Details

Time bar (total: 28.1s)

sample75.0ms

Algorithm
intervals
Results
32.0ms258×body80valid
7.0ms8×body1280valid
2.0ms3×body640valid
2.0ms5×body320valid
1.0ms3×body160valid

simplify4.7s

Counts
1 → 1
Iterations

Useful iterations: 4 (106.0ms)

IterNodesCost
02129
15029
29529
320729
449928
5120928
6480728
done500028

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(* K (+ m n))
0.0b
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
36.2b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite730.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
40×*-un-lft-identity
30×prod-diff
29×add-cube-cbrt
23×cos-sum
12×unpow-prod-down
11×associate-+r+ times-frac
10×fma-def
9×add-log-exp
7×pow1 add-exp-log
6×add-cbrt-cube
4×expm1-log1p-u associate-*r* log1p-expm1-u difference-of-squares
3×pow-unpow associate-*l* div-inv distribute-lft-out distribute-lft-out--
2×sub-neg flip3-+ associate-*r/ sum-log flip-+ sqr-pow
1×+-commutative distribute-rgt-in cos-diff pow-to-exp associate-+r- pow-pow distribute-lft-in diff-log pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 118
Calls
4 calls:
28.0ms
(* K (+ m n))
536.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
98.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series852.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* K (+ m n))
275.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
444.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
82.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify3.1s

Counts
130 → 130
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
03482962
16912434
214602132
345321966
done50001966

prune746.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite671.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×*-un-lft-identity
12×add-cube-cbrt unpow-prod-down
11×associate-+r+
10×fma-def
9×prod-diff
7×add-log-exp
4×difference-of-squares
3×pow1 add-exp-log pow-unpow distribute-lft-out--
2×expm1-log1p-u times-frac sum-log add-cbrt-cube log1p-expm1-u distribute-lft-out sqr-pow
1×+-commutative pow-to-exp associate-+r- sub-neg pow-pow flip3-+ diff-log pow-exp flip-+
Counts
2 → 60
Calls
2 calls:
594.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
73.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series703.0ms

Counts
2 → 6
Calls
2 calls:
328.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
374.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.7s

Counts
66 → 66
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01441073
1323956
2726889
32545876
done5001858

prune409.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
35.6b
(sin (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))
35.9b
(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-prod prod-diff
5×cos-sum sin-sum
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×sub-neg pow1/3
1×cos-diff sin-diff
Counts
4 → 56
Calls
4 calls:
2.0ms
(cbrt 2.0)
2.0ms
(cbrt 2.0)
96.0ms
(sin (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))
117.0ms
(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

series586.0ms

Counts
4 → 8
Calls
4 calls:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
286.0ms
(sin (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))
300.0ms
(cos (- (* (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0))) M))

simplify3.5s

Counts
64 → 64
Iterations

Useful iterations: 4 (617.0ms)

IterNodesCost
01291382
12201246
23831084
3718665
41374626
53266626
done5000626

prune654.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.9b

localize71.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.5b
(* (cbrt (+ m n)) (cbrt (+ m n)))
36.1b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite519.0ms

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
35×add-sqr-sqrt
32×cbrt-prod
27×add-cube-cbrt
23×cos-sum
21×prod-diff
16×cbrt-div
11×pow1
9×times-frac swap-sqr
8×flip3-+ pow1/3 flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
3×div-inv
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 cos-diff sub-neg pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 120
Calls
4 calls:
4.0ms
(cbrt (+ m n))
8.0ms
(cbrt (+ m n))
47.0ms
(* (cbrt (+ m n)) (cbrt (+ m n)))
456.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series884.0ms

Counts
4 → 12
Calls
4 calls:
235.0ms
(cbrt (+ m n))
216.0ms
(cbrt (+ m n))
253.0ms
(* (cbrt (+ m n)) (cbrt (+ m n)))
179.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify2.3s

Counts
132 → 132
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02943686
15393173
211232335
330121820
done50001798

prune796.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

regimes663.0ms

Accuracy

0% (0.3b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01619
12019
done2019

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.9s8099×body80valid
188.0ms111×body1280valid
161.0ms123×body320valid
129.0ms136×body640valid
15.0ms49×body160valid
3.0ms2×body2560valid