Details

Time bar (total: 19.5s)

sample74.0ms

Algorithm
intervals
Results
38.0ms379×body80valid
8.0ms139×body80nan

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 3 (18.0ms)

IterNodesCost
01215
12415
25313
310812
427012
5144212
done500112

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.6b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma k (+ 10.0 k) 1.0)
0.0b
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
2.6b
(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
101×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
48×unpow-prod-down
32×associate-/r*
18×add-exp-log
16×sqr-pow
10×div-exp add-cbrt-cube
6×div-inv associate-/l*
4×cbrt-undiv
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-to-exp frac-2neg pow-exp clear-num
1×associate-/r/ fma-udef
Counts
3 → 179
Calls
3 calls:
0.0ms
(fma k (+ 10.0 k) 1.0)
8.0ms
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
30.0ms
(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

series295.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(fma k (+ 10.0 k) 1.0)
89.0ms
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
170.0ms
(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

simplify580.0ms

Counts
188 → 188
Iterations

Useful iterations: done (560.0ms)

IterNodesCost
03374223
18854044
done50013879

prune783.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
0.1b
(* (/ 1 (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))))
8.4b
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
8.4b
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

rewrite368.0ms

Algorithm
rewrite-expression-head
Rules
694×times-frac
544×add-sqr-sqrt
392×sqrt-prod
299×*-un-lft-identity
269×add-cube-cbrt
133×unpow-prod-down
89×associate-*r* associate-*l*
66×unswap-sqr
61×sqr-pow
30×add-exp-log
28×associate-/r*
18×add-cbrt-cube
15×div-inv
10×pow1 div-exp
8×rem-sqrt-square prod-exp
5×cbrt-undiv sqrt-div
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×rec-exp pow-flip sqrt-pow1 pow1/2 1-exp associate-/r/ associate-/l*
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative inv-pow
Counts
4 → 488
Calls
4 calls:
22.0ms
(/ 1 (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
269.0ms
(* (/ 1 (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))))
10.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
18.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

series1.1s

Counts
4 → 12
Calls
4 calls:
186.0ms
(/ 1 (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m))))
147.0ms
(* (/ 1 (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))) (/ a (sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))))
183.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))
587.0ms
(sqrt (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

simplify1.5s

Counts
500 → 500
Iterations

Useful iterations: done (1.4s)

IterNodesCost
066216074
1204415152
done500113975

prune2.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 2.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma k (+ 10.0 k) 1.0)
0.0b
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
0.3b
(/ 1 (/ (/ (fma k (+ 10.0 k) 1.0) (pow k m)) a))
2.4b
(/ (/ (fma k (+ 10.0 k) 1.0) (pow k m)) a)

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
969×times-frac
454×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
156×unpow-prod-down
89×associate-/r*
57×add-exp-log
52×sqr-pow
41×div-exp
31×associate-/l*
23×div-inv
20×add-cbrt-cube
10×cbrt-undiv
5×pow1 pow-to-exp rec-exp 1-exp pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×pow-flip associate-/r/ fma-udef associate-/l/ inv-pow
Counts
4 → 531
Calls
4 calls:
1.0ms
(fma k (+ 10.0 k) 1.0)
15.0ms
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
69.0ms
(/ 1 (/ (/ (fma k (+ 10.0 k) 1.0) (pow k m)) a))
24.0ms
(/ (/ (fma k (+ 10.0 k) 1.0) (pow k m)) a)

series476.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(fma k (+ 10.0 k) 1.0)
118.0ms
(/ (fma k (+ 10.0 k) 1.0) (pow k m))
163.0ms
(/ 1 (/ (/ (fma k (+ 10.0 k) 1.0) (pow k m)) a))
169.0ms
(/ (/ (fma k (+ 10.0 k) 1.0) (pow k m)) a)

simplify2.7s

Counts
543 → 543
Iterations

Useful iterations: done (2.7s)

IterNodesCost
081715008
1240513653
done500013155

prune1.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 2.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (fma k (+ 10.0 k) 1.0)) (/ (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k m)) a))
0.3b
(/ 1 (* (sqrt (fma k (+ 10.0 k) 1.0)) (/ (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k m)) a)))
16.2b
(sqrt (fma k (+ 10.0 k) 1.0))
16.2b
(sqrt (fma k (+ 10.0 k) 1.0))

rewrite315.0ms

Algorithm
rewrite-expression-head
Rules
293×times-frac
194×add-sqr-sqrt
142×associate-*r*
138×add-cube-cbrt *-un-lft-identity
86×sqrt-prod
77×add-exp-log
58×unpow-prod-down
40×div-exp
27×add-cbrt-cube
22×sqr-pow
20×prod-exp
16×unswap-sqr
11×pow1
10×cbrt-undiv
6×rec-exp 1-exp associate-*l* cbrt-unprod
5×div-inv
4×expm1-log1p-u pow-to-exp pow-exp log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square pow-flip sqrt-pow1 pow1/2 associate-*r/ pow-prod-down
1×frac-2neg clear-num associate-/r* associate-/r/ *-commutative inv-pow
Counts
4 → 259
Calls
4 calls:
167.0ms
(* (sqrt (fma k (+ 10.0 k) 1.0)) (/ (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k m)) a))
104.0ms
(/ 1 (* (sqrt (fma k (+ 10.0 k) 1.0)) (/ (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k m)) a)))
3.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
3.0ms
(sqrt (fma k (+ 10.0 k) 1.0))

series505.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(* (sqrt (fma k (+ 10.0 k) 1.0)) (/ (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k m)) a))
186.0ms
(/ 1 (* (sqrt (fma k (+ 10.0 k) 1.0)) (/ (/ (sqrt (fma k (+ 10.0 k) 1.0)) (pow k m)) a)))
76.0ms
(sqrt (fma k (+ 10.0 k) 1.0))
85.0ms
(sqrt (fma k (+ 10.0 k) 1.0))

simplify1.1s

Counts
271 → 271
Iterations

Useful iterations: done (1.1s)

IterNodesCost
04977115
115226465
done50006079

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 2.5b

regimes105.0ms

Accuracy

0% (0.1b remaining)

Error of 2.0b against oracle of 1.9b and baseline of 2.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01427
11827
done1827

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.4s11959×body80valid
333.0ms4221×body80nan