Details

Time bar (total: 33.8s)

sample378.0ms

Algorithm
intervals
Results
62.0ms409×body80nan
38.0ms283×body80valid

simplify121.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize21.0ms

Local error

Found 4 expressions with local error:

6.7b
(* n (pow (/ l Om) 2.0))
7.3b
(/ (* l l) Om)
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.0b
(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:
14.0ms
(* n (pow (/ l Om) 2.0))
3.0ms
(/ (* l l) Om)
52.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
32.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.1s

Counts
4 → 12
Calls
4 calls:
141.0ms
(* n (pow (/ l Om) 2.0))
18.0ms
(/ (* l l) Om)
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.6s
(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 (24.0ms)

IterNodesCost
09641521
148051370
250021370

prune529.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 26.2b

localize17.0ms

Local error

Found 4 expressions with local error:

6.2b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.7b
(* n (pow (/ l Om) 2.0))
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
19.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite122.0ms

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:
22.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
16.0ms
(* n (pow (/ l Om) 2.0))
46.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
33.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.4s

Counts
4 → 12
Calls
4 calls:
354.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
136.0ms
(* n (pow (/ l Om) 2.0))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
4.7s
(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
131 → 131
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09871668
150011508

prune494.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 25.1b

localize19.0ms

Local error

Found 4 expressions with local error:

4.6b
(* n (pow (/ l Om) (/ 2.0 2)))
6.2b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
19.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
25×pow1 add-sqr-sqrt associate-*r*
24×add-cbrt-cube
22×associate-*r/
20×pow-exp
17×*-un-lft-identity
15×add-cube-cbrt unpow-prod-down
13×pow-prod-down cbrt-unprod
11×flip3-- flip--
10×pow-to-exp times-frac div-exp
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
5×associate-*l*
4×sqrt-pow1 associate--l+ 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 → 136
Calls
4 calls:
14.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
79.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
62.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
38.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series6.5s

Counts
4 → 12
Calls
4 calls:
153.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
352.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.2s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify52.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011132381
150012030

prune523.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 24.4b

localize20.0ms

Local error

Found 4 expressions with local error:

4.6b
(* n (pow (/ l Om) (/ 2.0 2)))
7.6b
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
10.6b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
19.0b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
30×unpow-prod-down associate-*r/
29×add-exp-log
25×*-un-lft-identity associate-*r*
23×pow1 add-cube-cbrt
21×associate-*l*
20×times-frac
17×add-cbrt-cube
14×prod-exp
12×pow-prod-down
11×flip3-- flip--
8×frac-sub cbrt-unprod unswap-sqr
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
4×sqrt-pow1 pow-exp associate--l+ add-log-exp sqr-pow
3×*-commutative
2×pow-to-exp div-exp div-inv
1×pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 136
Calls
4 calls:
14.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
21.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
57.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
36.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

series6.4s

Counts
4 → 12
Calls
4 calls:
164.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
334.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))
4.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))

simplify47.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010792179
150021964

prune623.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 24.2b

regimes524.0ms

Accuracy

3.6% (9.3b remaining)

Error of 31.1b against oracle of 21.9b and baseline of 31.5b

bsearch155.0ms

Steps
ItersRangePoint
9
1.0205019297313185e-238
1.461116172898857e-233
2.762753868964082e-236

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04160
14160

end0.0ms

sample4.1s

Algorithm
intervals
Results
2.0s14684×body80nan
1.2s9108×body80valid