Details

Time bar (total: 4.2s)

sample36.0ms

Algorithm
intervals
Results
16.0ms369×body80valid
5.0ms128×body80nan

simplify105.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0247
1487
2966
32566
48916
539636
650026

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* a (pow k m))
2.2b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
14×add-sqr-sqrt
11×add-cbrt-cube add-log-exp
9×add-cube-cbrt *-un-lft-identity
7×associate-*r*
6×prod-exp
4×pow1 unpow-prod-down div-exp sum-log
3×flip3-+ times-frac associate-*l* associate-/r* flip-+ unswap-sqr
2×cbrt-undiv +-commutative pow-to-exp pow-exp associate-/r/ cbrt-unprod sqr-pow
1×associate-+l+ frac-2neg clear-num *-commutative div-inv associate-/l*
Counts
4 → 74
Calls
4 calls:
3.0ms
(+ 1.0 (* 10.0 k))
5.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms
(* a (pow k m))
8.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ 1.0 (* 10.0 k))
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
62.0ms
(* a (pow k m))
115.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify65.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0457599
12146533
25001526

prune222.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(+ 1.0 (* 10.0 k))
0.0b
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
2.2b
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
70×add-exp-log
42×prod-exp
18×add-cbrt-cube
14×pow-to-exp pow-exp
13×div-exp
11×add-log-exp
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×associate-*r*
6×cbrt-unprod
4×pow1 sum-log
3×cbrt-undiv unpow-prod-down flip3-+ times-frac associate-/r* flip-+
2×+-commutative associate-/r/
1×associate-+l+ frac-2neg associate-*l* clear-num *-commutative div-inv associate-/l* sqr-pow
Counts
4 → 89
Calls
4 calls:
5.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
3.0ms
(+ 1.0 (* 10.0 k))
7.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
12.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
32.0ms
(+ 1.0 (* 10.0 k))
78.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
143.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify71.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0546993
12697816
25001786

prune237.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 2.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* (* a (pow k (/ m 2))) (pow k (/ (/ m 2) 2)))
2.2b
(/ (* (* (* a (pow k (/ m 2))) (pow k (/ (/ m 2) 2))) (pow k (/ (/ m 2) 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
178×add-exp-log
123×prod-exp
41×pow-to-exp pow-exp
40×div-exp
23×add-cbrt-cube
11×add-log-exp
9×cbrt-unprod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×associate-*r*
4×pow1 cbrt-undiv sum-log
3×unpow-prod-down flip3-+ times-frac associate-/r* flip-+
2×+-commutative associate-/r/
1×associate-+l+ frac-2neg associate-*l* clear-num *-commutative div-inv associate-/l* sqr-pow
Counts
4 → 117
Calls
4 calls:
3.0ms
(+ 1.0 (* 10.0 k))
5.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
8.0ms
(* (* a (pow k (/ m 2))) (pow k (/ (/ m 2) 2)))
17.0ms
(/ (* (* (* a (pow k (/ m 2))) (pow k (/ (/ m 2) 2))) (pow k (/ (/ m 2) 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series403.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ 1.0 (* 10.0 k))
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
130.0ms
(* (* a (pow k (/ m 2))) (pow k (/ (/ m 2) 2)))
218.0ms
(/ (* (* (* a (pow k (/ m 2))) (pow k (/ (/ m 2) 2))) (pow k (/ (/ m 2) 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify89.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07121762
133281362
250021296

prune250.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 2.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (pow k (* 2 (/ m 2))) a)
0.0b
(/ (/ (* (pow k (* 2 (/ m 2))) a) (* (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) 1)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
14.7b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
14.7b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
57×add-exp-log
49×times-frac
39×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
30×sqrt-prod
25×div-exp
24×add-cbrt-cube
20×sqrt-div prod-exp
16×associate-/r/
14×associate-*l/
10×flip3-+ flip-+
9×cbrt-undiv
8×div-inv
7×associate-*l* associate-/l*
6×pow1 associate-/r*
5×cbrt-unprod
4×pow-to-exp unpow-prod-down 1-exp pow-exp add-log-exp
3×associate-*r* unswap-sqr
2×rem-sqrt-square sqrt-pow1 pow1/2 sqr-pow
1×frac-2neg clear-num *-commutative associate-/l/
Counts
4 → 141
Calls
4 calls:
5.0ms
(* (pow k (* 2 (/ m 2))) a)
17.0ms
(/ (/ (* (pow k (* 2 (/ m 2))) a) (* (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) 1)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
4.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series329.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (pow k (* 2 (/ m 2))) a)
107.0ms
(/ (/ (* (pow k (* 2 (/ m 2))) a) (* (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) 1)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
58.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
68.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify97.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07492762
135362414
250022400

prune455.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 2.2b

regimes77.0ms

Accuracy

0% (0.0b remaining)

Error of 2.1b against oracle of 2.1b and baseline of 2.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02416
12416

end0.0ms

sample1.0s

Algorithm
intervals
Results
538.0ms11955×body80valid
155.0ms4227×body80nan