Details

Time bar (total: 5.1s)

sample118.0ms

Algorithm
intervals
Results
43.0ms237×body10240exit
38.0ms112×body1280valid
15.0ms75×body640valid
8.0ms40×body320valid
1.0ms16×body160valid
0.0ms13×body80valid

simplify47.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 7 (45.0ms)

IterNodesCost
0159
1249
2329
3449
4639
51799
611849
750017

prune6.0ms

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

localize9.0ms

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))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv expm1-udef
Counts
2 → 40
Calls
2 calls:
1.0ms
(fma 1 1 (exp (+ x x)))
3.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series91.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(fma 1 1 (exp (+ x x)))
70.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify75.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0150395
1512351
22464344
35002343

prune115.0ms

Filtered
46 candidates to 39 candidates (84.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New43346
Fresh000
Picked101
Done000
Total44347

Merged error: 0.7b

Counts
47 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

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-sub div-exp clear-num sum-log div-inv expm1-udef
Counts
2 → 53
Calls
2 calls:
8.0ms
(+ 1 (exp (+ x x)))
8.0ms
(/ (expm1 (+ x x)) (+ 1 (exp (+ x x))))

series63.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(+ 1 (exp (+ x x)))
51.0ms
(/ (expm1 (+ x x)) (+ 1 (exp (+ x x))))

simplify32.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0207469
1909421
25001412

prune129.0ms

Filtered
59 candidates to 46 candidates (78.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New59059
Fresh022
Picked011
Done000
Total59362

Merged error: 0.7b

Counts
62 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- x (* 1/3 (pow x 3)))
0.0b
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.1b
(* 1/3 (pow x 3))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×associate-*r*
9×add-cube-cbrt *-un-lft-identity
8×add-exp-log
5×add-cbrt-cube add-log-exp
4×unpow-prod-down cube-prod unswap-sqr
3×pow1 expm1-log1p-u fma-neg associate-*l* prod-diff prod-exp log1p-expm1-u
2×sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- diff-log unpow3 pow-exp *-commutative flip-- cbrt-unprod fma-udef
Counts
3 → 63
Calls
3 calls:
3.0ms
(- x (* 1/3 (pow x 3)))
1.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
7.0ms
(* 1/3 (pow x 3))

series165.0ms

Counts
3 → 9
Calls
3 calls:
77.0ms
(- x (* 1/3 (pow x 3)))
49.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
39.0ms
(* 1/3 (pow x 3))

simplify57.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0206338
1835292
25001292

prune369.0ms

Filtered
72 candidates to 48 candidates (66.7%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New71172
Fresh011
Picked011
Done011
Total71475

Merged error: 0.7b

Counts
75 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.0b
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.1b
(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
0.1b
(* 1/3 (pow x 3))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×associate-*r*
9×add-exp-log
8×add-cube-cbrt *-un-lft-identity
6×add-cbrt-cube
5×expm1-log1p-u
4×pow1 unpow-prod-down cube-prod log1p-expm1-u add-log-exp unswap-sqr
3×associate-*l* prod-exp
2×sqr-pow
1×cube-mult pow-to-exp log1p-udef expm1-log1p unpow3 log1p-expm1 pow-exp *-commutative cbrt-unprod fma-udef expm1-udef
Counts
4 → 65
Calls
4 calls:
1.0ms
(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
1.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
1.0ms
(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
7.0ms
(* 1/3 (pow x 3))

series336.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
54.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
153.0ms
(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
36.0ms
(* 1/3 (pow x 3))

simplify41.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0306465
11191409
25001389

prune202.0ms

Filtered
77 candidates to 55 candidates (71.4%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New75277
Fresh011
Picked011
Done112
Total76581

Merged error: 0.7b

Counts
81 → 5

regimes22.0ms

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
0126
1146
2146

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s7671×body10240exit
1.0s3364×body1280valid
430.0ms2366×body640valid
133.0ms1196×body320valid
46.0ms637×body160valid
16.0ms437×body80valid