Details

Time bar (total: 24.7s)

sample153.0ms

Algorithm
intervals
Results
42.0ms73×body10240exit
35.0ms61×body1280valid
24.0ms340×body80valid
13.0ms42×body640valid
4.0ms20×body320valid
2.0ms13×body160valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 4 (221.0ms)

IterNodesCost
01929
14729
212429
335327
4100826
5451426
done500026

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(exp (- (* (- 1.0 eps) x)))
1.9b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
74×exp-neg
72×frac-times
56×neg-sub0 exp-diff
38×associate-*l/
36×associate-*r/
28×flip3-- flip3-+ flip-- flip-+
18×un-div-inv
12×exp-prod
10×add-sqr-sqrt *-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u associate-*l* log1p-expm1-u rem-exp-log
3×associate-*r*
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in neg-log
1×sub-neg fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
4 → 158
Calls
4 calls:
34.0ms
(* (+ 1.0 eps) x)
8.0ms
(exp (- (* (+ 1.0 eps) x)))
9.0ms
(exp (- (* (- 1.0 eps) x)))
50.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series480.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (+ 1.0 eps) x)
55.0ms
(exp (- (* (+ 1.0 eps) x)))
49.0ms
(exp (- (* (- 1.0 eps) x)))
326.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify2.5s

Counts
170 → 170
Iterations

Useful iterations: done (2.4s)

IterNodesCost
03817574
110736798
238966366
done50006298

prune579.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
4.6b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite14.0ms

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:
1.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
12.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series176.0ms

Counts
2 → 6
Calls
2 calls:
109.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
67.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify3.7s

Counts
37 → 37
Iterations

Useful iterations: done (3.7s)

IterNodesCost
053544
1119518
2387468
32205433
done5000386

prune167.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
0.4b
(exp (log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
8.0b
(log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt add-cube-cbrt log-prod *-un-lft-identity
5×pow1
4×add-exp-log exp-prod
3×expm1-log1p-u exp-sum add-cbrt-cube log1p-expm1-u add-log-exp
2×log-pow
1×rem-log-exp fma-udef rem-exp-log
Counts
3 → 41
Calls
3 calls:
1.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
6.0ms
(exp (log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
3.0ms
(log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

series256.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
66.0ms
(exp (log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
129.0ms
(log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

simplify2.8s

Counts
50 → 50
Iterations

Useful iterations: 4 (1.4s)

IterNodesCost
089794
1177742
2421627
31103626
44028618
done5000618

prune258.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize30.0ms

Local error

Found 4 expressions with local error:

4.6b
(- (* (* (cbrt (fma 0.6666666666666667 (pow x 3) 2.0)) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (* 1.0 (pow x 2)))
8.6b
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
8.6b
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
8.6b
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow1/3
1×sub-neg flip3-- fma-neg diff-log prod-diff flip--
Counts
4 → 55
Calls
4 calls:
56.0ms
(- (* (* (cbrt (fma 0.6666666666666667 (pow x 3) 2.0)) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (* 1.0 (pow x 2)))
2.0ms
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
2.0ms
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
2.0ms
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* (* (cbrt (fma 0.6666666666666667 (pow x 3) 2.0)) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (cbrt (fma 0.6666666666666667 (pow x 3) 2.0))) (* 1.0 (pow x 2)))
603.0ms
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
567.0ms
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
695.0ms
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

simplify2.9s

Counts
67 → 67
Iterations

Useful iterations: 3 (983.0ms)

IterNodesCost
01191694
12981644
29461200
345381017
done50001017

prune386.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

regimes154.0ms

Accuracy

96.9% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.5b

bsearch150.0ms

Steps
ItersRangePoint
6
110.15968793260775
701.025784686831
336.42241444292944

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03349
14749
25549
done5549

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.2s1927×body10240exit
1.2s1737×body1280valid
864.0ms9990×body80valid
489.0ms1228×body640valid
179.0ms670×body320valid
56.0ms333×body160valid