Details

Time bar (total: 18.9s)

sample90.0ms

Algorithm
intervals
Results
38.0ms78×body1280valid
23.0ms31×body2560valid
11.0ms40×body640valid
4.0ms26×body320valid
3.0ms72×body80valid
1.0ms9×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
07232
110207
done10207

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (fma x x 1.0)))
2.1b
(log (+ x (sqrt (fma x x 1.0))))
16.8b
(sqrt (fma x x 1.0))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
7×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×log-prod add-exp-log
3×expm1-log1p-u fma-def add-cbrt-cube sqrt-prod log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 49
Calls
3 calls:
10.0ms
(+ x (sqrt (fma x x 1.0)))
9.0ms
(log (+ x (sqrt (fma x x 1.0))))
3.0ms
(sqrt (fma x x 1.0))

series421.0ms

Counts
3 → 9
Calls
3 calls:
93.0ms
(+ x (sqrt (fma x x 1.0)))
253.0ms
(log (+ x (sqrt (fma x x 1.0))))
74.0ms
(sqrt (fma x x 1.0))

simplify2.3s

Counts
58 → 58
Iterations

Useful iterations: done (2.3s)

IterNodesCost
012618143
128814293
284213647
3282813537
done501613487

prune316.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma -1/6 (/ (* x (* x x)) (* 1.0 (sqrt 1.0))) (+ (/ x (sqrt 1.0)) (log (sqrt 1.0))))
0.1b
(* x (* x x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
7×add-cbrt-cube add-exp-log
5×pow-prod-up
4×add-sqr-sqrt
3×*-un-lft-identity associate-*l* pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×pow2 pow-plus cube-unmult associate-*r* pow-sqr *-commutative fma-udef unswap-sqr
Counts
2 → 36
Calls
2 calls:
0.0ms
(fma -1/6 (/ (* x (* x x)) (* 1.0 (sqrt 1.0))) (+ (/ x (sqrt 1.0)) (log (sqrt 1.0))))
13.0ms
(* x (* x x))

series199.0ms

Counts
2 → 6
Calls
2 calls:
153.0ms
(fma -1/6 (/ (* x (* x x)) (* 1.0 (sqrt 1.0))) (+ (/ x (sqrt 1.0)) (log (sqrt 1.0))))
45.0ms
(* x (* x x))

simplify1.9s

Counts
42 → 42
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0609920
11178742
23838305
313798305
done50017875

prune196.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (fma 2 x (/ 0.5 x)) (/ 0.125 (* x (* x x))))
0.1b
(* x (* x x))
0.1b
(/ 0.125 (* x (* x x)))
11.2b
(log (- (fma 2 x (/ 0.5 x)) (/ 0.125 (* x (* x x)))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
26×*-un-lft-identity
22×add-cube-cbrt
21×prod-diff
19×pow1 add-exp-log
18×add-cbrt-cube
12×times-frac
6×prod-exp cbrt-unprod add-log-exp
5×log-prod pow-prod-up
4×expm1-log1p-u log1p-expm1-u div-inv
3×cbrt-undiv fma-neg div-exp associate-*l* pow-prod-down associate-/l*
2×log-div flip3-- flip-- distribute-lft-out-- difference-of-squares
1×pow2 clear-num associate-/r* sub-neg frac-2neg pow-plus diff-log cube-unmult rem-log-exp associate-*r* associate--l+ pow-sqr log-pow *-commutative fma-udef unswap-sqr
Counts
4 → 110
Calls
4 calls:
26.0ms
(- (fma 2 x (/ 0.5 x)) (/ 0.125 (* x (* x x))))
13.0ms
(* x (* x x))
14.0ms
(/ 0.125 (* x (* x x)))
23.0ms
(log (- (fma 2 x (/ 0.5 x)) (/ 0.125 (* x (* x x)))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(- (fma 2 x (/ 0.5 x)) (/ 0.125 (* x (* x x))))
36.0ms
(* x (* x x))
40.0ms
(/ 0.125 (* x (* x x)))
188.0ms
(log (- (fma 2 x (/ 0.5 x)) (/ 0.125 (* x (* x x)))))

simplify2.6s

Counts
122 → 122
Iterations

Useful iterations: done (2.6s)

IterNodesCost
021446129
148941024
2143836709
done500036094

prune505.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.125 (* x (* x x)))
0.2b
(/ 0.0625 (pow x 5))
13.4b
(log (- (- (/ 0.125 (* x (* x x))) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
19.5b
(- (/ 0.125 (* x (* x x))) (/ 0.0625 (pow x 5)))

rewrite371.0ms

Algorithm
rewrite-expression-head
Rules
253×times-frac
188×add-sqr-sqrt
180×*-un-lft-identity
175×prod-diff
173×add-cube-cbrt
76×unpow-prod-down
35×div-inv
26×sqr-pow
19×add-exp-log
15×add-cbrt-cube
8×associate-/r*
7×log-prod fma-neg
6×div-exp associate-/l* add-log-exp difference-of-squares
5×pow1 log-div frac-sub
4×expm1-log1p-u cbrt-undiv log1p-expm1-u distribute-lft-out--
3×flip3-- prod-exp cbrt-unprod flip--
2×clear-num frac-2neg
1×pow-to-exp sub-neg diff-log rem-log-exp pow-exp log-pow
Counts
4 → 297
Calls
4 calls:
13.0ms
(/ 0.125 (* x (* x x)))
6.0ms
(/ 0.0625 (pow x 5))
268.0ms
(log (- (- (/ 0.125 (* x (* x x))) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
69.0ms
(- (/ 0.125 (* x (* x x))) (/ 0.0625 (pow x 5)))

series492.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ 0.125 (* x (* x x)))
59.0ms
(/ 0.0625 (pow x 5))
211.0ms
(log (- (- (/ 0.125 (* x (* x x))) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
166.0ms
(- (/ 0.125 (* x (* x x))) (/ 0.0625 (pow x 5)))

simplify3.7s

Counts
309 → 309
Iterations

Useful iterations: done (3.6s)

IterNodesCost
0556295712
11316270405
24050203452
done5017202852

prune1.9s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes58.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.3b

bsearch130.0ms

Steps
ItersRangePoint
9
0.1909160003853501
166131308.15705827
0.8807071635272687
10
-27652538170.40468
-0.18371106458419734
-1.0266836572228921

simplify12.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0331320
1361320
done361320

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.8s2272×body1280valid
551.0ms1555×body640valid
371.0ms832×body2560valid
156.0ms795×body320valid
140.0ms2154×body80valid
46.0ms392×body160valid