Details

Time bar (total: 6.1s)

sample40.0ms

Algorithm
intervals
Results
19.0ms257×body80valid
2.0ms4×body1280valid
1.0ms3×body640valid
0.0ms2×body160valid
0.0ms1×body320valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
05016
19516
221116
355315
4197415
5500115

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b
(- (/ (* K (+ m n)) 2.0) M)
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
33.8b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite298.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
53×*-un-lft-identity
51×prod-diff
42×add-cube-cbrt
23×cos-sum times-frac
12×unpow-prod-down
11×associate-+r+ add-log-exp
10×fma-def
7×fma-neg div-inv
5×pow1 add-exp-log difference-of-squares
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u distribute-lft-out--
3×sub-neg pow-unpow
2×diff-log sum-log distribute-lft-out sqr-pow
1×+-commutative cos-diff pow-to-exp associate-+r- flip3-- pow-pow flip3-+ pow-exp flip-- flip-+
Counts
4 → 137
Calls
4 calls:
230.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
11.0ms
(- (/ (* K (+ m n)) 2.0) M)
31.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
21.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series562.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
56.0ms
(- (/ (* K (+ m n)) 2.0) M)
267.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify63.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06661925
118381487
250021476

prune537.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize15.0ms

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)

rewrite262.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×*-un-lft-identity
12×add-cube-cbrt unpow-prod-down
11×associate-+r+
10×fma-def
9×prod-diff
7×add-log-exp
4×difference-of-squares
3×pow1 add-exp-log pow-unpow distribute-lft-out--
2×expm1-log1p-u times-frac sum-log add-cbrt-cube log1p-expm1-u distribute-lft-out sqr-pow
1×+-commutative pow-to-exp associate-+r- sub-neg pow-pow flip3-+ diff-log pow-exp flip-+
Counts
2 → 60
Calls
2 calls:
229.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
31.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series449.0ms

Counts
2 → 6
Calls
2 calls:
185.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
264.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify126.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0326528
1945464
24380448
35001448

prune256.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M))
0.4b
(/ (+ m n) (sqrt 2.0))
0.4b
(/ K (sqrt 2.0))
33.9b
(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
42×times-frac
36×add-sqr-sqrt add-cube-cbrt
27×sqrt-prod
12×associate-/r*
8×add-exp-log add-cbrt-cube
7×distribute-lft-out associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv associate-/l/
1×cos-sum flip3-+ flip-+
Counts
4 → 111
Calls
4 calls:
0.0ms
(fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M))
8.0ms
(/ (+ m n) (sqrt 2.0))
3.0ms
(/ K (sqrt 2.0))
1.0ms
(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

series611.0ms

Counts
4 → 12
Calls
4 calls:
241.0ms
(fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M))
93.0ms
(/ (+ m n) (sqrt 2.0))
59.0ms
(/ K (sqrt 2.0))
218.0ms
(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

simplify94.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0301846
1906777
23539748
35001739

prune529.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos (/ (* K (+ m n)) 2.0)) (cos M)) (* (sin (/ (* K (+ m n)) 2.0)) (sin (- M))))
0.2b
(* (sin (/ (* K (+ m n)) 2.0)) (sin (- M)))
39.6b
(sin (/ (* K (+ m n)) 2.0))
39.8b
(cos (/ (* K (+ m n)) 2.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-*r* associate-*l* sin-mult
2×cos-mult
1×sub-neg flip3-- fma-neg diff-log prod-diff pow-prod-down prod-exp sin-neg *-commutative distribute-rgt-neg-out frac-sub flip-- cbrt-unprod sub-div unswap-sqr
Counts
4 → 58
Calls
4 calls:
5.0ms
(- (* (cos (/ (* K (+ m n)) 2.0)) (cos M)) (* (sin (/ (* K (+ m n)) 2.0)) (sin (- M))))
7.0ms
(* (sin (/ (* K (+ m n)) 2.0)) (sin (- M)))
2.0ms
(sin (/ (* K (+ m n)) 2.0))
2.0ms
(cos (/ (* K (+ m n)) 2.0))

series242.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(- (* (cos (/ (* K (+ m n)) 2.0)) (cos M)) (* (sin (/ (* K (+ m n)) 2.0)) (sin (- M))))
55.0ms
(* (sin (/ (* K (+ m n)) 2.0)) (sin (- M)))
29.0ms
(sin (/ (* K (+ m n)) 2.0))
16.0ms
(cos (/ (* K (+ m n)) 2.0))

simplify75.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0250779
1769695
22733663
35001652

prune388.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b

regimes287.0ms

Accuracy

0% (0.2b remaining)

Error of 1.5b against oracle of 1.3b 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
605.0ms8052×body80valid
65.0ms140×body1280valid
48.0ms142×body640valid
25.0ms110×body320valid
10.0ms64×body160valid
1.0ms1×body2560valid