Details

Time bar (total: 11.4s)

sample139.0ms

Algorithm
intervals
Results
90.0ms171×body10240exit
22.0ms336×body80valid
6.0ms175×body80nan

simplify102.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0247
1535
21065
32695
49045
539765
650015

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.3b
(* a (pow k m))
3.0b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
14×add-sqr-sqrt
10×add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
8×add-log-exp
7×associate-*r*
6×prod-exp
4×unpow-prod-down div-exp
3×pow1 expm1-log1p-u fma-def times-frac associate-*l* associate-/r* sum-log log1p-expm1-u unswap-sqr
2×cbrt-undiv pow-to-exp flip3-+ pow-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×+-commutative associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
3 → 72
Calls
3 calls:
10.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms
(* a (pow k m))
13.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series201.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
56.0ms
(* a (pow k m))
121.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify54.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0419575
12040495
25002476

prune227.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* a (pow k (/ m 2)))
0.0b
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
3.0b
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log
45×prod-exp
20×add-cbrt-cube
17×add-sqr-sqrt
15×pow-to-exp pow-exp
14×associate-*r*
13×div-exp
12×add-cube-cbrt *-un-lft-identity
9×add-log-exp
7×unpow-prod-down cbrt-unprod
4×pow1 expm1-log1p-u associate-*l* log1p-expm1-u
3×cbrt-undiv fma-def times-frac associate-/r* sum-log unswap-sqr sqr-pow
2×flip3-+ associate-/r/ *-commutative flip-+
1×+-commutative associate-+l+ frac-2neg clear-num div-inv associate-/l*
Counts
4 → 114
Calls
4 calls:
10.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms
(* a (pow k (/ m 2)))
16.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
20.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
75.0ms
(* a (pow k (/ m 2)))
82.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
140.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify79.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
05551139
12962935
25001884

prune500.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt k)
0.6b
(cbrt k)
0.6b
(cbrt k)
3.0b
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
30×prod-exp
16×div-exp
13×add-cbrt-cube
11×pow-exp
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×pow-to-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac pow1/3 associate-/r* cbrt-unprod
2×associate-/r/
1×frac-2neg flip3-+ clear-num flip-+ div-inv associate-/l*
Counts
4 → 79
Calls
4 calls:
0.0ms
(cbrt k)
0.0ms
(cbrt k)
0.0ms
(cbrt k)
21.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series887.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(cbrt k)
171.0ms
(cbrt k)
169.0ms
(cbrt k)
372.0ms
(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify62.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0514921
12446788
25001734

prune292.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ a (/ (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (pow k (* 2 (/ m 2))))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
0.3b
(/ a (/ (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (pow k (* 2 (/ m 2)))))
14.7b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
14.7b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
3012×times-frac
1349×add-sqr-sqrt
1345×add-cube-cbrt *-un-lft-identity
963×sqrt-prod
450×unpow-prod-down
150×sqr-pow
146×associate-/l*
52×associate-/r*
34×div-inv
30×add-exp-log
19×div-exp
18×add-cbrt-cube
10×associate-/r/
9×cbrt-undiv
6×pow1 sqrt-div
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num hypot-def
1×associate-/l/
Counts
4 → 1272
Calls
4 calls:
79.0ms
(/ (/ a (/ (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (pow k (* 2 (/ m 2))))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
22.0ms
(/ a (/ (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (pow k (* 2 (/ m 2)))))
11.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ (/ a (/ (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (pow k (* 2 (/ m 2))))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
163.0ms
(/ a (/ (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (pow k (* 2 (/ m 2)))))
53.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
47.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify385.0ms

Algorithm
egg-herbie
Counts
1284 → 1284
Iterations

Useful iterations: 1 (59.0ms)

IterNodesCost
0373039198
1500138098

prune3.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes87.0ms

Accuracy

98.3% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.8b

bsearch61.0ms

Steps
ItersRangePoint
7
1.0811805125093303e+153
2.58678130333839e+154
1.3393354591404545e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05238
15838
25838

end0.0ms

sample4.0s

Algorithm
intervals
Results
2.6s5092×body10240exit
751.0ms10678×body80valid
218.0ms5645×body80nan