Details

Time bar (total: 16.4s)

sample105.0ms

Algorithm
intervals
Results
26.0ms48×body1280valid
26.0ms69×body10240exit
17.0ms330×body80valid
11.0ms43×body640valid
4.0ms24×body320valid
1.0ms10×body160valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 4 (182.0ms)

IterNodesCost
01929
14729
212429
335327
4100826
5451426
done500026

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.6b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
31×flip3-- flip3-+ flip-- flip-+
21×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
14×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-lft-out difference-of-squares
1×sub-neg times-frac fma-neg diff-log prod-diff distribute-lft-out--
Counts
4 → 182
Calls
4 calls:
50.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
65.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
19.0ms
(* (+ 1.0 eps) x)
46.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series345.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
53.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
29.0ms
(* (+ 1.0 eps) x)
209.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify2.0s

Counts
194 → 194
Iterations

Useful iterations: 2 (968.0ms)

IterNodesCost
04078453
111577571
242597072
done50007072

prune492.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
6.8b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite10.0ms

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)
9.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series119.0ms

Counts
2 → 6
Calls
2 calls:
79.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
40.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify2.2s

Counts
37 → 37
Iterations

Useful iterations: done (2.2s)

IterNodesCost
053544
1119518
2387468
32205433
done5000386

prune94.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
0.0b
(- (* 0.6666666666666667 x) 1.0)
0.3b
(exp (log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
12.2b
(log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

rewrite14.0ms

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:
0.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
8.0ms
(- (* 0.6666666666666667 x) 1.0)
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))

series212.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
42.0ms
(- (* 0.6666666666666667 x) 1.0)
42.0ms
(exp (log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))
88.0ms
(log (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))

simplify1.1s

Counts
71 → 71
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0129999
1267913
2664779
31943767
done5000759

prune181.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

6.8b
(fma (* (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))))
12.6b
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
12.6b
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
12.6b
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
0.0ms
(fma (* (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))))
1.0ms
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
1.0ms
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
1.0ms
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
298.0ms
(fma (* (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))))
445.0ms
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
435.0ms
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))
412.0ms
(cbrt (fma 0.6666666666666667 (pow x 3) 2.0))

simplify1.6s

Counts
61 → 61
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01261526
12961478
29601209
34333995
done5000989

prune243.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

regimes94.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.4b

bsearch139.0ms

Steps
ItersRangePoint
9
1.4733657795017903
2551964808.6153555
19.564058406485834

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03153
14153
24353
done4353

end0.0ms

sample2.9s

Algorithm
intervals
Results
756.0ms1989×body10240exit
720.0ms1697×body1280valid
536.0ms10035×body80valid
317.0ms1292×body640valid
101.0ms641×body320valid
36.0ms320×body160valid