Details

Time bar (total: 8.9m)

sample89.0ms

Algorithm
intervals
Results
57.0ms260×body80valid
6.0ms5×body1280valid
3.0ms4×body640valid
1.0ms2×body320valid
1.0ms2×body160valid

simplify314.0ms

Calls
1 calls:
Slowest
314.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite500.0ms

Algorithm
rewrite-expression-head
Rules
178×add-sqr-sqrt
149×*-un-lft-identity
144×prod-diff
129×add-cube-cbrt
105×associate-*l*
81×times-frac
78×cos-sum
32×associate-*r*
24×fma-neg
18×frac-times unswap-sqr
10×flip3-+ flip-+
9×associate-/r* add-cbrt-cube associate-*l/ add-exp-log associate-/l*
8×associate--l+ *-commutative div-inv distribute-lft-out
6×distribute-rgt-in pow1 +-commutative distribute-lft-in add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×clear-num frac-2neg difference-of-squares
2×sub-neg prod-exp associate-*r/ cbrt-unprod distribute-lft-out--
1×cos-diff cbrt-undiv flip3-- diff-log div-exp pow-prod-down fma-udef flip--
Calls
4 calls:
Slowest
283.0ms
(cos (- (* (/ K 2) (+ m n)) M))
181.0ms
(- (* (/ K 2) (+ m n)) M)
28.0ms
(* (/ K 2) (+ m n))
0.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series395.0ms

Calls
4 calls:
Slowest
203.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
70.0ms
(- (* (/ K 2) (+ m n)) M)
63.0ms
(cos (- (* (/ K 2) (+ m n)) M))
59.0ms
(* (/ K 2) (+ m n))

simplify47.5s

Calls
344 calls:
Slowest
670.0ms
(fma (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ K (cbrt 2)) (+ m n)) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))
529.0ms
(* (cos (fma (/ (* (cbrt K) (cbrt K)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)) (- (* M 1)))) (cos (fma (- M) 1 (* M 1))))
529.0ms
(fma (/ (* (cbrt K) (cbrt K)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)) (- (* (sqrt M) (sqrt M))))
505.0ms
(* (cos (fma (/ (* (cbrt K) (cbrt K)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))
497.0ms
(* (cos (fma (/ (* (cbrt K) (cbrt K)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt K) (cbrt 2)) (+ m n)) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))

prune6.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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
11.0ms
(- (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)

series452.0ms

Calls
2 calls:
Slowest
227.0ms
(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
225.0ms
(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))

simplify6.8s

Calls
31 calls:
Slowest
510.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n)))))))
490.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (sqrt (fabs (- m n))) (sqrt (fabs (- m n))))))
459.0ms
(/ (exp (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (exp (fabs (- m n))))
435.0ms
(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (fabs (- m n)) 1)))
304.0ms
(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)))))))

prune834.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize33.0ms

Local error

Found 4 expressions with local error:

33.4b
(cos (- (* (* (/ K 2) (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) M))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))

rewrite3.9s

Algorithm
rewrite-expression-head
Rules
806×add-sqr-sqrt
360×unswap-sqr
356×cos-sum
354×prod-diff
264×associate-*l*
261×cbrt-prod
239×*-un-lft-identity
185×add-cube-cbrt
138×associate-*r*
108×times-frac
63×swap-sqr
27×*-commutative
24×distribute-lft-out
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ div-inv
1×cos-diff sub-neg
Calls
4 calls:
Slowest
3.8s
(cos (- (* (* (/ K 2) (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) M))
6.0ms
(cbrt (+ m n))
5.0ms
(cbrt (+ m n))
5.0ms
(cbrt (+ m n))

series732.0ms

Calls
4 calls:
Slowest
218.0ms
(cbrt (+ m n))
185.0ms
(cbrt (+ m n))
171.0ms
(cbrt (+ m n))
158.0ms
(cos (- (* (* (/ K 2) (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) M))

