Details

Time bar (total: 18.1s)

sample107.0ms

Algorithm
intervals
Results
37.0ms46×body2560valid
17.0ms87×body80valid
17.0ms35×body1280valid
15.0ms48×body640valid
6.0ms29×body320valid
2.0ms11×body160valid

simplify22.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1138
2218
3268
4288
done288

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b
(- 1.0 (cos x))
12.9b
(/ (- 1.0 (cos x)) (* x x))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-log-exp
3×fma-neg distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv expm1-log1p-u flip3-- div-exp flip-- log1p-expm1-u associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 58
Calls
2 calls:
21.0ms
(- 1.0 (cos x))
30.0ms
(/ (- 1.0 (cos x)) (* x x))

series125.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(- 1.0 (cos x))
86.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify2.3s

Counts
64 → 64
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0116808
1269678
2747566
32669526
done5001517

prune188.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
1.1b
(- 1.0 (cos x))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
54×*-un-lft-identity
46×times-frac
36×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp prod-diff
8×prod-exp distribute-lft-out-- difference-of-squares
6×unswap-sqr
5×pow1 cbrt-undiv associate-/l* add-log-exp
4×cbrt-unprod
3×expm1-log1p-u fma-neg associate-/r* log1p-expm1-u div-inv
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 132
Calls
3 calls:
51.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
23.0ms
(/ (- 1.0 (cos x)) x)
8.0ms
(- 1.0 (cos x))

series135.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
56.0ms
(/ (- 1.0 (cos x)) x)
26.0ms
(- 1.0 (cos x))

simplify2.1s

Counts
141 → 141
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02191855
15561581
217411364
done50011323

prune439.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* x (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
0.4b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
0.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
144×prod-diff
117×*-un-lft-identity
114×unpow-prod-down cube-prod
85×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
8×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×difference-cubes pow-unpow fma-def
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×+-commutative pow-to-exp sub-neg pow-pow frac-2neg flip3-+ diff-log div-sub pow-exp prod-exp clear-num associate-/r* sum-log cbrt-unprod flip-+ div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 304
Calls
4 calls:
140.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* x (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
7.0ms
(pow (cos x) 3)
7.0ms
(+ 1.0 (cos x))
57.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series332.0ms

Counts
4 → 12
Calls
4 calls:
225.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* x (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
39.0ms
(pow (cos x) 3)
11.0ms
(+ 1.0 (cos x))
56.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify2.2s

Counts
316 → 316
Iterations

Useful iterations: done (2.1s)

IterNodesCost
03419265
17835774
224504657
done50004655

prune708.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
0.1b
(/ (cos x) x)
1.2b
(- (/ 1.0 x) (/ (cos x) x))

rewrite318.0ms

Algorithm
rewrite-expression-head
Rules
751×times-frac
607×add-sqr-sqrt
593×*-un-lft-identity
576×add-cube-cbrt
507×prod-diff
171×distribute-rgt-in distribute-lft-in
85×div-inv
14×add-exp-log
13×fma-neg associate-*l*
12×associate-*r*
10×add-cbrt-cube
8×distribute-lft-out-- difference-of-squares
5×pow1 add-log-exp
4×frac-times associate-*r/ prod-exp
3×expm1-log1p-u sub-neg flip3-- div-exp associate-/r* frac-sub flip-- log1p-expm1-u associate-/l* sub-div unswap-sqr
2×cbrt-undiv distribute-rgt-out-- cbrt-unprod
1×rec-exp frac-2neg diff-log 1-exp pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 632
Calls
3 calls:
175.0ms
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
13.0ms
(/ (cos x) x)
43.0ms
(- (/ 1.0 x) (/ (cos x) x))

series260.0ms

Counts
3 → 9
Calls
3 calls:
133.0ms
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
47.0ms
(/ (cos x) x)
80.0ms
(- (/ 1.0 x) (/ (cos x) x))

simplify3.7s

Counts
641 → 641
Iterations

Useful iterations: 2 (2.5s)

IterNodesCost
079629807
1193926210
2448517472
done500017472

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes89.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.4b

bsearch103.0ms

Steps
ItersRangePoint
9
0.0033303272193615503
311302.39110615524
0.03577299125405769
9
-7.35943201301068
-4.403108084983288e-07
-0.028173748830909656

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03762
14562
done4562

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.7s1594×body2560valid
600.0ms1227×body1280valid
487.0ms1421×body640valid
176.0ms964×body320valid
171.0ms2318×body80valid
65.0ms476×body160valid