Details

sample96.0ms

Algorithm

intervals

Results

61.0ms	267×	body	80	valid
5.0ms	7×	body	640	valid
5.0ms	5×	body	1280	valid
2.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

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))))))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize82.0ms

Local error

Found 4 expressions with local error:

32.4b	(cos (- (/ (* K (+ m n)) 2) M))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
0.0b	(* K (+ m n))
0.0b	(- (/ (* K (+ m n)) 2) M)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `fma-neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `associate-r`
2×	`cos-sum` `sub-neg` `associate-*r/`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `flip3--` `pow-exp` `*-commutative` `flip-+` `div-inv` `flip--` `unpow2`

Calls

4 calls:

Slowest

8.0ms	(pow (- (/ (+ m n) 2) M) 2)
8.0ms	(cos (- (/ (* K (+ m n)) 2) M))
5.0ms	(- (/ (* K (+ m n)) 2) M)
1.0ms	(* K (+ m n))

series177.0ms

Calls

4 calls:

Slowest

54.0ms	(pow (- (/ (+ m n) 2) M) 2)
54.0ms	(cos (- (/ (* K (+ m n)) 2) M))
53.0ms	(- (/ (* K (+ m n)) 2) M)
16.0ms	(* K (+ m n))

simplify2.2s

Calls

30 calls:

Slowest

262.0ms	(- (pow M 2) (+ (* m M) (* M n)))
240.0ms	(- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M)
225.0ms	(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
201.0ms	(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
174.0ms	(+ (* 1/2 (* m n)) (+ (* 1/4 (pow m 2)) (* 1/4 (pow n 2))))

prune1.6s

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)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

3×	`unpow-prod-down`
2×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
1×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `add-cbrt-cube` `pow-exp` `insert-posit16` `log1p-expm1-u` `unpow2` `add-log-exp`

Calls

1 calls:

Slowest

7.0ms

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

series56.0ms

Calls

1 calls:

Slowest

56.0ms

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

simplify725.0ms

Calls

8 calls:

Slowest

256.0ms	(- (pow M 2) (+ (* m M) (* M n)))
195.0ms	(- (pow M 2) (+ (* m M) (* M n)))
140.0ms	(+ (* 1/2 (* m n)) (+ (* 1/4 (pow m 2)) (* 1/4 (pow n 2))))
58.0ms	(pow (* (cbrt (- (/ (+ m n) 2) M)) (cbrt (- (/ (+ m n) 2) M))) 2)
32.0ms	(pow (sqrt (- (/ (+ m n) 2) M)) 2)

prune293.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize36.0ms

Local error

Found 4 expressions with local error:

32.8b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))
15.4b	(cbrt (* K (+ m n)))
15.4b	(cbrt (* K (+ m n)))
15.4b	(cbrt (* K (+ m n)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*r/`
4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Calls

4 calls:

Slowest

18.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))
1.0ms	(cbrt (* K (+ m n)))
1.0ms	(cbrt (* K (+ m n)))
1.0ms	(cbrt (* K (+ m n)))

series434.0ms

Calls

4 calls:

Slowest

140.0ms	(cbrt (* K (+ m n)))
109.0ms	(cbrt (* K (+ m n)))
106.0ms	(cbrt (* K (+ m n)))
79.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))

simplify3.1s

Calls

24 calls:

Slowest

251.0ms	(cbrt (* K (- (* m m) (* n n))))
251.0ms	(exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K)))))
241.0ms	(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
241.0ms	(exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K)))))
236.0ms	(exp (* -1/3 (+ (log (/ 1 m)) (log (/ 1 K)))))

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 4 expressions with local error:

32.8b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))
15.4b	(cbrt (* K (+ m n)))
15.4b	(cbrt (* K (+ m n)))
15.4b	(cbrt (* K (+ m n)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*r/`
4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Calls

4 calls:

Slowest

20.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))
2.0ms	(cbrt (* K (+ m n)))
1.0ms	(cbrt (* K (+ m n)))
1.0ms	(cbrt (* K (+ m n)))

series465.0ms

Calls

4 calls:

Slowest

143.0ms	(cbrt (* K (+ m n)))
130.0ms	(cbrt (* K (+ m n)))
129.0ms	(cbrt (* K (+ m n)))
62.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))

simplify3.2s

Calls

24 calls:

Slowest

271.0ms	(cbrt (* K (- (* m m) (* n n))))
255.0ms	(exp (* -1/3 (+ (log (/ 1 m)) (log (/ 1 K)))))
239.0ms	(cbrt (* K (- (* m m) (* n n))))
236.0ms	(exp (* -1/3 (+ (log (/ 1 m)) (log (/ 1 K)))))
235.0ms	(exp (* -1/3 (+ (log (/ -1 m)) (log (/ -1 K)))))

prune1.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

regimes459.0ms

Accuracy

0% (0.2b remaining)

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

bsearch5.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.7s	8140×	body	80	valid
223.0ms	162×	body	640	valid
145.0ms	116×	body	1280	valid
68.0ms	96×	body	320	valid
26.0ms	57×	body	160	valid
17.0ms	7×	body	2560	valid