Details

Time bar (total: 52.1s)

sample58.0ms

Algorithm
intervals
Results
40.0ms258×body80valid
2.0ms3×body640valid
1.0ms3×body160valid
1.0ms1×body1280valid

simplify288.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
288.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize51.0ms

Local error

Found 4 expressions with local error:

35.0b
(cos (- (/ (* (+ m n) K) 2) M))
0.0b
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b
(* (+ m n) K)
0.0b
(- (/ (* (+ m n) K) 2) M)

rewrite227.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
28×*-un-lft-identity
13×pow1
10×associate-*l* add-cube-cbrt
9×associate-*r* difference-of-squares
8×add-cbrt-cube swap-sqr add-exp-log
7×flip3-- flip-- distribute-lft-out--
6×add-log-exp
4×frac-times sub-neg times-frac associate-*l/ insert-posit16
2×distribute-rgt-in cos-sum distribute-lft-in pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×pow2 cos-diff flip3-+ pow-plus diff-log pow-sqr pow-prod-up flip-+ distribute-lft-out
Counts
4 → 97
Calls
4 calls:
Slowest
167.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
22.0ms
(- (/ (* (+ m n) K) 2) M)
21.0ms
(cos (- (/ (* (+ m n) K) 2) M))
14.0ms
(* (+ m n) K)

series293.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(cos (- (/ (* (+ m n) K) 2) M))
84.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
63.0ms
(- (/ (* (+ m n) K) 2) M)
40.0ms
(* (+ m n) K)

simplify8.6s

Counts
82 → 109
Calls
82 calls:
Slowest
629.0ms
(* (* (* (+ m n) (+ m n)) (+ m n)) (* (* K K) K))
404.0ms
(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
378.0ms
(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))
359.0ms
(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))
350.0ms
(* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))))

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize35.0ms

Local error

Found 3 expressions with local error:

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

rewrite303.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
27×flip3-- flip--
23×*-un-lft-identity
16×frac-add
12×frac-times
10×pow1 add-log-exp
9×difference-of-squares
8×swap-sqr
7×add-cube-cbrt distribute-lft-out--
6×sub-neg associate-*r* associate-*l* associate-*l/ associate-*r/
5×add-cbrt-cube add-exp-log
4×distribute-rgt-in associate-+l+ distribute-lft-in times-frac
3×insert-posit16
2×associate-+r+ sum-log diff-log
1×pow2 +-commutative associate-+r- flip3-+ pow-plus pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ unswap-sqr
Counts
3 → 100
Calls
3 calls:
Slowest
187.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
104.0ms
(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
9.0ms
(- l (fabs (- m n)))

series349.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
221.0ms
(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
106.0ms
(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
22.0ms
(- l (fabs (- m n)))

simplify22.5s

Counts
106 → 109
Calls
106 calls:
Slowest
1.2s
(+ (* (* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (pow (/ (+ m n) 2) 3) (pow M 3))) (+ (* l l) (+ (* (fabs (- m n)) (fabs (- m n))) (* l (fabs (- m n)))))) (* (* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M)))) (- (pow l 3) (pow (fabs (- m n)) 3))))
889.0ms
(+ (* (* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M))) (+ (* l l) (+ (* (fabs (- m n)) (fabs (- m n))) (* l (fabs (- m n)))))) (* (* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M)) (- (pow l 3) (pow (fabs (- m n)) 3))))
710.0ms
(+ (* (* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M))) (+ l (fabs (- m n)))) (* (* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M)) (- (* l l) (* (fabs (- m n)) (fabs (- m n))))))
678.0ms
(+ (* (* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3))) (+ (* l l) (+ (* (fabs (- m n)) (fabs (- m n))) (* l (fabs (- m n)))))) (* (* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M)))) (- (pow l 3) (pow (fabs (- m n)) 3))))
633.0ms
(+ (* (* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (pow (/ (+ m n) 2) 3) (pow M 3))) (+ l (fabs (- m n)))) (* (* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M)))) (- (* l l) (* (fabs (- m n)) (fabs (- m n))))))

prune1.8s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize74.0ms

Local error

Found 4 expressions with local error:

