Details

Time bar (total: 6.9s)

sample143.0ms

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

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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-exp-log add-cbrt-cube add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 52
Calls
2 calls:
17.0ms
(/ (- 1.0 (cos x)) (sin x))
7.0ms
(- 1.0 (cos x))

series62.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(/ (- 1.0 (cos x)) (sin x))
20.0ms
(- 1.0 (cos x))

simplify79.0ms

Counts
58 → 58
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0233396
1673373
22654373
35001373
done5001373

prune152.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
21×*-un-lft-identity
16×difference-of-squares
15×unpow-prod-down cube-prod
9×add-cube-cbrt sqr-pow
8×add-log-exp
7×pow1 add-exp-log add-cbrt-cube
5×distribute-lft-out--
3×pow-unpow associate-*r* associate-*l*
2×flip3-+ associate-*l/ flip-+
1×difference-cubes +-commutative cube-mult pow-to-exp sub-neg flip3-- pow-pow diff-log unpow3 pow-prod-down pow-exp prod-exp sum-log *-commutative flip-- cbrt-unprod distribute-lft-out rem-cube-cbrt unswap-sqr
Counts
4 → 89
Calls
4 calls:
47.0ms
(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
3.0ms
(pow (cos x) 3)
6.0ms
(+ (cos x) 1.0)
26.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series176.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0)) (sin x))
33.0ms
(pow (cos x) 3)
11.0ms
(+ (cos x) 1.0)
48.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify62.0ms

Counts
101 → 101
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0434706
11921654
25003650
done5003650

prune273.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (cos x) 1.0)
0.5b
(+ (cos x) 1.0)
0.7b
(* (sqrt (+ (cos x) 1.0)) (sqrt (+ (cos x) 1.0)))
0.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
40×*-un-lft-identity
26×sqrt-prod
19×pow1
16×difference-of-squares
12×add-cube-cbrt unpow-prod-down sqrt-div cube-prod
11×swap-sqr
10×add-log-exp
8×sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out sqr-pow
7×associate-*r* associate-*l*
6×add-exp-log add-cbrt-cube
5×pow-prod-up distribute-lft-out--
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×+-commutative associate-*r/ associate-*l/ sum-log
1×difference-cubes pow2 sub-neg flip3-- pow-plus sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative flip-- cbrt-unprod
Counts
4 → 120
Calls
4 calls:
8.0ms
(+ (cos x) 1.0)
6.0ms
(+ (cos x) 1.0)
40.0ms
(* (sqrt (+ (cos x) 1.0)) (sqrt (+ (cos x) 1.0)))
26.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series80.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (cos x) 1.0)
11.0ms
(+ (cos x) 1.0)
11.0ms
(* (sqrt (+ (cos x) 1.0)) (sqrt (+ (cos x) 1.0)))
48.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify51.0ms

Counts
132 → 132
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0320787
11148733
25002719
done5002719

prune374.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ (cos x) 1.0)
0.6b
(log (exp (+ (cos x) 1.0)))
0.7b
(* (sqrt (+ (cos x) 1.0)) (sqrt (log (exp (+ (cos x) 1.0)))))
0.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
29×*-un-lft-identity
16×sqrt-prod difference-of-squares
12×unpow-prod-down cube-prod
11×add-cube-cbrt associate-*r*
10×pow1 log-pow
8×exp-prod add-log-exp sqr-pow
7×associate-*l*
6×add-exp-log add-cbrt-cube
5×distribute-lft-out--
4×log-prod distribute-lft-out unswap-sqr
3×pow-prod-down
2×sqrt-pow1 flip3-+ pow1/2 sqrt-div associate-*l/ flip-+
1×difference-cubes +-commutative sub-neg flip3-- sqrt-unprod diff-log rem-log-exp exp-sum prod-exp sum-log *-commutative flip-- cbrt-unprod
Counts
4 → 101
Calls
4 calls:
6.0ms
(+ (cos x) 1.0)
16.0ms
(log (exp (+ (cos x) 1.0)))
65.0ms
(* (sqrt (+ (cos x) 1.0)) (sqrt (log (exp (+ (cos x) 1.0)))))
26.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series85.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (cos x) 1.0)
11.0ms
(log (exp (+ (cos x) 1.0)))
11.0ms
(* (sqrt (+ (cos x) 1.0)) (sqrt (log (exp (+ (cos x) 1.0)))))
53.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify129.0ms

Counts
113 → 113
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0333742
11033634
24230612
35001612
done5001612

prune375.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

regimes176.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.1b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04739
14739
done4739

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.3s1566×body2560valid
1.2s2786×body1280valid
454.0ms1962×body640valid
156.0ms911×body320valid
52.0ms435×body160valid
21.0ms337×body80valid
11.0ms3×body5120valid