Details

Time bar (total: 1.1m)

sample75.0ms

Algorithm
intervals
Results
52.0ms257×body80valid
4.0ms4×body1280valid
3.0ms4×body640valid
1.0ms1×body320valid
1.0ms2×body160valid

simplify256.0ms

Calls
1 calls:
Slowest
256.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize87.0ms

Local error

Found 3 expressions with local error:

32.9b
(cos (- (/ (* K (+ m n)) 2) M))
0.0b
(pow (- (/ (+ m n) 2) M) 2)
0.0b
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

rewrite5.2s

Algorithm
rewrite-expression-head
Rules
180×add-sqr-sqrt
151×prod-diff
145×*-un-lft-identity
136×associate-*r*
133×exp-sum
71×add-cube-cbrt
66×unpow-prod-down
55×distribute-lft-neg-in distribute-rgt-neg-in
48×difference-of-squares
37×distribute-lft-out--
23×cos-sum
20×times-frac
11×unpow2 sqr-pow
6×pow1
5×neg-mul-1 add-cbrt-cube add-exp-log
3×expm1-log1p-u pow-unpow associate-*l* insert-posit16 log1p-expm1-u div-inv add-log-exp
2×sub-neg
1×cos-diff pow-to-exp pow-pow exp-diff pow-prod-down pow-exp prod-exp associate-*r/ *-commutative cbrt-unprod associate--r- unswap-sqr
Calls
3 calls:
Slowest
5.1s
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
64.0ms
(pow (- (/ (+ m n) 2) M) 2)
52.0ms
(cos (- (/ (* K (+ m n)) 2) M))

series712.0ms

Calls
3 calls:
Slowest
474.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
126.0ms
(pow (- (/ (+ m n) 2) M) 2)
111.0ms
(cos (- (/ (* K (+ m n)) 2) M))

simplify34.6s

Calls
187 calls:
Slowest
780.0ms
(* (exp (- (+ (* m M) (+ (* M n) (fabs (- m n)))) (+ (* 1/4 (pow m 2)) (+ (pow M 2) (+ (* 1/2 (* m n)) (+ l (* 1/4 (pow n 2)))))))) (cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M)))
589.0ms
(exp (fma (- (- l (fabs (- m n)))) 1 (* (- l (fabs (- m n))) 1)))
481.0ms
(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)
406.0ms
(* (* (* (cos (- (/ (* K (+ m n)) 2) M)) (cos (- (/ (* K (+ m n)) 2) M))) (cos (- (/ (* K (+ m n)) 2) M))) (* (* (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))
341.0ms
(* (exp (- (+ (* m M) (+ (* M n) (fabs (- m n)))) (+ (* 1/4 (pow m 2)) (+ (pow M 2) (+ (* 1/2 (* m n)) (+ l (* 1/4 (pow n 2)))))))) (cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M)))

prune4.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize40.0ms

Local error

Found 1 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2) M) 2)

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×unpow-prod-down
5×*-un-lft-identity
3×pow-unpow add-cube-cbrt
2×pow1 add-exp-log difference-of-squares
1×expm1-log1p-u pow-to-exp pow-pow times-frac add-cbrt-cube pow-exp insert-posit16 log1p-expm1-u distribute-lft-out-- unpow2 add-log-exp sqr-pow
Calls
1 calls:
Slowest
73.0ms
(pow (- (/ (+ m n) 2) M) 2)

series110.0ms

Calls
1 calls:
Slowest
110.0ms
(pow (- (/ (+ m n) 2) M) 2)

simplify1.7s

Calls
13 calls:
Slowest
415.0ms
(pow (+ (/ (sqrt (+ m n)) (sqrt 2)) (sqrt M)) 2)
272.0ms
(pow (* (cbrt (- (/ (+ m n) 2) M)) (cbrt (- (/ (+ m n) 2) M))) 2)
258.0ms
(- (pow M 2) (+ (* m M) (* M n)))
213.0ms
(pow (+ (sqrt (/ (+ m n) 2)) (sqrt M)) 2)
202.0ms
(- (pow M 2) (+ (* m M) (* M n)))

prune490.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize103.0ms

Local error

Found 4 expressions with local error:

33.3b
(sin (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* M 1))))
33.1b
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* M 1))))
0.5b
(/ (+ m n) (sqrt 2))
0.5b
(/ (+ m n) (sqrt 2))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
48×times-frac
38×add-sqr-sqrt add-cube-cbrt
30×sqrt-prod
14×distribute-lft-out
12×associate-/r*
8×add-cbrt-cube add-exp-log associate-/l*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp associate-/l/
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ fma-udef div-inv
1×cos-sum sin-sum
Calls
4 calls:
Slowest
19.0ms
(/ (+ m n) (sqrt 2))
15.0ms
(/ (+ m n) (sqrt 2))
3.0ms
(sin (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* M 1))))
2.0ms
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* M 1))))

series858.0ms

Calls
4 calls:
Slowest
300.0ms
(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* M 1))))
277.0ms
(sin (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- (* M 1))))
151.0ms
(/ (+ m n) (sqrt 2))
129.0ms
(/ (+ m n) (sqrt 2))

simplify3.4s

Calls
134 calls:
Slowest
358.0ms
(/ (* (* (+ m n) (+ m n)) (+ m n)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
352.0ms
(/ (* (* (+ m n) (+ m n)) (+ m n)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
233.0ms
(- (+ (/ (* K n) (pow (sqrt 2) 2)) (/ (* m K) (pow (sqrt 2) 2))) M)
179.0ms
(* (cos (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))) (cos (- (* M 1))))
146.0ms
(* (sin (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))) (cos (- (* M 1))))

prune4.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize147.0ms

Local error

Found 4 expressions with local error:

33.3b
(sin (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
33.1b
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
1.0b
(cbrt 2)
1.0b
(cbrt 2)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×pow1/3 fma-udef
1×cos-sum sin-sum
Calls
4 calls:
Slowest
2.0ms
(sin (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
2.0ms
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
1.0ms
(cbrt 2)
1.0ms
(cbrt 2)

series556.0ms

Calls
4 calls:
Slowest
279.0ms
(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
277.0ms
(sin (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- (* M 1))))
0.0ms
(cbrt 2)
0.0ms
(cbrt 2)

simplify2.1s

Calls
16 calls:
Slowest
267.0ms
(* (sin (* (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)))) (cos (- (* M 1))))
261.0ms
(cos (fma (/ K (pow (cbrt 2) 2)) (/ (+ m n) (cbrt 2)) (- M)))
250.0ms
(sin (fma (/ K (pow (cbrt 2) 2)) (/ (+ m n) (cbrt 2)) (* -1 M)))
247.0ms
(* (cos (* (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)))) (cos (- (* M 1))))
246.0ms
(cos (fma (/ K (pow (cbrt 2) 2)) (/ (+ m n) (cbrt 2)) (* -1 M)))

prune2.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

regimes746.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.9s8098×body80valid
246.0ms159×body640valid
211.0ms119×body1280valid
81.0ms101×body320valid
30.0ms60×body160valid
11.0ms5×body2560valid