Details

Time bar (total: 5.1s)

sample110.0ms

Algorithm
intervals
Results
47.0ms271×body10240exit
33.0ms109×body1280valid
14.0ms77×body640valid
4.0ms33×body320valid
2.0ms23×body160valid
0.0ms14×body80valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 7 (42.0ms)

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: 0.3b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1 1 (exp (+ x x)))
0.3b
(/ (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))))

series90.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(fma 1 1 (exp (+ x x)))
69.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify77.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0150395
1512351
22464344
35002343

prune111.0ms

Filtered
46 candidates to 39 candidates (84.8%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New44246
Fresh000
Picked101
Done000
Total45247

Merged error: 0.2b

Counts
47 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (log1p (exp (* 2 x))))
0.2b
(log1p (exp (* 2 x)))
0.3b
(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-cbrt-cube
4×add-exp-log expm1-log1p-u add-log-exp
3×pow1 exp-prod associate-/r* log1p-expm1-u associate-/l*
2×log1p-udef rem-exp-log
1×cbrt-undiv frac-2neg div-sub log1p-expm1 div-exp clear-num div-inv expm1-udef
Counts
3 → 55
Calls
3 calls:
2.0ms
(exp (log1p (exp (* 2 x))))
1.0ms
(log1p (exp (* 2 x)))
4.0ms
(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

series266.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(exp (log1p (exp (* 2 x))))
50.0ms
(log1p (exp (* 2 x)))
140.0ms
(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
0182523
1556477
22509465
35001451

prune133.0ms

Filtered
64 candidates to 50 candidates (78.1%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New64064
Fresh011
Picked011
Done000
Total64266

Merged error: 0.2b

Counts
66 → 2

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))

rewrite15.0ms

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))))
10.0ms
(* 1/3 (pow x 3))

series170.0ms

Counts
3 → 9
Calls
3 calls:
80.0ms
(- x (* 1/3 (pow x 3)))
55.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
36.0ms
(* 1/3 (pow x 3))

simplify36.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0206338
1835292
25001292

prune134.0ms

Filtered
72 candidates to 48 candidates (66.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New71172
Fresh000
Picked011
Done011
Total71374

Merged error: 0.2b

Counts
74 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.1b
(* 1/3 (pow x 3))
0.1b
(* 1/3 (pow x 3))
0.2b
(* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
30×associate-*r*
20×add-cube-cbrt *-un-lft-identity
19×pow1
18×sqrt-prod
16×add-exp-log
12×associate-*l* unswap-sqr
10×add-cbrt-cube
8×unpow-prod-down sqrt-pow1 pow1/2 cube-prod swap-sqr
7×prod-exp
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×pow-prod-down pow-sqr *-commutative cbrt-unprod
2×cube-mult pow-to-exp unpow3 pow-exp
1×pow2 pow-plus sqrt-unprod rem-square-sqrt fma-udef
Counts
4 → 127
Calls
4 calls:
1.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
6.0ms
(* 1/3 (pow x 3))
7.0ms
(* 1/3 (pow x 3))
6.0ms
(* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

series179.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
39.0ms
(* 1/3 (pow x 3))
34.0ms
(* 1/3 (pow x 3))
55.0ms
(* (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (sqrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))

simplify52.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0230794
11004692
25001660

prune280.0ms

Filtered
139 candidates to 76 candidates (54.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1381139
Fresh000
Picked101
Done022
Total1393142

Merged error: 0.2b

Counts
142 → 3

regimes15.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0157
1177
2177

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s7494×body10240exit
1.0s3366×body1280valid
437.0ms2403×body640valid
141.0ms1205×body320valid
44.0ms595×body160valid
16.0ms431×body80valid