Details

Time bar (total: 6.5s)

sample64.0ms

Algorithm
intervals
Results
37.0ms257×body80valid
3.0ms4×body1280valid
3.0ms4×body640valid
2.0ms4×body320valid
1.0ms1×body2560valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
05016
19516
221116
355315
4197415
5500115

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ (* K (+ m n)) 2.0) M)
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
32.1b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
42×prod-diff
40×add-sqr-sqrt
37×*-un-lft-identity
33×add-cube-cbrt
23×cos-sum
22×times-frac
7×fma-neg div-inv
6×unpow-prod-down
5×add-log-exp
4×pow1 add-exp-log
3×expm1-log1p-u pow-unpow add-cbrt-cube log1p-expm1-u difference-of-squares
2×sub-neg distribute-lft-out--
1×cos-diff pow-to-exp flip3-- pow-pow diff-log pow-exp flip-- sqr-pow
Counts
3 → 99
Calls
3 calls:
11.0ms
(- (/ (* K (+ m n)) 2.0) M)
30.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
23.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series365.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(- (/ (* K (+ m n)) 2.0) M)
256.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify52.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
05031571
113141191
250011184

prune368.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.4b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×unpow-prod-down
5×*-un-lft-identity
3×add-cube-cbrt pow-unpow
2×pow1 add-exp-log difference-of-squares
1×expm1-log1p-u pow-to-exp pow-pow times-frac pow-exp add-cbrt-cube log1p-expm1-u distribute-lft-out-- add-log-exp sqr-pow
Counts
1 → 22
Calls
1 calls:
32.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series250.0ms

Counts
1 → 3
Calls
1 calls:
250.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify44.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 3 (40.0ms)

IterNodesCost
0159174
1445168
21492167
35001162

prune110.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.2b
(expm1 (log1p (cos (- (/ (* K (+ m n)) 2.0) M))))
0.4b
(log1p (cos (- (/ (* K (+ m n)) 2.0) M)))
32.1b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
23×cos-sum
21×*-un-lft-identity prod-diff
19×add-cube-cbrt
10×times-frac
6×unpow-prod-down
5×pow1 add-exp-log expm1-log1p-u
4×add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-unpow div-inv
2×difference-of-squares
1×cos-diff pow-to-exp sub-neg log1p-udef expm1-log1p pow-pow log1p-expm1 pow-exp distribute-lft-out-- expm1-udef sqr-pow
Counts
4 → 77
Calls
4 calls:
29.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0ms
(expm1 (log1p (cos (- (/ (* K (+ m n)) 2.0) M))))
0.0ms
(log1p (cos (- (/ (* K (+ m n)) 2.0) M)))
22.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series576.0ms

Counts
4 → 12
Calls
4 calls:
253.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
151.0ms
(expm1 (log1p (cos (- (/ (* K (+ m n)) 2.0) M))))
116.0ms
(log1p (cos (- (/ (* K (+ m n)) 2.0) M)))
55.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify96.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
04621296
110511055
235151054
35001989

prune350.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.4b

localize39.0ms

Local error

Found 4 expressions with local error:

15.4b
(cbrt (/ (* K (+ m n)) 2.0))
15.4b
(cbrt (/ (* K (+ m n)) 2.0))
32.2b
(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))
32.3b
(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
14×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×times-frac
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×cbrt-div pow1/3 fma-udef div-inv
1×cos-sum sin-sum
Counts
4 → 56
Calls
4 calls:
5.0ms
(cbrt (/ (* K (+ m n)) 2.0))
3.0ms
(cbrt (/ (* K (+ m n)) 2.0))
1.0ms
(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))
1.0ms
(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))

series1.3s

Counts
4 → 12
Calls
4 calls:
163.0ms
(cbrt (/ (* K (+ m n)) 2.0))
154.0ms
(cbrt (/ (* K (+ m n)) 2.0))
498.0ms
(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))
482.0ms
(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))

simplify53.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0270940
1622851
21689835
35002831

prune631.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.4b

regimes272.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02110
12310
22310

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.1s8090×body80valid
90.0ms161×body640valid
72.0ms97×body1280valid
42.0ms101×body320valid
13.0ms45×body160valid
5.0ms5×body2560valid