ (+ 1 (* (sqrt (/ Om Omc)) (/ (sqrt Om) (sqrt Omc)))) (sqrt (fma (* (/ (/ t l) (cbrt l)) (/ t (* (cbrt l) (cbrt l)))) 2 1))))

prune3.2s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 5.3b

regimes715.0ms

Accuracy

98.5% (0.1b remaining)

Error of 5.8b against oracle of 5.7b and baseline of 10.3b

bsearch7.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.2s7841×body80nan
1.7s3817×body160valid
1.0s4183×body80valid