Details

Time bar (total: 1.7s)

sample16.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
2.0ms256×pre80true

simplify32.0ms

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: 14.6b

localize8.0ms

Local error

Found 1 expressions with local error:

14.1b
(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

rewrite63.0ms

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:
62.0ms
(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

series80.0ms

Counts
1 → 3
Calls
1 calls:
80.0ms
(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

simplify41.0ms

Counts
32 → 32
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0319406
11586285
25001285
done5001285

prune50.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
13.6b
(/ 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:
133.0ms
(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
46.0ms
(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

series158.0ms

Counts
2 → 6
Calls
2 calls:
78.0ms
(* (/ 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))

simplify63.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0549997
12561859
25001846
done5001846

prune179.0ms

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))
0.2b
(/ 1 (pow i 4))
0.4b
(/ 1 (pow i 2))

rewrite23.0ms

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))
10.0ms
(/ 1 (pow i 4))
8.0ms
(/ 1 (pow i 2))

series81.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(fma 0.00390625 (/ 1 (pow i 4)) (fma 0.015625 (/ 1 (pow i 2)) 0.0625))
28.0ms
(/ 1 (pow i 4))
17.0ms
(/ 1 (pow i 2))

simplify37.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0300623
11163535
25001459
done5001459

prune194.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes20.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 16.3b

bsearch43.0ms

Steps
ItersRangePoint
9
3.527561828140126
446184.5066440194
200.93090001216555

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02914
12914
done2914

end0.0ms

sample395.0ms

Algorithm
intervals
Results
216.0ms8000×body80valid
63.0ms8000×pre80true