Details

Time bar (total: 58.9s)

sample37.0ms

Algorithm
intervals
Results
16.0ms369×body80valid
5.0ms128×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: 2.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b
(* a (pow k m))
2.2b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite25.0ms

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:
3.0ms
(+ 1.0 (* 10.0 k))
5.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
5.0ms
(* a (pow k m))
9.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ 1.0 (* 10.0 k))
24.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
58.0ms
(* a (pow k m))
126.0ms
(/ (* 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

prune284.0ms

Pruning

4 alts after pruning (4 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
(+ 1.0 (* 10.0 k))
0.0b
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
2.2b
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
70×add-exp-log
42×prod-exp
18×add-cbrt-cube
14×pow-to-exp pow-exp
13×div-exp
11×add-log-exp
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×associate-*r*
6×fma-def cbrt-unprod
4×pow1 expm1-log1p-u sum-log log1p-expm1-u
3×cbrt-undiv unpow-prod-down flip3-+ times-frac associate-/r* flip-+
2×+-commutative associate-/r/
1×associate-+l+ frac-2neg associate-*l* clear-num *-commutative div-inv associate-/l* sqr-pow
Counts
4 → 103
Calls
4 calls:
5.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
3.0ms
(+ 1.0 (* 10.0 k))
7.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
12.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
39.0ms
(+ 1.0 (* 10.0 k))
78.0ms
(* (* a (pow k (/ m 2))) (pow k (/ m 2)))
146.0ms
(/ (* (* a (pow k (/ m 2))) (pow k (/ m 2))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify75.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
05671039
12826842
25002790

prune284.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

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)))

rewrite37.0ms

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))
16.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
4.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series280.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* a (pow k m))
123.0ms
(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
47.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
53.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify106.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07533189
137872815
250022804

prune515.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (/ a (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))) (/ (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (/ (pow k m) (sqrt (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)))
14.7b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite2.9s

Algorithm
rewrite-expression-head
Rules
52095×times-frac
31239×sqrt-prod
20879×add-sqr-sqrt
20873×add-cube-cbrt *-un-lft-identity
5508×unpow-prod-down
2502×sqrt-div
1836×sqr-pow
1283×associate-/r/
659×div-inv
627×flip3-+ flip-+
419×associate-/r*
41×add-exp-log
33×associate-/l*
29×div-exp
25×add-cbrt-cube
15×cbrt-undiv
7×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
2×pow-to-exp pow-exp
1×frac-2neg clear-num associate-/l/
Counts
4 → 14363
Calls
4 calls:
356.0ms
(/ (/ a (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))) (/ (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (/ (pow k m) (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))))
5.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
5.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (/ a (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))) (/ (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (/ (pow k m) (sqrt (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))))
50.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
47.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
57.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify6.4s

Algorithm
egg-herbie
Counts
14375 → 14375
Iterations

Useful iterations: 0 (128.0ms)

IterNodesCost
011440750604

prune45.7s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

97.6% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.1b

bsearch46.0ms

Steps
ItersRangePoint
6
1.4389056776079972e+117
1.818622262293009e+118
8.509642321498123e+117

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05238
15838
25838

end0.0ms

sample1.0s

Algorithm
intervals
Results
515.0ms11955×body80valid
145.0ms4227×body80nan