Details

Time bar (total: 16.3s)

sample16.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1108
2128
done128

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt times-frac
5×distribute-lft-out
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×fma-def associate-/l*
2×pow1 expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 52
Calls
2 calls:
21.0ms
(+ (exp x) (exp (- x)))
23.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

series73.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(+ (exp x) (exp (- x)))
45.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

simplify3.4s

Counts
58 → 58
Iterations

Useful iterations: 3 (263.0ms)

IterNodesCost
094681
1199650
2469597
3950593
43863593
done5000593

prune238.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize23.0ms

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))))

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
123×*-un-lft-identity
98×sqrt-prod
91×add-sqr-sqrt
90×times-frac
63×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×expm1-log1p-u sqrt-div log1p-expm1-u
3×fma-def 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 → 197
Calls
4 calls:
28.0ms
(+ (exp x) (exp (- x)))
178.0ms
(* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (sqrt (/ 2.0 (+ (exp x) (exp (- x))))))
28.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
40.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

series266.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (exp x) (exp (- x)))
129.0ms
(* (sqrt (/ 2.0 (+ (exp x) (exp (- x))))) (sqrt (/ 2.0 (+ (exp x) (exp (- x))))))
58.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
51.0ms
(/ 2.0 (+ (exp x) (exp (- x))))

simplify2.2s

Counts
209 → 209
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02204165
13882978
211332777
328452713
done50002651

prune772.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
31×add-sqr-sqrt times-frac
28×add-cube-cbrt
13×sqrt-prod
8×add-exp-log add-cbrt-cube
7×associate-/r*
6×associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u distribute-lft-out add-log-exp
3×div-inv
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num associate-/r/
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+ fma-udef
Counts
4 → 101
Calls
4 calls:
23.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
6.0ms
(fma 1/12 (pow x 4) 2)
5.0ms
(/ 2.0 (fma x x (fma 1/12 (pow x 4) 2)))
4.0ms
(sqrt (/ 2.0 (fma x x (fma 1/12 (pow x 4) 2))))

series521.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ 2.0 (+ (exp x) (exp (- x))))
106.0ms
(fma 1/12 (pow x 4) 2)
108.0ms
(/ 2.0 (fma x x (fma 1/12 (pow x 4) 2)))
257.0ms
(sqrt (/ 2.0 (fma x x (fma 1/12 (pow x 4) 2))))

simplify2.0s

Counts
113 → 113
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02141877
14211800
211211669
334661641
done50011638

prune531.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize36.0ms

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))))

rewrite750.0ms

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×expm1-log1p-u pow-pow pow-prod-up log1p-expm1-u
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 fma-neg diff-log unpow3 rgt-mult-inverse div-exp prod-diff pow-exp flip-- div-inv rem-cube-cbrt sqr-pow
Counts
4 → 164
Calls
4 calls:
8.0ms
(pow (exp x) 3)
31.0ms
(* (exp x) (exp (- x)))
640.0ms
(* (/ 2.0 (+ (pow (exp x) 3) (exp (* x -3)))) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))))
56.0ms
(- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))

series419.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(pow (exp x) 3)
86.0ms
(* (exp x) (exp (- x)))
223.0ms
(* (/ 2.0 (+ (pow (exp x) 3) (exp (* x -3)))) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))))
71.0ms
(- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))

simplify2.7s

Counts
176 → 176
Iterations

Useful iterations: done (2.7s)

IterNodesCost
03133591
18632658
234442006
done50001865

prune849.0ms

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

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01722
11922
done1922

end0.0ms

sample1.0s

Algorithm
intervals
Results
838.0ms8000×body80valid