Details

Time bar (total: 29.6s)

sample128.0ms

Algorithm
intervals
Results
67.0ms260×body80valid
29.0ms6×body640valid
3.0ms2×body1280valid
1.0ms2×body320valid
0.0ms1×body160valid

simplify341.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
340.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize88.0ms

Local error

Found 4 expressions with local error:

33.2b
(cos (- (/ (* K (+ m n)) 2) M))
0.0b
(pow (- (/ (+ m n) 2) M) 2)
0.0b
(* K (+ m n))
0.0b
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))

rewrite897.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
17×add-sqr-sqrt
14×add-log-exp
8×add-cube-cbrt
7×pow1 add-exp-log distribute-lft-out--
6×unpow-prod-down add-cbrt-cube diff-log
4×associate-*r* insert-posit16
3×pow-unpow sub-neg associate-*l* difference-of-squares
2×cos-sum distribute-rgt-neg-in neg-log associate-*r/ associate--r+
1×associate--l- neg-sub0 distribute-rgt-in cos-diff pow-to-exp pow-pow distribute-lft-in flip3-+ times-frac flip3-- pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod flip-+ flip-- distribute-lft-out unpow2 associate--r- unswap-sqr sqr-pow
Counts
4 → 82
Calls
4 calls:
Slowest
766.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
67.0ms
(pow (- (/ (+ m n) 2) M) 2)
38.0ms
(cos (- (/ (* K (+ m n)) 2) M))
25.0ms
(* K (+ m n))

series463.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
220.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
119.0ms
(pow (- (/ (+ m n) 2) M) 2)
82.0ms
(cos (- (/ (* K (+ m n)) 2) M))
42.0ms
(* K (+ m n))

simplify6.0s

Counts
53 → 94
Calls
53 calls:
Slowest
793.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
419.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
415.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
403.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
339.0ms
(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.2b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2) M) 2)
0.0b
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))

rewrite821.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
12×add-log-exp
11×add-sqr-sqrt
7×distribute-lft-out--
6×unpow-prod-down diff-log
4×add-cube-cbrt
3×pow1 pow-unpow add-exp-log difference-of-squares
2×sub-neg distribute-rgt-neg-in add-cbrt-cube neg-log insert-posit16 associate--r+
1×associate--l- neg-sub0 pow-to-exp pow-pow times-frac flip3-- pow-exp flip-- unpow2 associate--r- sqr-pow
Counts
2 → 47
Calls
2 calls:
Slowest
774.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
46.0ms
(pow (- (/ (+ m n) 2) M) 2)

series336.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
210.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
126.0ms
(pow (- (/ (+ m n) 2) M) 2)

simplify4.7s

Counts
29 → 53
Calls
29 calls:
Slowest
445.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
409.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
385.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
385.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
298.0ms
(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)

prune802.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.2b

localize97.0ms

Local error

Found 4 expressions with local error:

33.2b
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2) M))
0.6b
(cbrt K)
0.6b
(cbrt K)
0.6b
(cbrt K)

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
2×cos-sum
1×cos-diff sub-neg
Counts
4 → 47
Calls
4 calls:
Slowest
74.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2) M))
1.0ms
(cbrt K)
1.0ms
(cbrt K)
1.0ms
(cbrt K)

series982.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
290.0ms
(cbrt K)
284.0ms
(cbrt K)
272.0ms
(cbrt K)
136.0ms
(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2) M))

simplify1.6s

Counts
24 → 59
Calls
24 calls:
Slowest
328.0ms
(* (cos (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2)) (cos (- M)))
266.0ms
(* (cos (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2)) (cos M))
261.0ms
(* (cos (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2)) (cos (- M)))
145.0ms
(* (pow (* K -1) 1/3) (cbrt -1))
145.0ms
(* (pow (* K -1) 1/3) (cbrt -1))

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize134.0ms

Local error

Found 4 expressions with local error:

57.5b
(posit16->real (real->posit16 (cbrt K)))
33.2b
(cos (- (/ (* (* (cbrt K) (posit16->real (real->posit16 (cbrt K)))) (* (cbrt K) (+ m n))) 2) M))
0.6b
(cbrt K)
0.6b
(cbrt K)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×cos-sum pow1/3
1×cos-diff sub-neg remove-posit16
Counts
4 → 44
Calls
4 calls:
Slowest
53.0ms
(cos (- (/ (* (* (cbrt K) (posit16->real (real->posit16 (cbrt K)))) (* (cbrt K) (+ m n))) 2) M))
1.0ms
(cbrt K)
1.0ms
(cbrt K)
0.0ms
(posit16->real (real->posit16 (cbrt K)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
328.0ms
(cbrt K)
291.0ms
(cbrt K)
281.0ms
(posit16->real (real->posit16 (cbrt K)))
152.0ms
(cos (- (/ (* (* (cbrt K) (posit16->real (real->posit16 (cbrt K)))) (* (cbrt K) (+ m n))) 2) M))

simplify1.7s

Counts
21 → 56
Calls
21 calls:
Slowest
330.0ms
(* (cos (/ (* (* (cbrt K) (posit16->real (real->posit16 (cbrt K)))) (* (cbrt K) (+ m n))) 2)) (cos M))
295.0ms
(* (cos (/ (* (* (cbrt K) (posit16->real (real->posit16 (cbrt K)))) (* (cbrt K) (+ m n))) 2)) (cos (- M)))
268.0ms
(* (cos (/ (* (* (cbrt K) (posit16->real (real->posit16 (cbrt K)))) (* (cbrt K) (+ m n))) 2)) (cos (- M)))
160.0ms
(* (pow (* K -1) 1/3) (cbrt -1))
147.0ms
(* (pow (* K -1) 1/3) (cbrt -1))

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

regimes674.0ms

Accuracy

0% (0.2b remaining)

Error of 1.5b against oracle of 1.3b and baseline of 1.5b

bsearch5.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.7s8066×body80valid
201.0ms174×body640valid
150.0ms117×body1280valid
111.0ms111×body320valid
28.0ms53×body160valid
8.0ms4×body2560valid