Details

Time bar (total: 6.5s)

sample44.0ms

Algorithm
intervals
Results
24.0ms258×body80valid
2.0ms5×body640valid
1.0ms2×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

prune9.0ms

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))

rewrite109.0ms

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:
58.0ms
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
9.0ms
(* K (+ m n))
11.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
12.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series704.0ms

Counts
4 → 12
Calls
4 calls:
360.0ms
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
29.0ms
(* K (+ m n))
262.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
53.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify114.0ms

Algorithm
egg-herbie
Counts
236 → 236
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
012284982
137364262
250024261

prune680.0ms

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)

rewrite11.0ms

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:
11.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series257.0ms

Counts
1 → 3
Calls
1 calls:
257.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify47.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 3 (39.0ms)

IterNodesCost
0159174
1445168
21492167
35001162

prune111.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (+ m n) (sqrt 2.0))
0.5b
(/ (+ m n) (sqrt 2.0))
34.0b
(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
34.2b
(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
48×times-frac
38×add-sqr-sqrt add-cube-cbrt
30×sqrt-prod
14×distribute-lft-out
12×associate-/r*
8×add-exp-log add-cbrt-cube associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ fma-udef div-inv
1×cos-sum sin-sum
Counts
4 → 120
Calls
4 calls:
7.0ms
(/ (+ m n) (sqrt 2.0))
7.0ms
(/ (+ m n) (sqrt 2.0))
2.0ms
(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
2.0ms
(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

series597.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (+ m n) (sqrt 2.0))
90.0ms
(/ (+ m n) (sqrt 2.0))
207.0ms
(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
211.0ms
(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))

simplify73.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
02421020
1695946
22584919
35001918

prune783.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
34.0b
(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
34.6b
(cos (fma (/ K (sqrt 2.0)) (* (/ 1 (* (fabs (cbrt 2.0)) 1)) (/ (+ m n) (sqrt (cbrt 2.0)))) (- (* M 1))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow1/3 fma-udef
1×cos-sum sin-sum
Counts
4 → 46
Calls
4 calls:
1.0ms
(cbrt 2.0)
1.0ms
(cbrt 2.0)
2.0ms
(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
2.0ms
(cos (fma (/ K (sqrt 2.0)) (* (/ 1 (* (fabs (cbrt 2.0)) 1)) (/ (+ m n) (sqrt (cbrt 2.0)))) (- (* M 1))))

series792.0ms

Counts
4 → 8
Calls
4 calls:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
209.0ms
(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- (* M 1))))
583.0ms
(cos (fma (/ K (sqrt 2.0)) (* (/ 1 (* (fabs (cbrt 2.0)) 1)) (/ (+ m n) (sqrt (cbrt 2.0)))) (- (* M 1))))

simplify50.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0187582
1495523
21859516
35002513

prune486.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

regimes292.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02110
12310
22310

end0.0ms

sample1.1s

Algorithm
intervals
Results
679.0ms8080×body80valid
60.0ms117×body1280valid
52.0ms146×body640valid
26.0ms101×body320valid
8.0ms47×body160valid
2.0ms2×body2560valid