Details

Time bar (total: 27.3s)

sample256.0ms

Algorithm
intervals
Results
96.0ms359×body80valid
48.0ms60×body10240exit
42.0ms52×body1280valid
24.0ms48×body640valid
4.0ms12×body320valid
3.0ms13×body160valid

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 4 (295.0ms)

IterNodesCost
01929
14729
212429
335327
4100826
5451426
done500026

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.2b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
2.9b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite257.0ms

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:
9.0ms
(exp (- (* (+ 1.0 eps) x)))
80.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
74.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
68.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series421.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(exp (- (* (+ 1.0 eps) x)))
59.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
66.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
265.0ms
(- (* (+ 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
239357055
done50006999

prune903.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
8.4b
(- (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)))

series208.0ms

Counts
2 → 6
Calls
2 calls:
130.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
78.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify4.0s

Counts
37 → 37
Iterations

Useful iterations: done (4.0s)

IterNodesCost
053544
1119518
2387468
32205433
done5000386

prune207.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* 0.6666666666666667 x) 1.0)
0.0b
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
0.5b
(exp (log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
12.9b
(log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 log-prod add-log-exp
5×add-exp-log
4×expm1-log1p-u exp-prod add-cbrt-cube log1p-expm1-u
3×exp-sum prod-diff
2×log-pow
1×sub-neg flip3-- fma-neg diff-log rem-log-exp flip-- fma-udef rem-exp-log
Counts
4 → 59
Calls
4 calls:
9.0ms
(- (* 0.6666666666666667 x) 1.0)
0.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
3.0ms
(exp (log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
1.0ms
(log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

series309.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(- (* 0.6666666666666667 x) 1.0)
58.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
57.0ms
(exp (log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
138.0ms
(log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

simplify1.6s

Counts
71 → 71
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0129999
1267913
2664779
31947767
done5000759

prune351.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (fma 0.6666666666666667 (pow x 3) 2.0))
0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
0.1b
(log1p (expm1 (fma 0.6666666666666667 (pow x 3) 2.0)))
8.4b
(- (log1p (expm1 (fma 0.6666666666666667 (pow x 3) 2.0))) (* 1.0 (pow x 2)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
7×add-log-exp
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×log1p-expm1-u
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube
3×fma-neg prod-diff
2×log1p-udef diff-log
1×sub-neg expm1-log1p flip3-- log1p-expm1 flip-- fma-udef expm1-udef
Counts
4 → 53
Calls
4 calls:
1.0ms
(expm1 (fma 0.6666666666666667 (pow x 3) 2.0))
1.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
1.0ms
(log1p (expm1 (fma 0.6666666666666667 (pow x 3) 2.0)))
15.0ms
(- (log1p (expm1 (fma 0.6666666666666667 (pow x 3) 2.0))) (* 1.0 (pow x 2)))

series662.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(expm1 (fma 0.6666666666666667 (pow x 3) 2.0))
107.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
286.0ms
(log1p (expm1 (fma 0.6666666666666667 (pow x 3) 2.0)))
201.0ms
(- (log1p (expm1 (fma 0.6666666666666667 (pow x 3) 2.0))) (* 1.0 (pow x 2)))

simplify2.3s

Counts
65 → 65
Iterations

Useful iterations: done (2.3s)

IterNodesCost
091888
1189767
2568701
32745656
done5000651

prune249.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

regimes158.0ms

Accuracy

91.9% (1.3b remaining)

Error of 1.8b against oracle of 0.5b and baseline of 16.8b

bsearch196.0ms

Steps
ItersRangePoint
7
7.705379630644969e-17
8.69103209592137e-15
8.501320620640499e-15

simplify16.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04181
16181
27281
37381
done7381

end0.0ms

sample8.5s

Algorithm
intervals
Results
2.2s1949×body10240exit
2.1s9945×body80valid
2.1s1754×body1280valid
768.0ms1251×body640valid
580.0ms612×body320valid
114.0ms343×body160valid