Details

Time bar (total: 4.1s)

sample33.0ms

Algorithm
intervals
Results
14.0ms362×body80valid
4.0ms125×body80nan

simplify108.0ms

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

rewrite38.0ms

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:
2.0ms
(+ 1.0 (* 10.0 k))
6.0ms
(* a (pow k m))
14.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
14.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ 1.0 (* 10.0 k))
62.0ms
(* a (pow k m))
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
113.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify60.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0477629
12275544
25001524

prune282.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
16×*-un-lft-identity
15×add-sqr-sqrt
11×add-cbrt-cube
10×add-cube-cbrt
7×associate-*r*
6×prod-exp add-log-exp
4×pow1 expm1-log1p-u unpow-prod-down times-frac div-exp associate-/r* log1p-expm1-u
3×fma-def associate-*l* distribute-lft-out unswap-sqr
2×cbrt-undiv pow-to-exp flip3-+ pow-exp associate-/r/ cbrt-unprod flip-+ fma-udef sqr-pow
1×+-commutative associate-+r+ frac-2neg clear-num sum-log *-commutative div-inv associate-/l*
Counts
4 → 84
Calls
4 calls:
3.0ms
(+ 1.0 (fma 10.0 k (* k k)))
5.0ms
(* a (pow k m))
0.0ms
(fma 10.0 k (* k k))
8.0ms
(/ (* a (pow k m)) (+ 1.0 (fma 10.0 k (* k k))))

series251.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ 1.0 (fma 10.0 k (* k k)))
62.0ms
(* a (pow k m))
50.0ms
(fma 10.0 k (* k k))
119.0ms
(/ (* a (pow k m)) (+ 1.0 (fma 10.0 k (* k k))))

simplify55.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0395565
11854493
25002486

prune264.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log
45×prod-exp
20×add-cbrt-cube
16×add-sqr-sqrt
15×pow-to-exp *-un-lft-identity pow-exp
14×associate-*r*
13×div-exp
11×add-cube-cbrt
7×unpow-prod-down cbrt-unprod
4×pow1 expm1-log1p-u times-frac associate-*l* associate-/r* log1p-expm1-u add-log-exp
3×cbrt-undiv unswap-sqr sqr-pow
2×associate-/r/ *-commutative distribute-lft-out
1×frac-2neg flip3-+ clear-num flip-+ fma-udef div-inv associate-/l*
Counts
4 → 108
Calls
4 calls:
12.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
6.0ms
(* a (pow k (/ m 2)))
0.0ms
(fma 10.0 k (* k k))
15.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ 1.0 (fma 10.0 k (* k k))))

series340.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
67.0ms
(* a (pow k (/ m 2)))
55.0ms
(fma 10.0 k (* k k))
137.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ 1.0 (fma 10.0 k (* k k))))

simplify75.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
05031035
12651863
25002852

prune302.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 10.0 k (* k k))
0.0b
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (fma 10.0 k (* k k))))) (sqrt (+ 1.0 (fma 10.0 k (* k k)))))
14.5b
(sqrt (+ 1.0 (fma 10.0 k (* k k))))
14.5b
(sqrt (+ 1.0 (fma 10.0 k (* k k))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
147×times-frac
106×*-un-lft-identity
96×sqrt-prod
64×add-sqr-sqrt
58×add-cube-cbrt
24×distribute-lft-out
22×sqrt-div
20×add-exp-log
18×associate-/r/
13×add-cbrt-cube associate-/l*
11×flip3-+ flip-+
9×div-exp div-inv
7×associate-/r*
6×pow1
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×prod-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×pow-to-exp frac-2neg pow-exp clear-num cbrt-unprod fma-udef associate-/l/
Counts
4 → 182
Calls
4 calls:
0.0ms
(fma 10.0 k (* k k))
19.0ms
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (fma 10.0 k (* k k))))) (sqrt (+ 1.0 (fma 10.0 k (* k k)))))
4.0ms
(sqrt (+ 1.0 (fma 10.0 k (* k k))))
4.0ms
(sqrt (+ 1.0 (fma 10.0 k (* k k))))

series277.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(fma 10.0 k (* k k))
125.0ms
(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (fma 10.0 k (* k k))))) (sqrt (+ 1.0 (fma 10.0 k (* k k)))))
47.0ms
(sqrt (+ 1.0 (fma 10.0 k (* k k))))
54.0ms
(sqrt (+ 1.0 (fma 10.0 k (* k k))))

simplify94.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06893055
129322721
250012705

prune465.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes71.0ms

Accuracy

87.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 2.2b

bsearch57.0ms

Steps
ItersRangePoint
7
0.003342748024832997
0.12132668660207117
0.12004989461063595

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04937
15537
25537

end0.0ms

sample987.0ms

Algorithm
intervals
Results
488.0ms11935×body80valid
150.0ms4285×body80nan