Details

Time bar (total: 18.5s)

sample93.0ms

Algorithm
intervals
Results
60.0ms179×body1280valid
8.0ms274×body80valid
6.0ms36×body640valid
2.0ms22×body320valid
1.0ms12×body160valid

simplify177.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (exp x) 2.0)
5.2b
(+ (- (exp x) 2.0) (exp (- x)))

rewrite119.0ms

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:
22.0ms
(- (exp x) 2.0)
95.0ms
(+ (- (exp x) 2.0) (exp (- x)))

series97.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(- (exp x) 2.0)
74.0ms
(+ (- (exp x) 2.0) (exp (- x)))

simplify1.8s

Counts
41 → 41
Iterations

Useful iterations: 3 (596.0ms)

IterNodesCost
093511
1204465
2579445
32107432
done5000432

prune175.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

rewrite99.0ms

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:
11.0ms
(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
41.0ms
(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
25.0ms
(* 1/360 (pow x 6))
19.0ms
(* 1/12 (pow x 4))

series440.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
98.0ms
(+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
68.0ms
(* 1/360 (pow x 6))
50.0ms
(* 1/12 (pow x 4))

simplify4.3s

Counts
87 → 87
Iterations

Useful iterations: done (4.3s)

IterNodesCost
01331068
1331934
2952888
34364870
done5001868

prune393.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
29.9b
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
29.9b
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
29.9b
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

rewrite345.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
240.0ms
(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (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)))))
44.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
21.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

series813.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
172.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
208.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))
220.0ms
(cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))))

simplify2.3s

Counts
107 → 107
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01614106
13603755
29463511
329353006
done50002940

prune557.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/360 (pow x 6))
0.1b
(* 1/12 (pow x 4))
0.2b
(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
17.5b
(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×*-un-lft-identity
16×add-cube-cbrt unpow-prod-down
15×add-exp-log
14×cbrt-prod associate-*r*
9×add-cbrt-cube
8×cube-prod
6×associate-*l* prod-exp unswap-sqr sqr-pow
5×pow1
4×cube-div distribute-lft-out add-log-exp
3×pow-to-exp pow-unpow pow-exp
2×cube-mult cbrt-div flip3-+ unpow3 *-commutative cbrt-unprod flip-+
1×pow-pow pow1/3 rem-cbrt-cube rem-cube-cbrt
Counts
4 → 102
Calls
4 calls:
24.0ms
(* 1/360 (pow x 6))
12.0ms
(* 1/12 (pow x 4))
49.0ms
(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
65.0ms
(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

series283.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* 1/360 (pow x 6))
51.0ms
(* 1/12 (pow x 4))
80.0ms
(pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3)
62.0ms
(cbrt (pow (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))) 3))

simplify975.0ms

Counts
114 → 114
Iterations

Useful iterations: done (968.0ms)

IterNodesCost
01812128
14241835
212161643
done50011627

prune457.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

49% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.6b

bsearch48.0ms

Steps
ItersRangePoint
8
-0.7718806003288846
-0.0008047768791668974
-0.03372358286109268

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02842
13342
done3342

end0.0ms

sample4.6s

Algorithm
intervals
Results
3.2s5661×body1280valid
433.0ms1239×body640valid
376.0ms7952×body80valid
97.0ms634×body320valid
31.0ms318×body160valid