Details

Time bar (total: 21.5s)

sample151.0ms

Algorithm
intervals
Results
104.0ms189×body1280valid
12.0ms36×body640valid
12.0ms266×body80valid
4.0ms20×body320valid
1.0ms7×body160valid

simplify174.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1148
2268
3408
4498
5548
6638
7808
8958
91038
101118
done1118

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (exp x) 2.0)
3.3b
(+ (- (exp x) 2.0) (exp (- x)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity add-log-exp
4×add-sqr-sqrt frac-add
3×flip3-- flip--
2×pow1 add-exp-log neg-sub0 exp-neg add-cube-cbrt sub-neg associate-+l+ exp-diff diff-log sum-log add-cbrt-cube distribute-lft-out distribute-lft-out--
1×+-commutative associate-+l- flip3-+ flip-+ difference-of-squares
Counts
2 → 35
Calls
2 calls:
10.0ms
(- (exp x) 2.0)
100.0ms
(+ (- (exp x) 2.0) (exp (- x)))

series100.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- (exp x) 2.0)
84.0ms
(+ (- (exp x) 2.0) (exp (- x)))

simplify1.9s

Counts
41 → 41
Iterations

Useful iterations: 3 (570.0ms)

IterNodesCost
093511
1204465
2579445
32107432
done5000432

prune152.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
0.0b
(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
0.1b
(* 1/360 (pow x 6))
0.1b
(* 1/12 (pow x 4))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×add-exp-log associate-*r*
12×*-un-lft-identity
11×add-log-exp
10×add-cube-cbrt
8×unpow-prod-down add-cbrt-cube
6×associate-*l* prod-exp unswap-sqr
4×pow1 sum-log sqr-pow
2×+-commutative pow-to-exp flip3-+ pow-exp *-commutative cbrt-unprod flip-+
1×associate-+r+ distribute-lft-out
Counts
4 → 75
Calls
4 calls:
13.0ms
(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
25.0ms
(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
12.0ms
(* 1/360 (pow x 6))
12.0ms
(* 1/12 (pow x 4))

series416.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
78.0ms
(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
76.0ms
(* 1/360 (pow x 6))
53.0ms
(* 1/12 (pow x 4))

simplify4.2s

Counts
87 → 87
Iterations

Useful iterations: done (4.2s)

IterNodesCost
01331068
1331934
2952888
34364870
done5001868

prune363.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/12 (pow x 4))
0.1b
(* 1/12 (pow x 4))
30.6b
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
30.6b
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
16×*-un-lft-identity
14×add-exp-log associate-*r*
12×add-cube-cbrt
8×unpow-prod-down sqrt-prod add-cbrt-cube
6×pow1 associate-*l* prod-exp unswap-sqr
4×sqrt-div add-log-exp sqr-pow
2×pow-to-exp rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-exp *-commutative cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 82
Calls
4 calls:
24.0ms
(* 1/12 (pow x 4))
24.0ms
(* 1/12 (pow x 4))
77.0ms
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
52.0ms
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series462.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* 1/12 (pow x 4))
47.0ms
(* 1/12 (pow x 4))
173.0ms
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
187.0ms
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify2.2s

Counts
94 → 94
Iterations

Useful iterations: 3 (759.0ms)

IterNodesCost
01121420
12641228
27491184
324541162
done50001162

prune596.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (sqrt (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))))
30.6b
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
31.4b
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
31.4b
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
18×add-sqr-sqrt
13×cbrt-prod sqrt-prod
11×add-cube-cbrt
10×associate-*r*
7×pow1
6×add-exp-log cbrt-div add-cbrt-cube
4×flip3-+ sqrt-div flip-+ distribute-lft-out add-log-exp
3×associate-*l* unswap-sqr
2×pow1/3 associate-*r/
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
107.0ms
(* (fabs (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (sqrt (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))))
36.0ms
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
33.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
36.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series762.0ms

Counts
4 → 12
Calls
4 calls:
273.0ms
(* (fabs (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))) (sqrt (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))))
133.0ms
(sqrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
180.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
175.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify4.0s

Counts
85 → 85
Iterations

Useful iterations: done (4.0s)

IterNodesCost
02033140
14742930
213772694
346132541
done50002501

prune586.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01315
11715
done1715

end0.0ms

sample4.8s

Algorithm
intervals
Results
3.5s5704×body1280valid
429.0ms8021×body80valid
412.0ms1228×body640valid
156.0ms606×body320valid
35.0ms305×body160valid