Details

Time bar (total: 6.0s)

sample90.0ms

Algorithm
intervals
Results
61.0ms184×body1280valid
8.0ms296×body80valid
6.0ms33×body640valid
2.0ms20×body320valid
1.0ms16×body160valid

simplify233.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0145
1265
2415
3555
4675
51045
61615
73445
814545
950015

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.5b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (exp x) 2.0)
5.0b
(+ (- (exp x) 2.0) (exp (- x)))

rewrite16.0ms

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:
4.0ms
(- (exp x) 2.0)
9.0ms
(+ (- (exp x) 2.0) (exp (- x)))

series71.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- (exp x) 2.0)
53.0ms
(+ (- (exp x) 2.0) (exp (- x)))

simplify36.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0282506
11008381
25001367

prune145.0ms

Filtered
71 candidates to 51 candidates (71.8%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New69271
Fresh000
Picked101
Done000
Total70272

Merged error: 0.0b

Counts
72 → 2

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))

rewrite8.0ms

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:
1.0ms
(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
1.0ms
(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
5.0ms
(* 1/12 (pow x 4))

series224.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
123.0ms
(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
41.0ms
(* 1/12 (pow x 4))

simplify101.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0143265
1544240
22626237
35001237

prune110.0ms

Filtered
56 candidates to 39 candidates (69.6%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New56056
Fresh011
Picked011
Done000
Total56258

Merged error: 0.0b

Counts
58 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
24×times-frac
22×add-sqr-sqrt add-cube-cbrt
21×fma-def
9×distribute-lft-out
8×add-log-exp
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u flip3-+ associate-/r* associate-/r/ flip-+ log1p-expm1-u
3×associate-/l*
2×+-commutative frac-add sum-log div-inv
1×cbrt-undiv neg-sub0 exp-neg frac-2neg exp-diff div-exp clear-num fma-udef
Counts
4 → 96
Calls
4 calls:
1.0ms
(fma (- 2.0) 2.0 (exp (+ x x)))
4.0ms
(+ (exp x) 2.0)
6.0ms
(/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))
12.0ms
(+ (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (exp (- x)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(fma (- 2.0) 2.0 (exp (+ x x)))
8.0ms
(+ (exp x) 2.0)
63.0ms
(/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))
100.0ms
(+ (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (exp (- x)))

simplify44.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0341838
11209780
25001761

prune257.0ms

Filtered
108 candidates to 86 candidates (79.6%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1071108
Fresh000
Picked101
Done011
Total1082110

Merged error: 0.0b

Counts
110 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (exp (- x)) (exp (- x)))
0.0b
(* (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)))
0.0b
(/ (- (* (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))) (* (exp (- x)) (exp (- x)))) (- (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (exp (- x))))
5.3b
(- (* (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))) (* (exp (- x)) (exp (- x))))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
140×*-un-lft-identity
113×add-sqr-sqrt
93×times-frac
76×exp-prod
74×add-cube-cbrt
56×frac-sub
50×exp-neg
47×frac-times
43×neg-sub0 exp-diff
33×associate-*r/ associate-*l/
29×associate-/l/
27×swap-sqr
24×distribute-rgt-neg-in
21×associate-*r* associate-*l*
20×distribute-lft-neg-in add-cbrt-cube
18×pow1 add-exp-log distribute-lft-out difference-of-squares
16×pow-prod-down
14×pow-sqr pow-prod-up
12×associate-/r/
8×neg-mul-1
7×un-div-inv
6×associate-/r* add-log-exp
5×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv distribute-lft-out-- unswap-sqr
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u associate-/l*
3×flip3-- flip--
2×pow2 pow-plus *-commutative
1×sub-neg frac-2neg fma-neg diff-log div-sub prod-diff clear-num
Counts
4 → 290
Calls
4 calls:
14.0ms
(* (exp (- x)) (exp (- x)))
22.0ms
(* (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)))
31.0ms
(/ (- (* (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))) (* (exp (- x)) (exp (- x)))) (- (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (exp (- x))))
16.0ms
(- (* (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))) (* (exp (- x)) (exp (- x))))

series739.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (exp (- x)) (exp (- x)))
113.0ms
(* (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)))
438.0ms
(/ (- (* (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))) (* (exp (- x)) (exp (- x)))) (- (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (exp (- x))))
172.0ms
(- (* (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0)) (/ (fma (- 2.0) 2.0 (exp (+ x x))) (+ (exp x) 2.0))) (* (exp (- x)) (exp (- x))))

simplify84.0ms

Algorithm
egg-herbie
Counts
302 → 302
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012536293
150025815

prune694.0ms

Filtered
302 candidates to 186 candidates (61.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3002302
Fresh000
Picked101
Done011
Total3013304

Merged error: 0.0b

Counts
304 → 3

regimes18.0ms

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0115
1115

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.9s5647×body1280valid
238.0ms7931×body80valid
230.0ms1222×body640valid
77.0ms631×body320valid
26.0ms334×body160valid

Profiling

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