Details

Time bar (total: 4.7s)

sample102.0ms

Algorithm
intervals
Results
37.0ms237×body10240exit
33.0ms112×body1280valid
16.0ms75×body640valid
4.0ms40×body320valid
1.0ms16×body160valid
0.0ms13×body80valid

simplify45.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 7 (43.0ms)

IterNodesCost
0159
1249
2329
3449
4639
51799
611849
750027

prune5.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 0.8b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1 1 (exp (+ x x)))
0.8b
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
1×frac-2neg div-sub clear-num fma-udef div-inv expm1-udef
Counts
2 → 5
Calls
2 calls:
1.0ms
(fma 1 1 (exp (+ x x)))
2.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series87.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(fma 1 1 (exp (+ x x)))
67.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify123.0ms

Algorithm
egg-herbie
Counts
11 → 11
Iterations

Useful iterations: 3 (24.0ms)

IterNodesCost
07256
118956
270255
3304154
4500254

prune23.0ms

Filtered
11 candidates to 9 candidates (81.8%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New9211
Fresh000
Picked011
Done000
Total9312

Merged error: 0.7b

Counts
12 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (exp (* 2 x)) 1)
0.0b
(/ 1 (+ (exp (* 2 x)) 1))
0.8b
(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
4×associate-/r/
3×flip3-+ associate-*r/ associate-*r* clear-num flip-+
2×frac-2neg un-div-inv *-commutative div-inv
1×+-commutative fma-def exp-lft-sqr inv-pow
Counts
3 → 19
Calls
3 calls:
4.0ms
(+ (exp (* 2 x)) 1)
4.0ms
(/ 1 (+ (exp (* 2 x)) 1))
5.0ms
(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

series80.0ms

Counts
3 → 9
Calls
3 calls:
9.0ms
(+ (exp (* 2 x)) 1)
21.0ms
(/ 1 (+ (exp (* 2 x)) 1))
49.0ms
(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

simplify67.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0127111
1504101
2229396
3500192

prune61.0ms

Filtered
28 candidates to 20 candidates (71.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New26228
Fresh011
Picked101
Done011
Total27431

Merged error: 0.7b

Counts
31 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (exp x) (exp x) 1)
0.0b
(/ 1 (fma (exp x) (exp x) 1))
0.8b
(* (expm1 (+ x x)) (/ 1 (fma (exp x) (exp x) 1)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
3×associate-*r/ clear-num
2×frac-2neg un-div-inv div-inv
1×associate-*r* *-commutative fma-udef inv-pow
Counts
3 → 12
Calls
3 calls:
1.0ms
(fma (exp x) (exp x) 1)
2.0ms
(/ 1 (fma (exp x) (exp x) 1))
3.0ms
(* (expm1 (+ x x)) (/ 1 (fma (exp x) (exp x) 1)))

series129.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(fma (exp x) (exp x) 1)
33.0ms
(/ 1 (fma (exp x) (exp x) 1))
72.0ms
(* (expm1 (+ x x)) (/ 1 (fma (exp x) (exp x) 1)))

simplify36.0ms

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 3 (34.0ms)

IterNodesCost
09165
128062
2113261
3500160

prune42.0ms

Filtered
21 candidates to 13 candidates (61.9%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New21021
Fresh022
Picked011
Done011
Total21425

Merged error: 0.7b

Counts
25 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1)))
0.8b
(* (expm1 (+ x x)) (* (/ 1 (+ (pow (exp (* 2 x)) 3) 1)) (+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1)))))
0.8b
(* (/ 1 (+ (pow (exp (* 2 x)) 3) 1)) (+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1))))
4.9b
(- (* 1 1) (* (exp (* 2 x)) 1))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
71×*-commutative
56×associate-+r+
50×distribute-rgt-in distribute-lft-in
48×prod-diff
23×associate-*l*
22×exp-lft-sqr
15×associate-*r/
12×frac-times
11×flip3-+ flip-+
8×sub-neg
7×+-commutative
6×fma-def frac-2neg associate-*r* associate-*l/ clear-num
4×associate-/r/
2×distribute-rgt-out-- fma-neg div-inv distribute-lft-out--
1×associate-+r- flip3-- swap-sqr flip-- unswap-sqr
Counts
4 → 126
Calls
4 calls:
14.0ms
(+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1)))
23.0ms
(* (expm1 (+ x x)) (* (/ 1 (+ (pow (exp (* 2 x)) 3) 1)) (+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1)))))
21.0ms
(* (/ 1 (+ (pow (exp (* 2 x)) 3) 1)) (+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1))))
6.0ms
(- (* 1 1) (* (exp (* 2 x)) 1))

series301.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1)))
161.0ms
(* (expm1 (+ x x)) (* (/ 1 (+ (pow (exp (* 2 x)) 3) 1)) (+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1)))))
88.0ms
(* (/ 1 (+ (pow (exp (* 2 x)) 3) 1)) (+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1))))
19.0ms
(- (* 1 1) (* (exp (* 2 x)) 1))

simplify84.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06262639
131032185
250012160

prune259.0ms

Filtered
138 candidates to 62 candidates (44.9%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1380138
Fresh011
Picked011
Done022
Total1384142

Merged error: 0.7b

Counts
142 → 4

regimes17.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0137
1157
2157

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.3s7671×body10240exit
1.0s3364×body1280valid
419.0ms2366×body640valid
132.0ms1196×body320valid
43.0ms637×body160valid
16.0ms437×body80valid