Details

Time bar (total: 15.1s)

sample44.0ms

Algorithm
intervals
Results
15.0ms391×body80valid
5.0ms168×body80nan

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 3 (17.0ms)

IterNodesCost
01215
12415
25313
310712
425412
573512
6272912
done500112

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
2.3b
(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
100×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
48×unpow-prod-down
32×associate-/r*
17×add-exp-log
16×sqr-pow
10×div-exp
9×add-cbrt-cube
6×div-inv associate-/l*
4×cbrt-undiv
2×pow1 expm1-log1p-u pow-to-exp frac-2neg pow-exp clear-num log1p-expm1-u add-log-exp
1×associate-/r/
Counts
2 → 169
Calls
2 calls:
7.0ms
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
17.0ms
(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

series192.0ms

Counts
2 → 6
Calls
2 calls:
74.0ms
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
118.0ms
(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

simplify1.1s

Counts
175 → 175
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03314107
17133899
223573762
done50003717

prune506.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ a (sqrt (fma k (+ 10.0 k) 1.0)))
0.0b
(/ (/ a (sqrt (fma k (+ 10.0 k) 1.0))) (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k m)))
12.1b
(sqrt (fma k (+ 10.0 k) 1.0))
12.1b
(sqrt (fma k (+ 10.0 k) 1.0))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
2842×times-frac
1255×add-sqr-sqrt
1253×add-cube-cbrt *-un-lft-identity
924×sqrt-prod
414×unpow-prod-down
138×sqr-pow
72×div-inv
52×associate-/r*
30×add-exp-log
25×associate-/l*
19×div-exp
18×add-cbrt-cube
9×cbrt-undiv
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num
1×associate-/r/ associate-/l/
Counts
4 → 1177
Calls
4 calls:
6.0ms
(/ a (sqrt (fma k (+ 10.0 k) 1.0)))
44.0ms
(/ (/ a (sqrt (fma k (+ 10.0 k) 1.0))) (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k m)))
1.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
1.0ms
(sqrt (fma k (+ 10.0 k) 1.0))

series332.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ a (sqrt (fma k (+ 10.0 k) 1.0)))
116.0ms
(/ (/ a (sqrt (fma k (+ 10.0 k) 1.0))) (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k m)))
57.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
50.0ms
(sqrt (fma k (+ 10.0 k) 1.0))

simplify2.3s

Counts
1189 → 1189
Iterations

Useful iterations: done (2.2s)

IterNodesCost
0145054472
1397548600
done500147185

prune2.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (pow k m) a)
0.3b
(/ 1 (fma k (+ 10.0 k) 1.0))
2.1b
(* (/ 1 (fma k (+ 10.0 k) 1.0)) (* (pow k m) a))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
56×add-exp-log
31×prod-exp
26×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
20×associate-*l*
19×add-cbrt-cube
18×times-frac
10×div-exp
7×cbrt-unprod
6×pow1
5×pow-to-exp rec-exp 1-exp pow-exp
4×unpow-prod-down associate-*r*
3×cbrt-undiv expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×*-commutative div-inv sqr-pow
1×pow-flip frac-2neg pow-prod-down associate-*l/ clear-num inv-pow
Counts
3 → 106
Calls
3 calls:
11.0ms
(* (pow k m) a)
5.0ms
(/ 1 (fma k (+ 10.0 k) 1.0))
32.0ms
(* (/ 1 (fma k (+ 10.0 k) 1.0)) (* (pow k m) a))

series256.0ms

Counts
3 → 9
Calls
3 calls:
102.0ms
(* (pow k m) a)
39.0ms
(/ 1 (fma k (+ 10.0 k) 1.0))
115.0ms
(* (/ 1 (fma k (+ 10.0 k) 1.0)) (* (pow k m) a))

simplify1.3s

Counts
115 → 115
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01921704
14561498
213861317
done50001281

prune247.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

12.1b
(sqrt (fma k (+ 10.0 k) 1.0))
12.1b
(sqrt (fma k (+ 10.0 k) 1.0))
12.6b
(cbrt (fma k (+ 10.0 k) 1.0))
12.6b
(cbrt (fma k (+ 10.0 k) 1.0))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
1.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
1.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
1.0ms
(cbrt (fma k (+ 10.0 k) 1.0))
1.0ms
(cbrt (fma k (+ 10.0 k) 1.0))

series346.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
60.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
116.0ms
(cbrt (fma k (+ 10.0 k) 1.0))
118.0ms
(cbrt (fma k (+ 10.0 k) 1.0))

simplify2.1s

Counts
68 → 68
Iterations

Useful iterations: 4 (1.2s)

IterNodesCost
089842
1200776
2515724
31403702
44412696
done5000696

prune398.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes82.0ms

Accuracy

97.3% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch61.0ms

Steps
ItersRangePoint
9
6.524589428332346e+47
1.6525700559986095e+56
4.3724534202259655e+54

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03254
13850
done3850

end0.0ms

sample1.1s

Algorithm
intervals
Results
468.0ms11914×body80valid
144.0ms4329×body80nan