Details

Time bar (total: 20.9s)

sample156.0ms

Algorithm
intervals
Results
77.0ms57×body2560valid
41.0ms82×body1280valid
16.0ms58×body640valid
9.0ms38×body320valid
2.0ms13×body160valid
1.0ms8×body80valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done16
316
214
111
06

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.3b
(- 1.0 (cos x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
2 → 52
Calls
2 calls:
13.0ms
(/ (- 1.0 (cos x)) (sin x))
6.0ms
(- 1.0 (cos x))

series70.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(/ (- 1.0 (cos x)) (sin x))
23.0ms
(- 1.0 (cos x))

simplify797.0ms

Counts
58 → 58
Iterations
IterNodes
done5000
2805
1240
0106

prune379.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sin x))
0.2b
(/ (cos x) (sin x))
1.5b
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
29×*-un-lft-identity
28×times-frac
21×add-cube-cbrt
7×add-cbrt-cube add-exp-log
6×associate-/r* associate-/l*
5×add-log-exp
4×div-inv distribute-lft-out-- difference-of-squares
3×pow1
2×cbrt-undiv clear-num frac-2neg div-exp
1×sub-neg flip3-- distribute-rgt-out-- diff-log frac-sub flip-- sub-div
Counts
3 → 77
Calls
3 calls:
8.0ms
(/ 1.0 (sin x))
13.0ms
(/ (cos x) (sin x))
32.0ms
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series157.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(/ 1.0 (sin x))
28.0ms
(/ (cos x) (sin x))
103.0ms
(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify1.7s

Counts
86 → 86
Iterations
IterNodes
done5000
34056
2868
1302
0146

prune514.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos x) (cos x))
0.3b
(pow (cos x) 3)
0.4b
(+ (cos x) 1.0)
1.2b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
23×*-un-lft-identity
16×difference-of-squares
15×unpow-prod-down cube-prod
12×pow1
11×add-cube-cbrt
9×sqr-pow
8×add-log-exp
7×add-cbrt-cube add-exp-log
5×distribute-lft-out--
3×pow-unpow swap-sqr associate-*r* associate-*l*
1×pow2 cube-mult pow-to-exp difference-cubes +-commutative sqr-cos sum-log sub-neg pow-pow flip3-+ pow-plus flip3-- diff-log unpow3 pow-prod-down pow-exp prod-exp pow-sqr cos-mult *-commutative pow-prod-up cbrt-unprod flip-+ flip-- distribute-lft-out rem-cube-cbrt unswap-sqr
Counts
4 → 96
Calls
4 calls:
15.0ms
(* (cos x) (cos x))
5.0ms
(pow (cos x) 3)
9.0ms
(+ (cos x) 1.0)
40.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series195.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (cos x) (cos x))
55.0ms
(pow (cos x) 3)
17.0ms
(+ (cos x) 1.0)
92.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify4.3s

Counts
108 → 108
Iterations
IterNodes
done5001
23372
1420
0154

prune740.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.1b

localize93.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cos x) (cos x))
0.3b
(cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x))))
0.4b
(+ (cos x) 1.0)
1.2b
(- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x)))))

rewrite796.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt associate-*l/
13×cos-mult
12×*-un-lft-identity
11×pow1
8×add-cube-cbrt add-log-exp
7×cbrt-div
6×add-cbrt-cube add-exp-log
5×frac-times
4×pow3 difference-of-squares
3×swap-sqr associate-*r* associate-*l* pow-prod-down associate-*r/
2×rem-cbrt-cube
1×cbrt-prod pow2 +-commutative sqr-cos sum-log sub-neg unpow-prod-down flip3-+ pow-plus flip3-- pow1/3 diff-log cube-prod prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ flip-- distribute-lft-out distribute-lft-out-- unswap-sqr sqr-pow
Counts
4 → 74
Calls
4 calls:
15.0ms
(* (cos x) (cos x))
741.0ms
(cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x))))
9.0ms
(+ (cos x) 1.0)
29.0ms
(- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x)))))

series142.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (cos x) (cos x))
42.0ms
(cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x))))
11.0ms
(+ (cos x) 1.0)
66.0ms
(- (pow 1.0 3) (cbrt (* (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos x) (cos x)) (cos x))) (* (* (cos x) (cos x)) (cos x)))))

simplify2.0s

Counts
86 → 86
Iterations
IterNodes
done5000
22624
1386
0152

prune475.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

regimes319.0ms

Accuracy

96.9% (1.0b remaining)

Error of 1.1b against oracle of 0.2b and baseline of 30.8b

bsearch2.0ms

simplify24.0ms

Iterations
IterNodes
done69
169
053

end0.0ms

sample7.7s

Algorithm
intervals
Results
3.2s1642×body2560valid
2.3s2753×body1280valid
1.2s1876×body640valid
651.0ms927×body320valid
117.0ms452×body160valid
43.0ms5×body5120valid
35.0ms345×body80valid