Details

Time bar (total: 6.4s)

sample42.0ms

Algorithm
intervals
Results
21.0ms260×body80valid
2.0ms7×body640valid
1.0ms2×body320valid
1.0ms3×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
05016
19516
221116
355315
4197415
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

localize26.0ms

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))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
42×prod-diff
40×add-sqr-sqrt *-un-lft-identity
36×add-cube-cbrt
24×times-frac
23×cos-sum
11×add-exp-log add-cbrt-cube
8×div-inv
7×fma-neg
6×pow1 add-log-exp
4×expm1-log1p-u associate-*r/ associate-*r* log1p-expm1-u
3×associate-*l* associate-/r*
2×cbrt-undiv sub-neg 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-- distribute-lft-out associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 127
Calls
4 calls:
9.0ms
(- (/ (* K (+ m n)) 2.0) M)
6.0ms
(* K (+ m n))
6.0ms
(/ (* K (+ m n)) 2.0)
11.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series179.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- (/ (* K (+ m n)) 2.0) M)
27.0ms
(* K (+ m n))
41.0ms
(/ (* K (+ m n)) 2.0)
57.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify59.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05491609
117621211
250021208

prune453.0ms

Filtered
139 candidates to 81 candidates (58.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize14.0ms

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)

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
33×add-sqr-sqrt
23×add-cube-cbrt
14×times-frac
12×unpow-prod-down
11×associate-+r+
10×fma-def
9×prod-diff
8×add-log-exp
6×pow-flip
5×pow1 add-exp-log exp-prod add-cbrt-cube
4×exp-sum associate-/r* distribute-lft-out distribute-lft-out-- difference-of-squares
3×expm1-log1p-u pow-unpow log1p-expm1-u associate-/l*
2×associate-+r- div-exp sum-log sqr-pow
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
Counts
3 → 103
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)

series591.0ms

Counts
3 → 9
Calls
3 calls:
158.0ms
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
173.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
260.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify56.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04901187
118421061
250011034

prune359.0ms

Filtered
112 candidates to 76 candidates (67.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize27.0ms

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) (fma (- M) 1 M)))

rewrite55.0ms

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×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
2×frac-2neg clear-num associate-/l/
1×cos-diff frac-times associate-+l- cos-sum flip3-+ associate-*r/ pow-prod-down associate-*l/ *-commutative flip-+
Counts
4 → 183
Calls
4 calls:
21.0ms
(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
4.0ms
(/ K (sqrt 2.0))
6.0ms
(/ (+ m n) (sqrt 2.0))
16.0ms
(cos (+ (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M) (fma (- M) 1 M)))

series669.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
55.0ms
(/ K (sqrt 2.0))
87.0ms
(/ (+ m n) (sqrt 2.0))
352.0ms
(cos (+ (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M) (fma (- M) 1 M)))

simplify65.0ms

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05701523
125921410
250011351

prune803.0ms

Filtered
195 candidates to 122 candidates (62.6%)
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) (fma (- M) 1 M)))

rewrite74.0ms

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×expm1-log1p-u sqrt-pow1 cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp 1-exp
2×frac-2neg pow1/2 clear-num associate-/l/
1×cos-diff frac-times associate-+l- cos-sum flip3-+ associate-*r/ pow-prod-down associate-*l/ *-commutative flip-+ inv-pow
Counts
4 → 238
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)))
21.0ms
(cos (+ (- (* (* (/ 1 (sqrt (sqrt 2.0))) (/ K (sqrt (sqrt 2.0)))) (/ (+ m n) (sqrt 2.0))) M) (fma (- M) 1 M)))

series503.0ms

Counts
4 → 10
Calls
4 calls:
62.0ms
(* (/ 1 (sqrt (sqrt 2.0))) (/ K (sqrt (sqrt 2.0))))
88.0ms
(/ (+ m n) (sqrt 2.0))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))
353.0ms
(cos (+ (- (* (* (/ 1 (sqrt (sqrt 2.0))) (/ K (sqrt (sqrt 2.0)))) (/ (+ m n) (sqrt 2.0))) M) (fma (- M) 1 M)))

simplify86.0ms

Algorithm
egg-herbie
Counts
248 → 248
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
07292371
134612091
250021967

prune904.0ms

Filtered
248 candidates to 124 candidates (50.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

regimes185.0ms

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

sample1.1s

Algorithm
intervals
Results
665.0ms8081×body80valid
56.0ms112×body1280valid
54.0ms155×body640valid
29.0ms114×body320valid
11.0ms62×body160valid
2.0ms3×body2560valid