Details

Time bar (total: 3.5s)

sample62.0ms

Algorithm
intervals
Results
32.0ms64×body2560valid
9.0ms39×body1280valid
6.0ms41×body640valid
3.0ms26×body320valid
2.0ms71×body80valid
1.0ms15×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0134
1214
2264
3284
4284

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: 33.5b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b
(- 1.0 (cos x))
17.7b
(/ (- 1.0 (cos x)) (* x x))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-log-exp
3×fma-neg distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv expm1-log1p-u flip3-- div-exp flip-- log1p-expm1-u associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 58
Calls
2 calls:
4.0ms
(- 1.0 (cos x))
12.0ms
(/ (- 1.0 (cos x)) (* x x))

series59.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- 1.0 (cos x))
42.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0279446
11006326
25001317

prune131.0ms

Filtered
64 candidates to 43 candidates (67.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New55964
Fresh000
Picked011
Done000
Total551065

Merged error: 0.1b

Counts
65 → 10

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 1/24 (pow x 2))
12.9b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×associate-*r*
7×add-exp-log
5×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
1×pow-to-exp pow-exp *-commutative cbrt-unprod fma-udef
Counts
2 → 39
Calls
2 calls:
6.0ms
(* 1/24 (pow x 2))
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series72.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(* 1/24 (pow x 2))
47.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify108.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 3 (103.0ms)

IterNodesCost
0139194
1532171
22601171
35001170

prune110.0ms

Filtered
45 candidates to 30 candidates (66.7%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New44145
Fresh088
Picked011
Done011
Total441155

Merged error: 0.1b

Counts
55 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

12.0b
(cbrt (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2)))))
12.9b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
12.9b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
12.9b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod fma-udef
1×pow1/3
Counts
4 → 43
Calls
4 calls:
1.0ms
(cbrt (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2)))))
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series262.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(cbrt (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2)))))
44.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
40.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
44.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify64.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0151462
1465414
21944397
35002393

prune181.0ms

Filtered
55 candidates to 45 candidates (81.8%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New54155
Fresh088
Picked101
Done022
Total551166

Merged error: 0.1b

Counts
66 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

12.9b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
12.9b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
12.9b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
12.9b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
4 → 40
Calls
4 calls:
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series170.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
40.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
45.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
40.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify213.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
040356
1142312
2664312
34949312
45001312

prune190.0ms

Filtered
52 candidates to 40 candidates (76.9%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New52052
Fresh088
Picked011
Done022
Total521163

Merged error: 0.1b

Counts
63 → 11

regimes99.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.9b

bsearch57.0ms

Steps
ItersRangePoint
6
0.018000635171863108
0.09117784756913819
0.03010910821075468
10
-1421.6155834850151
-1.485944467815708e-07
-0.03323288645356819

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0269
1269

end0.0ms

sample1.6s

Algorithm
intervals
Results
750.0ms1643×body2560valid
280.0ms1221×body1280valid
207.0ms1450×body640valid
97.0ms914×body320valid
68.0ms2291×body80valid
34.0ms481×body160valid