Details

Time bar (total: 37.0s)

sample68.0ms

Algorithm
intervals
Results
29.0ms256×body80valid
5.0ms9×body640valid
2.0ms3×body1280valid
1.0ms2×body320valid
0.0ms1×body160valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 4 (138.0ms)

IterNodesCost
02129
15029
29529
322029
468028
5321028
done500128

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b
(* (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))
33.0b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite12.4s

Algorithm
rewrite-expression-head
Rules
342×add-sqr-sqrt
282×*-un-lft-identity
270×prod-diff
132×unpow-prod-down
130×add-cube-cbrt associate-*r*
123×exp-sum
112×distribute-rgt-neg-in
110×distribute-lft-neg-in
93×difference-of-squares
76×distribute-lft-out--
31×times-frac
24×fma-neg
23×cos-sum
22×sqr-pow
14×add-log-exp
11×neg-mul-1 associate--r+
8×pow1 add-cbrt-cube
7×add-exp-log
6×diff-log associate-*l*
4×expm1-log1p-u sub-neg log1p-expm1-u
3×associate-*r/ div-inv
2×pow-prod-down neg-log prod-exp *-commutative cbrt-unprod associate--r- unswap-sqr
1×associate--l- neg-sub0 distribute-rgt-in cos-diff flip3-- distribute-lft-in flip3-+ exp-diff flip-- flip-+ distribute-lft-out
Counts
4 → 381
Calls
4 calls:
2.0s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
10.2s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
35.0ms
(* K (+ m n))
67.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series950.0ms

Counts
4 → 12
Calls
4 calls:
273.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
560.0ms
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
33.0ms
(* K (+ m n))
84.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.8s

Counts
393 → 393
Iterations

Useful iterations: done (2.8s)

IterNodesCost
066617794
1135414743
2492612648
done500012647

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.9b

localize36.0ms

Local error

Found 2 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))))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
179×add-sqr-sqrt
148×*-un-lft-identity
129×prod-diff
78×unpow-prod-down
64×add-cube-cbrt
62×distribute-rgt-neg-in
60×distribute-lft-neg-in
51×difference-of-squares
43×distribute-lft-out--
24×fma-neg
13×times-frac sqr-pow
12×add-log-exp
11×associate--r+
6×neg-mul-1 diff-log
3×pow1 add-exp-log pow-unpow
2×expm1-log1p-u sub-neg neg-log add-cbrt-cube log1p-expm1-u
1×associate--l- neg-sub0 pow-to-exp flip3-- pow-pow pow-exp flip-- associate--r-
Counts
2 → 201
Calls
2 calls:
104.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
2.0s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series687.0ms

Counts
2 → 6
Calls
2 calls:
406.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
280.0ms
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify2.2s

Counts
207 → 207
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02749396
16497425
220486187
done50005080

prune720.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.9b

localize78.0ms

Local error

Found 4 expressions with local error:

13.9b
(cbrt (* K (+ m n)))
13.9b
(cbrt (* K (+ m n)))
13.9b
(cbrt (* K (+ m n)))
33.3b
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite127.0ms

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:
14.0ms
(cbrt (* K (+ m n)))
14.0ms
(cbrt (* K (+ m n)))
15.0ms
(cbrt (* K (+ m n)))
78.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series646.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(cbrt (* K (+ m n)))
163.0ms
(cbrt (* K (+ m n)))
182.0ms
(cbrt (* K (+ m n)))
122.0ms
(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify1.9s

Counts
84 → 84
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02283327
14302926
28791839
324501392
done50001266

prune625.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.8b

localize107.0ms

Local error

Found 4 expressions with local error:

13.9b
(cbrt (* K (+ m n)))
13.9b
(cbrt (* K (+ m n)))
32.7b
(sin (fma (/ (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (sqrt 2.0)) (/ (cbrt (* K (+ m n))) (sqrt 2.0)) (- M)))
33.1b
(cos (fma (/ (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (sqrt 2.0)) (/ (cbrt (* K (+ m n))) (sqrt 2.0)) (- M)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt cbrt-div *-un-lft-identity associate-*r/ add-cbrt-cube log1p-expm1-u add-log-exp
2×cbrt-prod flip3-+ pow1/3 flip-+ fma-udef
1×cos-sum sin-sum
Counts
4 → 46
Calls
4 calls:
25.0ms
(cbrt (* K (+ m n)))
13.0ms
(cbrt (* K (+ m n)))
4.0ms
(sin (fma (/ (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (sqrt 2.0)) (/ (cbrt (* K (+ m n))) (sqrt 2.0)) (- M)))
5.0ms
(cos (fma (/ (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (sqrt 2.0)) (/ (cbrt (* K (+ m n))) (sqrt 2.0)) (- M)))

series2.5s

Counts
4 → 12
Calls
4 calls:
143.0ms
(cbrt (* K (+ m n)))
153.0ms
(cbrt (* K (+ m n)))
1.1s
(sin (fma (/ (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (sqrt 2.0)) (/ (cbrt (* K (+ m n))) (sqrt 2.0)) (- M)))
1.0s
(cos (fma (/ (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (sqrt 2.0)) (/ (cbrt (* K (+ m n))) (sqrt 2.0)) (- M)))

simplify1.4s

Counts
58 → 58
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01281422
12951377
2717901
32399651
done5002605

prune813.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.8b

regimes454.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01720
12118
22218
done2218

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.6s8098×body80valid
109.0ms151×body640valid
69.0ms100×body1280valid
67.0ms100×body320valid
15.0ms59×body160valid
4.0ms3×body2560valid