Details

Time bar (total: 4.0s)

sample59.0ms

Algorithm
intervals
Results
27.0ms59×body2560valid
8.0ms59×body640valid
8.0ms38×body1280valid
5.0ms18×body320valid
2.0ms70×body80valid
1.0ms12×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

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize6.0ms

Local error

Found 2 expressions with local error:

1.3b
(- 1.0 (cos x))
18.5b
(/ (- 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))
8.0ms
(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(- 1.0 (cos x))
43.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify31.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0279446
11006326
25001317

prune133.0ms

Filtered
64 candidates to 43 candidates (67.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(* 1/24 (pow x 2))
13.4b
(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))))

series71.0ms

Counts
2 → 6
Calls
2 calls:
24.0ms
(* 1/24 (pow x 2))
47.0ms
(fma (pow x 4) 1/720 (- 1/2 (* 1/24 (pow x 2))))

simplify104.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
0139194
1532171
22601171
35001170

prune114.0ms

Filtered
45 candidates to 30 candidates (66.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- 1.0 (cos x))) x)
0.1b
(/ (sqrt (- 1.0 (cos x))) x)
1.3b
(- 1.0 (cos x))
1.3b
(- 1.0 (cos x))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt *-un-lft-identity
52×add-cube-cbrt
48×times-frac
40×sqrt-prod
18×prod-diff
16×associate-/l*
10×distribute-lft-out-- difference-of-squares
8×add-exp-log add-cbrt-cube add-log-exp
6×fma-neg associate-/r*
4×pow1 expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u associate-/l/
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 158
Calls
4 calls:
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
7.0ms
(/ (sqrt (- 1.0 (cos x))) x)
5.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series220.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (sqrt (- 1.0 (cos x))) x)
92.0ms
(/ (sqrt (- 1.0 (cos x))) x)
18.0ms
(- 1.0 (cos x))
18.0ms
(- 1.0 (cos x))

simplify178.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 3 (164.0ms)

IterNodesCost
03011368
19361148
249531118
350011112

prune376.0ms

Filtered
170 candidates to 110 candidates (64.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.5b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.1b
(- (pow 1.0 3) (pow (cos x) 3))
1.3b
(- 1.0 (cos x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
153×prod-diff
115×add-sqr-sqrt
101×*-un-lft-identity
90×unpow-prod-down cube-prod
89×add-cube-cbrt
34×sqr-pow
26×cube-mult unpow3
17×difference-of-squares
15×fma-neg
10×add-log-exp
6×distribute-lft-out--
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow
2×sub-neg flip3-- diff-log flip--
1×difference-cubes +-commutative pow-to-exp sqr-cos associate-+l+ distribute-rgt-out pow-pow fma-def flip3-+ pow-exp sum-log flip-+ rem-cube-cbrt
Counts
4 → 261
Calls
4 calls:
3.0ms
(pow (cos x) 3)
5.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
16.0ms
(- (pow 1.0 3) (pow (cos x) 3))
4.0ms
(- 1.0 (cos x))

series145.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (cos x) 3)
46.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
47.0ms
(- (pow 1.0 3) (pow (cos x) 3))
24.0ms
(- 1.0 (cos x))

simplify140.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
06732891
127151964
250021933

prune421.0ms

Filtered
273 candidates to 82 candidates (30.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes97.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.9b

bsearch85.0ms

Steps
ItersRangePoint
10
4.9177062248324165e-05
42925490.781275615
0.03263027133962249
8
-1.0806682141483241
-0.0004106978961831668
-0.026802849257838823

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04424
14424

end0.0ms

sample1.6s

Algorithm
intervals
Results
722.0ms1585×body2560valid
291.0ms1257×body1280valid
226.0ms1538×body640valid
98.0ms905×body320valid
85.0ms2254×body80valid
33.0ms461×body160valid