Details

Time bar (total: 36.8s)

sample93.0ms

Algorithm
intervals
Results
30.0ms484×body80nan
18.0ms288×body80valid

simplify121.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115514
268414
3389814
4500114

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize21.0ms

Local error

Found 4 expressions with local error:

6.3b
(* n (pow (/ l Om) 2.0))
9.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
10.3b
(/ (* l l) Om)
22.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×add-exp-log
23×pow1
20×add-cube-cbrt *-un-lft-identity associate-*r/ associate-*r* add-cbrt-cube
15×unpow-prod-down
13×times-frac
12×prod-diff pow-prod-down
11×prod-exp
10×distribute-rgt-in flip3-- distribute-lft-in associate--l+ flip--
8×frac-sub cbrt-unprod
6×sqrt-div
4×expm1-log1p-u sub-neg sqrt-pow1 associate-*l* log1p-expm1-u 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 → 132
Calls
4 calls:
24.0ms
(* n (pow (/ l Om) 2.0))
131.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.0ms
(/ (* l l) Om)
99.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.0s

Counts
4 → 12
Calls
4 calls:
133.0ms
(* n (pow (/ l Om) 2.0))
1.2s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
17.0ms
(/ (* l l) Om)
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify46.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010791948
150011746

prune629.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 25.1b

localize27.0ms

Local error

Found 4 expressions with local error:

5.4b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.3b
(* n (pow (/ l Om) 2.0))
9.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
22.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite312.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
35×add-exp-log
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
25×pow1 associate-*r*
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
20×add-cbrt-cube
19×prod-exp
15×unpow-prod-down
13×pow-prod-down
11×flip3-- flip--
10×times-frac associate--l+ cbrt-unprod
8×frac-sub
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u 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 → 157
Calls
4 calls:
48.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
26.0ms
(* n (pow (/ l Om) 2.0))
131.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
100.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.3s

Counts
4 → 12
Calls
4 calls:
353.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
135.0ms
(* n (pow (/ l Om) 2.0))
1.2s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify52.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012272457
150022136

prune627.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.8b

localize33.0ms

Local error

Found 4 expressions with local error:

5.3b
(* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0))
5.4b
(* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*))
9.5b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*))))
22.3b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))

rewrite522.0ms

Algorithm
rewrite-expression-head
Rules
188×add-exp-log
126×prod-exp
41×pow-exp
33×add-sqr-sqrt
30×prod-diff
28×div-exp
27×*-un-lft-identity
25×pow1 add-cube-cbrt
24×add-cbrt-cube
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
17×associate-*r*
13×pow-to-exp pow-prod-down cbrt-unprod
11×flip3-- flip--
10×associate--l+
8×frac-sub
7×unpow-prod-down
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×times-frac sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 181
Calls
4 calls:
29.0ms
(* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0))
186.0ms
(* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*))
169.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*))))
129.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))

series6.4s

Counts
4 → 12
Calls
4 calls:
178.0ms
(* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0))
366.0ms
(* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2.0)) (pow (/ (cbrt l) (cbrt Om)) 2.0)) (- U U*)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
193 → 193
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013944996
150014416

prune980.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.5b

localize28.0ms

Local error

Found 4 expressions with local error:

11.2b
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.2b
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
11.2b
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
22.3b
(sqrt (* (* (* (* 2.0 n) U) (* (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))) (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

rewrite938.0ms

Algorithm
rewrite-expression-head
Rules
984×associate-*r/
900×cbrt-div
750×flip3-- flip--
600×frac-sub
540×frac-times
342×sqrt-div
90×associate-*l/
34×pow1
22×pow-prod-down
9×cbrt-prod
8×sqrt-pow1
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×pow1/2 sqrt-prod
Counts
4 → 418
Calls
4 calls:
22.0ms
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
23.0ms
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
22.0ms
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
776.0ms
(sqrt (* (* (* (* 2.0 n) U) (* (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))) (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

series6.2s

Counts
4 → 12
Calls
4 calls:
608.0ms
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
593.0ms
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
599.0ms
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.4s
(sqrt (* (* (* (* 2.0 n) U) (* (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))) (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))

simplify407.0ms

Algorithm
egg-herbie
Counts
430 → 430
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0332544085
1500143974

prune3.3s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 22.5b

regimes654.0ms

Accuracy

10.6% (8.2b remaining)

Error of 30.2b against oracle of 22.1b and baseline of 31.2b

bsearch83.0ms

Steps
ItersRangePoint
5
1.0011276807577403e-148
2.3890075056810385e-148
1.0468514204986157e-148

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04251
14251

end0.0ms

sample2.7s

Algorithm
intervals
Results
939.0ms14793×body80nan
595.0ms9236×body80valid