Details

Time bar (total: 6.9s)

sample40.0ms

Algorithm
intervals
Results
20.0ms255×body80valid
2.0ms5×body640valid
1.0ms4×body320valid
0.0ms1×body160valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (10.0ms)

IterNodesCost
05016
19516
221116
355315
4197415
5500115

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize26.0ms

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))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
34.1b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite290.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
40×*-un-lft-identity
30×prod-diff
29×add-cube-cbrt
23×cos-sum
12×unpow-prod-down
11×associate-+r+ times-frac
10×fma-def
9×add-log-exp
7×pow1 add-exp-log
6×add-cbrt-cube
4×expm1-log1p-u associate-*r* log1p-expm1-u difference-of-squares
3×pow-unpow associate-*l* div-inv distribute-lft-out distribute-lft-out--
2×sub-neg flip3-+ associate-*r/ sum-log flip-+ sqr-pow
1×+-commutative distribute-rgt-in cos-diff pow-to-exp associate-+r- pow-pow distribute-lft-in diff-log pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 118
Calls
4 calls:
223.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
12.0ms
(* K (+ m n))
30.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series502.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
24.0ms
(* K (+ m n))
253.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
55.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify61.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
07091542
121391259
250011252

prune510.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize14.0ms

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)

rewrite255.0ms

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:
220.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
32.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series428.0ms

Counts
2 → 6
Calls
2 calls:
171.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
257.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify124.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0326528
1945464
24380448
35001448

prune261.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
34.1b
(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
34.2b
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite4.0ms

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:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
1.0ms
(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
1.0ms
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

series403.0ms

Counts
4 → 8
Calls
4 calls:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
203.0ms
(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
200.0ms
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify114.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
0162536
1394479
2986470
32961468
45003468

prune445.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.0b

localize40.0ms

Local error

Found 4 expressions with local error:

15.6b
(cbrt (/ (* K (+ m n)) 2.0))
15.6b
(cbrt (/ (* K (+ m n)) 2.0))
34.0b
(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))
34.0b
(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))

rewrite10.0ms

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:
3.0ms
(cbrt (/ (* K (+ m n)) 2.0))
3.0ms
(cbrt (/ (* K (+ m n)) 2.0))
1.0ms
(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))
1.0ms
(cos (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:
164.0ms
(cbrt (/ (* K (+ m n)) 2.0))
158.0ms
(cbrt (/ (* K (+ m n)) 2.0))
492.0ms
(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- (* M 1))))
503.0ms
(cos (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

prune609.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.0b

regimes254.0ms

Accuracy

0% (0.2b remaining)

Error of 1.1b against oracle of 0.9b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02010
12010

end0.0ms

sample1.1s

Algorithm
intervals
Results
640.0ms8142×body80valid
59.0ms120×body1280valid
46.0ms140×body640valid
23.0ms85×body320valid
8.0ms49×body160valid
6.0ms7×body2560valid