Details

Time bar (total: 16.0s)

sample113.0ms

Algorithm
intervals
Results
64.0ms390×body80valid
23.0ms144×body80nan

simplify1.3s

Counts
1 → 1
Iterations
IterNodes
done2000
62000
5639
4204
387
247
126
012

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.8b

localize34.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ k 10) k)
2.8b
(/ (* (pow k m) a) (+ (* (+ k 10) k) 1))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log
9×add-cbrt-cube
8×add-sqr-sqrt *-un-lft-identity
6×add-cube-cbrt
4×pow1 div-exp associate-*l* prod-exp
3×associate-/r* times-frac associate-*r*
2×cbrt-undiv flip3-+ associate-*l/ associate-/r/ cbrt-unprod flip-+ insert-posit16 add-log-exp
1×pow-to-exp clear-num frac-2neg pow-prod-down pow-exp *-commutative div-inv distribute-lft-out associate-/l* unswap-sqr
Counts
2 → 48
Calls
2 calls:
14.0ms
(* (+ k 10) k)
42.0ms
(/ (* (pow k m) a) (+ (* (+ k 10) k) 1))

series183.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(* (+ k 10) k)
122.0ms
(/ (* (pow k m) a) (+ (* (+ k 10) k) 1))

simplify1.4s

Counts
54 → 54
Iterations
IterNodes
done2264
32264
21232
1380
0140

prune232.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 2.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ k 10) k)
0.0b
(* (/ (pow k m) (sqrt (+ (* (+ k 10) k) 1))) (/ a (sqrt (+ (* (+ k 10) k) 1))))
15.0b
(sqrt (+ (* (+ k 10) k) 1))
15.0b
(sqrt (+ (* (+ k 10) k) 1))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
120×add-sqr-sqrt
92×times-frac
52×associate-*l* sqrt-prod
50×*-un-lft-identity
48×add-cube-cbrt
30×add-exp-log
27×associate-*r*
24×unpow-prod-down
22×unswap-sqr
18×add-cbrt-cube
12×sqr-pow
10×pow1 div-exp
9×prod-exp
8×sqrt-div
5×flip3-+ cbrt-unprod flip-+
4×cbrt-undiv associate-/r/ insert-posit16 add-log-exp
3×associate-*l/
2×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down pow-exp *-commutative div-inv
1×frac-times associate-*r/ distribute-lft-out
Counts
4 → 172
Calls
4 calls:
22.0ms
(* (+ k 10) k)
92.0ms
(* (/ (pow k m) (sqrt (+ (* (+ k 10) k) 1))) (/ a (sqrt (+ (* (+ k 10) k) 1))))
11.0ms
(sqrt (+ (* (+ k 10) k) 1))
12.0ms
(sqrt (+ (* (+ k 10) k) 1))

series235.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (+ k 10) k)
113.0ms
(* (/ (pow k m) (sqrt (+ (* (+ k 10) k) 1))) (/ a (sqrt (+ (* (+ k 10) k) 1))))
39.0ms
(sqrt (+ (* (+ k 10) k) 1))
32.0ms
(sqrt (+ (* (+ k 10) k) 1))

simplify1.3s

Counts
184 → 184
Iterations
IterNodes
done2002
22002
1816
0276

prune997.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b
(* k (+ (* k (* k k)) 1000))
0.1b
(* k (* k k))
2.8b
(/ (* (pow k m) a) (+ (/ (* k (+ (* k (* k k)) 1000)) (+ (* k k) (- (* 10 10) (* k 10)))) 1))
21.0b
(/ (* k (+ (* k (* k k)) 1000)) (+ (* k k) (- (* 10 10) (* k 10))))

