Details

Time bar (total: 12.8s)

sample131.0ms

Algorithm
intervals
Results
57.0ms44×body2560valid
39.0ms88×body1280valid
16.0ms53×body640valid
5.0ms32×body320valid
4.0ms25×body160valid
1.0ms14×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
1117
2147
3167
done167

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
1.9b
(- 1.0 (cos x))

rewrite16.0ms

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:
10.0ms
(/ (- 1.0 (cos x)) (sin x))
4.0ms
(- 1.0 (cos x))

series66.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(/ (- 1.0 (cos x)) (sin x))
20.0ms
(- 1.0 (cos x))

simplify1.4s

Counts
74 → 74
Iterations

Useful iterations: done (1.4s)

IterNodesCost
0134964
1291831
2741731
32756719
done5000718

prune205.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0 (cos x)) (sin x))
0.3b
(exp (/ (- 1.0 (cos x)) (sin x)))
1.3b
(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.9b
(- 1.0 (cos x))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt *-un-lft-identity
45×times-frac
40×add-cube-cbrt
38×exp-prod
20×log-pow
11×distribute-lft-out-- difference-of-squares
9×prod-diff
7×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×log-prod fma-neg div-sub associate-/r* div-inv
2×flip3-- exp-diff flip-- associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg diff-log div-exp rem-log-exp clear-num rem-exp-log
Counts
4 → 132
Calls
4 calls:
9.0ms
(/ (- 1.0 (cos x)) (sin x))
11.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
16.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms
(- 1.0 (cos x))

series144.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ (- 1.0 (cos x)) (sin x))
45.0ms
(exp (/ (- 1.0 (cos x)) (sin x)))
42.0ms
(log (exp (/ (- 1.0 (cos x)) (sin x))))
20.0ms
(- 1.0 (cos x))

simplify1.5s

Counts
144 → 144
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01951743
13671509
28571372
330111333
done50011332

prune387.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (sin x))
0.2b
(* (/ 1 (sin x)) (- 1.0 (cos x)))
1.9b
(- 1.0 (cos x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
43×*-un-lft-identity
38×add-cube-cbrt
27×prod-diff
20×times-frac
16×add-exp-log
13×associate-*l*
11×distribute-rgt-in distribute-lft-in
10×add-cbrt-cube
6×pow1
5×associate-*r* add-log-exp
4×div-exp prod-exp
3×expm1-log1p-u sub-neg flip3-- fma-neg associate-/r* flip-- log1p-expm1-u associate-/l* unswap-sqr
2×cbrt-undiv frac-times rec-exp 1-exp associate-*r/ cbrt-unprod div-inv distribute-lft-out-- difference-of-squares
1×pow-flip frac-2neg diff-log pow-prod-down associate-*l/ clear-num *-commutative inv-pow
Counts
3 → 126
Calls
3 calls:
2.0ms
(/ 1 (sin x))
19.0ms
(* (/ 1 (sin x)) (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))

series74.0ms

Counts
3 → 9
Calls
3 calls:
14.0ms
(/ 1 (sin x))
41.0ms
(* (/ 1 (sin x)) (- 1.0 (cos x)))
19.0ms
(- 1.0 (cos x))

simplify2.1s

Counts
135 → 135
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
02042041
14781557
212311206
338191089
done50011089

prune249.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
0.4b
(pow (cos x) 3)
0.5b
(+ 1.0 (cos x))
1.7b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite101.0ms

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:
60.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
1.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
21.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series276.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (* (sin x) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
31.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
55.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify968.0ms

Counts
316 → 316
Iterations

Useful iterations: 2 (334.0ms)

IterNodesCost
03429345
17075855
223704730
done50014730

prune656.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.2b

regimes226.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.2b

bsearch3.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03682
14082
done4082

end0.0ms

sample4.3s

Algorithm
intervals
Results
2.1s1609×body2560valid
1.2s2698×body1280valid
490.0ms1887×body640valid
163.0ms953×body320valid
56.0ms472×body160valid
25.0ms378×body80valid
14.0ms3×body5120valid