simplify2.3m

Calls
387 calls:
Slowest
1.2s
(* (cos (fma (* (* (/ (sqrt K) (sqrt 2)) (* (cbrt (sqrt (+ m n))) (cbrt (sqrt (+ m n))))) (sqrt (cbrt (+ m n)))) (* (* (/ (sqrt K) (sqrt 2)) (* (cbrt (sqrt (+ m n))) (cbrt (sqrt (+ m n))))) (sqrt (cbrt (+ m n)))) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
892.0ms
(* (cos (fma (* (* (/ (sqrt K) (sqrt 2)) (* (sqrt (cbrt (+ m n))) (cbrt (sqrt (+ m n))))) (cbrt (sqrt (+ m n)))) (* (* (/ (sqrt K) (sqrt 2)) (* (sqrt (cbrt (+ m n))) (cbrt (sqrt (+ m n))))) (cbrt (sqrt (+ m n)))) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
778.0ms
(* (cos (fma (* (* (/ (sqrt K) (sqrt 2)) (* (cbrt (sqrt (+ m n))) (cbrt (sqrt (+ m n))))) (sqrt (cbrt (+ m n)))) (* (* (/ (sqrt K) (sqrt 2)) (* (cbrt (sqrt (+ m n))) (cbrt (sqrt (+ m n))))) (sqrt (cbrt (+ m n)))) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))
775.0ms
(* (cos (fma (* (/ (sqrt K) (sqrt 2)) (* (sqrt (cbrt (+ m n))) (cbrt (sqrt (+ m n))))) (* (* (/ (sqrt K) (sqrt 2)) (* (sqrt (cbrt (+ m n))) (cbrt (sqrt (+ m n))))) (cbrt (+ m n))) (- (* M 1)))) (cos (fma (- M) 1 (* M 1))))
771.0ms
(* (cos (fma (* (* (/ (sqrt K) (sqrt 2)) (* (cbrt (sqrt (+ m n))) (sqrt (cbrt (+ m n))))) (cbrt (sqrt (+ m n)))) (* (* (/ (sqrt K) (sqrt 2)) (* (cbrt (sqrt (+ m n))) (sqrt (cbrt (+ m n))))) (cbrt (sqrt (+ m n)))) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))

prune13.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

localize22.0ms

Local error

Found 4 expressions with local error:

33.2b
(cos (- (/ (* (/ K (sqrt 2)) (+ m n)) (sqrt 2)) M))
0.5b
(/ K (sqrt 2))
0.4b
(/ (* (/ K (sqrt 2)) (+ m n)) (sqrt 2))
0.2b
(* (/ K (sqrt 2)) (+ m n))

rewrite559.0ms

Algorithm
rewrite-expression-head
Rules
1354×times-frac
1119×add-sqr-sqrt
963×*-un-lft-identity
911×add-cube-cbrt
701×sqrt-prod
626×cos-sum
624×prod-diff
572×associate-*l*
104×associate-*r*
78×unswap-sqr
55×associate-/l*
48×frac-times associate-/r*
38×associate-/l/
31×div-inv
26×flip3-+ *-commutative flip-+ distribute-lft-out
24×associate-*l/
20×add-cbrt-cube add-exp-log
8×clear-num frac-2neg
6×pow1 cbrt-undiv div-exp
4×expm1-log1p-u prod-exp associate-*r/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×distribute-rgt-in +-commutative distribute-lft-in
1×cos-diff sub-neg pow-prod-down
Calls
4 calls:
Slowest
397.0ms
(cos (- (/ (* (/ K (sqrt 2)) (+ m n)) (sqrt 2)) M))
65.0ms
(/ (* (/ K (sqrt 2)) (+ m n)) (sqrt 2))
33.0ms
(* (/ K (sqrt 2)) (+ m n))
9.0ms
(/ K (sqrt 2))

series943.0ms

Calls
4 calls:
Slowest
408.0ms
(cos (- (/ (* (/ K (sqrt 2)) (+ m n)) (sqrt 2)) M))
241.0ms
(/ (* (/ K (sqrt 2)) (+ m n)) (sqrt 2))
191.0ms
(* (/ K (sqrt 2)) (+ m n))
104.0ms
(/ K (sqrt 2))

simplify4.7m

Calls
1275 calls:
Slowest
963.0ms
(* (cos (fma (/ (/ (* (cbrt K) (cbrt K)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt 1)) (/ (* (/ (cbrt K) (cbrt (sqrt 2))) (+ m n)) (sqrt 2)) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
933.0ms
(* (cos (fma (/ (/ (* (cbrt K) (cbrt K)) (sqrt (sqrt 2))) (sqrt (* (cbrt 2) (cbrt 2)))) (/ (* (/ (cbrt K) (sqrt (sqrt 2))) (+ m n)) (sqrt (cbrt 2))) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))
858.0ms
(* (cos (fma (/ (/ (* (cbrt K) (cbrt K)) (sqrt (* (cbrt 2) (cbrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (* (/ (cbrt K) (sqrt (cbrt 2))) (+ m n)) (cbrt (sqrt 2))) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
832.0ms
(* (cos (fma (/ (/ (* (cbrt K) (cbrt K)) (sqrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (* (/ (cbrt K) (sqrt (sqrt 2))) (+ m n)) (cbrt (sqrt 2))) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))
812.0ms
(* (cos (fma (/ (/ (* (cbrt K) (cbrt K)) (sqrt (* (cbrt 2) (cbrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (* (/ (cbrt K) (sqrt (cbrt 2))) (+ m n)) (cbrt (sqrt 2))) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))

prune30.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

regimes538.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch4.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.0s8068×body80valid
241.0ms114×body1280valid
161.0ms159×body640valid
91.0ms111×body320valid
33.0ms64×body160valid
6.0ms3×body2560valid