Details

Time bar (total: 11.2s)

sample47.0ms

Algorithm
intervals
Results
21.0ms259×body80valid
6.0ms10×body640valid
2.0ms4×body1280valid
1.0ms3×body160valid
0.0ms2×body320valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (8.0ms)

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: 15.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* K (+ m n))
0.0b
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
33.9b
(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:
9.0ms
(* K (+ m n))
3.6s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
34.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series698.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* K (+ m n))
356.0ms
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
263.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
53.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify110.0ms

Algorithm
egg-herbie
Counts
236 → 236
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
012284982
137364262
250024261

prune722.0ms

Filtered
236 candidates to 109 candidates (46.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite732.0ms

Algorithm
rewrite-expression-head
Rules
179×add-sqr-sqrt
148×*-un-lft-identity
129×prod-diff
78×unpow-prod-down
64×add-cube-cbrt
62×distribute-rgt-neg-in
60×distribute-lft-neg-in
51×difference-of-squares
43×distribute-lft-out--
24×fma-neg
13×times-frac sqr-pow
12×add-log-exp
11×associate--r+
6×neg-mul-1 diff-log
3×pow1 add-exp-log pow-unpow
2×expm1-log1p-u sub-neg neg-log add-cbrt-cube log1p-expm1-u
1×associate--l- neg-sub0 pow-to-exp flip3-- pow-pow pow-exp flip-- associate--r-
Counts
2 → 201
Calls
2 calls:
681.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
35.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series455.0ms

Counts
2 → 6
Calls
2 calls:
186.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
269.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify74.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
06085050
116933609
250013001

prune410.0ms

Filtered
207 candidates to 71 candidates (34.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
34.1b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
23×cos-sum
21×prod-diff
20×add-sqr-sqrt add-cube-cbrt
12×cbrt-prod
9×times-frac
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ div-inv distribute-lft-out
1×cos-diff sub-neg
Counts
4 → 81
Calls
4 calls:
2.0ms
(cbrt (+ m n))
2.0ms
(cbrt (+ m n))
2.0ms
(cbrt (+ m n))
152.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series489.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(cbrt (+ m n))
126.0ms
(cbrt (+ m n))
133.0ms
(cbrt (+ m n))
99.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify87.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
04271747
19061467
231541458
350011308

prune456.0ms

Filtered
93 candidates to 63 candidates (67.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ m n))
0.5b
(cbrt (+ m n))
0.6b
(log (exp (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))))
34.1b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite460.0ms

Algorithm
rewrite-expression-head
Rules
46×cos-sum
42×prod-diff
38×*-un-lft-identity
34×add-sqr-sqrt add-cube-cbrt
23×log-div exp-diff
18×times-frac
8×cbrt-prod
6×div-inv
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div log-prod log-pow add-cbrt-cube log1p-expm1-u add-log-exp
3×exp-prod
2×cos-diff sub-neg flip3-+ pow1/3 flip-+ distribute-lft-out
1×rem-log-exp exp-sum
Counts
4 → 106
Calls
4 calls:
2.0ms
(cbrt (+ m n))
2.0ms
(cbrt (+ m n))
298.0ms
(log (exp (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))))
152.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series464.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(cbrt (+ m n))
133.0ms
(cbrt (+ m n))
102.0ms
(log (exp (cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))))
102.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify106.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
06373262
112962707
237782701
350012409

prune522.0ms

Filtered
118 candidates to 69 candidates (58.5%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

regimes236.0ms

Accuracy

0% (0.3b remaining)

Error of 1.6b against oracle of 1.3b and baseline of 1.6b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02110
12310
22310

end0.0ms

sample1.1s

Algorithm
intervals
Results
654.0ms8091×body80valid
62.0ms122×body1280valid
61.0ms174×body640valid
28.0ms113×body320valid
11.0ms67×body160valid
1.0ms1×body2560valid