Details

Time bar (total: 14.4s)

sample97.0ms

Algorithm
intervals
Results
34.0ms273×body80nan
23.0ms107×body160valid
17.0ms149×body80valid

simplify123.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
14910
210110
327910
4102910
5438410
6500210

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.5b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
65×times-frac
51×*-un-lft-identity
37×add-cube-cbrt
30×sqrt-prod
28×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×associate-/r/ add-log-exp
3×pow-unpow associate-/r* div-inv
2×rem-sqrt-square flip3-+ div-exp pow-exp flip-+ 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 → 130
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
40.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
32.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series609.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ t l) 2.0)
211.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
316.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06481882
120471787
250011774

prune559.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.6b
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.6b
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.8b
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite320.0ms

Algorithm
rewrite-expression-head
Rules
215×add-sqr-sqrt
151×unpow-prod-down
131×times-frac
120×difference-of-squares
90×cube-prod
67×sqr-pow
61×sqrt-prod
49×associate-/l*
46×*-un-lft-identity
16×add-cube-cbrt associate-/r/
15×distribute-lft-out--
12×add-exp-log flip3-+ flip-+
9×add-cbrt-cube
8×frac-times
6×pow1
4×associate-*r/ associate-*l/ add-log-exp
3×difference-cubes pow-unpow div-exp div-inv
2×cbrt-undiv pow-exp 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
Counts
4 → 232
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
169.0ms
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
0.0ms
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
129.0ms
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ t l) 2.0)
714.0ms
(/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
45.0ms
(asin (sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
897.0ms
(sqrt (/ (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3)) (* (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify158.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011455722
149865485
250015485

prune963.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.5b
(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.6b
(asin (* (sqrt (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)))) (sqrt (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.8b
(sqrt (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite320.0ms

Algorithm
rewrite-expression-head
Rules
599×add-sqr-sqrt
506×sqrt-prod
379×times-frac
335×unpow-prod-down
280×difference-of-squares
210×cube-prod
202×*-un-lft-identity
155×sqr-pow
132×add-cube-cbrt
52×associate-/l*
35×distribute-lft-out--
9×add-exp-log
7×difference-cubes
6×pow1 add-cbrt-cube
4×associate-/r/ add-log-exp
3×rem-sqrt-square pow-unpow sqrt-div associate-/r* div-inv
2×flip3-+ div-exp pow-exp flip-+ associate-/l/
1×cbrt-undiv pow-to-exp asin-acos flip3-- pow-pow frac-2neg sqrt-pow1 pow1/2 clear-num flip--
Counts
4 → 438
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
153.0ms
(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.0ms
(asin (* (sqrt (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)))) (sqrt (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
121.0ms
(sqrt (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series700.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ t l) 2.0)
256.0ms
(/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
42.0ms
(asin (* (sqrt (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ (* (pow (/ Om Omc) 2.0) (+ (pow (/ Om Omc) 2.0) 1.0)) (* 1.0 1.0)))) (sqrt (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
339.0ms
(sqrt (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify168.0ms

Algorithm
egg-herbie
Counts
450 → 450
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
0117910374
1367310175
2500110132

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.1b

localize31.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
31.4b
(cbrt (pow (/ t l) 2.0))
31.4b
(cbrt (pow (/ t l) 2.0))
31.4b
(cbrt (pow (/ t l) 2.0))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
310×sqrt-prod
290×add-sqr-sqrt
209×times-frac
177×unpow-prod-down
120×difference-of-squares
117×*-un-lft-identity
90×cube-prod
87×add-cube-cbrt
69×sqr-pow
51×cbrt-prod
15×distribute-lft-out--
5×pow1
4×add-exp-log add-cbrt-cube div-inv add-log-exp
3×difference-cubes rem-sqrt-square pow1/3
2×associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 250
Calls
4 calls:
115.0ms
(sqrt (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
3.0ms
(cbrt (pow (/ t l) 2.0))
7.0ms
(cbrt (pow (/ t l) 2.0))
4.0ms
(cbrt (pow (/ t l) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
336.0ms
(sqrt (/ (sqrt (- (pow 1.0 3) (pow (pow (/ Om Omc) 2.0) 3))) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
271.0ms
(cbrt (pow (/ t l) 2.0))
268.0ms
(cbrt (pow (/ t l) 2.0))
269.0ms
(cbrt (pow (/ t l) 2.0))

simplify121.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
09308571
121318457
250018346

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.1b

regimes682.0ms

Accuracy

0% (0.1b remaining)

Error of 10.0b against oracle of 9.9b and baseline of 10.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03330
13330

end0.0ms

sample2.7s

Algorithm
intervals
Results
886.0ms8082×body80nan
852.0ms3798×body160valid
473.0ms4202×body80valid