Details

Time bar (total: 17.6s)

sample65.0ms

Algorithm
intervals
Results
23.0ms369×body80valid
14.0ms133×body80nan

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01215
12415
24813
39513
423913
571813
6274513
done500013

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.4b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (* 10.0 k))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
1.4b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
10×add-log-exp
8×add-cbrt-cube
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×div-exp sum-log
3×pow1 flip3-+ times-frac prod-exp associate-/r* flip-+
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 → 49
Calls
3 calls:
8.0ms
(+ 1.0 (* 10.0 k))
23.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
65.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series287.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(+ 1.0 (* 10.0 k))
24.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
215.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.2s

Counts
58 → 58
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01411027
1399876
21441782
done5000737

prune219.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(* k (+ 10.0 k))
0.2b
(/ 1 (+ 1.0 (* k (+ 10.0 k))))
1.2b
(* (* a (pow k m)) (/ 1 (+ 1.0 (* k (+ 10.0 k)))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
53×add-exp-log
29×prod-exp
22×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
19×associate-*r* add-cbrt-cube
18×times-frac
10×div-exp
8×pow1
7×cbrt-unprod
5×rec-exp 1-exp
4×pow-to-exp associate-*l* pow-exp associate-/r/
3×cbrt-undiv flip3-+ associate-*r/ associate-/r* flip-+ associate-/l* add-log-exp
2×pow-prod-down *-commutative div-inv
1×distribute-rgt-in pow-flip frac-2neg distribute-lft-in clear-num un-div-inv distribute-lft-out inv-pow unswap-sqr
Counts
3 → 103
Calls
3 calls:
32.0ms
(* k (+ 10.0 k))
20.0ms
(/ 1 (+ 1.0 (* k (+ 10.0 k))))
76.0ms
(* (* a (pow k m)) (/ 1 (+ 1.0 (* k (+ 10.0 k)))))

series300.0ms

Counts
3 → 9
Calls
3 calls:
87.0ms
(* k (+ 10.0 k))
46.0ms
(/ 1 (+ 1.0 (* k (+ 10.0 k))))
167.0ms
(* (* a (pow k m)) (/ 1 (+ 1.0 (* k (+ 10.0 k)))))

simplify1.6s

Counts
112 → 112
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02031785
15481558
218211370
done50011337

prune383.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
1.2b
(* (* a (pow k m)) (/ (/ 1 (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
13.2b
(sqrt (+ 1.0 (* (+ 10.0 k) k)))
13.2b
(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
522×times-frac
276×add-sqr-sqrt
274×add-cube-cbrt *-un-lft-identity
270×sqrt-prod
150×associate-*r*
83×add-exp-log
35×prod-exp
34×sqrt-div
30×div-exp associate-/r/ add-cbrt-cube
24×associate-/l*
17×flip3-+ flip-+
15×div-inv
9×cbrt-undiv cbrt-unprod
8×pow1
6×associate-/r*
5×pow-to-exp rec-exp 1-exp pow-exp
4×add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*r/ associate-*l* pow-prod-down clear-num *-commutative associate-/l/
Counts
4 → 410
Calls
4 calls:
59.0ms
(/ (/ 1 (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
134.0ms
(* (* a (pow k m)) (/ (/ 1 (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
12.0ms
(sqrt (+ 1.0 (* (+ 10.0 k) k)))
11.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

series366.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ (/ 1 (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
172.0ms
(* (* a (pow k m)) (/ (/ 1 (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
62.0ms
(sqrt (+ 1.0 (* (+ 10.0 k) k)))
83.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify2.1s

Counts
422 → 422
Iterations

Useful iterations: done (2.1s)

IterNodesCost
052914029
1147211117
2356010117
done50029754

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 10.0 k) k)
0.0b
(* (/ (* (pow k m) a) (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (/ 1 (sqrt (+ 1.0 (* k (+ 10.0 k))))))
13.2b
(sqrt (+ 1.0 (* (+ 10.0 k) k)))
13.2b
(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log
40×add-sqr-sqrt
33×prod-exp
28×*-un-lft-identity times-frac
27×associate-*r* add-cbrt-cube
26×div-exp
24×add-cube-cbrt
20×sqrt-prod
16×associate-*l*
10×pow1
9×cbrt-unprod
8×sqrt-div
7×cbrt-undiv
6×unswap-sqr
5×rec-exp flip3-+ 1-exp flip-+
4×pow-to-exp pow-exp associate-/r/ add-log-exp
3×associate-*l/
2×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down *-commutative div-inv
1×frac-times associate-*r/ un-div-inv distribute-lft-out
Counts
4 → 131
Calls
4 calls:
22.0ms
(* (+ 10.0 k) k)
96.0ms
(* (/ (* (pow k m) a) (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (/ 1 (sqrt (+ 1.0 (* k (+ 10.0 k))))))
11.0ms
(sqrt (+ 1.0 (* (+ 10.0 k) k)))
10.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

series332.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (+ 10.0 k) k)
143.0ms
(* (/ (* (pow k m) a) (sqrt (+ 1.0 (* (+ 10.0 k) k)))) (/ 1 (sqrt (+ 1.0 (* k (+ 10.0 k))))))
63.0ms
(sqrt (+ 1.0 (* (+ 10.0 k) k)))
68.0ms
(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify2.0s

Counts
143 → 143
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02883412
17622983
225652279
done50022264

prune536.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes126.0ms

Accuracy

97.3% (0.0b remaining)

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

bsearch119.0ms

Steps
ItersRangePoint
8
6.078647819315964e+130
2.9949035539067785e+135
4.309780576654703e+132

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03561
14761
done4761

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.6s11910×body80valid
368.0ms4225×body80nan