Details

Time bar (total: 4.3s)

sample34.0ms

Algorithm
intervals
Results
14.0ms362×body80valid
5.0ms136×body80nan

simplify105.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0247
1535
21065
32695
49045
539765
650015

prune11.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.7b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
10×add-log-exp
8×add-cbrt-cube
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×fma-def
4×div-exp sum-log
3×pow1 expm1-log1p-u flip3-+ times-frac prod-exp associate-/r* flip-+ log1p-expm1-u
2×cbrt-undiv +-commutative associate-/r/
1×pow-to-exp associate-+l+ frac-2neg pow-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
3 → 61
Calls
3 calls:
2.0ms
(+ 1.0 (* 10.0 k))
10.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
14.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series174.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ 1.0 (* 10.0 k))
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
116.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify49.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0421510
11910434
25001411

prune207.0ms

Filtered
70 candidates to 55 candidates (78.6%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
14.9b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
14.9b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
66×sqrt-prod
58×add-sqr-sqrt
54×add-cube-cbrt *-un-lft-identity
20×add-exp-log sqrt-div
16×associate-/r/
13×add-cbrt-cube
12×associate-/l*
11×flip3-+ flip-+
9×div-exp add-log-exp
8×div-inv
6×pow1 associate-/r*
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u
3×fma-def prod-exp sum-log
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×+-commutative pow-to-exp associate-+l+ frac-2neg pow-exp clear-num cbrt-unprod associate-/l/
Counts
4 → 167
Calls
4 calls:
10.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
40.0ms
(/ (/ (* 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)))
11.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
127.0ms
(/ (/ (* 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)))
57.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify90.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07433165
133082789
250022776

prune524.0ms

Filtered
179 candidates to 116 candidates (64.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma k 10.0 1.0)
0.1b
(/ 1 (/ (fma k k (fma k 10.0 1.0)) (* a (pow k m))))
1.7b
(/ (fma k k (fma k 10.0 1.0)) (* a (pow k m)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
51×add-exp-log
36×times-frac
26×div-exp
21×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×add-cbrt-cube
12×prod-exp
8×associate-/r*
7×cbrt-undiv
6×div-inv associate-/l*
5×rec-exp 1-exp
4×pow1 pow-to-exp pow-exp
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num cbrt-unprod
1×pow-flip associate-/r/ fma-udef inv-pow
Counts
3 → 99
Calls
3 calls:
0.0ms
(fma k 10.0 1.0)
8.0ms
(/ 1 (/ (fma k k (fma k 10.0 1.0)) (* a (pow k m))))
4.0ms
(/ (fma k k (fma k 10.0 1.0)) (* a (pow k m)))

series271.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(fma k 10.0 1.0)
114.0ms
(/ 1 (/ (fma k k (fma k 10.0 1.0)) (* a (pow k m))))
116.0ms
(/ (fma k k (fma k 10.0 1.0)) (* a (pow k m)))

simplify64.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0501947
12339836
25001792

prune243.0ms

Filtered
108 candidates to 61 candidates (56.5%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 2 (* (fabs (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) 2))
14.9b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.5b
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.5b
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×cbrt-prod
5×pow1
4×expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×flip3-+ times-frac sqrt-prod flip-+ associate-/l*
2×cbrt-undiv pow1/3 sqrt-div div-exp
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num associate-/r* cbrt-unprod hypot-def div-inv
Counts
4 → 71
Calls
4 calls:
3.0ms
(/ 2 (* (fabs (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) 2))
16.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
6.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ 2 (* (fabs (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) 2))
59.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
116.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
117.0ms
(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify47.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0366799
11404712
25001680

prune603.0ms

Filtered
83 candidates to 73 candidates (88.0%)
Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

95.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.2b

bsearch55.0ms

Steps
ItersRangePoint
7
1.02823751487715e+109
1.074385189532799e+111
1.9591962514676314e+110

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05041
15641
25641

end0.0ms

sample972.0ms

Algorithm
intervals
Results
480.0ms11793×body80valid
147.0ms4206×body80nan