Details

Time bar (total: 1.7s)

sample18.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
2.0ms256×pre80true

simplify31.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
03212
117211
29749
350018
done50018

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize8.0ms

Local error

Found 1 expressions with local error:

15.3b
(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log add-cbrt-cube
9×prod-exp cbrt-unprod
6×cbrt-undiv div-exp
2×associate-*l/ associate-/r/
1×pow1 add-sqr-sqrt expm1-log1p-u add-cube-cbrt flip3-- frac-2neg *-un-lft-identity times-frac clear-num associate-/r* flip-- log1p-expm1-u div-inv associate-/l* add-log-exp
Counts
1 → 29
Calls
1 calls:
60.0ms
(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

series81.0ms

Counts
1 → 3
Calls
1 calls:
81.0ms
(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

simplify43.0ms

Counts
32 → 32
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0319406
11586285
25001285
done5001285

prune53.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
14.7b
(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
31×times-frac
25×add-exp-log add-cbrt-cube
21×add-cube-cbrt *-un-lft-identity
18×associate-*l*
8×cbrt-undiv div-exp prod-exp cbrt-unprod
7×associate-*r* difference-of-squares
4×pow1 associate-/r* associate-/r/ unswap-sqr
3×div-inv associate-/l*
2×expm1-log1p-u flip3-- flip-- log1p-expm1-u add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
2 → 90
Calls
2 calls:
132.0ms
(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
48.0ms
(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

series159.0ms

Counts
2 → 6
Calls
2 calls:
79.0ms
(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
80.0ms
(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

simplify64.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0549997
12561859
25001846
done5001846

prune181.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 0.00390625 (/ 1 (pow i 4)) (fma 0.015625 (/ 1 (pow i 2)) 0.0625))
0.3b
(/ 1 (pow i 2))
0.3b
(/ 1 (pow i 4))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
36×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
21×add-exp-log
15×associate-/r*
12×div-exp
8×sqr-pow
7×add-cbrt-cube
6×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
4×unpow2
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv pow-flip frac-2neg clear-num div-inv inv-pow
1×fma-udef
Counts
3 → 124
Calls
3 calls:
0.0ms
(fma 0.00390625 (/ 1 (pow i 4)) (fma 0.015625 (/ 1 (pow i 2)) 0.0625))
8.0ms
(/ 1 (pow i 2))
8.0ms
(/ 1 (pow i 4))

series81.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(fma 0.00390625 (/ 1 (pow i 4)) (fma 0.015625 (/ 1 (pow i 2)) 0.0625))
17.0ms
(/ 1 (pow i 2))
32.0ms
(/ 1 (pow i 4))

simplify36.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0300623
11168535
25001459
done5001459

prune191.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes17.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch40.0ms

Steps
ItersRangePoint
7
13.84420111739038
2682.073445789064
383.24648239598304

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02914
12914
done2914

end0.0ms

sample406.0ms

Algorithm
intervals
Results
220.0ms8000×body80valid
64.0ms8000×pre80true