Details

Time bar (total: 23.3s)

sample204.0ms

Algorithm
intervals
Results
109.0ms59×body2560valid
55.0ms91×body1280valid
21.0ms58×body640valid
6.0ms22×body320valid
2.0ms11×body160valid
1.0ms15×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06202
111202
214202
316202
done16202

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize65.0ms

Local error

Found 2 expressions with local error:

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

rewrite44.0ms

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-cbrt-cube add-exp-log add-log-exp
3×associate-/r* fma-neg
2×expm1-log1p-u pow1 flip3-- log1p-expm1-u flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
2 → 68
Calls
2 calls:
29.0ms
(/ (- 1.0 (cos x)) (sin x))
11.0ms
(- 1.0 (cos x))

series101.0ms

Counts
2 → 6
Calls
2 calls:
66.0ms
(/ (- 1.0 (cos x)) (sin x))
35.0ms
(- 1.0 (cos x))

simplify2.5s

Counts
74 → 74
Iterations

Useful iterations: done (2.5s)

IterNodesCost
013425270
130822964
277421137
3233420972
done500219518

prune427.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (cos x))
0.2b
(* (cos x) (cos x))
0.4b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.8b
(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1
16×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log add-log-exp
6×swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u
3×sqr-cos
2×pow2 pow-plus pow3 pow-prod-down prod-exp pow-sqr cos-mult *-commutative pow-prod-up cbrt-unprod unswap-sqr
1×difference-cubes +-commutative associate-+l+ sum-log sub-neg fma-def flip3-+ distribute-rgt-out flip3-- fma-neg diff-log prod-diff flip-+ flip--
Counts
4 → 91
Calls
4 calls:
17.0ms
(* (cos x) (cos x))
16.0ms
(* (cos x) (cos x))
10.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
31.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))

series208.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (cos x) (cos x))
30.0ms
(* (cos x) (cos x))
73.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
75.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (cos x) (cos x)) (cos x)))

simplify4.1s

Counts
103 → 103
Iterations

Useful iterations: 3 (2.8s)

IterNodesCost
012624927
135619394
2132519103
3410318993
done500018993

prune674.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (cos x))
0.3b
(+ 1/2 (* (cos (+ x x)) 1/2))
0.4b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.8b
(- (* (* 1.0 1.0) 1.0) (* (+ 1/2 (* (cos (+ x x)) 1/2)) (cos x)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt pow1
10×*-un-lft-identity add-log-exp
9×add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u fma-def log1p-expm1-u
3×swap-sqr associate-*r* associate-*l*
2×+-commutative sqr-cos sum-log flip3-+ distribute-rgt-out flip-+
1×pow2 associate-+l+ sub-neg pow-plus flip3-- fma-neg diff-log prod-diff pow-prod-down distribute-rgt1-in prod-exp pow-sqr cos-mult *-commutative pow-prod-up cbrt-unprod flip-- unswap-sqr
Counts
4 → 79
Calls
4 calls:
16.0ms
(* (cos x) (cos x))
9.0ms
(+ 1/2 (* (cos (+ x x)) 1/2))
20.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
39.0ms
(- (* (* 1.0 1.0) 1.0) (* (+ 1/2 (* (cos (+ x x)) 1/2)) (cos x)))

series279.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (cos x) (cos x))
30.0ms
(+ 1/2 (* (cos (+ x x)) 1/2))
76.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
144.0ms
(- (* (* 1.0 1.0) 1.0) (* (+ 1/2 (* (cos (+ x x)) 1/2)) (cos x)))

simplify1.9s

Counts
91 → 91
Iterations

Useful iterations: done (1.9s)

IterNodesCost
015626934
146221415
2172621022
done500020908

prune713.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ 1/2 (* (cos (+ x x)) 1/2))
0.4b
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.8b
(fma (* 1.0 1.0) 1.0 (- (* (cos x) (+ 1/2 (* (cos (+ x x)) 1/2)))))
31.6b
(fma (- (cos x)) (+ 1/2 (* (cos (+ x x)) 1/2)) (* (cos x) (+ 1/2 (* (cos (+ x x)) 1/2))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
8×add-log-exp
6×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt
4×expm1-log1p-u pow1 fma-def add-cbrt-cube add-exp-log log1p-expm1-u
2×+-commutative sum-log flip3-+ distribute-rgt-out flip-+ fma-udef
1×sqr-cos associate-+l+ distribute-rgt1-in
Counts
4 → 54
Calls
4 calls:
5.0ms
(+ 1/2 (* (cos (+ x x)) 1/2))
20.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
1.0ms
(fma (* 1.0 1.0) 1.0 (- (* (cos x) (+ 1/2 (* (cos (+ x x)) 1/2)))))
1.0ms
(fma (- (cos x)) (+ 1/2 (* (cos (+ x x)) 1/2)) (* (cos x) (+ 1/2 (* (cos (+ x x)) 1/2))))

series419.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ 1/2 (* (cos (+ x x)) 1/2))
56.0ms
(+ (* (cos x) (cos x)) (* 1.0 (cos x)))
162.0ms
(fma (* 1.0 1.0) 1.0 (- (* (cos x) (+ 1/2 (* (cos (+ x x)) 1/2)))))
168.0ms
(fma (- (cos x)) (+ 1/2 (* (cos (+ x x)) 1/2)) (* (cos x) (+ 1/2 (* (cos (+ x x)) 1/2))))

simplify1.5s

Counts
66 → 66
Iterations

Useful iterations: done (1.4s)

IterNodesCost
012421337
132417650
2110217094
done500016990

prune566.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

regimes395.0ms

Accuracy

98.2% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.0b

bsearch2.0ms

simplify14.0ms

Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0472009
1572009
done572009

end0.0ms

sample8.9s

Algorithm
intervals
Results
4.4s1554×body2560valid
2.7s2855×body1280valid
989.0ms1841×body640valid
362.0ms930×body320valid
92.0ms350×body80valid
89.0ms464×body160valid
26.0ms6×body5120valid