Details

Time bar (total: 29.2s)

sample128.0ms

Algorithm
intervals
Results
80.0ms257×body80valid
10.0ms8×body640valid
8.0ms6×body1280valid
2.0ms3×body160valid
1.0ms1×body320valid

simplify925.0ms

Counts
1 → 1
Iterations
IterNodes
done2004
52004
4821
3262
2104
151
021

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2) M) 2)
37.2b
(cos (- (/ (* K (+ m n)) 2) M))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
204×add-sqr-sqrt
173×*-un-lft-identity
160×prod-diff
83×add-cube-cbrt
78×unpow-prod-down
68×distribute-rgt-neg-in
66×distribute-lft-neg-in
53×difference-of-squares
45×distribute-lft-out--
26×fma-neg
23×cos-sum
22×times-frac
14×add-log-exp
13×unpow2 sqr-pow
11×associate--r+
7×pow1 add-exp-log
6×neg-mul-1 add-cbrt-cube diff-log
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u
3×pow-unpow sub-neg associate-*l* div-inv
2×neg-log associate-*r/
1×associate--l- neg-sub0 distribute-rgt-in cos-diff pow-to-exp pow-pow distribute-lft-in flip3-+ flip3-- pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod flip-+ flip-- distribute-lft-out associate--r- unswap-sqr
Counts
4 → 276
Calls
4 calls:
1.0s
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
25.0ms
(* K (+ m n))
63.0ms
(pow (- (/ (+ m n) 2) M) 2)
49.0ms
(cos (- (/ (* K (+ m n)) 2) M))

series480.0ms

Counts
4 → 12
Calls
4 calls:
268.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
28.0ms
(* K (+ m n))
97.0ms
(pow (- (/ (+ m n) 2) M) 2)
86.0ms
(cos (- (/ (* K (+ m n)) 2) M))

simplify1.1s

Counts
288 → 288
Iterations
IterNodes
done2001
22001
11039
0474

prune5.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.3b

localize58.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b
(pow (- (/ (+ m n) 2) M) 2)

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
185×add-sqr-sqrt
154×*-un-lft-identity
139×prod-diff
78×unpow-prod-down
68×distribute-rgt-neg-in
66×distribute-lft-neg-in add-cube-cbrt
53×difference-of-squares
45×distribute-lft-out--
26×fma-neg
13×times-frac unpow2 sqr-pow
12×add-log-exp
11×associate--r+
6×neg-mul-1 diff-log
3×pow1 pow-unpow add-exp-log
2×expm1-log1p-u sub-neg add-cbrt-cube neg-log insert-posit16 log1p-expm1-u
1×associate--l- neg-sub0 pow-to-exp pow-pow flip3-- pow-exp flip-- associate--r-
Counts
2 → 216
Calls
2 calls:
951.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
46.0ms
(pow (- (/ (+ m n) 2) M) 2)

series339.0ms

Counts
2 → 6
Calls
2 calls:
235.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
104.0ms
(pow (- (/ (+ m n) 2) M) 2)

simplify1.1s

Counts
222 → 222
Iterations
IterNodes
done2001
32001
21318
1644
0269

prune4.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

localize143.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 2)
1.0b
(cbrt 2)
37.2b
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
37.6b
(sin (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×pow1/3 fma-udef
1×cos-sum sin-sum
Counts
4 → 50
Calls
4 calls:
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)
2.0ms
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
2.0ms
(sin (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))

series921.0ms

Counts
4 → 8
Calls
4 calls:
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)
223.0ms
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
698.0ms
(sin (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))

simplify1.4s

Counts
58 → 58
Iterations
IterNodes
done2075
52075
41066
3520
2245
1136
081

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

localize162.0ms

Local error

Found 4 expressions with local error:

37.2b
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
37.2b
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
37.2b
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
37.6b
(sin (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
3×cos-sum
1×sin-sum
Counts
4 → 44
Calls
4 calls:
2.0ms
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
2.0ms
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
4.0ms
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
5.0ms
(sin (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))

series1.2s

Counts
4 → 12
Calls
4 calls:
314.0ms
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
284.0ms
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
282.0ms
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
287.0ms
(sin (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))

simplify1.3s

Counts
56 → 56
Iterations
IterNodes
done2001
52001
41013
3477
2214
1112
063

prune2.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.3b

regimes576.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 0.9b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done21
121
017

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.6s8120×body80valid
257.0ms164×body640valid
220.0ms116×body1280valid
69.0ms96×body320valid
24.0ms54×body160valid