Details

Time bar (total: 9.1s)

sample99.0ms

Algorithm
intervals
Results
31.0ms129×body160valid
31.0ms273×body80nan
15.0ms127×body80valid

simplify125.0ms

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: 11.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.8b
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
10.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×times-frac
38×*-un-lft-identity
32×add-cube-cbrt unpow-prod-down
30×sqrt-prod
12×difference-of-squares
10×add-exp-log
7×pow1
6×pow-unpow
5×sqr-pow
4×pow-exp add-cbrt-cube add-log-exp
3×div-inv distribute-lft-out--
2×pow-to-exp rem-sqrt-square pow-pow div-exp associate-/r/
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 106
Calls
4 calls:
3.0ms
(pow (/ t l) 2.0)
4.0ms
(pow (/ Om Omc) 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)))))

series451.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(pow (/ t l) 2.0)
63.0ms
(pow (/ Om Omc) 2.0)
17.0ms
(asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))))
308.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))

simplify54.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
06951235
120431164
250021152

prune445.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ t l) 2.0)
0.2b
(pow (/ Om Omc) 2.0)
0.8b
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
10.6b
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
26×unpow-prod-down
22×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac
10×add-exp-log
7×pow1
6×pow-unpow
4×pow-exp add-cbrt-cube add-log-exp
3×sqrt-prod
2×pow-to-exp pow-pow sqrt-div div-exp div-inv sqr-pow
1×rem-sqrt-square asin-acos sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 79
Calls
4 calls:
3.0ms
(pow (/ t l) 2.0)
3.0ms
(pow (/ Om Omc) 2.0)
0.0ms
(asin (fabs (/ (sqrt (- 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))))

series313.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(pow (/ t l) 2.0)
62.0ms
(pow (/ Om Omc) 2.0)
17.0ms
(asin (fabs (/ (sqrt (- 1.0 (pow (/ Om Omc) 2.0))) (sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))
177.0ms
(sqrt (+ 1.0 (* 2.0 (pow (/ t l) 2.0))))

simplify46.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0547658
11773608
25002608

prune386.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.3b

localize22.0ms

Local error

Found 4 expressions with local error:

10.4b
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
32.8b
(cbrt (pow (/ t l) 2.0))
32.8b
(cbrt (pow (/ t l) 2.0))
32.8b
(cbrt (pow (/ t l) 2.0))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
55×times-frac
51×cbrt-prod
46×*-un-lft-identity
45×unpow-prod-down
40×add-cube-cbrt
30×sqrt-prod
12×difference-of-squares
6×sqr-pow
5×pow1
4×add-exp-log add-cbrt-cube div-inv add-log-exp
3×pow1/3 distribute-lft-out--
2×rem-sqrt-square associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 117
Calls
4 calls:
27.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 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))
3.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
317.0ms
(sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (* (* (cbrt (pow (/ t l) 2.0)) (cbrt (pow (/ t l) 2.0))) (cbrt (pow (/ t l) 2.0)))))))
257.0ms
(cbrt (pow (/ t l) 2.0))
256.0ms
(cbrt (pow (/ t l) 2.0))
260.0ms
(cbrt (pow (/ t l) 2.0))

simplify121.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 3 (101.0ms)

IterNodesCost
05162189
112052120
248302084
350012075

prune630.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.3b

localize22.0ms

Local error

Found 4 expressions with local error:

32.8b
(cbrt (pow (/ t l) 2.0))
32.8b
(cbrt (pow (/ t l) 2.0))
32.8b
(cbrt (pow (/ t l) 2.0))
32.8b
(cbrt (pow (/ t l) 2.0))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
68×cbrt-prod
52×unpow-prod-down
36×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
4×pow1 add-exp-log pow1/3 add-cbrt-cube div-inv add-log-exp sqr-pow
Counts
4 → 100
Calls
4 calls:
3.0ms
(cbrt (pow (/ t l) 2.0))
6.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))
3.0ms
(cbrt (pow (/ t l) 2.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
264.0ms
(cbrt (pow (/ t l) 2.0))
260.0ms
(cbrt (pow (/ t l) 2.0))
260.0ms
(cbrt (pow (/ t l) 2.0))
263.0ms
(cbrt (pow (/ t l) 2.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
02371064
14891036
213031028
333351016
450011016

prune596.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.3b

regimes663.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample2.7s

Algorithm
intervals
Results
918.0ms8086×body80nan
882.0ms3915×body160valid
465.0ms4085×body80valid