Details

Time bar (total: 5.9s)

sample43.0ms

Algorithm
intervals
Results
22.0ms260×body80valid
3.0ms7×body640valid
1.0ms3×body160valid
1.0ms2×body320valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
05016
19316
220016
351715
4189315
5500115

prune9.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ (* K (+ m n)) 2.0) M)
0.0b
(* K (+ m n))
0.2b
(/ (* K (+ m n)) 2.0)
32.9b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
8×add-cube-cbrt
6×pow1 add-log-exp
4×associate-*r/ associate-*r*
3×times-frac associate-*l* associate-/r*
2×cbrt-undiv sub-neg cos-sum flip3-+ div-exp prod-exp cbrt-unprod flip-+ associate-/l/
1×distribute-rgt-in cos-diff flip3-- frac-2neg distribute-lft-in diff-log pow-prod-down clear-num *-commutative flip-- div-inv distribute-lft-out associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 70
Calls
4 calls:
8.0ms
(- (/ (* K (+ m n)) 2.0) M)
9.0ms
(* K (+ m n))
6.0ms
(/ (* K (+ m n)) 2.0)
8.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series178.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (/ (* K (+ m n)) 2.0) M)
24.0ms
(* K (+ m n))
43.0ms
(/ (* K (+ m n)) 2.0)
53.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify39.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0324439
11291389
25001386

prune304.0ms

Filtered
82 candidates to 58 candidates (70.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- 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)

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
20×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
8×add-log-exp
6×unpow-prod-down pow-flip
5×pow1 add-exp-log exp-prod add-cbrt-cube
4×exp-sum associate-/r* distribute-lft-out
3×pow-unpow associate-/l* distribute-lft-out--
2×associate-+r- associate-+r+ div-exp sum-log difference-of-squares
1×cbrt-undiv +-commutative pow-to-exp sub-neg rec-exp pow-pow frac-2neg flip3-+ exp-diff diff-log 1-exp pow-exp clear-num associate-/r/ flip-+ div-inv inv-pow sqr-pow
Counts
3 → 78
Calls
3 calls:
20.0ms
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
17.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
10.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series605.0ms

Counts
3 → 9
Calls
3 calls:
166.0ms
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
175.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
264.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify48.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04121005
11568934
25001910

prune261.0ms

Filtered
87 candidates to 55 candidates (63.2%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
0.4b
(/ K (sqrt 2.0))
0.4b
(/ (+ m n) (sqrt 2.0))
33.2b
(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
94×add-sqr-sqrt
90×*-un-lft-identity
64×add-cube-cbrt
54×sqrt-prod
28×associate-*r*
22×associate-*l*
20×add-exp-log add-cbrt-cube
13×distribute-lft-out
12×associate-/r*
9×unswap-sqr
7×associate-/l*
6×pow1 cbrt-undiv div-exp
4×prod-exp cbrt-unprod div-inv add-log-exp
2×cos-sum frac-2neg clear-num associate-/l/
1×cos-diff frac-times sub-neg flip3-+ associate-*r/ pow-prod-down associate-*l/ *-commutative flip-+
Counts
4 → 176
Calls
4 calls:
20.0ms
(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
7.0ms
(/ K (sqrt 2.0))
6.0ms
(/ (+ m n) (sqrt 2.0))
12.0ms
(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

series665.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
54.0ms
(/ K (sqrt 2.0))
90.0ms
(/ (+ m n) (sqrt 2.0))
333.0ms
(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

simplify70.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05291443
124671336
250021280

prune671.0ms

Filtered
188 candidates to 114 candidates (60.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (sqrt 2.0))) (/ K (sqrt (sqrt 2.0))))
0.4b
(/ (+ m n) (sqrt 2.0))
1.0b
(/ 1 (sqrt (sqrt 2.0)))
33.6b
(cos (- (* (* (/ 1 (sqrt (sqrt 2.0))) (/ K (sqrt (sqrt 2.0)))) (/ (+ m n) (sqrt 2.0))) M))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
170×add-sqr-sqrt
150×times-frac sqrt-prod
107×*-un-lft-identity
81×add-cube-cbrt
32×add-exp-log
31×associate-*r* associate-*l*
28×unswap-sqr
20×add-cbrt-cube
15×associate-/r*
11×div-exp
9×pow1
8×prod-exp
7×distribute-lft-out associate-/l*
6×cbrt-undiv
5×pow-flip
4×sqrt-pow1 cbrt-unprod div-inv add-log-exp
3×rec-exp 1-exp
2×cos-sum frac-2neg pow1/2 clear-num associate-/l/
1×cos-diff frac-times sub-neg flip3-+ associate-*r/ pow-prod-down associate-*l/ *-commutative flip-+ inv-pow
Counts
4 → 231
Calls
4 calls:
26.0ms
(* (/ 1 (sqrt (sqrt 2.0))) (/ K (sqrt (sqrt 2.0))))
6.0ms
(/ (+ m n) (sqrt 2.0))
6.0ms
(/ 1 (sqrt (sqrt 2.0)))
20.0ms
(cos (- (* (* (/ 1 (sqrt (sqrt 2.0))) (/ K (sqrt (sqrt 2.0)))) (/ (+ m n) (sqrt 2.0))) M))

series478.0ms

Counts
4 → 10
Calls
4 calls:
61.0ms
(* (/ 1 (sqrt (sqrt 2.0))) (/ K (sqrt (sqrt 2.0))))
88.0ms
(/ (+ m n) (sqrt 2.0))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))
329.0ms
(cos (- (* (* (/ 1 (sqrt (sqrt 2.0))) (/ K (sqrt (sqrt 2.0)))) (/ (+ m n) (sqrt 2.0))) M))

simplify77.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06882287
133372014
250021890

prune758.0ms

Filtered
241 candidates to 116 candidates (48.1%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

regimes188.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02010
12010

end0.0ms

sample1.2s

Algorithm
intervals
Results
714.0ms8081×body80valid
62.0ms112×body1280valid
57.0ms155×body640valid
30.0ms114×body320valid
11.0ms62×body160valid
2.0ms3×body2560valid