Details

Time bar (total: 14.2s)

sample82.0ms

Algorithm
intervals
Results
33.0ms49×body2560valid
14.0ms37×body1280valid
11.0ms51×body640valid
6.0ms34×body320valid
4.0ms69×body80valid
2.0ms16×body160valid

simplify51.0ms

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: 31.2b

localize9.0ms

Local error

Found 2 expressions with local error:

2.6b
(- 1.0 (cos x))
14.5b
(/ (- 1.0 (cos x)) (* x x))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 42
Calls
2 calls:
6.0ms
(- 1.0 (cos x))
40.0ms
(/ (- 1.0 (cos x)) (* x x))

series88.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(- 1.0 (cos x))
68.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify628.0ms

Counts
48 → 48
Iterations

Useful iterations: 2 (177.0ms)

IterNodesCost
088507
1232489
21094441
done5001441

prune203.0ms

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
(/ (- 1.0 (cos x)) x)
0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
2.6b
(- 1.0 (cos x))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
29×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp
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×associate-/r* 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 → 114
Calls
3 calls:
31.0ms
(/ (- 1.0 (cos x)) x)
51.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
11.0ms
(- 1.0 (cos x))

series134.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(/ (- 1.0 (cos x)) x)
58.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
26.0ms
(- 1.0 (cos x))

simplify1.7s

Counts
123 → 123
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01891536
15411395
230581239
done50001227

prune666.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
0.3b
(+ 1.0 (cos x))
0.4b
(pow (cos x) 3)
2.5b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
89×*-un-lft-identity
80×difference-of-squares
75×times-frac
63×unpow-prod-down cube-prod
41×sqr-pow
37×add-cube-cbrt
25×associate-/l* distribute-lft-out--
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
3×pow-unpow associate-/r*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative cube-mult pow-to-exp sub-neg pow-pow frac-2neg diff-log unpow3 div-sub div-exp pow-exp clear-num sum-log div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 189
Calls
4 calls:
127.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
10.0ms
(+ 1.0 (cos x))
5.0ms
(pow (cos x) 3)
36.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series297.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0)))
16.0ms
(+ 1.0 (cos x))
41.0ms
(pow (cos x) 3)
74.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify1.7s

Counts
201 → 201
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02605407
16845088
229954980
done50014978

prune762.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(log (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
0.3b
(+ 1.0 (cos x))
0.4b
(pow (cos x) 3)
2.5b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
132×add-sqr-sqrt
81×log-prod
78×*-un-lft-identity
75×times-frac
64×difference-of-squares
51×unpow-prod-down cube-prod
36×add-cube-cbrt
33×sqr-pow
20×distribute-lft-out--
8×add-exp-log add-log-exp
6×pow1
5×add-cbrt-cube
4×difference-cubes
3×pow-unpow
2×flip3-+ rem-log-exp associate-/r/ flip-+
1×+-commutative cube-mult pow-to-exp sub-neg log-div flip3-- pow-pow diff-log unpow3 div-exp pow-exp sum-log log-pow flip-- div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 161
Calls
4 calls:
53.0ms
(log (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
7.0ms
(+ 1.0 (cos x))
3.0ms
(pow (cos x) 3)
43.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series459.0ms

Counts
4 → 12
Calls
4 calls:
335.0ms
(log (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ 1.0 (cos x))) (* 1.0 1.0))))
14.0ms
(+ 1.0 (cos x))
32.0ms
(pow (cos x) 3)
77.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify2.1s

Counts
173 → 173
Iterations

Useful iterations: 2 (714.0ms)

IterNodesCost
03374999
18484682
232224589
done50014589

prune756.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes105.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.8b

bsearch92.0ms

Steps
ItersRangePoint
8
0.01136632641909174
309.51167567074003
0.03249397456549535
10
-1950712569354.648
-0.00015980627971116164
-0.03059660473543996

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03972
15072
25172
done5172

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.5s1566×body2560valid
1.0s1493×body640valid
649.0ms1239×body1280valid
201.0ms950×body320valid
135.0ms2271×body80valid
64.0ms481×body160valid