Details

Time bar (total: 3.9s)

sample48.0ms

Algorithm
intervals
Results
20.0ms48×body2560valid
9.0ms43×body1280valid
6.0ms42×body640valid
3.0ms31×body320valid
3.0ms78×body80valid
1.0ms14×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: 31.1b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 42
Calls
2 calls:
2.0ms
(- 1.0 (cos x))
9.0ms
(/ (- 1.0 (cos x)) (* x x))

series68.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(- 1.0 (cos x))
50.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify59.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune114.0ms

Filtered
48 candidates to 34 candidates (70.8%)
Pruning

10 alts after pruning (10 fresh and 0 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)
2.2b
(- 1.0 (cos x))
2.2b
(- 1.0 (cos x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
48×times-frac
40×sqrt-prod
38×add-cube-cbrt
16×associate-/l*
10×distribute-lft-out-- difference-of-squares
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r*
4×pow1 flip3-- sqrt-div flip-- associate-/l/
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 126
Calls
4 calls:
8.0ms
(/ (sqrt (- 1.0 (cos x))) x)
8.0ms
(/ (sqrt (- 1.0 (cos x))) x)
2.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))

series233.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (sqrt (- 1.0 (cos x))) x)
96.0ms
(/ (sqrt (- 1.0 (cos x))) x)
19.0ms
(- 1.0 (cos x))
24.0ms
(- 1.0 (cos x))

simplify96.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
02421020
1706972
22968960
35002960

prune301.0ms

Filtered
138 candidates to 92 candidates (66.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.4b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.9b
(- (pow 1.0 3) (pow (cos x) 3))
2.2b
(- 1.0 (cos x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
19×*-un-lft-identity
17×difference-of-squares
15×unpow-prod-down cube-prod
10×add-log-exp
9×sqr-pow
7×add-cube-cbrt
6×distribute-lft-out--
5×pow1 add-exp-log add-cbrt-cube
3×pow-unpow
2×sub-neg flip3-- diff-log flip--
1×difference-cubes +-commutative cube-mult pow-to-exp sqr-cos associate-+l+ distribute-rgt-out pow-pow flip3-+ unpow3 pow-exp sum-log flip-+ rem-cube-cbrt
Counts
4 → 84
Calls
4 calls:
2.0ms
(pow (cos x) 3)
4.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))
5.0ms
(- 1.0 (cos x))

series141.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (cos x) 3)
43.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
52.0ms
(- (pow 1.0 3) (pow (cos x) 3))
19.0ms
(- 1.0 (cos x))

simplify64.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0361583
11558544
25003524

prune319.0ms

Filtered
96 candidates to 59 candidates (61.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
0.4b
(pow (pow (cos x) 3) 3)
1.9b
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))
2.2b
(- 1.0 (cos x))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
53×unpow-prod-down cube-prod
45×difference-of-squares
40×cbrt-prod
26×sqr-pow
15×*-un-lft-identity
11×add-cube-cbrt
10×add-log-exp
6×add-exp-log
5×add-cbrt-cube
4×pow1 pow-exp
3×cube-mult pow-unpow unpow3
2×pow-to-exp sub-neg flip3-- diff-log flip-- distribute-lft-out--
1×+-commutative sqr-cos associate-+l+ distribute-rgt-out pow-pow flip3-+ sum-log flip-+ rem-cube-cbrt
Counts
4 → 127
Calls
4 calls:
4.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
4.0ms
(pow (pow (cos x) 3) 3)
37.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))
3.0ms
(- 1.0 (cos x))

series178.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
56.0ms
(pow (pow (cos x) 3) 3)
55.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))
20.0ms
(- 1.0 (cos x))

simplify73.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
04871079
119101002
25002993

prune370.0ms

Filtered
139 candidates to 67 candidates (48.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes55.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.0b

bsearch59.0ms

Steps
ItersRangePoint
9
0.0004320794088804456
4086.0217424804537
0.029942885905857714
7
-0.37949367736095085
-0.007251023403816859
-0.030582628052299624

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03015
13015

end0.0ms

sample1.5s

Algorithm
intervals
Results
724.0ms1593×body2560valid
294.0ms1297×body1280valid
200.0ms1435×body640valid
92.0ms928×body320valid
72.0ms2297×body80valid
31.0ms450×body160valid