Details

Time bar (total: 3.3s)

sample51.0ms

Algorithm
intervals
Results
21.0ms48×body2560valid
10.0ms45×body1280valid
7.0ms54×body640valid
3.0ms26×body320valid
2.0ms65×body80valid
1.0ms18×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 32.2b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.2b
(- 1.0 (cos x))
14.6b
(/ (- 1.0 (cos x)) (* x x))

rewrite13.0ms

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))
7.0ms
(/ (- 1.0 (cos x)) (* x x))

series67.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
49.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify33.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0279446
11006326
25001317

prune128.0ms

Filtered
64 candidates to 43 candidates (67.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New531164
Fresh000
Picked101
Done000
Total541165

Merged error: 0.0b

Counts
65 → 11

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(* 1/24 (pow x 2))
12.4b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

rewrite7.0ms

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:
5.0ms
(* 1/24 (pow x 2))
1.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

series73.0ms

Counts
2 → 6
Calls
2 calls:
26.0ms
(* 1/24 (pow x 2))
47.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify101.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0139203
1565171
22616171
35001170

prune101.0ms

Filtered
45 candidates to 30 candidates (66.7%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New44145
Fresh1910
Picked011
Done000
Total451156

Merged error: 0.0b

Counts
56 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 1/24 (pow x 2))
0.7b
(expm1 (log1p (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))))
12.4b
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
23.1b
(log1p (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2)))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×add-exp-log
8×associate-*r*
7×add-cube-cbrt *-un-lft-identity
6×add-cbrt-cube
5×expm1-log1p-u
4×pow1 unpow-prod-down log1p-expm1-u add-log-exp unswap-sqr
3×associate-*l* prod-exp
2×unpow2 sqr-pow
1×pow-to-exp log1p-udef expm1-log1p log1p-expm1 pow-exp *-commutative cbrt-unprod fma-udef expm1-udef
Counts
4 → 61
Calls
4 calls:
5.0ms
(* 1/24 (pow x 2))
1.0ms
(expm1 (log1p (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
(log1p (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2)))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* 1/24 (pow x 2))
133.0ms
(expm1 (log1p (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))))
47.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))
91.0ms
(log1p (fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2)))))

simplify36.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0285449
11022396
25001376

prune181.0ms

Filtered
73 candidates to 53 candidates (72.6%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New73073
Fresh099
Picked011
Done011
Total731184

Merged error: 0.0b

Counts
84 → 11

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (- 1.0 (cos x)) x) x)
0.1b
(/ (- 1.0 (cos x)) x)
2.2b
(- 1.0 (cos x))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
110×add-sqr-sqrt *-un-lft-identity
76×add-cube-cbrt
24×associate-/l*
17×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
9×prod-diff
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u fma-neg div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg diff-log
Counts
3 → 165
Calls
3 calls:
12.0ms
(/ (/ (- 1.0 (cos x)) x) x)
6.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series112.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(/ (/ (- 1.0 (cos x)) x) x)
44.0ms
(/ (- 1.0 (cos x)) x)
19.0ms
(- 1.0 (cos x))

simplify60.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05921453
122121292
250011283

prune235.0ms

Filtered
174 candidates to 115 candidates (66.1%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1704174
Fresh268
Picked101
Done022
Total17312185

Merged error: 0.0b

Counts
185 → 12

regimes92.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.7b

bsearch62.0ms

Steps
ItersRangePoint
7
0.00999808388340962
0.475758948552502
0.030798941289724838
9
-164485.30314980465
-0.009598081335721272
-0.03106715975092916

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02912
12912

end0.0ms

sample1.6s

Algorithm
intervals
Results
737.0ms1621×body2560valid
269.0ms1232×body1280valid
225.0ms1497×body640valid
95.0ms946×body320valid
79.0ms2270×body80valid
30.0ms434×body160valid