Details

Time bar (total: 55.0s)

sample99.0ms

Algorithm
intervals
Results
69.0ms256×body80valid
4.0ms4×body640valid
4.0ms3×body1280valid
2.0ms3×body320valid

simplify283.0ms

Calls
1 calls:
Slowest
282.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.9b

localize76.0ms

Local error

Found 4 expressions with local error:

34.8b
(cos (- (/ (* (+ m n) K) 2) M))
0.0b
(- (/ (* (+ m n) K) 2) M)
0.0b
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b
(* (+ m n) K)

rewrite667.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
28×*-un-lft-identity
13×pow1
11×difference-of-squares
10×associate-*l* add-cube-cbrt
9×associate-*r*
8×add-cbrt-cube swap-sqr add-exp-log
7×flip3-- flip-- distribute-lft-out--
6×times-frac add-log-exp
4×frac-times sub-neg associate-*l/ insert-posit16
3×unswap-sqr
2×distribute-rgt-in cos-sum distribute-lft-in pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod
1×pow2 cos-diff flip3-+ pow-plus diff-log pow-sqr pow-prod-up flip-+ distribute-lft-out
Calls
4 calls:
Slowest
252.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
251.0ms
(cos (- (/ (* (+ m n) K) 2) M))
134.0ms
(- (/ (* (+ m n) K) 2) M)
30.0ms
(* (+ m n) K)

series300.0ms

Calls
4 calls:
Slowest
103.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
83.0ms
(- (/ (* (+ m n) K) 2) M)
77.0ms
(cos (- (/ (* (+ m n) K) 2) M))
37.0ms
(* (+ m n) K)

simplify8.9s

Calls
86 calls:
Slowest
571.0ms
(* (* (* (+ m n) (+ m n)) (+ m n)) (* (* K K) K))
442.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
399.0ms
(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
376.0ms
(* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))))
372.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (/ (+ m n) 2) M))

prune2.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize38.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
28×add-sqr-sqrt
26×flip3-- flip--
16×frac-add
12×frac-times
11×distribute-lft-out--
10×associate-*l*
9×pow1
8×swap-sqr difference-of-squares
7×add-log-exp
6×associate-*r* associate-*l/ associate-*r/ add-cube-cbrt distribute-lft-out
5×sub-neg
4×distribute-rgt-in associate-+l+ distribute-lft-in times-frac add-cbrt-cube add-exp-log
2×associate-+r+ sum-log insert-posit16
1×pow2 +-commutative associate-+r- flip3-+ pow-plus diff-log pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ unswap-sqr
Calls
2 calls:
Slowest
993.0ms
(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
267.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

series295.0ms

Calls
2 calls:
Slowest
203.0ms
(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
92.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify24.1s

Calls
105 calls:
Slowest
884.0ms
(+ (* (* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (pow (/ (+ m n) 2) 3) (pow M 3))) (+ (* l l) (+ (* (fabs (- m n)) (fabs (- m n))) (* l (fabs (- m n)))))) (* (* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M)))) (- (pow l 3) (pow (fabs (- m n)) 3))))
813.0ms
(+ (* (* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M))) (+ (* l l) (+ (* (fabs (- m n)) (fabs (- m n))) (* l (fabs (- m n)))))) (* (* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M)) (- (pow l 3) (pow (fabs (- m n)) 3))))
782.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
685.0ms
(+ (* (* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3))) (+ (* l l) (+ (* (fabs (- m n)) (fabs (- m n))) (* l (fabs (- m n)))))) (* (* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M)))) (- (pow l 3) (pow (fabs (- m n)) 3))))
670.0ms
(+ (* (* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M))) (+ l (fabs (- m n)))) (* (* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M)) (- (* l l) (* (fabs (- m n)) (fabs (- m n))))))

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize69.0ms

Local error

Found 4 expressions with local error:

34.6b
(cos (- (/ (* (* (+ m n) (* (cbrt K) (cbrt K))) (cbrt K)) 2) M))
0.6b
(cbrt K)
0.6b
(cbrt K)
0.6b
(cbrt K)

rewrite1.7s

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
Calls
4 calls:
Slowest
1.7s
(cos (- (/ (* (* (+ m n) (* (cbrt K) (cbrt K))) (cbrt K)) 2) M))
1.0ms
(cbrt K)
1.0ms
(cbrt K)
1.0ms
(cbrt K)

series1.0s

Calls
4 calls:
Slowest
321.0ms
(cbrt K)
285.0ms
(cbrt K)
256.0ms
(cbrt K)
140.0ms
(cos (- (/ (* (* (+ m n) (* (cbrt K) (cbrt K))) (cbrt K)) 2) M))

simplify1.2s

Calls
24 calls:
Slowest
206.0ms
(* (cos (/ (* (* (+ m n) (* (cbrt K) (cbrt K))) (cbrt K)) 2)) (cos (- M)))
179.0ms
(* (cos (/ (* (* (+ m n) (* (cbrt K) (cbrt K))) (cbrt K)) 2)) (cos (- M)))
172.0ms
(* (pow (* K -1) 1/3) (cbrt -1))
162.0ms
(* (cos (/ (* (* (+ m n) (* (cbrt K) (cbrt K))) (cbrt K)) 2)) (cos M))
112.0ms
(* (pow (* K -1) 1/3) (cbrt -1))

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize79.0ms

Local error

Found 4 expressions with local error:

57.8b
(posit16->real (real->posit16 (cbrt K)))
34.6b
(cos (- (/ (* (* (+ m n) (* (cbrt K) (cbrt K))) (posit16->real (real->posit16 (cbrt K)))) 2) M))
0.6b
(cbrt K)
0.6b
(cbrt K)

rewrite1.6s

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
Calls
4 calls:
Slowest
1.6s
(cos (- (/ (* (* (+ m n) (* (cbrt K) (cbrt K))) (posit16->real (real->posit16 (cbrt K)))) 2) M))
1.0ms
(cbrt K)
1.0ms
(cbrt K)
0.0ms
(posit16->real (real->posit16 (cbrt K)))

series1.0s

Calls
4 calls:
Slowest
347.0ms
(cbrt K)
260.0ms
(cbrt K)
250.0ms
(posit16->real (real->posit16 (cbrt K)))
156.0ms
(cos (- (/ (* (* (+ m n) (* (cbrt K) (cbrt K))) (posit16->real (real->posit16 (cbrt K)))) 2) M))

simplify2.0s

Calls
21 calls:
Slowest
755.0ms
(* (cos (/ (* (* (+ m n) (* (cbrt K) (cbrt K))) (posit16->real (real->posit16 (cbrt K)))) 2)) (cos (- M)))
269.0ms
(* (cos (/ (* (* (+ m n) (* (cbrt K) (cbrt K))) (posit16->real (real->posit16 (cbrt K)))) 2)) (cos M))
251.0ms
(* (cos (/ (* (* (+ m n) (* (cbrt K) (cbrt K))) (posit16->real (real->posit16 (cbrt K)))) 2)) (cos (- M)))
138.0ms
(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
135.0ms
(* (pow (* K -1) 1/3) (cbrt -1))

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

regimes574.0ms

Accuracy

0% (0.3b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch3.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.4s8123×body80valid
172.0ms140×body640valid
144.0ms111×body1280valid
72.0ms107×body320valid
27.0ms60×body160valid
1.0ms1×body2560valid