Details

Time bar (total: 24.2s)

sample211.0ms

Algorithm
intervals
Results
61.0ms139×body80valid
59.0ms117×body160valid
53.0ms219×body80nan

simplify786.0ms

Counts
1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.6b

localize44.0ms

Local error

Found 4 expressions with local error:

7.5b
(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))))))
0.5b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (* 2 (/ t l)) (/ t l))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite74.0ms

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
37.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (* 2 (/ t l)) (/ t l))))
24.0ms
(* (/ Om Omc) (/ Om Omc))
8.0ms
(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))))))

series322.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (* 2 (/ t l)) (/ t l)))))
105.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (* 2 (/ t l)) (/ t l))))
40.0ms
(* (/ Om Omc) (/ Om Omc))
12.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* (* 2 (/ t l)) (/ t l))))))

simplify982.0ms

Counts
164 → 164

prune2.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.6b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

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
(* (/ Om Omc) (/ Om Omc))
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))))))

series277.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
97.0ms
(sqrt (+ 1 (* (* 2 (/ t l)) (/ t l))))
28.0ms
(* (/ Om Omc) (/ Om Omc))
11.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l))))))

simplify803.0ms

Counts
185 → 185

prune3.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.0b

localize53.0ms

Local error

Found 4 expressions with local error:

9.8b
(sqrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
9.8b
(sqrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
8.0b
(sqrt (+ 1 (* (* 2 (/ t l)) (/ t l))))
8.0b
(sqrt (+ 1 (* (* 2 (/ t l)) (/ t l))))

rewrite16.0ms

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))))

series503.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
193.0ms
(sqrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
150.0ms
(sqrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
87.0ms
(sqrt (+ 1 (* (* 2 (/ t l)) (/ t l))))
73.0ms
(sqrt (+ 1 (* (* 2 (/ t l)) (/ t l))))

simplify2.9s

Counts
88 → 88

prune1.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.0b

localize111.0ms

Local error

Found 4 expressions with local error:

10.0b
(cbrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
10.0b
(cbrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
10.0b
(cbrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
9.8b
(sqrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
19×sqrt-prod
18×cbrt-prod
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
10×sqrt-div
6×pow1 cbrt-div
4×sqrt-pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
3×pow1/3
2×rem-sqrt-square pow1/2
Counts
4 → 73
Calls
4 calls:
Slowest
10.0ms
(cbrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
6.0ms
(sqrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
4.0ms
(cbrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
4.0ms
(cbrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))

series698.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
197.0ms
(cbrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
174.0ms
(cbrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
166.0ms
(cbrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))
161.0ms
(sqrt (sqrt (+ 1 (* (* 2 (/ t l)) (/ t l)))))

simplify595.0ms

Counts
85 → 85

prune1.8s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.0b

regimes671.0ms

Accuracy

98.9% (0.1b remaining)

Error of 5.6b against oracle of 5.5b and baseline of 10.0b

bsearch8.0ms

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.9s8151×body80nan
1.6s3875×body160valid
1.2s4125×body80valid