Details

Time bar (total: 47.7s)

sample36.0ms

Algorithm
intervals
Results
15.0ms378×body80valid
5.0ms147×body80nan

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 3 (16.0ms)

IterNodesCost
01215
12415
25213
310112
423212
566212
6235412
done500012

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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:
2.0ms
(+ 1.0 (* 10.0 k))
6.0ms
(* a (pow k m))
11.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
14.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ 1.0 (* 10.0 k))
57.0ms
(* a (pow k m))
19.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
123.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify753.0ms

Counts
100 → 100
Iterations

Useful iterations: done (751.0ms)

IterNodesCost
01791340
14751136
21615982
done5001978

prune284.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.4b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
59×cbrt-prod
46×add-sqr-sqrt
29×add-exp-log
23×unpow-prod-down
22×add-cube-cbrt *-un-lft-identity
20×pow1 associate-*r*
17×add-cbrt-cube
16×unswap-sqr
13×prod-exp cbrt-unprod sqr-pow
11×associate-*l*
10×swap-sqr
9×add-log-exp
8×pow-prod-down
6×pow1/3
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×fma-def times-frac associate-/r* sum-log
2×flip3-+ associate-/r/ pow-sqr *-commutative pow-prod-up flip-+
1×+-commutative pow2 associate-+l+ frac-2neg pow-plus clear-num div-inv associate-/l*
Counts
4 → 143
Calls
4 calls:
60.0ms
(* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m)))
11.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
13.0ms
(* (cbrt (pow k m)) (cbrt (pow k m)))
67.0ms
(/ (* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m)))
19.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
108.0ms
(* (cbrt (pow k m)) (cbrt (pow k m)))
120.0ms
(/ (* (* a (* (cbrt (pow k m)) (cbrt (pow k m)))) (cbrt (pow k m))) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.0s

Counts
155 → 155
Iterations

Useful iterations: 2 (376.0ms)

IterNodesCost
02473060
16372786
226002103
done50012103

prune481.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (cbrt (pow k m)) 3)
0.1b
(/ (/ a (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow (cbrt (pow k m)) 3))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
15.4b
(sqrt (fma k (+ 10.0 k) 1.0))
15.4b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite741.0ms

Algorithm
rewrite-expression-head
Rules
9546×times-frac
4110×add-sqr-sqrt
4107×add-cube-cbrt *-un-lft-identity
3102×sqrt-prod
2032×unpow-prod-down
1778×cbrt-prod
1270×cube-prod
485×associate-/l*
381×sqr-pow
127×cube-mult unpow3
29×div-inv
21×add-exp-log
13×add-cbrt-cube
12×div-exp
9×associate-/r/
7×pow1
6×cbrt-undiv associate-/r*
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×pow-unpow
2×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 flip3-+ pow1/2 pow-exp flip-+
1×frac-2neg pow1/3 clear-num hypot-def associate-/l/ rem-cube-cbrt
Counts
4 → 3497
Calls
4 calls:
4.0ms
(pow (cbrt (pow k m)) 3)
203.0ms
(/ (/ a (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow (cbrt (pow k m)) 3))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
1.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
13.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(pow (cbrt (pow k m)) 3)
177.0ms
(/ (/ a (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow (cbrt (pow k m)) 3))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
58.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
49.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.2s

Counts
3509 → 3509
Iterations

Useful iterations: 0 (381.0ms)

IterNodesCost
02820200036
done5000200036

prune11.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 1 (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow (cbrt (pow k m)) 3))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
1.3b
(* (/ a 1) (/ (/ 1 (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow (cbrt (pow k m)) 3))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
15.4b
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.4b
(sqrt (fma k (+ 10.0 k) 1.0))

rewrite2.7s

Algorithm
rewrite-expression-head
Rules
19077×times-frac
8918×add-sqr-sqrt
7967×*-un-lft-identity
7754×add-cube-cbrt
6210×sqrt-prod
3888×unpow-prod-down
3420×cbrt-prod
2916×associate-*r*
2436×cube-prod
774×sqr-pow
485×associate-/l*
261×unswap-sqr
234×cube-mult unpow3
207×add-exp-log
148×div-exp
55×div-inv
45×add-cbrt-cube
42×prod-exp
30×1-exp
22×cbrt-undiv
17×associate-/r/
16×rec-exp
13×associate-*l*
12×pow-to-exp pow-exp
8×pow1 cbrt-unprod
6×sqrt-div associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative hypot-def associate-/l/
Counts
4 → 6719
Calls
4 calls:
208.0ms
(/ (/ 1 (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow (cbrt (pow k m)) 3))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
1.3s
(* (/ a 1) (/ (/ 1 (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow (cbrt (pow k m)) 3))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
12.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
1.0ms
(sqrt (fma k (+ 10.0 k) 1.0))

series480.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(/ (/ 1 (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow (cbrt (pow k m)) 3))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
182.0ms
(* (/ a 1) (/ (/ 1 (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow (cbrt (pow k m)) 3))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
55.0ms
(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
53.0ms
(sqrt (fma k (+ 10.0 k) 1.0))

simplify2.3s

Counts
6731 → 6731
Iterations

Useful iterations: 0 (909.0ms)

IterNodesCost
04205330948
done5000330948

prune21.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.4b

regimes83.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01526
12026
done2026

end0.0ms

sample918.0ms

Algorithm
intervals
Results
454.0ms11895×body80valid
136.0ms4267×body80nan