Details

Time bar (total: 8.2s)

sample53.0ms

Algorithm
intervals
Results
26.0ms260×body80valid
3.0ms5×body1280valid
2.0ms6×body640valid
1.0ms4×body320valid
0.0ms1×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
05016
19516
221116
355315
4197415
5500115

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b
(* K (+ m n))
34.2b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite503.0ms

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:
385.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
55.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
19.0ms
(* K (+ m n))
39.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series487.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
243.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
28.0ms
(* K (+ m n))
50.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify65.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
07091542
121391259
250011252

prune866.0ms

Pruning

4 alts after pruning (4 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)

rewrite439.0ms

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:
380.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
57.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series409.0ms

Counts
2 → 6
Calls
2 calls:
162.0ms
(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
247.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify131.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0326528
1945464
24380448
35001448

prune398.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt K)
0.5b
(cbrt K)
0.6b
(* (cbrt K) (cbrt K))
33.8b
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
27×add-cube-cbrt *-un-lft-identity
23×cos-sum
22×cbrt-prod
21×prod-diff
11×pow1
9×times-frac
8×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
3×div-inv
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 cos-diff sub-neg pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 101
Calls
4 calls:
1.0ms
(cbrt K)
1.0ms
(cbrt K)
11.0ms
(* (cbrt K) (cbrt K))
92.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series657.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(cbrt K)
178.0ms
(cbrt K)
204.0ms
(* (cbrt K) (cbrt K))
94.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify61.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04341577
112551304
250011284

prune879.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

localize26.0ms

Local error

Found 4 expressions with local error:

14.5b
(cbrt (* K (+ m n)))
14.5b
(cbrt (* K (+ m n)))
14.5b
(cbrt (* K (+ m n)))
33.6b
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
23×cos-sum
21×prod-diff
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×cbrt-div associate-*r/
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod flip3-+ pow1/3 flip-+ div-inv
1×cos-diff sub-neg
Counts
4 → 72
Calls
4 calls:
6.0ms
(cbrt (* K (+ m n)))
7.0ms
(cbrt (* K (+ m n)))
7.0ms
(cbrt (* K (+ m n)))
56.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series345.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(cbrt (* K (+ m n)))
99.0ms
(cbrt (* K (+ m n)))
98.0ms
(cbrt (* K (+ m n)))
50.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify63.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
04261888
17861586
218781562
350021391

prune826.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.9b

regimes248.0ms

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
02010
12010

end0.0ms

sample1.2s

Algorithm
intervals
Results
741.0ms8120×body80valid
66.0ms122×body1280valid
62.0ms161×body640valid
30.0ms109×body320valid
14.0ms64×body160valid
2.0ms2×body2560valid