Details

Time bar (total: 43.1s)

sample109.0ms

Algorithm
intervals
Results
69.0ms262×body80valid
5.0ms3×body1280valid
4.0ms5×body320valid
4.0ms4×body640valid
1.0ms2×body160valid

simplify282.0ms

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×*-un-lft-identity
20×add-cube-cbrt
13×associate-*l*
12×exp-sum prod-diff
10×times-frac
9×add-cbrt-cube add-exp-log
7×cos-sum add-log-exp
6×pow1
5×exp-prod
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u
3×associate--l+
2×distribute-rgt-in frac-times sub-neg distribute-lft-in flip3-+ prod-exp associate-*r/ cbrt-unprod flip-+ fma-udef unswap-sqr rem-exp-log
1×cos-diff cbrt-undiv exp-diff diff-log div-exp pow-prod-down associate-*l/ *-commutative div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 101
Calls
4 calls:
Slowest
58.0ms
(cos (- (* (/ K 2) (+ m n)) M))
35.0ms
(* (/ K 2) (+ m n))
22.0ms
(exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n))))
0.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series515.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
216.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
147.0ms
(exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n))))
84.0ms
(cos (- (* (/ K 2) (+ m n)) M))
68.0ms
(* (/ K 2) (+ m n))

simplify10.3s

Counts
73 → 113
Calls
73 calls:
Slowest
800.0ms
(exp (fma (sqrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (sqrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n))))))))
461.0ms
(exp (- (fma (- (+ (* 1/2 m) (* 1/2 n)) M) (- (+ (* 1/2 m) (* 1/2 n)) M) l) (fabs (- m n))))
435.0ms
(exp (* (cbrt (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))) (cbrt (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n))))))
415.0ms
(exp (- (fma (- (+ (* 1/2 m) (* 1/2 n)) M) (- (+ (* 1/2 m) (* 1/2 n)) M) l) (fabs (- m n))))
409.0ms
(exp (fma (* (cbrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (cbrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))) (cbrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n))))))))

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.1b

localize51.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×exp-sum
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
5×exp-prod add-log-exp
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log fma-udef insert-posit16 log1p-expm1-u rem-exp-log
1×sub-neg exp-diff diff-log associate--l+ distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
Slowest
13.0ms
(exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n))))
1.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series316.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
182.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
134.0ms
(exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n))))

simplify7.0s

Counts
26 → 47
Calls
26 calls:
Slowest
497.0ms
(exp (- (fma (- (+ (* 1/2 m) (* 1/2 n)) M) (- (+ (* 1/2 m) (* 1/2 n)) M) l) (fabs (- m n))))
447.0ms
(exp (fma (sqrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (sqrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n))))))))
413.0ms
(exp (fma (* (cbrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (cbrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))) (cbrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n))))))))
400.0ms
(exp (* (cbrt (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))) (cbrt (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n))))))
400.0ms
(exp (- (fma (- (+ (* 1/2 m) (* 1/2 n)) M) (- (+ (* 1/2 m) (* 1/2 n)) M) l) (fabs (- m n))))

prune703.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

localize110.0ms

Local error

Found 4 expressions with local error:

36.4b
(cos (- (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* (/ (cbrt K) (sqrt 2)) (+ m n))) M))
0.6b
(cbrt K)
0.6b
(cbrt K)
0.6b
(cbrt K)

rewrite243.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod cos-sum
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×distribute-rgt-in expm1-log1p-u pow1 distribute-lft-in add-cbrt-cube associate--l+ add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 prod-diff
1×cos-diff sub-neg
Counts
4 → 62
Calls
4 calls:
Slowest
240.0ms
(cos (- (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* (/ (cbrt K) (sqrt 2)) (+ m n))) M))
1.0ms
(cbrt K)
1.0ms
(cbrt K)
1.0ms
(cbrt K)

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
429.0ms
(cos (- (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* (/ (cbrt K) (sqrt 2)) (+ m n))) M))
320.0ms
(cbrt K)
285.0ms
(cbrt K)
272.0ms
(cbrt K)

simplify4.7s

Counts
31 → 74
Calls
31 calls:
Slowest
450.0ms
(* (cos (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* (/ (cbrt K) (sqrt 2)) (+ m n)))) (cos M))
416.0ms
(* (cos (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* (/ (cbrt K) (sqrt 2)) (+ m n)))) (cos (- M)))
407.0ms
(* (cos (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* (/ (cbrt K) (sqrt 2)) (+ m n)))) (cos (- M)))
395.0ms
(* (cos (fma (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* (/ (cbrt K) (sqrt 2)) (+ m n)) (- (* M 1)))) (cos (fma (- M) 1 (* M 1))))
336.0ms
(* (cos (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* m (/ (cbrt K) (sqrt 2))))) (cos (- (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* n (/ (cbrt K) (sqrt 2)))) M)))

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize152.0ms

Local error

Found 4 expressions with local error:

29.2b
(cos (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* m (/ (cbrt K) (sqrt 2)))))
28.8b
(sin (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* m (/ (cbrt K) (sqrt 2)))))
26.0b
(cos (- (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* n (/ (cbrt K) (sqrt 2)))) M))
25.9b
(sin (- (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* n (/ (cbrt K) (sqrt 2)))) M))

rewrite493.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity prod-diff add-cube-cbrt
5×cos-sum sin-sum
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×sub-neg
1×cos-diff sin-diff
Counts
4 → 52
Calls
4 calls:
Slowest
202.0ms
(sin (- (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* n (/ (cbrt K) (sqrt 2)))) M))
174.0ms
(cos (- (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* n (/ (cbrt K) (sqrt 2)))) M))
58.0ms
(sin (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* m (/ (cbrt K) (sqrt 2)))))
57.0ms
(cos (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* m (/ (cbrt K) (sqrt 2)))))

series693.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
241.0ms
(sin (- (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* n (/ (cbrt K) (sqrt 2)))) M))
226.0ms
(cos (- (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* n (/ (cbrt K) (sqrt 2)))) M))
118.0ms
(cos (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* m (/ (cbrt K) (sqrt 2)))))
108.0ms
(sin (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* m (/ (cbrt K) (sqrt 2)))))

simplify5.8s

Counts
24 → 64
Calls
24 calls:
Slowest
713.0ms
(* (sin (fma (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* n (/ (cbrt K) (sqrt 2))) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))
405.0ms
(* (sin (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* n (/ (cbrt K) (sqrt 2))))) (cos (- M)))
396.0ms
(* (sin (fma (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* n (/ (cbrt K) (sqrt 2))) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
355.0ms
(* (sin (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* n (/ (cbrt K) (sqrt 2))))) (cos M))
343.0ms
(* (cos (* (* (cbrt K) (/ (cbrt K) (sqrt 2))) (* n (/ (cbrt K) (sqrt 2))))) (cos (- M)))

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.1b

regimes714.0ms

Accuracy

0% (0.2b remaining)

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

bsearch5.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.8s8094×body80valid
213.0ms166×body640valid
187.0ms110×body1280valid
129.0ms112×body320valid
36.0ms66×body160valid
1.0ms1×body2560valid