Details

Time bar (total: 4.7s)

sample103.0ms

Algorithm
intervals
Results
49.0ms60×body2560valid
16.0ms33×body1280valid
13.0ms40×body640valid
6.0ms80×body80valid
5.0ms22×body320valid
3.0ms21×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b
(- 1.0 (cos x))
16.7b
(/ (- 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))

series65.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- 1.0 (cos x))
47.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify62.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune106.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos x) 1.0)
0.4b
(pow (cos x) 3)
1.3b
(- (pow 1.0 3) (pow (cos x) 3))
16.7b
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (* x x))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
233×add-sqr-sqrt
231×times-frac
137×*-un-lft-identity
112×difference-of-squares
87×unpow-prod-down cube-prod
81×associate-/l*
65×add-cube-cbrt
57×sqr-pow
35×distribute-lft-out--
17×add-exp-log add-cbrt-cube
8×add-log-exp
7×difference-cubes
6×cbrt-undiv div-exp
5×pow1
4×associate-/r/
3×pow-unpow flip3-+ flip-+ div-inv
2×div-sub prod-exp cbrt-unprod
1×+-commutative cube-mult pow-to-exp sub-neg flip3-- pow-pow frac-2neg diff-log unpow3 pow-exp clear-num associate-/r* sum-log flip-- associate-/l/ distribute-lft-out rem-cube-cbrt
Counts
4 → 252
Calls
4 calls:
3.0ms
(+ (cos x) 1.0)
1.0ms
(pow (cos x) 3)
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))
69.0ms
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (* x x))

series247.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (cos x) 1.0)
32.0ms
(pow (cos x) 3)
47.0ms
(- (pow 1.0 3) (pow (cos x) 3))
158.0ms
(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (* x x))

simplify131.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
010444274
145474109
250024017

prune564.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos x) 1.0)
0.4b
(+ (cos x) 1.0)
0.4b
(pow (cos x) 3)
1.3b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
21×*-un-lft-identity
16×difference-of-squares
15×unpow-prod-down cube-prod
10×add-log-exp
9×sqr-pow
7×add-cube-cbrt
5×pow1 add-exp-log add-cbrt-cube distribute-lft-out--
3×pow-unpow
2×+-commutative flip3-+ sum-log flip-+ distribute-lft-out
1×difference-cubes cube-mult pow-to-exp sub-neg flip3-- pow-pow diff-log unpow3 pow-exp flip-- rem-cube-cbrt
Counts
4 → 81
Calls
4 calls:
3.0ms
(+ (cos x) 1.0)
3.0ms
(+ (cos x) 1.0)
2.0ms
(pow (cos x) 3)
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series98.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (cos x) 1.0)
9.0ms
(+ (cos x) 1.0)
27.0ms
(pow (cos x) 3)
52.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify42.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0277507
11082479
25001459

prune294.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (cos x) 1.0)
0.4b
(pow (cos x) 3)
1.3b
(- (pow 1.0 3) (pow (cos x) 3))
1.5b
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
32×difference-of-squares
31×*-un-lft-identity
27×unpow-prod-down cube-prod
26×log-pow
25×exp-prod
17×sqr-pow
10×distribute-lft-out--
9×add-cube-cbrt
8×add-log-exp
6×pow1
5×add-exp-log log-prod add-cbrt-cube
3×pow-unpow
2×difference-cubes sub-neg exp-sum
1×+-commutative cube-mult pow-to-exp log-div flip3-- pow-pow flip3-+ exp-diff diff-log unpow3 rem-log-exp pow-exp sum-log flip-- flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 109
Calls
4 calls:
3.0ms
(+ (cos x) 1.0)
1.0ms
(pow (cos x) 3)
15.0ms
(- (pow 1.0 3) (pow (cos x) 3))
52.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

series136.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (cos x) 1.0)
28.0ms
(pow (cos x) 3)
51.0ms
(- (pow 1.0 3) (pow (cos x) 3))
47.0ms
(log (exp (- (pow 1.0 3) (pow (cos x) 3))))

simplify48.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0348673
11242636
25001608

prune376.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes70.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.9b

bsearch99.0ms

Steps
ItersRangePoint
8
0.007618006570916684
21.02059315853866
0.03447109155992608
11
-7.192008941699975e+16
-0.00038629318802677867
-0.02946646932882836

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06452
16652
26652

end0.0ms

sample2.0s

Algorithm
intervals
Results
900.0ms1617×body2560valid
364.0ms1223×body1280valid
298.0ms1502×body640valid
134.0ms902×body320valid
112.0ms2243×body80valid
56.0ms513×body160valid