Details

Time bar (total: 37.2s)

sample94.0ms

Algorithm
intervals
Results
29.0ms471×body80nan
21.0ms293×body80valid

simplify116.0ms

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: 35.6b

localize22.0ms

Local error

Found 4 expressions with local error:

6.8b
(/ (* l l) Om)
7.3b
(* n (pow (/ l Om) 2.0))
13.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.6b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite253.0ms

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:
12.0ms
(/ (* l l) Om)
25.0ms
(* n (pow (/ l Om) 2.0))
129.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
82.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series6.6s

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ (* l l) Om)
152.0ms
(* 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*))))
5.1s
(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 (23.0ms)

IterNodesCost
09641525
147931370
250011370

prune516.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 27.0b

localize18.0ms

Local error

Found 4 expressions with local error:

6.1b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
7.3b
(* n (pow (/ l Om) 2.0))
13.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
18.6b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite292.0ms

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:
47.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
25.0ms
(* n (pow (/ l Om) 2.0))
129.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
86.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series7.1s

Counts
4 → 12
Calls
4 calls:
405.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
160.0ms
(* 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*))))
5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify44.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
09871664
150011508

prune525.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 25.4b

localize28.0ms

Local error

Found 4 expressions with local error:

4.6b
(* n (pow (/ l Om) (/ 2.0 2)))
6.1b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
13.4b
(* (* (* 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*))))
18.6b
(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*)))))

rewrite505.0ms

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:
27.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
154.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
192.0ms
(* (* (* 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*))))
125.0ms
(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*)))))

series7.2s

Counts
4 → 12
Calls
4 calls:
170.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
377.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
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*))))
5.3s
(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*)))))

simplify52.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011132381
150022030

prune545.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 25.3b

localize31.0ms

Local error

Found 4 expressions with local error:

4.0b
(* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2)))
6.1b
(* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
13.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
18.6b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
803×add-exp-log
611×prod-exp
246×pow-exp
153×div-exp
93×pow-to-exp
40×1-exp
34×associate-*r*
32×add-cbrt-cube
25×pow1
22×add-sqr-sqrt unpow-prod-down *-un-lft-identity associate-*r/
20×add-cube-cbrt
19×cbrt-unprod
18×times-frac
13×pow-prod-down
11×flip3-- flip--
9×cbrt-prod
8×frac-sub
6×distribute-rgt-in sub-neg distribute-lft-in sqrt-div
4×sqrt-pow1 associate--l+ add-log-exp
3×associate-*l* *-commutative
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 281
Calls
4 calls:
55.0ms
(* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2)))
483.0ms
(* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
296.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
192.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series7.8s

Counts
4 → 12
Calls
4 calls:
332.0ms
(* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2)))
792.0ms
(* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.4s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify90.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
017826288
150015889

prune747.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 24.6b

regimes598.0ms

Accuracy

23.3% (7.9b remaining)

Error of 29.5b against oracle of 21.5b and baseline of 31.9b

bsearch296.0ms

Steps
ItersRangePoint
6
1.3891809080235205e+20
9.477762236175723e+20
2.5897331506828896e+20
10
-3.305190560513696e-63
-2.1629086601828642e-74
-1.3487365281994786e-70
3
-2.000159998393285e+186
-1.6157597536252222e+186
-1.9761349830952812e+186

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08692
19292
29392
39392

end0.0ms

sample2.6s

Algorithm
intervals
Results
915.0ms14732×body80nan
570.0ms9197×body80valid