Details

Time bar (total: 5.4s)

sample75.0ms

Algorithm
intervals
Results
49.0ms173×body1280valid
7.0ms48×body640valid
5.0ms253×body80valid
1.0ms17×body320valid
1.0ms14×body160valid

simplify225.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0145
1265
2415
3555
4675
51045
61615
73445
814545
950015
done50015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (exp x) 2.0)
4.4b
(+ (- (exp x) 2.0) (exp (- x)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
20×add-sqr-sqrt
18×prod-diff
16×add-cube-cbrt
11×associate-+l+
9×add-log-exp
5×fma-def
4×frac-add
3×flip3-- fma-neg flip-- distribute-lft-out--
2×pow1 add-exp-log neg-sub0 exp-neg expm1-log1p-u sub-neg exp-diff diff-log sum-log add-cbrt-cube log1p-expm1-u distribute-lft-out difference-of-squares
1×+-commutative associate-+l- flip3-+ flip-+
Counts
2 → 65
Calls
2 calls:
11.0ms
(- (exp x) 2.0)
56.0ms
(+ (- (exp x) 2.0) (exp (- x)))

series72.0ms

Counts
2 → 6
Calls
2 calls:
13.0ms
(- (exp x) 2.0)
59.0ms
(+ (- (exp x) 2.0) (exp (- x)))

simplify34.0ms

Counts
71 → 71
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0282506
11008381
25001367
done5001367

prune158.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×add-exp-log
7×associate-*r*
6×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down
3×pow1 expm1-log1p-u associate-*l* prod-exp log1p-expm1-u add-log-exp unswap-sqr
2×fma-udef sqr-pow
1×pow-to-exp pow-exp *-commutative cbrt-unprod
Counts
3 → 47
Calls
3 calls:
0.0ms
(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0ms
(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
15.0ms
(* 1/12 (pow x 4))

series215.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
122.0ms
(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
36.0ms
(* 1/12 (pow x 4))

simplify99.0ms

Counts
56 → 56
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0143265
1544240
22626237
35001237
done5001237

prune138.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3))
0.0b
(pow (exp x) 3)
0.0b
(pow (exp x) 3)
4.2b
(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×pow-pow
6×pow1 unpow-prod-down pow-unpow exp-prod cube-prod add-cbrt-cube
4×add-exp-log expm1-log1p-u log1p-expm1-u add-log-exp
2×cube-mult pow-to-exp unpow3 pow-exp fma-udef rem-cube-cbrt sqr-pow
Counts
4 → 76
Calls
4 calls:
0.0ms
(fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3))
4.0ms
(pow (exp x) 3)
4.0ms
(pow (exp x) 3)
0.0ms
(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

series239.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3))
23.0ms
(pow (exp x) 3)
22.0ms
(pow (exp x) 3)
120.0ms
(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

simplify38.0ms

Counts
88 → 88
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0228446
1940404
25001393
done5001393

prune287.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.9b
(cbrt (fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3)))
0.9b
(cbrt (fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3)))
1.0b
(* (cbrt (fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3))) (cbrt (fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3))))
4.2b
(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
11×pow1
8×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 78
Calls
4 calls:
1.0ms
(cbrt (fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3)))
1.0ms
(cbrt (fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3)))
13.0ms
(* (cbrt (fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3))) (cbrt (fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3))))
0.0ms
(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

series759.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(cbrt (fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3)))
205.0ms
(cbrt (fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3)))
233.0ms
(* (cbrt (fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3))) (cbrt (fma (exp x) (fma 2.0 2.0 (* (exp x) 2.0)) (pow (exp x) 3))))
118.0ms
(fma (exp x) (- (pow (exp x) 3) (pow 2.0 3)) (fma 2.0 (+ (exp x) 2.0) (exp (+ x x))))

simplify146.0ms

Counts
90 → 90
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02981400
110751266
248761151
350011151
done50011151

prune367.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes16.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0115
1115
done115

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.6s5686×body1280valid
180.0ms1209×body640valid
168.0ms8093×body80valid
57.0ms626×body320valid
19.0ms321×body160valid