Details

Time bar (total: 23.6s)

sample130.0ms

Algorithm
intervals
Results
35.0ms260×body80nan
27.0ms122×body160valid
15.0ms134×body80valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
01619
12919
25118
310818
427918
583518
6311618
done500018

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
0.6b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
11.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
65×times-frac
51×*-un-lft-identity
37×add-cube-cbrt
28×sqrt-prod difference-of-squares
27×unpow-prod-down
9×add-exp-log
8×associate-/l* sqr-pow
7×distribute-lft-out--
6×pow1 add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square div-exp pow-exp associate-/l/
1×cbrt-undiv pow-to-exp asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub clear-num flip--
Counts
4 → 134
Calls
4 calls:
8.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
95.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
49.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series804.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(pow (/ Om Omc) 2.0)
13.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
277.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
433.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify2.0s

Counts
146 → 146
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02763461
15123355
210953196
331763184
done50003181

prune900.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))))
0.6b
(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))
11.0b
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0)))))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt times-frac
16×add-cube-cbrt *-un-lft-identity
13×unpow-prod-down
12×add-exp-log
10×sqrt-prod
9×add-cbrt-cube
6×pow1
4×expm1-log1p-u associate-*r/ associate-/r/ log1p-expm1-u associate-/l* add-log-exp
3×pow-unpow div-exp div-inv difference-of-squares
2×cbrt-undiv flip3-+ pow-exp flip-+ associate-/l/
1×pow-to-exp rem-sqrt-square asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub prod-exp clear-num associate-/r* flip-- cbrt-unprod sqr-pow
Counts
4 → 93
Calls
4 calls:
13.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))))
63.0ms
(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))
60.0ms
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0)))))

series2.1s

Counts
4 → 12
Calls
4 calls:
77.0ms
(pow (/ Om Omc) 2.0)
27.0ms
(asin (sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))))
861.0ms
(/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))
1.2s
(sqrt (/ (- (* 1.0 1.0) (* (pow (/ Om Omc) 2.0) (pow (/ Om Omc) 2.0))) (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0)))))

simplify1.2s

Counts
105 → 105
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02513208
15862764
220152499
done50002025

prune714.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
0.6b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
11.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
65×times-frac
51×*-un-lft-identity
37×add-cube-cbrt
28×sqrt-prod difference-of-squares
27×unpow-prod-down
9×add-exp-log
8×associate-/l* sqr-pow
7×distribute-lft-out--
6×pow1 add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square div-exp pow-exp associate-/l/
1×cbrt-undiv pow-to-exp asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub clear-num flip--
Counts
4 → 134
Calls
4 calls:
12.0ms
(pow (/ Om Omc) 2.0)
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
119.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
46.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series789.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(pow (/ Om Omc) 2.0)
23.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
290.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
391.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify1.9s

Counts
146 → 146
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02763461
15123355
210953196
331763184
done50003181

prune929.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) (* 2 2.0))
0.3b
(asin (/ (sqrt (- (* 1.0 1.0) (pow (/ Om Omc) (* 2 2.0)))) (sqrt (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))))
0.6b
(/ (sqrt (- (* 1.0 1.0) (pow (/ Om Omc) (* 2 2.0)))) (sqrt (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0)))))
11.3b
(sqrt (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
52×add-sqr-sqrt
47×sqrt-prod
32×add-cube-cbrt *-un-lft-identity
23×unpow-prod-down
20×difference-of-squares
10×associate-/l*
9×add-exp-log
8×pow1
6×sqrt-div add-cbrt-cube sqr-pow
4×expm1-log1p-u associate-*r/ associate-/r* log1p-expm1-u add-log-exp
2×sqrt-pow1 flip3-+ div-exp pow-exp associate-/r/ flip-+ div-inv associate-/l/
1×cbrt-undiv pow-to-exp asin-acos pow-unpow sqrt-undiv flip3-- pow-pow frac-2neg pow1/2 pow-prod-down clear-num flip--
Counts
4 → 126
Calls
4 calls:
7.0ms
(pow (/ Om Omc) (* 2 2.0))
1.0ms
(asin (/ (sqrt (- (* 1.0 1.0) (pow (/ Om Omc) (* 2 2.0)))) (sqrt (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))))
84.0ms
(/ (sqrt (- (* 1.0 1.0) (pow (/ Om Omc) (* 2 2.0)))) (sqrt (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0)))))
25.0ms
(sqrt (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
89.0ms
(pow (/ Om Omc) (* 2 2.0))
20.0ms
(asin (/ (sqrt (- (* 1.0 1.0) (pow (/ Om Omc) (* 2 2.0)))) (sqrt (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))))
525.0ms
(/ (sqrt (- (* 1.0 1.0) (pow (/ Om Omc) (* 2 2.0)))) (sqrt (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0)))))
383.0ms
(sqrt (* (fma 2.0 (pow (/ t l) 2.0) 1.0) (+ 1.0 (pow (/ Om Omc) 2.0))))

simplify2.6s

Counts
138 → 138
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
03264828
16164635
214364394
342804354
done50004354

prune1.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.1b

regimes502.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01934
12134
done2134

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.1s8238×body80nan
693.0ms3815×body160valid
384.0ms4185×body80valid