Details

Time bar (total: 10.4s)

sample243.0ms

Algorithm
intervals
Results
112.0ms51×body2560valid
76.0ms92×body1280valid
19.0ms45×body640valid
13.0ms39×body320valid
5.0ms1×body5120valid
5.0ms20×body160valid
1.0ms8×body80valid

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
1117
2147
3167
done167

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize22.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
2.0b
(- 1.0 (cos x))

rewrite62.0ms

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:
42.0ms
(/ (- 1.0 (cos x)) (sin x))
15.0ms
(- 1.0 (cos x))

series90.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(/ (- 1.0 (cos x)) (sin x))
38.0ms
(- 1.0 (cos x))

simplify1.8s

Counts
74 → 74
Iterations

Useful iterations: done (1.8s)

IterNodesCost
0134964
1295831
2743731
32333692
done5000683

prune237.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
0.2b
(fma 1/240 (pow x 5) (* 1/2 x))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
0.0ms
(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
0.0ms
(fma 1/240 (pow x 5) (* 1/2 x))

series299.0ms

Counts
2 → 6
Calls
2 calls:
91.0ms
(fma 1/24 (pow x 3) (fma 1/240 (pow x 5) (* 1/2 x)))
208.0ms
(fma 1/240 (pow x 5) (* 1/2 x))

simplify1.1s

Counts
26 → 26
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
036358
162349
2177307
3967307
done5001307

prune158.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (+ 1.0 (cos x)))
0.3b
(+ 1.0 (cos x))
0.3b
(pow (cos x) 3)
1.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
111×add-sqr-sqrt
99×*-un-lft-identity
90×unpow-prod-down cube-prod
85×add-cube-cbrt
34×sqr-pow
26×cube-mult unpow3
16×difference-of-squares
12×fma-neg
8×add-log-exp
7×pow1 add-exp-log add-cbrt-cube
5×distribute-lft-out--
4×expm1-log1p-u associate-*r* log1p-expm1-u
3×pow-unpow fma-def associate-*l*
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×difference-cubes +-commutative distribute-rgt-in pow-to-exp sub-neg flip3-- pow-pow distribute-lft-in diff-log pow-prod-down pow-exp prod-exp sum-log *-commutative flip-- cbrt-unprod rem-cube-cbrt unswap-sqr
Counts
4 → 259
Calls
4 calls:
26.0ms
(* (cos x) (+ 1.0 (cos x)))
12.0ms
(+ 1.0 (cos x))
7.0ms
(pow (cos x) 3)
60.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series174.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (cos x) (+ 1.0 (cos x)))
18.0ms
(+ 1.0 (cos x))
51.0ms
(pow (cos x) 3)
63.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify2.0s

Counts
271 → 271
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02737533
16124117
219633101
done50012379

prune552.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

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)))
2.0b
(- 1.0 (cos x))

rewrite93.0ms

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:
36.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
32.0ms
(/ (sin x) (- 1.0 (cos x)))
9.0ms
(- 1.0 (cos x))

series154.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(/ 1 (/ (sin x) (- 1.0 (cos x))))
46.0ms
(/ (sin x) (- 1.0 (cos x)))
32.0ms
(- 1.0 (cos x))

simplify2.6s

Counts
186 → 186
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02693021
15612564
212262279
334722188
done50002178

prune356.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes80.0ms

bsearch2.0ms