Details

Time bar (total: 48.7s)

sample133.0ms

Algorithm
intervals
Results
85.0ms262×body80valid
5.0ms4×body640valid
5.0ms3×body1280valid
4.0ms5×body320valid
1.0ms2×body160valid

simplify379.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
378.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize81.0ms

Local error

Found 4 expressions with local error:

35.9b
(cos (- (/ (* (+ m n) K) 2) M))
0.0b
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b
(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))
0.0b
(* (+ m n) K)

rewrite548.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
27×*-un-lft-identity
13×pow1
11×add-cube-cbrt
10×associate-*l* add-log-exp
9×associate-*r*
8×add-cbrt-cube swap-sqr add-exp-log difference-of-squares
6×flip3-- flip-- distribute-lft-out--
4×frac-times times-frac associate-*l/ insert-posit16
3×exp-prod sub-neg rem-exp-log
2×distribute-rgt-in cos-sum sum-log distribute-lft-in pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×pow2 cos-diff associate-+r- flip3-+ pow-plus exp-diff diff-log exp-sum pow-sqr pow-prod-up flip-+ distribute-lft-out
Counts
4 → 98
Calls
4 calls:
Slowest
254.0ms
(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))
217.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
45.0ms
(cos (- (/ (* (+ m n) K) 2) M))
29.0ms
(* (+ m n) K)

series381.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))
116.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
87.0ms
(cos (- (/ (* (+ m n) K) 2) M))
40.0ms
(* (+ m n) K)

simplify10.5s

Counts
86 → 110
Calls
86 calls:
Slowest
535.0ms
(* (* (* (+ m n) (+ m n)) (+ m n)) (* (* K K) K))
431.0ms
(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
400.0ms
(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
400.0ms
(* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))))
386.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize44.0ms

Local error

Found 2 expressions with local error:

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

rewrite490.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
21×*-un-lft-identity
9×pow1
8×swap-sqr add-log-exp difference-of-squares
7×add-cube-cbrt
6×flip3-- associate-*r* associate-*l* flip-- distribute-lft-out--
4×frac-times times-frac add-cbrt-cube add-exp-log
3×exp-prod rem-exp-log
2×distribute-rgt-in sum-log sub-neg distribute-lft-in associate-*l/ associate-*r/ insert-posit16
1×pow2 associate-+r- pow-plus exp-diff diff-log exp-sum pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
Counts
2 → 65
Calls
2 calls:
Slowest
282.0ms
(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))
207.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

series257.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
166.0ms
(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))
91.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify9.7s

Counts
66 → 71
Calls
66 calls:
Slowest
677.0ms
(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))
495.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
460.0ms
(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
450.0ms
(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
428.0ms
(exp (* (cbrt (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))) (cbrt (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize119.0ms

Local error

Found 4 expressions with local error:

50.5b
(posit16->real (real->posit16 (* (+ m n) K)))
35.9b
(cos (- (/ (posit16->real (real->posit16 (* (+ m n) K))) 2) M))
0.0b
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b
(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))

rewrite519.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
23×*-un-lft-identity
11×pow1
10×add-log-exp
9×add-cube-cbrt
8×swap-sqr difference-of-squares
6×flip3-- add-cbrt-cube associate-*r* associate-*l* add-exp-log flip-- distribute-lft-out--
4×frac-times times-frac insert-posit16
3×exp-prod sub-neg rem-exp-log
2×distribute-rgt-in cos-sum sum-log distribute-lft-in associate-*l/ associate-*r/
1×pow2 cos-diff associate-+r- pow-plus exp-diff diff-log exp-sum pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod remove-posit16 unswap-sqr
Counts
4 → 85
Calls
4 calls:
Slowest
258.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
238.0ms
(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))
19.0ms
(cos (- (/ (posit16->real (real->posit16 (* (+ m n) K))) 2) M))
1.0ms
(posit16->real (real->posit16 (* (+ m n) K)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))
92.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
79.0ms
(cos (- (/ (posit16->real (real->posit16 (* (+ m n) K))) 2) M))
32.0ms
(posit16->real (real->posit16 (* (+ m n) K)))

simplify9.6s

Counts
76 → 97
Calls
76 calls:
Slowest
409.0ms
(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
396.0ms
(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
391.0ms
(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
389.0ms
(exp (* (cbrt (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))) (cbrt (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))))
387.0ms
(exp (sqrt (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))))

prune3.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize101.0ms

Local error

Found 4 expressions with local error:

36.1b
(cos (- (/ (* (* (cbrt (+ m n)) (cbrt (+ m n))) (* (cbrt (+ m n)) K)) 2) M))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
2×cos-sum
1×cos-diff sub-neg
Counts
4 → 56
Calls
4 calls:
Slowest
120.0ms
(cos (- (/ (* (* (cbrt (+ m n)) (cbrt (+ m n))) (* (cbrt (+ m n)) K)) 2) M))
3.0ms
(cbrt (+ m n))
3.0ms
(cbrt (+ m n))
3.0ms
(cbrt (+ m n))

series721.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
219.0ms
(cbrt (+ m n))
181.0ms
(cbrt (+ m n))
165.0ms
(cos (- (/ (* (* (cbrt (+ m n)) (cbrt (+ m n))) (* (cbrt (+ m n)) K)) 2) M))
156.0ms
(cbrt (+ m n))

simplify3.1s

Counts
33 → 68
Calls
33 calls:
Slowest
437.0ms
(- (+ (* 1/3 (* m (pow (/ 1 (pow n 2)) 1/3))) (pow n 1/3)) (* 1/9 (* (pow m 2) (pow (/ 1 (pow n 5)) 1/3))))
425.0ms
(- (+ (* 1/3 (* m (pow (/ 1 (pow n 2)) 1/3))) (pow n 1/3)) (* 1/9 (* (pow m 2) (pow (/ 1 (pow n 5)) 1/3))))
368.0ms
(- (+ (* 1/3 (* m (pow (/ 1 (pow n 2)) 1/3))) (pow n 1/3)) (* 1/9 (* (pow m 2) (pow (/ 1 (pow n 5)) 1/3))))
198.0ms
(* (cos (/ (* (* (cbrt (+ m n)) (cbrt (+ m n))) (* (cbrt (+ m n)) K)) 2)) (cos M))
175.0ms
(* (pow (* m -1) 1/3) (cbrt -1))

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

regimes538.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.7s8094×body80valid
226.0ms166×body640valid
136.0ms110×body1280valid
76.0ms112×body320valid
30.0ms66×body160valid
2.0ms1×body2560valid