Details

Time bar (total: 33.5s)

sample91.0ms

Algorithm
intervals
Results
35.0ms465×body80nan
21.0ms299×body80valid

simplify115.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize21.0ms

Local error

Found 4 expressions with local error:

5.4b
(* n (pow (/ l Om) 2.0))
6.2b
(/ (* l l) Om)
10.9b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
24×add-sqr-sqrt
23×pow1
20×associate-*r/ associate-*r* add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
13×times-frac
12×pow-prod-down
11×prod-exp
10×flip3-- flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 associate-*l* associate--l+ add-log-exp unswap-sqr
3×div-exp associate-/r*
2×cbrt-undiv pow-exp *-commutative div-inv sqr-pow
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod associate-/l*
Counts
4 → 112
Calls
4 calls:
17.0ms
(* n (pow (/ l Om) 2.0))
4.0ms
(/ (* l l) Om)
48.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
34.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.3s

Counts
4 → 12
Calls
4 calls:
145.0ms
(* n (pow (/ l Om) 2.0))
25.0ms
(/ (* l l) Om)
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify127.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09641521
148051370
250021370

prune531.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.8b

localize27.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.4b
(* n (pow (/ l Om) 2.0))
10.9b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
35×add-exp-log
25×pow1 add-sqr-sqrt associate-*r*
22×associate-*r/
20×add-cbrt-cube
19×prod-exp
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
13×pow-prod-down
11×flip3-- flip--
10×times-frac cbrt-unprod
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×associate-*l*
4×sqrt-pow1 pow-exp associate--l+ add-log-exp unswap-sqr
3×*-commutative
2×pow-to-exp div-exp sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 119
Calls
4 calls:
23.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
17.0ms
(* n (pow (/ l Om) 2.0))
49.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
31.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.8s

Counts
4 → 12
Calls
4 calls:
388.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
145.0ms
(* n (pow (/ l Om) 2.0))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09871664
150011508

prune546.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.1b

localize22.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
5.4b
(* n (pow (/ l Om) 2.0))
5.7b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
20.8b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log
34×associate-*r/
31×pow1
24×add-sqr-sqrt
23×associate-*r* add-cbrt-cube
21×prod-exp
18×distribute-rgt-in distribute-lft-in
17×pow-prod-down
16×*-un-lft-identity
15×unpow-prod-down
14×add-cube-cbrt
12×cbrt-unprod
11×flip3-- flip--
10×sub-neg times-frac
8×associate--l+ frac-sub
6×sqrt-div
5×sqrt-pow1 associate-*l*
4×pow-exp add-log-exp unswap-sqr
3×*-commutative
2×pow-to-exp div-exp sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 129
Calls
4 calls:
27.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
15.0ms
(* n (pow (/ l Om) 2.0))
56.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
39.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series7.0s

Counts
4 → 12
Calls
4 calls:
366.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
148.0ms
(* n (pow (/ l Om) 2.0))
1.3s
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.2s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify47.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010521826
150011638

prune515.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.6b

localize24.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
5.6b
(* n (pow (/ l Om) (/ 2.0 2)))
5.7b
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
20.8b
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
102×add-exp-log
69×prod-exp
34×associate-*r/
31×pow1
27×add-cbrt-cube
24×add-sqr-sqrt
23×associate-*r*
20×pow-exp
18×distribute-rgt-in distribute-lft-in
17×pow-prod-down
16×*-un-lft-identity
15×unpow-prod-down cbrt-unprod
14×add-cube-cbrt
11×flip3-- flip--
10×pow-to-exp sub-neg times-frac div-exp
8×associate--l+ frac-sub
6×sqrt-div
5×sqrt-pow1 associate-*l*
4×add-log-exp unswap-sqr
3×*-commutative
2×sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 146
Calls
4 calls:
87.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
15.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
80.0ms
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
60.0ms
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

series6.8s

Counts
4 → 12
Calls
4 calls:
377.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
168.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.4s
(* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.9s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

simplify50.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011782588
150012182

prune515.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.2b

regimes608.0ms

Accuracy

31.6% (8.7b remaining)

Error of 27.4b against oracle of 18.6b and baseline of 31.4b

bsearch156.0ms

Steps
ItersRangePoint
2
1.7331756575409306e+31
1.8939131288578974e+31
1.7532678414555514e+31
8
-1.038894416666328e-47
-1.465946927530174e-51
-9.704663980464789e-48

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07452
18052
28152
38152

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.0s14972×body80nan
644.0ms9184×body80valid