Details

Time bar (total: 5.8s)

sample34.0ms

Algorithm
intervals
Results
15.0ms375×body80valid
4.0ms135×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: 2.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* a (pow k m))
2.8b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite34.0ms

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:
11.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms
(* a (pow k m))
16.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series187.0ms

Counts
3 → 9
Calls
3 calls:
17.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
58.0ms
(* a (pow k m))
111.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify57.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0419575
12040495
25002476

prune224.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
66×sqrt-prod
65×add-sqr-sqrt
56×add-cube-cbrt *-un-lft-identity
25×add-exp-log
20×sqrt-div
16×associate-/r/
15×add-cbrt-cube
12×associate-/l*
10×flip3-+ flip-+
9×div-exp
8×div-inv
7×associate-*r*
6×pow1 prod-exp associate-/r*
5×cbrt-undiv
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
3×associate-*l* unswap-sqr
2×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-exp cbrt-unprod hypot-def sqr-pow
1×frac-2neg clear-num *-commutative associate-/l/
Counts
4 → 176
Calls
4 calls:
5.0ms
(* a (pow k m))
34.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
11.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* a (pow k m))
114.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
50.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
46.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify99.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07533189
137872815
250022804

prune478.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (fma k k (fma k 10.0 1.0)) a) (pow k m))
0.0b
(fma k 10.0 1.0)
0.1b
(/ 1 (/ (/ (fma k k (fma k 10.0 1.0)) a) (pow k m)))
5.9b
(/ (fma k k (fma k 10.0 1.0)) a)

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
1073×times-frac
496×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
198×unpow-prod-down
105×associate-/r*
68×add-exp-log
66×sqr-pow
51×div-exp
43×div-inv
20×add-cbrt-cube
19×associate-/l*
10×cbrt-undiv
8×pow-to-exp pow-exp
7×rec-exp 1-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×pow-flip associate-/r/ fma-udef associate-/l/ inv-pow
Counts
4 → 593
Calls
4 calls:
8.0ms
(/ (/ (fma k k (fma k 10.0 1.0)) a) (pow k m))
0.0ms
(fma k 10.0 1.0)
22.0ms
(/ 1 (/ (/ (fma k k (fma k 10.0 1.0)) a) (pow k m)))
2.0ms
(/ (fma k k (fma k 10.0 1.0)) a)

series302.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (/ (fma k k (fma k 10.0 1.0)) a) (pow k m))
32.0ms
(fma k 10.0 1.0)
116.0ms
(/ 1 (/ (/ (fma k k (fma k 10.0 1.0)) a) (pow k m)))
43.0ms
(/ (fma k k (fma k 10.0 1.0)) a)

simplify121.0ms

Algorithm
egg-herbie
Counts
605 → 605
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
020648184
150017772

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (+ (fma 1.0 (/ 1 a) (* 10.0 (/ k a))) (/ (pow k 2) a)) (pow k m)))
0.3b
(* 10.0 (/ k a))
0.7b
(+ (fma 1.0 (/ 1 a) (* 10.0 (/ k a))) (/ (pow k 2) a))
9.5b
(/ (pow k 2) a)

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
242×times-frac
185×*-un-lft-identity
132×add-sqr-sqrt
127×add-cube-cbrt
60×unpow-prod-down
36×add-exp-log
35×associate-/r*
29×distribute-lft-out
21×div-exp
20×sqr-pow
16×add-cbrt-cube
13×associate-*r*
11×associate-/l*
7×pow1 div-inv
6×add-log-exp
5×cbrt-undiv
4×expm1-log1p-u pow-to-exp rec-exp 1-exp pow-exp log1p-expm1-u unpow2
3×fma-def associate-*l*
2×frac-2neg prod-exp clear-num cbrt-unprod unswap-sqr
1×+-commutative associate-+l+ pow-flip flip3-+ associate-*r/ pow-prod-down sum-log associate-/r/ *-commutative flip-+ fma-udef inv-pow
Counts
4 → 263
Calls
4 calls:
33.0ms
(/ 1 (/ (+ (fma 1.0 (/ 1 a) (* 10.0 (/ k a))) (/ (pow k 2) a)) (pow k m)))
7.0ms
(* 10.0 (/ k a))
12.0ms
(+ (fma 1.0 (/ 1 a) (* 10.0 (/ k a))) (/ (pow k 2) a))
4.0ms
(/ (pow k 2) a)

series197.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ 1 (/ (+ (fma 1.0 (/ 1 a) (* 10.0 (/ k a))) (/ (pow k 2) a)) (pow k m)))
18.0ms
(* 10.0 (/ k a))
49.0ms
(+ (fma 1.0 (/ 1 a) (* 10.0 (/ k a))) (/ (pow k 2) a))
19.0ms
(/ (pow k 2) a)

simplify128.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
09833481
148863215
250013211

prune690.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

0% (1.8b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0179
1179

end0.0ms

sample963.0ms

Algorithm
intervals
Results
479.0ms11990×body80valid
146.0ms4349×body80nan