Details

Time bar (total: 24.3s)

sample115.0ms

Algorithm
intervals
Results
33.0ms286×body80nan
32.0ms129×body160valid
16.0ms127×body80valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
01619
12919
25118
310818
427918
583518
6311618
done500018

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
0.3b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
9.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

rewrite193.0ms

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:
7.0ms
(pow (/ Om Omc) 2.0)
102.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
1.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
77.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

series928.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(pow (/ Om Omc) 2.0)
298.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))
23.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0))))
482.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (fma 2.0 (pow (/ t l) 2.0) 1.0)))

simplify2.3s

Counts
146 → 146
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02763461
15123355
210953196
331783184
done50013181

prune858.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- (* 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))))
0.3b
(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))))))
9.4b
(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)))))

rewrite100.0ms

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:
7.0ms
(pow (/ Om Omc) 2.0)
47.0ms
(/ (- (* 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))))
1.0ms
(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))))))
40.0ms
(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)))))

series1.9s

Counts
4 → 12
Calls
4 calls:
82.0ms
(pow (/ Om Omc) 2.0)
818.0ms
(/ (- (* 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))))
43.0ms
(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))))))
957.0ms
(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)))))

simplify1.3s

Counts
105 → 105
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02513208
15862764
220152499
done50012025

prune610.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
9.4b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
9.4b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
9.4b
(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
153×add-sqr-sqrt
86×times-frac
74×sqrt-prod
56×difference-of-squares
53×*-un-lft-identity
39×add-cube-cbrt
28×unpow-prod-down
14×sqr-pow
12×associate-/l*
9×pow1
7×distribute-lft-out--
6×add-exp-log associate-/r* add-cbrt-cube
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×pow1/2 sqrt-div
2×rem-sqrt-square associate-/l/
1×cbrt-undiv frac-times flip3-- frac-2neg div-sub associate-*r/ div-exp pow-prod-down associate-*l/ clear-num flip-- div-inv
Counts
4 → 153
Calls
4 calls:
116.0ms
(/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
2.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
2.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
83.0ms
(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
400.0ms
(/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
146.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
414.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
448.0ms
(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

simplify1.6s

Counts
165 → 165
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02105348
14154948
28944710
324014710
done50004692

prune866.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
9.4b
(sqrt (fma (pow (/ (/ -1 l) (/ -1 t)) 2.0) 2.0 1.0))
9.4b
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
9.4b
(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma (pow (/ (/ -1 l) (/ -1 t)) 2.0) 2.0 1.0))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
153×add-sqr-sqrt
86×times-frac
74×sqrt-prod
56×difference-of-squares
53×*-un-lft-identity
39×add-cube-cbrt
28×unpow-prod-down
14×sqr-pow
12×associate-/l*
9×pow1
7×distribute-lft-out--
6×add-exp-log associate-/r* add-cbrt-cube
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×pow1/2 sqrt-div
2×rem-sqrt-square associate-/l/
1×cbrt-undiv frac-times flip3-- frac-2neg div-sub associate-*r/ div-exp pow-prod-down associate-*l/ clear-num flip-- div-inv
Counts
4 → 153
Calls
4 calls:
125.0ms
(/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
3.0ms
(sqrt (fma (pow (/ (/ -1 l) (/ -1 t)) 2.0) 2.0 1.0))
3.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
86.0ms
(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma (pow (/ (/ -1 l) (/ -1 t)) 2.0) 2.0 1.0))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
361.0ms
(/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))
154.0ms
(sqrt (fma (pow (/ (/ -1 l) (/ -1 t)) 2.0) 2.0 1.0))
159.0ms
(sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0))
501.0ms
(sqrt (* (/ (+ (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma (pow (/ (/ -1 l) (/ -1 t)) 2.0) 2.0 1.0))) (/ (- (sqrt 1.0) (pow (/ Om Omc) (/ 2.0 2))) (sqrt (fma 2.0 (pow (/ t l) 2.0) 1.0)))))

simplify1.9s

Counts
165 → 165
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02285490
14485089
29684953
326034895
done50004690

prune957.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 10.1b

regimes626.0ms

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

sample3.7s

Algorithm
intervals
Results
1.4s3861×body160valid
1.1s8023×body80nan
546.0ms4139×body80valid