35.2b
(cos (- (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2) M))
16.6b
(cbrt (* (+ m n) K))
16.6b
(cbrt (* (+ m n) K))
16.6b
(cbrt (* (+ m n) K))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-div associate-*l/
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
3×cbrt-prod flip3-+ pow1/3 flip-+
2×cos-sum
1×cos-diff sub-neg
Counts
4 → 47
Calls
4 calls:
Slowest
27.0ms
(cos (- (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2) M))
9.0ms
(cbrt (* (+ m n) K))
9.0ms
(cbrt (* (+ m n) K))
9.0ms
(cbrt (* (+ m n) K))

series517.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(cbrt (* (+ m n) K))
135.0ms
(cbrt (* (+ m n) K))
128.0ms
(cbrt (* (+ m n) K))
113.0ms
(cos (- (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2) M))

simplify4.9s

Counts
24 → 59
Calls
24 calls:
Slowest
391.0ms
(- (+ (* 1/3 (* m (exp (* 1/3 (- (log K) (* 2 (log n))))))) (exp (* 1/3 (+ (log K) (log n))))) (* 1/9 (* (exp (* 1/3 (- (log K) (* 5 (log n))))) (pow m 2))))
387.0ms
(- (+ (* 1/3 (* m (exp (* 1/3 (- (log K) (* 2 (log n))))))) (exp (* 1/3 (+ (log K) (log n))))) (* 1/9 (* (exp (* 1/3 (- (log K) (* 5 (log n))))) (pow m 2))))
381.0ms
(exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K)))))
379.0ms
(exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K)))))
350.0ms
(- (+ (* 1/3 (* m (exp (* 1/3 (- (log K) (* 2 (log n))))))) (exp (* 1/3 (+ (log K) (log n))))) (* 1/9 (* (exp (* 1/3 (- (log K) (* 5 (log n))))) (pow m 2))))

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize127.0ms

Local error

Found 4 expressions with local error:

39.1b
(cos (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2))
38.8b
(sin (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2))
16.6b
(cbrt (* (+ m n) K))
16.6b
(cbrt (* (+ m n) K))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 cbrt-div *-un-lft-identity add-cbrt-cube associate-*l/ add-exp-log add-cube-cbrt insert-posit16 add-log-exp
2×cbrt-prod flip3-+ pow1/3 flip-+
Counts
4 → 40
Calls
4 calls:
Slowest
10.0ms
(cbrt (* (+ m n) K))
6.0ms
(cbrt (* (+ m n) K))
4.0ms
(cos (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2))
3.0ms
(sin (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
130.0ms
(cbrt (* (+ m n) K))
128.0ms
(cbrt (* (+ m n) K))
53.0ms
(cos (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2))
30.0ms
(sin (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2))

simplify2.9s

Counts
18 → 52
Calls
18 calls:
Slowest
356.0ms
(- (+ (* 1/3 (* m (exp (* 1/3 (- (log K) (* 2 (log n))))))) (exp (* 1/3 (+ (log K) (log n))))) (* 1/9 (* (exp (* 1/3 (- (log K) (* 5 (log n))))) (pow m 2))))
355.0ms
(- (+ (* 1/3 (* m (exp (* 1/3 (- (log K) (* 2 (log n))))))) (exp (* 1/3 (+ (log K) (log n))))) (* 1/9 (* (exp (* 1/3 (- (log K) (* 5 (log n))))) (pow m 2))))
303.0ms
(exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K)))))
298.0ms
(exp (* -1/3 (+ (log (/ 1 m)) (log (/ 1 K)))))
289.0ms
(exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K)))))

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes480.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
2.8s8126×body80valid
151.0ms111×body1280valid
142.0ms139×body640valid
111.0ms111×body320valid
25.0ms54×body160valid
7.0ms3×body2560valid