Details

Time bar (total: 3.7m)

sample115.0ms

Algorithm
intervals
Results
77.0ms256×body80valid
5.0ms3×body1280valid
5.0ms4×body640valid
3.0ms3×body320valid

simplify380.0ms

Calls
1 calls:
Slowest
380.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.9b

localize84.0ms

Local error

Found 4 expressions with local error:

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

rewrite489.0ms

Algorithm
rewrite-expression-head
Rules
187×add-sqr-sqrt
158×*-un-lft-identity
153×prod-diff
136×add-cube-cbrt
105×associate-*l*
81×times-frac
78×cos-sum
32×associate-*r*
27×fma-neg
18×frac-times unswap-sqr
10×flip3-+ flip-+
9×associate-/r* add-cbrt-cube associate-*l/ associate--l+ add-exp-log associate-/l*
8×*-commutative div-inv distribute-lft-out add-log-exp
6×distribute-rgt-in pow1 +-commutative distribute-lft-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×clear-num sub-neg frac-2neg distribute-lft-out--
2×flip3-- diff-log prod-exp associate-*r/ cbrt-unprod flip--
1×cos-diff cbrt-undiv div-exp pow-prod-down fma-udef
Calls
4 calls:
Slowest
259.0ms
(cos (- (* (/ K 2) (+ m n)) M))
188.0ms
(- (* (/ K 2) (+ m n)) M)
20.0ms
(* (/ K 2) (+ m n))
10.0ms
(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))

series479.0ms

Calls
4 calls:
Slowest
258.0ms
(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))
100.0ms
(- (* (/ K 2) (+ m n)) M)
72.0ms
(cos (- (* (/ K 2) (+ m n)) M))
49.0ms
(* (/ K 2) (+ m n))

simplify54.7s

Calls
369 calls:
Slowest
707.0ms
(* (cos (fma (/ (* (cbrt K) (cbrt K)) 1) (* (/ (cbrt K) 2) (+ m n)) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))
607.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n)))))))
502.0ms
(fma (/ (* (cbrt K) (cbrt K)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)) (- (* M 1)))
501.0ms
(fma (- (fabs (- m n))) 1 (* (fabs (- m n)) 1))
494.0ms
(fma (/ (* (cbrt K) (cbrt K)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))

prune6.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize46.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log fma-udef insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log associate--l+ flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
5.0ms
(- (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)

series407.0ms

Calls
2 calls:
Slowest
208.0ms
(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))
199.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

simplify6.8s

Calls
31 calls:
Slowest
560.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n)))))))
512.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (sqrt (fabs (- m n))) (sqrt (fabs (- m n))))))
425.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (fabs (- m n)) 1)))
392.0ms
(/ (exp (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (exp (fabs (- m n))))
337.0ms
(fma (sqrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (sqrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (- (* (fabs (- m n)) 1)))

prune757.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize49.0ms

Local error

Found 4 expressions with local error:

34.9b
(cos (- (/ (+ m n) (/ 2 K)) M))
0.2b
(/ (+ m n) (/ 2 K))
0.0b
(- (/ (+ m n) (/ 2 K)) M)
0.0b
(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
716×times-frac
714×*-un-lft-identity
511×add-sqr-sqrt
500×add-cube-cbrt
399×prod-diff
197×cos-sum
105×distribute-lft-out
72×associate-/r/
68×fma-neg
41×div-inv
37×associate-/r*
28×associate-/l*
9×clear-num frac-2neg add-cbrt-cube add-exp-log
8×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u difference-of-squares
3×cbrt-undiv sub-neg div-exp
2×flip3-- diff-log flip-- distribute-lft-out-- associate-/l/
1×cos-diff flip3-+ associate--l+ flip-+ fma-udef
Calls
4 calls:
Slowest
127.0ms
(cos (- (/ (+ m n) (/ 2 K)) M))
114.0ms
(- (/ (+ m n) (/ 2 K)) M)
37.0ms
(/ (+ m n) (/ 2 K))
10.0ms
(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))

series435.0ms

Calls
4 calls:
Slowest
213.0ms
(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))
102.0ms
(cos (- (/ (+ m n) (/ 2 K)) M))
73.0ms
(- (/ (+ m n) (/ 2 K)) M)
47.0ms
(/ (+ m n) (/ 2 K))

simplify2.2m

Calls
829 calls:
Slowest
925.0ms
(fma (/ 1 (/ (sqrt 2) (sqrt K))) (/ (+ m n) (/ (sqrt 2) (sqrt K))) (- (* M 1)))
758.0ms
(* (cos (fma (/ (sqrt (+ m n)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt K) (cbrt K)))) (/ (sqrt (+ m n)) (/ (cbrt 2) (cbrt K))) (- (* M 1)))) (cos (fma (- M) 1 (* M 1))))
676.0ms
(fma (/ (* (cbrt (+ m n)) (cbrt (+ m n))) (/ 1 (sqrt K))) (/ (cbrt (+ m n)) (/ 2 (sqrt K))) (- (* M 1)))
669.0ms
(* (cos (fma (/ (* (cbrt (+ m n)) (cbrt (+ m n))) (/ 1 (sqrt K))) (/ (cbrt (+ m n)) (/ 2 (sqrt K))) (- (* M 1)))) (cos (fma (- M) 1 (* M 1))))
658.0ms
(* (cos (fma (/ (* (cbrt (+ m n)) (cbrt (+ m n))) (/ 1 (sqrt K))) (/ (cbrt (+ m n)) (/ 2 (sqrt K))) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))

prune13.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize102.0ms

Local error

Found 4 expressions with local error:

35.1b
(cos (- (/ (/ (+ m n) (* (cbrt (/ 2 K)) (cbrt (/ 2 K)))) (cbrt (/ 2 K))) M))
0.5b
(cbrt (/ 2 K))
0.5b
(cbrt (/ 2 K))
0.5b
(cbrt (/ 2 K))

rewrite4.4s

Algorithm
rewrite-expression-head
Rules
46320×times-frac
31325×*-un-lft-identity
29981×add-sqr-sqrt
26016×cbrt-prod
25373×add-cube-cbrt
16889×cos-sum
16887×prod-diff
8694×cbrt-div
4779×associate-/r/
3888×frac-times
3072×swap-sqr associate-*r* associate-*l*
2976×distribute-lft-out
2898×associate-/r* associate-/l*
1875×div-inv
1728×unswap-sqr
966×clear-num frac-2neg
432×associate-*l/ associate-*r/
192×*-commutative
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×cos-diff sub-neg
Calls
4 calls:
Slowest
1.6s
(cos (- (/ (/ (+ m n) (* (cbrt (/ 2 K)) (cbrt (/ 2 K)))) (cbrt (/ 2 K))) M))
22.0ms
(cbrt (/ 2 K))
2.0ms
(cbrt (/ 2 K))
2.0ms
(cbrt (/ 2 K))

series1.1s

Calls
4 calls:
Slowest
307.0ms
(cos (- (/ (/ (+ m n) (* (cbrt (/ 2 K)) (cbrt (/ 2 K)))) (cbrt (/ 2 K))) M))
298.0ms
(cbrt (/ 2 K))
262.0ms
(cbrt (/ 2 K))
246.0ms
(cbrt (/ 2 K))