Details

Time bar (total: 7.2s)

sample137.0ms

Algorithm
intervals
Results
71.0ms57×body2560valid
41.0ms102×body1280valid
10.0ms48×body640valid
4.0ms26×body320valid
1.0ms11×body160valid
1.0ms12×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.5b
(- 1.0 (cos x))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 68
Calls
2 calls:
25.0ms
(/ (- 1.0 (cos x)) (sin x))
7.0ms
(- 1.0 (cos x))

series52.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(/ (- 1.0 (cos x)) (sin x))
18.0ms
(- 1.0 (cos x))

simplify36.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0292569
1965460
25002460

prune192.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b
(/ (sin x) (- 1.0 (cos x)))
1.5b
(- 1.0 (cos x))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
112×add-sqr-sqrt *-un-lft-identity
78×add-cube-cbrt
26×associate-/r*
17×distribute-lft-out-- difference-of-squares
16×add-exp-log
11×associate-/r/
10×add-cbrt-cube
9×prod-diff
8×div-exp
6×flip3-- flip-- div-inv associate-/l*
5×add-log-exp
4×pow1 cbrt-undiv
3×expm1-log1p-u fma-neg log1p-expm1-u
2×rec-exp frac-2neg 1-exp clear-num
1×sub-neg pow-flip diff-log inv-pow
Counts
3 → 177
Calls
3 calls:
18.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
16.0ms
(/ (sin x) (- 1.0 (cos x)))
7.0ms
(- 1.0 (cos x))

series93.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
34.0ms
(/ (sin x) (- 1.0 (cos x)))
18.0ms
(- 1.0 (cos x))

simplify69.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05721779
126361549
250011441

prune302.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos x) (cos x))
0.4b
(pow (cos x) 3)
0.5b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.3b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
112×add-sqr-sqrt
96×*-un-lft-identity
90×unpow-prod-down cube-prod
86×add-cube-cbrt
34×sqr-pow
26×cube-mult unpow3
16×difference-of-squares
12×pow1 fma-neg
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow swap-sqr associate-*r* associate-*l*
2×sqr-cos
1×difference-cubes +-commutative pow2 pow-to-exp sub-neg associate-+l+ distribute-rgt-out flip3-- pow-pow fma-def flip3-+ pow-plus diff-log pow-prod-down pow-exp prod-exp sum-log pow-sqr cos-mult *-commutative pow-prod-up flip-- cbrt-unprod flip-+ rem-cube-cbrt unswap-sqr
Counts
4 → 262
Calls
4 calls:
13.0ms
(* (cos x) (cos x))
3.0ms
(pow (cos x) 3)
12.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
31.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series135.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (cos x) (cos x))
27.0ms
(pow (cos x) 3)
46.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
47.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify148.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 2 (114.0ms)

IterNodesCost
06562815
127541911
250011872

prune388.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos x) (cos x))
0.4b
(pow (cos x) 3)
0.5b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
30.6b
(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
37×*-un-lft-identity
36×prod-diff
35×add-cube-cbrt
16×unpow-prod-down cube-prod
12×pow1 fma-neg
8×add-log-exp
7×add-exp-log add-cbrt-cube
6×sqr-pow
5×cube-mult unpow3
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×pow-unpow swap-sqr associate-*r* associate-*l*
2×sqr-cos
1×+-commutative pow2 pow-to-exp sub-neg associate-+l+ distribute-rgt-out flip3-- pow-pow fma-def flip3-+ pow-plus diff-log pow-prod-down pow-exp prod-exp sum-log pow-sqr cos-mult *-commutative pow-prod-up flip-- cbrt-unprod flip-+ distribute-lft-out-- expm1-udef associate--r- rem-cube-cbrt unswap-sqr
Counts
4 → 138
Calls
4 calls:
10.0ms
(* (cos x) (cos x))
3.0ms
(pow (cos x) 3)
12.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
21.0ms
(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

series294.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (cos x) (cos x))
27.0ms
(pow (cos x) 3)
40.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
205.0ms
(- (pow 1.0 3) (expm1 (log1p (pow (cos x) 3))))

simplify118.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
04811252
12458813
25001796

prune369.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

regimes293.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.4b

bsearch77.0ms

Steps
ItersRangePoint
9
1.3330246063773173e-09
3.618674152218468
0.02321496743503862
7
-0.23317146499959118
-0.002309702793432406
-0.02503568567500278

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05043
15043

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.1s1592×body2560valid
1.2s2800×body1280valid
448.0ms1866×body640valid
135.0ms892×body320valid
51.0ms475×body160valid
24.0ms372×body80valid
16.0ms3×body5120valid