Details

Time bar (total: 9.6s)

sample53.0ms

Algorithm
intervals
Results
26.0ms258×body80valid
2.0ms5×body640valid
2.0ms2×body1280valid
0.0ms1×body320valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
05016
19516
221116
355315
4197415
5500115

prune13.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
34.3b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite3.7s

Algorithm
rewrite-expression-head
Rules
179×add-sqr-sqrt
144×*-un-lft-identity
141×prod-diff
130×associate-*r*
123×exp-sum
72×add-cube-cbrt
66×unpow-prod-down
50×distribute-lft-neg-in distribute-rgt-neg-in
46×difference-of-squares
35×distribute-lft-out--
23×cos-sum
20×times-frac
11×sqr-pow
9×pow1
8×add-exp-log add-cbrt-cube
6×associate-*l*
5×neg-mul-1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r/ div-inv
2×sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in cos-diff pow-to-exp pow-pow distribute-lft-in flip3-+ exp-diff pow-exp flip-+ distribute-lft-out associate--r-
Counts
4 → 224
Calls
4 calls:
3.6s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
10.0ms
(* K (+ m n))
34.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series699.0ms

Counts
4 → 12
Calls
4 calls:
357.0ms
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
24.0ms
(* K (+ m n))
265.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
53.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify115.0ms

Algorithm
egg-herbie
Counts
236 → 236
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
012284982
137364262
250024261

prune716.0ms

Filtered
236 candidates to 109 candidates (46.2%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite35.0ms

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:
34.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series265.0ms

Counts
1 → 3
Calls
1 calls:
265.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify56.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0159174
1445168
21492167
35001162

prune122.0ms

Filtered
25 candidates to 19 candidates (76.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt K)
0.6b
(cbrt K)
0.6b
(cbrt K)
33.7b
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
23×cos-sum
21×prod-diff
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×cbrt-prod times-frac
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3 div-inv
1×cos-diff sub-neg
Counts
4 → 72
Calls
4 calls:
0.0ms
(cbrt K)
0.0ms
(cbrt K)
1.0ms
(cbrt K)
54.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series660.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(cbrt K)
190.0ms
(cbrt K)
183.0ms
(cbrt K)
102.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify85.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
03561441
17401183
225301177
350021054

prune390.0ms

Filtered
84 candidates to 57 candidates (67.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt K)
0.6b
(cbrt K)
0.6b
(pow (cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M)) 3)
33.7b
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
23×cos-sum
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
21×prod-diff
9×times-frac
6×cbrt-prod
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow cube-prod div-inv
2×pow1/3
1×cos-diff cube-mult pow-to-exp sub-neg pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 84
Calls
4 calls:
1.0ms
(cbrt K)
1.0ms
(cbrt K)
9.0ms
(pow (cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M)) 3)
51.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series619.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(cbrt K)
174.0ms
(cbrt K)
167.0ms
(pow (cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M)) 3)
103.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify47.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
04241775
111091478
250011470

prune432.0ms

Filtered
96 candidates to 60 candidates (62.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

regimes299.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02110
12310
22310

end0.0ms

sample1.1s

Algorithm
intervals
Results
637.0ms8080×body80valid
57.0ms117×body1280valid
52.0ms146×body640valid
24.0ms101×body320valid
8.0ms47×body160valid
1.0ms2×body2560valid