Details

Time bar (total: 9.6s)

sample61.0ms

Algorithm
intervals
Results
15.0ms263×body80nan
15.0ms124×body160valid
8.0ms132×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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ Om Omc) 2.0)
0.3b
(/ (- 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))))))
8.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite78.0ms

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:
3.0ms
(pow (/ Om Omc) 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))))))
29.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series618.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(pow (/ Om Omc) 2.0)
213.0ms
(/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
17.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
324.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
06341882
120171787
250011774

prune559.0ms

Filtered
142 candidates to 114 candidates (80.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(asin (sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
8.7b
(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
8.7b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
8.7b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
8×add-sqr-sqrt
7×sqrt-div sqrt-prod
6×add-cube-cbrt *-un-lft-identity
4×add-exp-log sqrt-pow1 add-cbrt-cube add-log-exp
3×pow1/2
2×rem-sqrt-square flip3-+ flip-+
1×frac-times asin-acos associate-*r/ pow-prod-down associate-*l/
Counts
4 → 52
Calls
4 calls:
0.0ms
(asin (sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
23.0ms
(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
3.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series768.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(asin (sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))))
387.0ms
(sqrt (* (/ 1 (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))) (/ (- 1.0 (pow (/ Om Omc) 2.0)) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
182.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
180.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify103.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0265790
1811728
23959726
35002726

prune310.0ms

Filtered
64 candidates to 54 candidates (84.4%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.7b

localize18.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.5b
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
8.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
8.7b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
190×sqrt-prod
164×add-sqr-sqrt
112×times-frac
78×*-un-lft-identity
54×add-cube-cbrt
48×difference-of-squares
24×unpow-prod-down
12×distribute-lft-out-- sqr-pow
10×pow1 rem-sqrt-square sqrt-pow1
8×associate-/r/
6×pow1/2 sqrt-div
4×add-exp-log flip3-+ add-cbrt-cube flip-+ div-inv add-log-exp
Counts
4 → 180
Calls
4 calls:
31.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
33.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
28.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
31.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

series1.4s

Counts
4 → 12
Calls
4 calls:
353.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
352.0ms
(sqrt (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
329.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))
332.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify112.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
04143314
19113236
233593216
350023184

prune1.0s

Filtered
192 candidates to 154 candidates (80.2%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.7b

localize32.0ms

Local error

Found 4 expressions with local error:

10.7b
(sqrt (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
15.7b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.7b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
15.7b
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
13×sqrt-prod
9×cbrt-prod add-sqr-sqrt flip3-+ flip-+
8×add-cube-cbrt *-un-lft-identity associate-/r/
5×pow1
4×add-exp-log frac-times add-cbrt-cube add-log-exp
3×pow1/3
2×rem-sqrt-square times-frac associate-*r/ associate-*l/
1×sqrt-pow1 pow1/2 sqrt-div div-inv
Counts
4 → 64
Calls
4 calls:
38.0ms
(sqrt (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
1.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
2.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
348.0ms
(sqrt (/ (* (cbrt (- 1.0 (pow (/ Om Omc) 2.0))) (cbrt (- 1.0 (pow (/ Om Omc) 2.0)))) (* (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))) (cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
253.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
252.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))
253.0ms
(cbrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify83.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
03101212
17821115
228781090
350011086

prune568.0ms

Filtered
76 candidates to 68 candidates (89.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 9.7b

regimes648.0ms

Accuracy

0% (0.1b remaining)

Error of 10.6b against oracle of 10.6b and baseline of 10.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample1.7s

Algorithm
intervals
Results
492.0ms8082×body80nan
458.0ms3856×body160valid
250.0ms4144×body80valid