Details

Time bar (total: 44.3s)

sample1.2s

Algorithm
intervals
Results
932.0ms761×body10240exit
129.0ms1016×body80nan
23.0ms126×body160valid
13.0ms130×body80valid

simplify125.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02910
15110
210710
329010
4105410
5444510
6500110

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.4b
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
7.8b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite89.0ms

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×expm1-log1p-u associate-/r/ log1p-expm1-u 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 → 138
Calls
4 calls:
4.0ms
(pow (/ t l) 2.0)
50.0ms
(/ (- 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))))))
30.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series633.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ t l) 2.0)
233.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
16.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
323.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify73.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06641948
121061846
250011828

prune632.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ t l) 2.0)
0.4b
(/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.7b
(asin (sqrt (* (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
7.8b
(sqrt (* (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
46×times-frac
40×*-un-lft-identity
32×cbrt-prod add-cube-cbrt
26×cbrt-div
21×unpow-prod-down
17×sqrt-div
16×frac-times difference-of-squares
13×flip3-- flip--
12×associate-*l/
11×pow1 associate-/l*
9×add-exp-log
5×associate-*r/ add-cbrt-cube sqr-pow
4×expm1-log1p-u log1p-expm1-u distribute-lft-out-- add-log-exp
3×pow-unpow sqrt-pow1 pow-prod-down associate-/r*
2×div-exp pow-exp associate-/r/ div-inv associate-/l/
1×cbrt-undiv pow-to-exp asin-acos pow-pow frac-2neg flip3-+ pow1/2 clear-num sqrt-prod flip-+
Counts
4 → 136
Calls
4 calls:
5.0ms
(pow (/ t l) 2.0)
38.0ms
(/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
0.0ms
(asin (sqrt (* (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
122.0ms
(sqrt (* (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

series872.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(pow (/ t l) 2.0)
475.0ms
(/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
18.0ms
(asin (sqrt (* (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
320.0ms
(sqrt (* (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))

simplify76.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
07932478
123662373
250032343

prune704.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (sqrt (* (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (* (pow (sqrt (/ t l)) 2.0) (pow (sqrt (/ t l)) 2.0))))))))
7.8b
(sqrt (* (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (* (pow (sqrt (/ t l)) 2.0) (pow (sqrt (/ t l)) 2.0)))))))
15.0b
(sqrt (/ t l))
15.0b
(sqrt (/ t l))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
27×sqrt-prod
24×add-sqr-sqrt cbrt-div
20×times-frac
19×sqrt-div
18×add-cube-cbrt *-un-lft-identity
16×frac-times
12×pow1 flip3-- associate-*l/ flip--
5×sqrt-pow1 associate-*r/
4×add-exp-log expm1-log1p-u rem-sqrt-square add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/2 pow-prod-down
2×div-inv
1×asin-acos
Counts
4 → 95
Calls
4 calls:
0.0ms
(asin (sqrt (* (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (* (pow (sqrt (/ t l)) 2.0) (pow (sqrt (/ t l)) 2.0))))))))
123.0ms
(sqrt (* (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (* (pow (sqrt (/ t l)) 2.0) (pow (sqrt (/ t l)) 2.0)))))))
2.0ms
(sqrt (/ t l))
3.0ms
(sqrt (/ t l))

series438.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(asin (sqrt (* (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (* (pow (sqrt (/ t l)) 2.0) (pow (sqrt (/ t l)) 2.0))))))))
326.0ms
(sqrt (* (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (/ (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (+ 1.0 (* 2.0 (* (pow (sqrt (/ t l)) 2.0) (pow (sqrt (/ t l)) 2.0)))))))
46.0ms
(sqrt (/ t l))
49.0ms
(sqrt (/ t l))

simplify49.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
04761715
112351604
250011592

prune566.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
2.0b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
13.3b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
13.3b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
82×add-sqr-sqrt
56×times-frac
54×sqrt-prod
41×*-un-lft-identity
31×cbrt-prod
29×add-cube-cbrt
24×difference-of-squares
12×unpow-prod-down
6×cbrt-div distribute-lft-out-- sqr-pow
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-+ flip-+
2×pow1/3 associate-/r/
1×asin-acos sqrt-pow1 pow1/2 sqrt-div div-inv
Counts
4 → 109
Calls
4 calls:
0.0ms
(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
32.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series872.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(asin (* (fabs (/ 1 (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))) (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
350.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
248.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
245.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify54.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
05582127
114022035
250022026

prune663.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.1b

regimes698.0ms

Accuracy

0% (0.2b remaining)

Error of 10.1b against oracle of 9.9b and baseline of 10.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02426
12426

end0.0ms

sample36.2s

Algorithm
intervals
Results
29.1s24096×body10240exit
3.9s31747×body80nan
725.0ms3859×body160valid
454.0ms4141×body80valid