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
21×add-cbrt-cube
20×pow1
15×*-un-lft-identity
14×add-sqr-sqrt
11×add-cube-cbrt
8×prod-exp
7×associate-/r* times-frac
6×div-exp associate-*l* cbrt-unprod
5×pow-prod-up
4×cbrt-undiv flip3-+ associate-*r* pow-prod-down associate-*r/ associate-/r/ flip-+ insert-posit16 add-log-exp
2×clear-num frac-2neg *-commutative div-inv distribute-lft-out associate-/l* unswap-sqr associate-/l/
1×pow2 distribute-rgt-in pow-to-exp distribute-lft-in pow-plus cube-unmult pow-exp pow-sqr
Counts
4 → 102
Calls
4 calls:
54.0ms
(* k (+ (* k (* k k)) 1000))
27.0ms
(* k (* k k))
170.0ms
(/ (* (pow k m) a) (+ (/ (* k (+ (* k (* k k)) 1000)) (+ (* k k) (- (* 10 10) (* k 10)))) 1))
76.0ms
(/ (* k (+ (* k (* k k)) 1000)) (+ (* k k) (- (* 10 10) (* k 10))))

series700.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(* k (+ (* k (* k k)) 1000))
60.0ms
(* k (* k k))
209.0ms
(/ (* (pow k m) a) (+ (/ (* k (+ (* k (* k k)) 1000)) (+ (* k k) (- (* 10 10) (* k 10)))) 1))
305.0ms
(/ (* k (+ (* k (* k k)) 1000)) (+ (* k k) (- (* 10 10) (* k 10))))

simplify1.3s

Counts
114 → 114
Iterations
IterNodes
done2008
22008
1664
0223

prune641.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (/ a k) (/ (exp (- (- (* m (log k))))) (* k k)))
4.2b
(/ (exp (- (- (* m (log k))))) (* k k))
8.1b
(/ (* (* 99 a) (exp (- (- (* m (log k)))))) (* (* k k) (* k k)))
9.6b
(- (/ (* (* 99 a) (exp (- (- (* m (log k)))))) (* (* k k) (* k k))) (* 10 (* (/ a k) (/ (exp (- (- (* m (log k))))) (* k k)))))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
99×add-cbrt-cube
83×add-exp-log
48×prod-exp cbrt-unprod
44×distribute-neg-in
41×add-sqr-sqrt
38×times-frac
24×cbrt-undiv div-exp
22×log-prod exp-sum
21×*-un-lft-identity add-cube-cbrt
13×associate-*r* associate-*l*
11×distribute-rgt-in distribute-lft-in
10×associate-/l*
8×unswap-sqr
7×associate-*r/
6×pow1 add-log-exp
5×associate-/l/
4×insert-posit16 div-inv
3×exp-neg frac-sub
2×neg-sub0 frac-times clear-num associate-/r* frac-2neg exp-diff associate-*l/
1×sub-neg flip3-- diff-log pow-prod-down un-div-inv *-commutative flip--
Counts
4 → 158
Calls
4 calls:
54.0ms
(* (/ a k) (/ (exp (- (- (* m (log k))))) (* k k)))
35.0ms
(/ (exp (- (- (* m (log k))))) (* k k))
55.0ms
(/ (* (* 99 a) (exp (- (- (* m (log k)))))) (* (* k k) (* k k)))
113.0ms
(- (/ (* (* 99 a) (exp (- (- (* m (log k)))))) (* (* k k) (* k k))) (* 10 (* (/ a k) (/ (exp (- (- (* m (log k))))) (* k k)))))

series513.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (/ a k) (/ (exp (- (- (* m (log k))))) (* k k)))
80.0ms
(/ (exp (- (- (* m (log k))))) (* k k))
119.0ms
(/ (* (* 99 a) (exp (- (- (* m (log k)))))) (* (* k k) (* k k)))
204.0ms
(- (/ (* (* 99 a) (exp (- (- (* m (log k)))))) (* (* k k) (* k k))) (* 10 (* (/ a k) (/ (exp (- (- (* m (log k))))) (* k k)))))

simplify1.3s

Counts
170 → 170
Iterations
IterNodes
done2020
22020
11091
0358

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes143.0ms

Accuracy

98.7% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.0b

bsearch70.0ms

Steps
ItersRangePoint
4
2.8377692699023555e+153
4.746104912308318e+153
3.2541396121661334e+153

simplify13.0ms

Iterations
IterNodes
done62
362
257
150
033

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.0s11958×body80valid
680.0ms4280×body80nan