Details

Time bar (total: 8.3s)

sample98.0ms

Algorithm
intervals
Results
25.0ms59×body10240exit
20.0ms49×body1280valid
16.0ms321×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

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
76×exp-neg frac-times
57×neg-sub0 exp-diff
40×associate-*l/
38×associate-*r/
31×flip3-- flip--
29×flip3-+ flip-+
19×un-div-inv
17×add-sqr-sqrt
14×*-un-lft-identity
10×associate-*l*
8×pow1 add-cube-cbrt add-cbrt-cube add-log-exp
7×add-exp-log
6×associate-*r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out difference-of-squares unswap-sqr
1×+-commutative sub-neg times-frac diff-log sum-log distribute-lft-out--
Counts
4 → 156
Calls
4 calls:
10.0ms
(+ 1.0 (/ 1.0 eps))
67.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
22.0ms
(* (+ 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)))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ 1.0 (/ 1.0 eps))
52.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
33.0ms
(* (+ 1.0 eps) x)
202.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify141.0ms

Counts
168 → 168
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
012173851
145893582
250013573
done50013573

prune422.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
8.2b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log add-log-exp
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 diff-log sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- unpow3 pow-exp associate--l+ sum-log *-commutative flip-- cbrt-unprod
Counts
2 → 45
Calls
2 calls:
13.0ms
(* 0.6666666666666667 (pow x 3))
59.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series80.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(* 0.6666666666666667 (pow x 3))
39.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify34.0ms

Counts
51 → 51
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0207270
1894242
25002238
done5002238

prune117.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

8.2b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
13.0b
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
13.0b
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
13.0b
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite147.0ms

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:
57.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
29.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
31.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
29.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

series488.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
143.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
152.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
149.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify132.0ms

Counts
65 → 65
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0252983
1905918
24257836
35002836
done5002836

prune260.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

12.6b
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
13.0b
(/ (cbrt (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))) (cbrt (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)) (+ (* (* 1.0 (pow x 2)) (* 1.0 (pow x 2))) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))))))
13.0b
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
13.0b
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite662.0ms

Algorithm
rewrite-expression-head
Rules
148×cbrt-prod
134×add-sqr-sqrt
96×times-frac
70×*-un-lft-identity
64×difference-of-squares
54×add-cube-cbrt
48×sqr-pow
24×cbrt-div
21×flip3-+ flip-+
18×associate-/r/
16×unpow-prod-down cube-prod frac-add associate-/l*
8×difference-cubes frac-times distribute-lft-out--
6×add-exp-log associate-/r* add-log-exp
4×pow1 flip3-- associate-*r/ associate-*l/ add-cbrt-cube flip--
2×pow1/3 associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 198
Calls
4 calls:
117.0ms
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
325.0ms
(/ (cbrt (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))) (cbrt (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)) (+ (* (* 1.0 (pow x 2)) (* 1.0 (pow x 2))) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))))))
179.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
29.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

series599.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
218.0ms
(/ (cbrt (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))) (cbrt (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)) (+ (* (* 1.0 (pow x 2)) (* 1.0 (pow x 2))) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))))))
143.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
142.0ms
(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify197.0ms

Counts
210 → 210
Iterations

Useful iterations: 2 (121.0ms)

IterNodesCost
0102010040
143929923
250019919
done50019919

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

regimes83.0ms

Accuracy

96.2% (0.6b remaining)

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

bsearch152.0ms

Steps
ItersRangePoint
9
0.02319676823116778
6068.335987417336
273.9633798024049

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07194
18494
28494
done8494

end0.0ms

sample2.9s

Algorithm
intervals
Results
755.0ms1951×body10240exit
715.0ms1705×body1280valid
537.0ms10034×body80valid
302.0ms1209×body640valid
115.0ms676×body320valid
29.0ms284×body160valid