Details

Time bar (total: 7.6s)

sample136.0ms

Algorithm
intervals
Results
66.0ms44×body2560valid
33.0ms77×body1280valid
15.0ms66×body640valid
10.0ms38×body320valid
2.0ms17×body80valid
1.0ms14×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0114
1144
2164
3164
done164

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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:
19.0ms
(/ (- 1.0 (cos x)) (sin x))
7.0ms
(- 1.0 (cos x))

series64.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(/ (- 1.0 (cos x)) (sin x))
21.0ms
(- 1.0 (cos x))

simplify36.0ms

Counts
74 → 74
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0292569
1965460
25002460
done5002460

prune180.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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)))) (sin x)))
0.4b
(pow (cos x) 3)
0.4b
(fma (cos x) (cos x) (* 1.0 (cos x)))
1.3b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite137.0ms

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:
82.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))
3.0ms
(pow (cos x) 3)
0.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
36.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series318.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x)))
28.0ms
(pow (cos x) 3)
51.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
52.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify137.0ms

Counts
309 → 309
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
07683882
129222862
250022805
done50022805

prune449.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.2b
(exp (/ (- 1.0 (cos x)) (sin x)))
1.1b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.5b
(- 1.0 (cos x))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt *-un-lft-identity
45×times-frac
40×add-cube-cbrt
38×exp-prod
20×log-pow
11×distribute-lft-out-- difference-of-squares
9×prod-diff
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×log-prod fma-neg div-sub associate-/r* div-inv
2×flip3-- exp-diff flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg diff-log div-exp rem-log-exp clear-num rem-exp-log
Counts
4 → 132
Calls
4 calls:
19.0ms
(/ (- 1.0 (cos x)) (sin x))
21.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
27.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
7.0ms
(- 1.0 (cos x))

series145.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ (- 1.0 (cos x)) (sin x))
49.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
37.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
22.0ms
(- 1.0 (cos x))

simplify38.0ms

Counts
144 → 144
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03681009
11099873
25002871
done5002871

prune363.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (pow (pow (cos x) 3) 3))
0.4b
(pow (cos x) 3)
0.4b
(fma (cos x) (cos x) (* 1.0 (cos x)))
1.3b
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
430×cbrt-prod
396×prod-diff
374×unpow-prod-down cube-prod
277×add-sqr-sqrt
214×*-un-lft-identity
212×add-cube-cbrt
97×sqr-pow
74×cube-mult unpow3
44×difference-of-squares
12×fma-neg
6×add-log-exp
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow
1×pow-to-exp sub-neg flip3-- pow-pow pow1/3 diff-log pow-exp flip-- rem-cbrt-cube fma-udef distribute-lft-out-- rem-cube-cbrt
Counts
4 → 543
Calls
4 calls:
6.0ms
(cbrt (pow (pow (cos x) 3) 3))
4.0ms
(pow (cos x) 3)
0.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
65.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series155.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(cbrt (pow (pow (cos x) 3) 3))
28.0ms
(pow (cos x) 3)
52.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
47.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify157.0ms

Counts
555 → 555
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
08569810
122455042
250014983
done50014983

prune375.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

regimes142.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.6b

bsearch76.0ms

Steps
ItersRangePoint
8
0.016621422887445694
5.276955647516397
0.020904349932135746
9
-0.05800990145057735
-1.1864783425707322e-08
-0.02322762662824426

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03935
13935
done3935

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.1s1604×body2560valid
1.4s2719×body1280valid
471.0ms1920×body640valid
151.0ms940×body320valid
59.0ms460×body160valid
22.0ms354×body80valid
12.0ms3×body5120valid