Details

Time bar (total: 3.7s)

sample20.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
6.0ms256×pre80true

simplify378.0ms

Counts
1 → 1
Iterations

Useful iterations: done (377.0ms)

IterNodesCost
01025
13225
216723
389319
done500017

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize8.0ms

Local error

Found 1 expressions with local error:

17.0b
(/ (* i i) (* (- (* (* 2.0 i) (* 2.0 i)) 1.0) (* 2.0 2.0)))

rewrite22.0ms

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:
21.0ms
(/ (* 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)))

simplify457.0ms

Counts
32 → 32
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
098851
1312830
21467578
done5000578

prune59.0ms

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)))
16.3b
(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

rewrite81.0ms

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:
56.0ms
(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
20.0ms
(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

series168.0ms

Counts
2 → 6
Calls
2 calls:
83.0ms
(* (/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0)) (/ i (* 2.0 2.0)))
85.0ms
(/ i (- (* (* 2.0 i) (* 2.0 i)) 1.0))

simplify870.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (182.0ms)

IterNodesCost
01922054
15571988
225131693
done50001693

prune195.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 0.00390625 (pow i 4))
0.3b
(/ 0.015625 (pow i 2))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
35×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
15×associate-/r*
12×add-exp-log
8×sqr-pow
6×div-exp add-cbrt-cube associate-/l*
4×unpow2
2×pow1 cbrt-undiv expm1-log1p-u pow-to-exp frac-2neg pow-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
2 → 98
Calls
2 calls:
3.0ms
(/ 0.00390625 (pow i 4))
4.0ms
(/ 0.015625 (pow i 2))

series65.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ 0.00390625 (pow i 4))
29.0ms
(/ 0.015625 (pow i 2))

simplify547.0ms

Counts
104 → 104
Iterations

Useful iterations: done (544.0ms)

IterNodesCost
01701064
1296966
21087870
done5001862

prune224.0ms

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 15.1b

bsearch40.0ms

Steps
ItersRangePoint
7
12.705855632074393
434.2008027916323
245.4970352238536

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02434
12834
done2834

end0.0ms

sample394.0ms

Algorithm
intervals
Results
222.0ms8000×body80valid
72.0ms8000×pre80true