Details

Time bar (total: 7.5s)

sample144.0ms

Algorithm
intervals
Results
76.0ms60×body2560valid
42.0ms102×body1280valid
11.0ms49×body640valid
4.0ms26×body320valid
1.0ms8×body160valid
1.0ms11×body80valid

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: 29.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) (sin x))
1.0b
(- 1.0 (cos x))

rewrite32.0ms

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:
23.0ms
(/ (- 1.0 (cos x)) (sin x))
7.0ms
(- 1.0 (cos x))

series55.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(/ (- 1.0 (cos x)) (sin x))
19.0ms
(- 1.0 (cos x))

simplify33.0ms

Counts
74 → 74
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0292569
1965460
25002460
done5002460

prune180.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
0.3b
(pow (cos x) 3)
0.5b
(+ 1.0 (cos x))
0.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
233×add-sqr-sqrt
165×*-un-lft-identity
144×prod-diff
138×unpow-prod-down cube-prod
113×add-cube-cbrt
80×difference-of-squares
75×times-frac
66×sqr-pow
26×cube-mult unpow3
25×associate-/l* distribute-lft-out--
12×fma-neg
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-def associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative pow-to-exp sub-neg pow-pow frac-2neg flip3-+ diff-log div-sub div-exp pow-exp clear-num sum-log flip-+ div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 354
Calls
4 calls:
79.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
3.0ms
(pow (cos x) 3)
6.0ms
(+ 1.0 (cos x))
31.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series207.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
27.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
52.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify143.0ms

Counts
366 → 366
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
08284951
132444033
250023940
done50023940

prune524.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
0.3b
(pow (cos x) 3)
0.5b
(fma (cos x) (cos x) (* 1.0 (cos x)))
0.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
110×add-sqr-sqrt
94×*-un-lft-identity
90×unpow-prod-down cube-prod
84×add-cube-cbrt
34×sqr-pow
26×cube-mult unpow3
16×difference-of-squares
12×fma-neg
7×pow1 add-exp-log add-cbrt-cube
6×add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow associate-*r* associate-*l*
1×difference-cubes pow-to-exp sub-neg flip3-- pow-pow diff-log pow-prod-down pow-exp prod-exp *-commutative flip-- cbrt-unprod fma-udef rem-cube-cbrt unswap-sqr
Counts
4 → 247
Calls
4 calls:
9.0ms
(* (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)))
33.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series231.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (fma 1.0 1.0 (fma (cos x) (cos x) (* 1.0 (cos x)))) (sin x))
33.0ms
(pow (cos x) 3)
46.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
52.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify100.0ms

Counts
259 → 259
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
06162913
121531995
250021966
done50021966

prune349.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (- (pow 1.0 3) (pow (cos x) 3)))
0.3b
(pow (cos x) 3)
0.5b
(fma (cos x) (cos x) (* 1.0 (cos x)))
0.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
106×add-sqr-sqrt
92×*-un-lft-identity
90×unpow-prod-down cube-prod
82×add-cube-cbrt
34×sqr-pow
26×cube-mult unpow3
16×difference-of-squares
12×fma-neg
6×add-log-exp
5×pow1 add-exp-log add-cbrt-cube log1p-expm1-u distribute-lft-out--
4×expm1-log1p-u
3×pow-unpow
1×difference-cubes pow-to-exp sub-neg expm1-log1p flip3-- pow-pow diff-log pow-exp flip-- fma-udef expm1-udef rem-cube-cbrt
Counts
4 → 238
Calls
4 calls:
0.0ms
(expm1 (- (pow 1.0 3) (pow (cos x) 3)))
3.0ms
(pow (cos x) 3)
0.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
30.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series224.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(expm1 (- (pow 1.0 3) (pow (cos x) 3)))
27.0ms
(pow (cos x) 3)
50.0ms
(fma (cos x) (cos x) (* 1.0 (cos x)))
47.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify89.0ms

Counts
250 → 250
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
05502757
117771867
250011838
done50011838

prune319.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

regimes95.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.1b

bsearch78.0ms

Steps
ItersRangePoint
10
4.250299402880914e-15
0.02319676823116778
0.02029306521166552
7
-0.15939393977811658
-0.001391736753177052
-0.02373580573239165

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04340
14340
done4340

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.1s1566×body2560valid
1.4s2786×body1280valid
463.0ms1962×body640valid
139.0ms911×body320valid
47.0ms435×body160valid
27.0ms337×body80valid
11.0ms3×body5120valid