Details

Time bar (total: 15.8s)

sample28.0ms

Algorithm
intervals
Results
14.0ms256×body80valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1108
2128
done128

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 2 expressions with local error:

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

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
12×times-frac
11×add-sqr-sqrt add-cube-cbrt
5×distribute-lft-out
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 45
Calls
2 calls:
30.0ms
(+ (exp x) (exp (- x)))
40.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

series88.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(+ (exp x) (exp (- x)))
61.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

simplify3.3s

Counts
51 → 51
Iterations

Useful iterations: 3 (271.0ms)

IterNodesCost
090649
1190620
2439568
3859566
43442566
done5001566

prune141.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (exp x) (exp (- x)))
0.0b
(* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (sqrt (/ 2.0 (+ (exp x) (exp (- x))))))
0.0b
(/ 2.0 (+ (exp x) (exp (- x))))
0.0b
(/ 2.0 (+ (exp x) (exp (- x))))

rewrite245.0ms

Algorithm
rewrite-expression-head
Rules
122×*-un-lft-identity
98×sqrt-prod
90×add-sqr-sqrt times-frac
62×add-cube-cbrt
29×swap-sqr
27×distribute-lft-out
21×associate-*r* associate-*l*
19×pow1
12×associate-/r/
10×add-exp-log add-cbrt-cube
9×unswap-sqr
8×sqrt-pow1 pow1/2 associate-/r*
7×flip3-+ flip-+
6×div-inv associate-/l* add-log-exp
5×pow-prod-up
4×sqrt-div
3×pow-prod-down pow-sqr
2×cbrt-undiv frac-2neg div-exp clear-num
1×+-commutative pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 186
Calls
4 calls:
15.0ms
(+ (exp x) (exp (- x)))
155.0ms
(* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (sqrt (/ 2.0 (+ (exp x) (exp (- x))))))
33.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
29.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

series275.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(+ (exp x) (exp (- x)))
121.0ms
(* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (sqrt (/ 2.0 (+ (exp x) (exp (- x))))))
56.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
54.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

simplify2.2s

Counts
198 → 198
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02144075
13762914
210922715
326932656
done50002595

prune665.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (+ (exp x) (exp (- x))))
0.0b
(/ 2.0 (+ (pow x 2) (+ (* 1/12 (pow x 4)) 2)))
0.1b
(* 1/12 (pow x 4))
5.8b
(sqrt (/ 2.0 (+ (pow x 2) (+ (* 1/12 (pow x 4)) 2))))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
41×add-sqr-sqrt
37×times-frac
33×add-cube-cbrt
18×sqrt-prod
13×add-exp-log
11×distribute-lft-out
10×add-cbrt-cube
8×associate-/r*
7×associate-*r*
6×associate-/r/ associate-/l*
5×pow1
4×unpow-prod-down add-log-exp
3×flip3-+ associate-*l* prod-exp flip-+ div-inv unswap-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num sqr-pow
1×pow-to-exp sqrt-pow1 pow1/2 sqrt-div pow-exp *-commutative cbrt-unprod
Counts
4 → 121
Calls
4 calls:
29.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
55.0ms
(/ 2.0 (+ (pow x 2) (+ (* 1/12 (pow x 4)) 2)))
16.0ms
(* 1/12 (pow x 4))
74.0ms
(sqrt (/ 2.0 (+ (pow x 2) (+ (* 1/12 (pow x 4)) 2))))

series464.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
90.0ms
(/ 2.0 (+ (pow x 2) (+ (* 1/12 (pow x 4)) 2)))
51.0ms
(* 1/12 (pow x 4))
249.0ms
(sqrt (/ 2.0 (+ (pow x 2) (+ (* 1/12 (pow x 4)) 2))))

simplify1.3s

Counts
133 → 133
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02572327
15552193
214952049
done50002022

prune774.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (exp x) 3)
1.0b
(* (exp x) (exp (- x)))
1.0b
(* (/ 2.0 (+ (pow (exp x) 3) (exp (* x -3)))) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))))
4.5b
(- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))

rewrite932.0ms

Algorithm
rewrite-expression-head
Rules
61×exp-neg
44×associate-*r/
39×neg-sub0 exp-diff
32×*-un-lft-identity
30×add-sqr-sqrt
27×frac-sub
23×add-cube-cbrt
21×associate-*l* un-div-inv
19×exp-prod
15×sub-div
14×frac-times
13×times-frac associate-*l/
12×add-cbrt-cube
9×pow1 add-exp-log
6×associate-*r* pow-prod-down add-log-exp
4×pow-pow pow-prod-up
3×distribute-lft-neg-in unpow-prod-down pow-unpow distribute-rgt-neg-in flip3-+ cube-prod prod-exp cbrt-unprod flip-+ distribute-lft-out unswap-sqr
2×associate-/r/ *-commutative
1×cbrt-undiv distribute-rgt-in cube-mult pow-to-exp neg-mul-1 sub-neg flip3-- distribute-rgt-out-- distribute-lft-in diff-log unpow3 rgt-mult-inverse div-exp pow-exp flip-- div-inv rem-cube-cbrt sqr-pow
Counts
4 → 154
Calls
4 calls:
5.0ms
(pow (exp x) 3)
40.0ms
(* (exp x) (exp (- x)))
801.0ms
(* (/ 2.0 (+ (pow (exp x) 3) (exp (* x -3)))) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))))
77.0ms
(- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))

series505.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(pow (exp x) 3)
110.0ms
(* (exp x) (exp (- x)))
286.0ms
(* (/ 2.0 (+ (pow (exp x) 3) (exp (* x -3)))) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))))
77.0ms
(- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))

simplify3.0s

Counts
166 → 166
Iterations

Useful iterations: done (3.0s)

IterNodesCost
03013437
17882540
232031928
done50001927

prune847.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes20.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01924
12424
done2424

end0.0ms

sample663.0ms

Algorithm
intervals
Results
463.0ms8000×body80valid