Details

Time bar (total: 17.4s)Debug log

sample117.0ms

Algorithm
intervals
Results
78.0ms262×body80valid
5.0ms3×body1280valid
3.0ms3×body320valid
3.0ms2×body640valid
2.0ms3×body160valid

simplify100.0ms

Calls
1 calls:
Slowest
100.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize49.0ms

Local error

Found 4 expressions with local error:

31.4b
(cos (- (/ (* K (+ m n)) 2) M))
0.0b
(pow (- (/ (+ m n) 2) M) 2)
0.0b
(- (/ (* K (+ m n)) 2) M)
0.0b
(* K (+ m n))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
6×add-cube-cbrt
6×*-un-lft-identity
6×add-sqr-sqrt
5×add-exp-log
5×pow1
4×add-log-exp
4×add-cbrt-cube
3×associate-*r*
3×unpow-prod-down
2×associate-*r/
2×sub-neg
2×cos-sum
1×unpow2
1×flip--
1×flip-+
1×*-commutative
1×pow-exp
1×flip3--
1×flip3-+
1×distribute-lft-in
1×pow-pow
1×pow-to-exp
1×cos-diff
1×distribute-rgt-in
Calls
4 calls:
Slowest
10.0ms
(cos (- (/ (* K (+ m n)) 2) M))
10.0ms
(pow (- (/ (+ m n) 2) M) 2)
6.0ms
(- (/ (* K (+ m n)) 2) M)
2.0ms
(* K (+ m n))

series237.0ms

Calls
4 calls:
Slowest
90.0ms
(cos (- (/ (* K (+ m n)) 2) M))
64.0ms
(pow (- (/ (+ m n) 2) M) 2)
55.0ms
(- (/ (* K (+ m n)) 2) M)
27.0ms
(* K (+ m n))

simplify886.0ms

Calls
27 calls:
Slowest
95.0ms
(- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M)
89.0ms
(- (pow M 2) (+ (* m M) (* M n)))
79.0ms
(- (pow M 2) (+ (* m M) (* M n)))
76.0ms
(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
66.0ms
(- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M)

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize3.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
3×unpow-prod-down
2×add-cube-cbrt
2×add-exp-log
2×*-un-lft-identity
2×pow1
2×add-sqr-sqrt
1×add-log-exp
1×unpow2
1×pow-exp
1×add-cbrt-cube
1×pow-pow
1×pow-to-exp
Calls
1 calls:
Slowest
5.0ms
(pow (- (/ (+ m n) 2) M) 2)

series52.0ms

Calls
1 calls:
Slowest
52.0ms
(pow (- (/ (+ m n) 2) M) 2)

simplify657.0ms

Calls
8 calls:
Slowest
434.0ms
(+ (* 1/2 (* m n)) (+ (* 1/4 (pow m 2)) (* 1/4 (pow n 2))))
99.0ms
(- (pow M 2) (+ (* m M) (* M n)))
87.0ms
(- (pow M 2) (+ (* m M) (* M n)))
15.0ms
(pow (* (cbrt (- (/ (+ m n) 2) M)) (cbrt (- (/ (+ m n) 2) M))) 2)
12.0ms
(pow (sqrt (- (/ (+ m n) 2) M)) 2)

prune257.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize29.0ms

Local error

Found 4 expressions with local error:

31.6b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2) M))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-cube-cbrt
7×*-un-lft-identity
7×add-sqr-sqrt
6×cbrt-div
4×add-log-exp
4×add-exp-log
4×add-cbrt-cube
4×pow1
3×flip-+
3×pow1/3
3×flip3-+
2×cos-sum
1×sub-neg
1×cos-diff
Calls
4 calls:
Slowest
15.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2) M))
1.0ms
(cbrt (+ m n))
1.0ms
(cbrt (+ m n))
1.0ms
(cbrt (+ m n))

series542.0ms

Calls
4 calls:
Slowest
156.0ms
(cbrt (+ m n))
155.0ms
(cbrt (+ m n))
130.0ms
(cbrt (+ m n))
101.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2) M))

simplify1.0s

Calls
30 calls:
Slowest
179.0ms
(- (+ (* 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))))
152.0ms
(- (+ (* 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))))
136.0ms
(- (+ (* 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))))
104.0ms
(* (cos (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2)) (cos (- M)))
97.0ms
(* (cos (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2)) (cos M))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize46.0ms

Local error

Found 4 expressions with local error:

28.2b
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1))) 2) M))
1.4b
(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
0.6b
(cbrt (+ m n))
0.6b
(cbrt (+ m n))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
16×cbrt-div
10×associate-*r/
10×associate-*l/
9×add-exp-log
9×pow1
8×flip-+
8×flip3-+
7×add-cbrt-cube
6×add-cube-cbrt
6×*-un-lft-identity
6×add-sqr-sqrt
6×cbrt-prod
4×add-log-exp
4×frac-times
3×cbrt-unprod
3×prod-exp
3×pow-prod-down
2×pow1/3
2×cos-sum
1×*-commutative
1×associate-*l*
1×associate-*r*
1×sub-neg
1×cos-diff
Calls
4 calls:
Slowest
43.0ms
(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
31.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1))) 2) M))
1.0ms
(cbrt (+ m n))
1.0ms
(cbrt (+ m n))

series754.0ms

Calls
4 calls:
Slowest
284.0ms
(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1))) 2) M))
185.0ms
(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
151.0ms
(cbrt (+ m n))
134.0ms
(cbrt (+ m n))

simplify4.5s

Calls
40 calls:
Slowest
504.0ms
(* (* (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* K (* (cbrt (+ m n)) (cbrt (+ m n))))) (* K (* (cbrt (+ m n)) (cbrt (+ m n))))) (* (- m) -1))
308.0ms
(* (* K (* (cbrt (+ (pow m 3) (pow n 3))) (cbrt (- (* m m) (* n n))))) (* (cbrt (- m)) (cbrt -1)))
297.0ms
(* (* K (* (cbrt (- (* m m) (* n n))) (cbrt (+ (pow m 3) (pow n 3))))) (* (cbrt (- m)) (cbrt -1)))
275.0ms
(* (* K (* (cbrt (+ m n)) (cbrt (- (* m m) (* n n))))) (* (cbrt (- m)) (cbrt -1)))
269.0ms
(* (* K (* (cbrt (- (* m m) (* n n))) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes440.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.7s8074×body80valid
193.0ms112×body1280valid
182.0ms155×body640valid
106.0ms111×body320valid
65.0ms60×body160valid
9.0ms4×body2560valid