Details

Time bar (total: 37.6s)

sample84.0ms

Algorithm
intervals
Results
32.0ms434×body80nan
19.0ms291×body80valid

simplify118.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04914
115314
265214
3362414
4500214

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize19.0ms

Local error

Found 4 expressions with local error:

7.8b
(* n (pow (/ l Om) 2.0))
10.3b
(/ (* l l) Om)
13.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.7b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite104.0ms

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:
15.0ms
(* n (pow (/ l Om) 2.0))
3.0ms
(/ (* l l) Om)
50.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
31.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.2s

Counts
4 → 12
Calls
4 calls:
143.0ms
(* 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*))))
4.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify128.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09641525
147931370
250011370

prune538.0ms

Filtered
124 candidates to 87 candidates (70.2%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 26.3b

localize24.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.8b
(* n (pow (/ l Om) 2.0))
13.1b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.7b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite123.0ms

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))
47.0ms
(* (* (* 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*)))))

series6.6s

Counts
4 → 12
Calls
4 calls:
372.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
140.0ms
(* 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*))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify41.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09871664
150011508

prune529.0ms

Filtered
131 candidates to 86 candidates (65.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.8b

localize21.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
6.0b
(* n (pow (/ l Om) (/ 2.0 2)))
13.1b
(* (* (* 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*))))
20.7b
(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*)))))

rewrite214.0ms

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:
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)))
62.0ms
(* (* (* 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*))))
44.0ms
(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:
360.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
156.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
1.3s
(* (* (* 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*))))
5.0s
(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
148 → 148
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011132381
150022030

prune558.0ms

Filtered
148 candidates to 89 candidates (60.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 24.3b

localize24.0ms

Local error

Found 4 expressions with local error:

5.5b
(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
6.3b
(* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
7.8b
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
20.7b
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
25×associate-*r*
23×add-exp-log
19×*-un-lft-identity
17×add-cube-cbrt add-cbrt-cube
16×unpow-prod-down
15×pow1
11×prod-exp
10×times-frac associate-*l*
8×cbrt-unprod
7×pow-prod-down
5×sqrt-prod unswap-sqr
4×associate-*r/ add-log-exp sqr-pow
3×*-commutative
2×distribute-rgt-in sub-neg rem-sqrt-square flip3-- distribute-lft-in associate-*l/ pow-exp flip--
1×distribute-lft-neg-out distribute-lft-neg-in pow-to-exp neg-mul-1 distribute-rgt-neg-in sqrt-pow1 pow1/2 div-exp div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 106
Calls
4 calls:
14.0ms
(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
96.0ms
(* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
15.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
4.0ms
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

series11.6s

Counts
4 → 12
Calls
4 calls:
291.0ms
(* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))
1.3s
(* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U)
147.0ms
(* n (pow (/ l Om) (* 2 (/ 2.0 2))))
9.9s
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))

simplify119.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
07701582
141311372
250011364

prune516.0ms

Filtered
118 candidates to 89 candidates (75.4%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.6b

regimes515.0ms

Accuracy

17.3% (10.2b remaining)

Error of 28.8b against oracle of 18.6b and baseline of 30.9b

bsearch106.0ms

Steps
ItersRangePoint
8
9.170912651718186e-258
9.631104734655604e-255
9.333968041762941e-258

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06943
18443
28643
38643

end0.0ms

sample2.4s

Algorithm
intervals
Results
957.0ms14599×body80nan
596.0ms9217×body80valid