Details

Time bar (total: 28.3s)

sample174.0ms

Algorithm
intervals
Results
56.0ms327×body80valid
37.0ms52×body10240exit
30.0ms43×body1280valid
18.0ms44×body640valid
4.0ms15×body320valid
2.0ms10×body160valid

simplify4.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (351.0ms)

IterNodesCost
01929
14729
212429
335327
4100826
5451426
done500026

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (- (* (+ 1.0 eps) x)))
0.3b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.3b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
1.5b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite311.0ms

Algorithm
rewrite-expression-head
Rules
81×exp-neg frac-sub
80×frac-times
61×neg-sub0 exp-diff
40×associate-*r/ associate-*l/
31×flip3-- flip--
30×flip3-+ flip-+
20×un-div-inv
18×add-sqr-sqrt
13×*-un-lft-identity
10×associate-*l*
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-log-exp
6×add-exp-log exp-prod associate-*r*
4×expm1-log1p-u log1p-expm1-u
2×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log difference-of-squares unswap-sqr
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in times-frac fma-neg diff-log prod-diff neg-log distribute-lft-out distribute-lft-out--
Counts
4 → 178
Calls
4 calls:
15.0ms
(exp (- (* (+ 1.0 eps) x)))
88.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
119.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
70.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series522.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(exp (- (* (+ 1.0 eps) x)))
74.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
77.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
315.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify2.8s

Counts
190 → 190
Iterations

Useful iterations: done (2.8s)

IterNodesCost
03908431
111057547
239387055
done50006999

prune879.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
6.2b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
3×fma-neg prod-diff
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube fma-udef log1p-expm1-u
1×sub-neg flip3-- diff-log associate--l+ flip--
Counts
2 → 31
Calls
2 calls:
0.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
7.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series150.0ms

Counts
2 → 6
Calls
2 calls:
91.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
59.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify3.6s

Counts
37 → 37
Iterations

Useful iterations: done (3.6s)

IterNodesCost
053544
1119518
2387468
32205433
done5000386

prune162.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0) 3)
0.0b
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
3.3b
(cbrt (pow (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0) 3))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
4×pow1 add-exp-log add-cbrt-cube
3×expm1-log1p-u pow-unpow log1p-expm1-u add-log-exp
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube fma-udef rem-cube-cbrt
Counts
3 → 58
Calls
3 calls:
3.0ms
(pow (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0) 3)
0.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
4.0ms
(cbrt (pow (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0) 3))

series212.0ms

Counts
3 → 9
Calls
3 calls:
92.0ms
(pow (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0) 3)
55.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
65.0ms
(cbrt (pow (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0) 3))

simplify3.7s

Counts
67 → 67
Iterations

Useful iterations: done (3.6s)

IterNodesCost
0861239
11811049
2495918
33080909
done5001908

prune258.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma (pow x 2) (- (* x 8.0) 12.0) 8.0)
10.9b
(cbrt (fma (pow x 2) (- (* x 8.0) 12.0) 8.0))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
3×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
1×pow1/3 fma-udef
Counts
2 → 23
Calls
2 calls:
0.0ms
(fma (pow x 2) (- (* x 8.0) 12.0) 8.0)
1.0ms
(cbrt (fma (pow x 2) (- (* x 8.0) 12.0) 8.0))

series257.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(fma (pow x 2) (- (* x 8.0) 12.0) 8.0)
189.0ms
(cbrt (fma (pow x 2) (- (* x 8.0) 12.0) 8.0))

simplify1.9s

Counts
29 → 29
Iterations

Useful iterations: done (1.9s)

IterNodesCost
087566
1199551
2547502
31876452
done5001432

prune133.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

regimes162.0ms

Accuracy

96.1% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.5b

bsearch252.0ms

Steps
ItersRangePoint
9
0.12160444842987421
18133.886566758163
356.35535311208105

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03557
14457
25057
done5057

end0.0ms

sample8.7s

Algorithm
intervals
Results
2.3s9978×body80valid
2.3s1747×body1280valid
2.3s1975×body10240exit
748.0ms1239×body640valid
230.0ms647×body320valid
71.0ms316×body160valid