Details

Time bar (total: 4.5s)

sample68.0ms

Algorithm
intervals
Results
38.0ms375×body80valid
14.0ms155×body80nan

simplify102.0ms

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: 1.7b

localize10.0ms

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))
1.7b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
16×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
7×associate-*r*
6×fma-def prod-exp
4×pow1 expm1-log1p-u unpow-prod-down div-exp sum-log log1p-expm1-u
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 → 88
Calls
4 calls:
13.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
2.0ms
(+ 1.0 (* 10.0 k))
5.0ms
(* a (pow k m))
13.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
38.0ms
(+ 1.0 (* 10.0 k))
56.0ms
(* a (pow k m))
115.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify58.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0477629
12275544
25001524

prune294.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* a (pow k m))
0.1b
(fma 10.0 k 1.0)
1.7b
(/ (* a (pow k m)) (fma k k (fma 10.0 k 1.0)))

rewrite11.0ms

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:
5.0ms
(* a (pow k m))
0.0ms
(fma 10.0 k 1.0)
4.0ms
(/ (* a (pow k m)) (fma k k (fma 10.0 k 1.0)))

series210.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(* a (pow k m))
37.0ms
(fma 10.0 k 1.0)
117.0ms
(/ (* a (pow k m)) (fma k k (fma 10.0 k 1.0)))

simplify47.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0327406
11538360
25001358

prune200.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma 10.0 k 1.0)
0.1b
(fma 10.0 k 1.0)
12.6b
(sqrt (fma k k (fma 10.0 k 1.0)))
12.6b
(sqrt (fma k k (fma 10.0 k 1.0)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 50
Calls
4 calls:
0.0ms
(fma 10.0 k 1.0)
0.0ms
(fma 10.0 k 1.0)
1.0ms
(sqrt (fma k k (fma 10.0 k 1.0)))
1.0ms
(sqrt (fma k k (fma 10.0 k 1.0)))

series180.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(fma 10.0 k 1.0)
31.0ms
(fma 10.0 k 1.0)
59.0ms
(sqrt (fma k k (fma 10.0 k 1.0)))
53.0ms
(sqrt (fma k k (fma 10.0 k 1.0)))

simplify36.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (32.0ms)

IterNodesCost
0106230
1297218
21090210
35001206

prune224.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
0.1b
(fma 10.0 k 1.0)
0.3b
(* a (pow k (/ m 2)))
1.7b
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (fma k k (fma 10.0 k 1.0)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log
45×prod-exp
20×add-cbrt-cube
16×add-sqr-sqrt
15×pow-to-exp pow-exp
14×associate-*r*
13×div-exp
11×add-cube-cbrt *-un-lft-identity
7×unpow-prod-down cbrt-unprod
4×pow1 expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac associate-/r* unswap-sqr sqr-pow
2×*-commutative
1×frac-2neg clear-num fma-udef div-inv associate-/l*
Counts
4 → 104
Calls
4 calls:
11.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
0.0ms
(fma 10.0 k 1.0)
5.0ms
(* a (pow k (/ m 2)))
11.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (fma k k (fma 10.0 k 1.0)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
31.0ms
(fma 10.0 k 1.0)
67.0ms
(* a (pow k (/ m 2)))
137.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (fma k k (fma 10.0 k 1.0)))

simplify68.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0463939
12429776
25001768

prune297.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

97.7% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.9b

bsearch50.0ms

Steps
ItersRangePoint
5
5.299326542122988e+129
1.2838874600995062e+130
9.480969675725085e+129

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05343
15943
25943

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.2s11947×body80valid
318.0ms4299×body80nan