Details

Time bar (total: 18.9s)

sample56.0ms

Algorithm
intervals
Results
22.0ms376×body80valid
8.0ms157×body80nan

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01215
12415
24813
39613
425613
5140813
done500013

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.7b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(* a (pow k m))
0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
2.7b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
13×add-sqr-sqrt
10×add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity add-log-exp
7×associate-*r*
6×prod-exp
4×unpow-prod-down div-exp
3×pow1 times-frac associate-*l* associate-/r* sum-log 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 → 63
Calls
3 calls:
21.0ms
(* a (pow k m))
24.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
56.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series356.0ms

Counts
3 → 9
Calls
3 calls:
119.0ms
(* a (pow k m))
34.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
203.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.0s

Counts
72 → 72
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01551140
14261079
22062887
done5000875

prune284.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (* k (+ 10.0 k)) 1.0) a) (pow k m))
0.0b
(* k (+ 10.0 k))
0.1b
(/ 1 (/ (/ (+ (* k (+ 10.0 k)) 1.0) a) (pow k m)))
3.9b
(/ (+ (* k (+ 10.0 k)) 1.0) a)

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
1073×times-frac
500×add-sqr-sqrt *-un-lft-identity
498×add-cube-cbrt
198×unpow-prod-down
105×associate-/r*
70×add-exp-log
66×sqr-pow
51×div-exp
43×div-inv
22×add-cbrt-cube
19×associate-/l*
10×cbrt-undiv
8×pow-to-exp pow-exp
7×pow1 rec-exp 1-exp
4×associate-*r* add-log-exp
3×frac-2neg associate-*l* clear-num associate-/l/
2×flip3-+ associate-*r/ flip-+
1×distribute-rgt-in pow-flip distribute-lft-in pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod distribute-lft-out inv-pow unswap-sqr
Counts
4 → 602
Calls
4 calls:
57.0ms
(/ (/ (+ (* k (+ 10.0 k)) 1.0) a) (pow k m))
29.0ms
(* k (+ 10.0 k))
85.0ms
(/ 1 (/ (/ (+ (* k (+ 10.0 k)) 1.0) a) (pow k m)))
51.0ms
(/ (+ (* k (+ 10.0 k)) 1.0) a)

series466.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (/ (+ (* k (+ 10.0 k)) 1.0) a) (pow k m))
70.0ms
(* k (+ 10.0 k))
167.0ms
(/ 1 (/ (/ (+ (* k (+ 10.0 k)) 1.0) a) (pow k m)))
52.0ms
(/ (+ (* k (+ 10.0 k)) 1.0) a)

simplify2.9s

Counts
614 → 614
Iterations

Useful iterations: done (2.9s)

IterNodesCost
089817811
1270516206
done500115662

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ a (cbrt (+ (* (+ 10.0 k) k) 1.0))) (cbrt (+ (* (+ 10.0 k) k) 1.0)))
15.2b
(cbrt (+ (* (+ 10.0 k) k) 1.0))
15.2b
(cbrt (+ (* (+ 10.0 k) k) 1.0))
15.2b
(cbrt (+ (* (+ 10.0 k) k) 1.0))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
270×times-frac
148×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
147×cbrt-prod
24×associate-/l*
22×cbrt-div
16×associate-/r/
11×flip3-+ flip-+
9×add-exp-log
8×div-inv
6×associate-/r* add-cbrt-cube
4×pow1 add-log-exp
3×cbrt-undiv pow1/3 div-exp
1×frac-2neg clear-num associate-/l/
Counts
4 → 230
Calls
4 calls:
83.0ms
(/ (/ a (cbrt (+ (* (+ 10.0 k) k) 1.0))) (cbrt (+ (* (+ 10.0 k) k) 1.0)))
11.0ms
(cbrt (+ (* (+ 10.0 k) k) 1.0))
17.0ms
(cbrt (+ (* (+ 10.0 k) k) 1.0))
11.0ms
(cbrt (+ (* (+ 10.0 k) k) 1.0))

series799.0ms

Counts
4 → 12
Calls
4 calls:
318.0ms
(/ (/ a (cbrt (+ (* (+ 10.0 k) k) 1.0))) (cbrt (+ (* (+ 10.0 k) k) 1.0)))
161.0ms
(cbrt (+ (* (+ 10.0 k) k) 1.0))
139.0ms
(cbrt (+ (* (+ 10.0 k) k) 1.0))
181.0ms
(cbrt (+ (* (+ 10.0 k) k) 1.0))

simplify2.3s

Counts
242 → 242
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03838449
19398174
246327964
done50007796

prune1.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 2.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (pow k m) (sqrt (+ (* (+ 10.0 k) k) 1.0)))
0.1b
(* (/ a (sqrt (+ (* (+ 10.0 k) k) 1.0))) (/ (pow k m) (sqrt (+ (* (+ 10.0 k) k) 1.0))))
14.7b
(sqrt (+ (* (+ 10.0 k) k) 1.0))
14.7b
(sqrt (+ (* (+ 10.0 k) k) 1.0))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
146×add-sqr-sqrt
134×times-frac
76×add-cube-cbrt *-un-lft-identity sqrt-prod
48×associate-*r*
45×unpow-prod-down
33×add-exp-log
24×associate-*l*
21×unswap-sqr
19×sqr-pow
18×add-cbrt-cube
13×div-exp
10×sqrt-div
8×pow1 prod-exp
7×associate-/l*
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod add-log-exp
3×pow-to-exp pow-exp div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 218
Calls
4 calls:
52.0ms
(/ (pow k m) (sqrt (+ (* (+ 10.0 k) k) 1.0)))
188.0ms
(* (/ a (sqrt (+ (* (+ 10.0 k) k) 1.0))) (/ (pow k m) (sqrt (+ (* (+ 10.0 k) k) 1.0))))
32.0ms
(sqrt (+ (* (+ 10.0 k) k) 1.0))
17.0ms
(sqrt (+ (* (+ 10.0 k) k) 1.0))

series506.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(/ (pow k m) (sqrt (+ (* (+ 10.0 k) k) 1.0)))
172.0ms
(* (/ a (sqrt (+ (* (+ 10.0 k) k) 1.0))) (/ (pow k m) (sqrt (+ (* (+ 10.0 k) k) 1.0))))
87.0ms
(sqrt (+ (* (+ 10.0 k) k) 1.0))
75.0ms
(sqrt (+ (* (+ 10.0 k) k) 1.0))

simplify592.0ms

Counts
230 → 230
Iterations

Useful iterations: done (575.0ms)

IterNodesCost
03266183
19315784
done50005541

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 2.6b

regimes125.0ms

Accuracy

0% (0.2b remaining)

Error of 2.1b against oracle of 1.9b and baseline of 2.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01315
11815
done1815

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.5s11820×body80valid
338.0ms4127×body80nan