Details

Time bar (total: 6.2s)

sample38.0ms

Algorithm
intervals
Results
19.0ms261×body80valid
1.0ms3×body640valid
1.0ms4×body320valid
0.0ms1×body1280valid

simplify51.0ms

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: 17.7b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
35.3b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
35×*-un-lft-identity
30×prod-diff
26×add-cube-cbrt
23×cos-sum
12×unpow-prod-down
11×associate-+r+ times-frac
10×fma-def
8×add-log-exp
4×pow1 add-exp-log difference-of-squares
3×expm1-log1p-u pow-unpow add-cbrt-cube log1p-expm1-u div-inv distribute-lft-out--
2×sub-neg sum-log distribute-lft-out sqr-pow
1×+-commutative cos-diff pow-to-exp associate-+r- pow-pow flip3-+ diff-log pow-exp flip-+
Counts
3 → 93
Calls
3 calls:
30.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
221.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
23.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series483.0ms

Counts
3 → 9
Calls
3 calls:
258.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
172.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
53.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify49.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
06011450
115261177
250011161

prune375.0ms

Pruning

3 alts after pruning (3 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)

rewrite257.0ms

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:
221.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
33.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series440.0ms

Counts
2 → 6
Calls
2 calls:
177.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
263.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify120.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0326528
1945464
24380448
35001448

prune243.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.0b

localize39.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
35.1b
(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
35.3b
(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))))

series422.0ms

Counts
4 → 8
Calls
4 calls:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
211.0ms
(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
210.0ms
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify117.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 3 (25.0ms)

IterNodesCost
0162536
1394479
2986470
32961468
45003468

prune441.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.0b

localize51.0ms

Local error

Found 4 expressions with local error:

35.1b
(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
35.3b
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
35.3b
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
35.3b
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
3×cos-sum
1×sin-sum
Counts
4 → 40
Calls
4 calls:
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))))
1.0ms
(cos (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))))

series845.0ms

Counts
4 → 12
Calls
4 calls:
210.0ms
(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
208.0ms
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
214.0ms
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
213.0ms
(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify56.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
0108754
1251653
2596652
31348652
45002652

prune479.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.0b

regimes284.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02010
12010

end0.0ms

sample1.0s

Algorithm
intervals
Results
616.0ms8086×body80valid
54.0ms115×body1280valid
52.0ms161×body640valid
27.0ms107×body320valid
6.0ms38×body160valid
2.0ms3×body2560valid