Details

Time bar (total: 6.2s)

sample76.0ms

Algorithm
intervals
Results
33.0ms56×body2560valid
15.0ms39×body1280valid
10.0ms45×body640valid
4.0ms26×body320valid
4.0ms77×body80valid
1.0ms13×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize6.0ms

Local error

Found 2 expressions with local error:

1.4b
(- 1.0 (cos x))
17.7b
(/ (- 1.0 (cos x)) (* x x))

rewrite14.0ms

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:
3.0ms
(- 1.0 (cos x))
10.0ms
(/ (- 1.0 (cos x)) (* x x))

series8.0ms

Counts
2 → 6
Calls
2 calls:
2.0ms
(- 1.0 (cos x))
6.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0279446
11006326
25001317

prune298.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- 1.0 (cos x)) x) x)
0.2b
(/ (- 1.0 (cos x)) x)
1.4b
(- 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:
11.0ms
(/ (/ (- 1.0 (cos x)) x) x)
8.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

series14.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(/ (/ (- 1.0 (cos x)) x) x)
5.0ms
(/ (- 1.0 (cos x)) x)
2.0ms
(- 1.0 (cos x))

simplify57.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05921453
122121292
250011283

prune740.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
0.3b
(pow (cos x) 3)
0.3b
(fma (cos x) (cos x) (* 1.0 (cos x)))
1.3b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
156×add-sqr-sqrt
144×prod-diff
114×unpow-prod-down *-un-lft-identity cube-prod
84×add-cube-cbrt
50×sqr-pow
48×difference-of-squares
26×cube-mult unpow3
25×times-frac associate-/l*
15×distribute-lft-out--
12×fma-neg
10×add-exp-log add-cbrt-cube
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×difference-cubes pow-unpow
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub pow-exp prod-exp clear-num associate-/r* cbrt-unprod fma-udef div-inv rem-cube-cbrt
Counts
4 → 297
Calls
4 calls:
54.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
1.0ms
(pow (cos x) 3)
0.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
22.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series58.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
5.0ms
(pow (cos x) 3)
8.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
7.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify127.0ms

Algorithm
egg-herbie
Counts
309 → 309
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
07663804
129492790
250012733

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.3b
(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
0.3b
(fma (cos x) (cos x) (* 1.0 (cos x)))
30.6b
(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
39×*-un-lft-identity
36×prod-diff
33×add-cube-cbrt
18×unpow-prod-down cube-prod
12×fma-neg difference-of-squares
10×add-exp-log add-cbrt-cube
8×times-frac associate-/l* sqr-pow
6×add-log-exp
5×pow1 cube-mult unpow3
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow distribute-lft-out--
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub pow-exp prod-exp clear-num associate-/r* cbrt-unprod fma-udef div-inv expm1-udef associate--r- rem-cube-cbrt
Counts
4 → 139
Calls
4 calls:
1.0ms
(pow (cos x) 3)
27.0ms
(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
0.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
12.0ms
(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

series101.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(pow (cos x) 3)
63.0ms
(/ (- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3)))) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) x))
7.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
25.0ms
(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

simplify92.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
05481814
124261305
250011293

prune967.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes130.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 29.9b

bsearch39.0ms

Steps
ItersRangePoint
9
0.006665254470786589
7065.8830381017015
0.033493863120598724
9
-14674.600957416102
-0.00012459925560949148
-0.0343424885078094

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03932
13932

end0.0ms

sample2.1s

Algorithm
intervals
Results
876.0ms1542×body2560valid
432.0ms1264×body1280valid
324.0ms1501×body640valid
146.0ms925×body320valid
114.0ms2295×body80valid
52.0ms473×body160valid