Details

Time bar (total: 4.3s)

sample38.0ms

Algorithm
intervals
Results
17.0ms383×body80valid
5.0ms146×body80nan

simplify105.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0247
1535
21065
32695
49045
539765
650015

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.2b
(* a (pow k m))
2.9b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite20.0ms

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:
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)))

series185.0ms

Counts
3 → 9
Calls
3 calls:
17.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
57.0ms
(* a (pow k m))
110.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify56.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0419575
12040495
25002476

prune224.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma k 10.0 1.0)
0.2b
(* a (pow k m))
2.9b
(/ (* a (pow k m)) (fma k k (fma k 10.0 1.0)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
13×add-sqr-sqrt
10×add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
7×associate-*r*
6×prod-exp
4×unpow-prod-down div-exp
3×pow1 expm1-log1p-u times-frac associate-*l* associate-/r* log1p-expm1-u add-log-exp unswap-sqr
2×cbrt-undiv pow-to-exp pow-exp cbrt-unprod sqr-pow
1×frac-2neg clear-num *-commutative fma-udef div-inv associate-/l*
Counts
3 → 62
Calls
3 calls:
1.0ms
(fma k 10.0 1.0)
5.0ms
(* a (pow k m))
5.0ms
(/ (* a (pow k m)) (fma k k (fma k 10.0 1.0)))

series199.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(fma k 10.0 1.0)
58.0ms
(* a (pow k m))
111.0ms
(/ (* a (pow k m)) (fma k k (fma k 10.0 1.0)))

simplify48.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0329406
11540360
25001358

prune197.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* a (sqrt (pow k m)))
0.2b
(sqrt (pow k m))
0.2b
(sqrt (pow k m))
2.9b
(/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
24×sqrt-prod
15×add-exp-log add-cbrt-cube
14×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
10×associate-*r*
6×pow1 rem-sqrt-square sqr-pow
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×cbrt-undiv times-frac div-exp associate-*l* associate-/r*
2×sqrt-pow1 pow1/2 associate-/r/
1×frac-2neg flip3-+ pow-prod-down clear-num *-commutative flip-+ div-inv associate-/l*
Counts
4 → 99
Calls
4 calls:
9.0ms
(* a (sqrt (pow k m)))
2.0ms
(sqrt (pow k m))
2.0ms
(sqrt (pow k m))
13.0ms
(/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* a (sqrt (pow k m)))
58.0ms
(sqrt (pow k m))
61.0ms
(sqrt (pow k m))
110.0ms
(/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify62.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0469809
12337693
25002659

prune343.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

2.9b
(/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))
2.9b
(/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.6b
(sqrt (/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k))))
5.6b
(sqrt (/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log add-cbrt-cube
18×sqrt-prod
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity times-frac
8×associate-/r/
6×pow1 cbrt-undiv div-exp prod-exp associate-/r* cbrt-unprod
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u div-inv add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 sqrt-div clear-num associate-/l*
Counts
4 → 98
Calls
4 calls:
13.0ms
(/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))
17.0ms
(/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))
10.0ms
(sqrt (/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k))))
11.0ms
(sqrt (/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k))))

series634.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))
114.0ms
(/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))
202.0ms
(sqrt (/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k))))
203.0ms
(sqrt (/ (* (* a (sqrt (pow k m))) (sqrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k))))

simplify63.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04981742
122751498
250021424

prune441.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

98.4% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.3b

bsearch51.0ms

Steps
ItersRangePoint
7
7.232028391489847e+54
8.011735395639846e+56
5.517677918177175e+56

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04332
14932
24932

end0.0ms

sample1.0s

Algorithm
intervals
Results
535.0ms11882×body80valid
160.0ms4350×body80nan