Details

Time bar (total: 6.9s)

sample97.0ms

Algorithm
intervals
Results
23.0ms59×body10240exit
21.0ms49×body1280valid
17.0ms321×body80valid
11.0ms46×body640valid
3.0ms18×body320valid
1.0ms11×body160valid

simplify35.0ms

Counts
1 → 1
Iterations

Useful iterations: 4 (34.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115
done500115

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
0.0b
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
2.2b
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite392.0ms

Algorithm
rewrite-expression-head
Rules
122×*-un-lft-identity
106×times-frac
94×add-sqr-sqrt
36×add-cube-cbrt
26×distribute-lft-out--
17×difference-of-squares
11×distribute-lft-out
10×add-cbrt-cube associate-/l*
8×add-exp-log
6×pow1 associate-/r* add-log-exp
4×associate-*l* div-inv associate-/l/
3×div-sub associate-*r*
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp associate-*l/ clear-num flip-- flip-+
1×sub-neg distribute-rgt-out-- diff-log pow-prod-down prod-exp *-commutative frac-sub cbrt-unprod sub-div associate--r- unswap-sqr
Counts
4 → 137
Calls
4 calls:
19.0ms
(* (+ 1.0 eps) x)
39.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
43.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
284.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series304.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (+ 1.0 eps) x)
42.0ms
(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
49.0ms
(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
186.0ms
(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify67.0ms

Counts
149 → 149
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
06891986
122651877
250031876
done50031876

prune418.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
0.1b
(* 0.33333333333333337 (pow x 3))
8.2b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
20×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp unswap-sqr
7×add-cbrt-cube
6×associate-*l* prod-exp
4×cube-prod sqr-pow
3×pow1
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
1×cube-mult sub-neg flip3-- unpow3 associate--l+ sum-log flip--
Counts
3 → 72
Calls
3 calls:
11.0ms
(* 0.5 (pow x 2))
13.0ms
(* 0.33333333333333337 (pow x 3))
54.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

series103.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(* 0.5 (pow x 2))
39.0ms
(* 0.33333333333333337 (pow x 3))
39.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))

simplify44.0ms

Counts
81 → 81
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0281367
11210327
25001314
done5001314

prune153.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

8.2b
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
12.3b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
12.3b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
12.3b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-log-exp
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log flip3-- add-cbrt-cube flip--
3×pow1/3
2×diff-log
1×sub-neg associate--l+ sum-log
Counts
4 → 53
Calls
4 calls:
52.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
27.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
26.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
28.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series466.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2)))
141.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
141.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
140.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify135.0ms

Counts
65 → 65
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0253983
1904924
24251839
35001839
done5001839

prune273.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

11.4b
(- (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0)) (* (* 0.5 (pow x 2)) (* 0.5 (pow x 2))))
12.3b
(cbrt (+ (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
12.3b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
12.3b
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×flip3-- pow1/3 flip--
2×associate--l+
1×distribute-rgt-in sub-neg distribute-lft-in flip3-+ diff-log flip-+ difference-of-squares
Counts
4 → 54
Calls
4 calls:
53.0ms
(- (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0)) (* (* 0.5 (pow x 2)) (* 0.5 (pow x 2))))
22.0ms
(cbrt (+ (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
26.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
29.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

series476.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(- (* (+ (* 0.33333333333333337 (pow x 3)) 1.0) (+ (* 0.33333333333333337 (pow x 3)) 1.0)) (* (* 0.5 (pow x 2)) (* 0.5 (pow x 2))))
131.0ms
(cbrt (+ (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
146.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))
146.0ms
(cbrt (- (+ (* 0.33333333333333337 (pow x 3)) 1.0) (* 0.5 (pow x 2))))

simplify50.0ms

Counts
66 → 66
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03741120
114881025
25002948
done5002948

prune357.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

regimes63.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 17.4b

bsearch145.0ms

Steps
ItersRangePoint
9
0.02319676823116778
6068.335987417336
273.9633798024049

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06554
16554
done6554

end0.0ms

sample2.9s

Algorithm
intervals
Results
781.0ms1951×body10240exit
740.0ms1705×body1280valid
546.0ms10034×body80valid
306.0ms1209×body640valid
111.0ms676×body320valid
33.0ms284×body160valid