Details

sample63.0ms

Algorithm

intervals

Results

43.0ms	265×	body	80	valid
3.0ms	4×	body	640	valid
2.0ms	5×	body	320	valid
0.0ms	1×	body	160	valid

simplify296.0ms

Calls

1 calls:

Slowest

296.0ms

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

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize83.0ms

Local error

Found 4 expressions with local error:

37.0b	(cos (- (/ K (/ 2 (+ m n))) M))
0.2b	(/ K (/ 2 (+ m n)))
0.0b	(- (/ K (/ 2 (+ m n))) M)
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1`
7×	`add-sqr-sqrt` `*-un-lft-identity` `flip3--` `add-cube-cbrt` `flip--`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`frac-times` `sub-neg` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/r/`
2×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `associate-l/` `associate-r/` `div-inv`
1×	`pow2` `cos-diff` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `pow-prod-down` `prod-exp` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+`

Calls

4 calls:

Slowest

19.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
6.0ms	(cos (- (/ K (/ 2 (+ m n))) M))
3.0ms	(- (/ K (/ 2 (+ m n))) M)
1.0ms	(/ K (/ 2 (+ m n)))

series169.0ms

Calls

4 calls:

Slowest

61.0ms	(cos (- (/ K (/ 2 (+ m n))) M))
43.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
33.0ms	(- (/ K (/ 2 (+ m n))) M)
32.0ms	(/ K (/ 2 (+ m n)))

simplify6.1s

Calls

49 calls:

Slowest

580.0ms	(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))
465.0ms	(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
391.0ms	(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
363.0ms	(* (+ (/ (+ m n) 2) M) (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))))
341.0ms	(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `flip3--` `flip--`
6×	`add-sqr-sqrt` `sub-neg` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `associate--l+` `associate-r/`
1×	`associate--l-` `pow2` `pow-plus` `pow-prod-down` `prod-exp` `*-commutative` `pow-prod-up` `cbrt-unprod`

Calls

4 calls:

Slowest

32.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
21.0ms	(- (- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) l)
10.0ms	(- (/ (+ m n) 2) M)
7.0ms	(- (/ (+ m n) 2) M)

series241.0ms

Calls

4 calls:

Slowest

129.0ms	(- (- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) l)
65.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
25.0ms	(- (/ (+ m n) 2) M)
21.0ms	(- (/ (+ m n) 2) M)

simplify5.9s

Calls

42 calls:

Slowest

670.0ms	(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (/ (+ m n) 2) M))
540.0ms	(* (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)) (- (pow (/ (+ m n) 2) 3) (pow M 3)))
502.0ms	(* (- (pow (/ (+ m n) 2) 3) (pow M 3)) (- (* (/ (+ m n) 2) (/ (+ m n) 2)) (* M M)))
378.0ms	(* (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)) (* (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- (/ (+ m n) 2) M)))
356.0ms	(* (+ (* (/ (+ m n) 2) (/ (+ m n) 2)) (+ (* M M) (* (/ (+ m n) 2) M))) (+ (/ (+ m n) 2) M))

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize18.0ms

Local error

Found 4 expressions with local error:

44.5b	(cos (* (* (cbrt (- (/ K (/ 2 (+ m n))) M)) (cbrt (- (/ K (/ 2 (+ m n))) M))) (cbrt (- (/ K (/ 2 (+ m n))) M))))
13.7b	(cbrt (- (/ K (/ 2 (+ m n))) M))
13.7b	(cbrt (- (/ K (/ 2 (+ m n))) M))
13.7b	(cbrt (- (/ K (/ 2 (+ m n))) M))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`

Calls

4 calls:

Slowest

53.0ms	(cos (* (* (cbrt (- (/ K (/ 2 (+ m n))) M)) (cbrt (- (/ K (/ 2 (+ m n))) M))) (cbrt (- (/ K (/ 2 (+ m n))) M))))
4.0ms	(cbrt (- (/ K (/ 2 (+ m n))) M))
4.0ms	(cbrt (- (/ K (/ 2 (+ m n))) M))
4.0ms	(cbrt (- (/ K (/ 2 (+ m n))) M))

series738.0ms

Calls

4 calls:

Slowest

220.0ms	(cbrt (- (/ K (/ 2 (+ m n))) M))
217.0ms	(cbrt (- (/ K (/ 2 (+ m n))) M))
213.0ms	(cbrt (- (/ K (/ 2 (+ m n))) M))
88.0ms	(cos (* (* (cbrt (- (/ K (/ 2 (+ m n))) M)) (cbrt (- (/ K (/ 2 (+ m n))) M))) (cbrt (- (/ K (/ 2 (+ m n))) M))))

simplify4.8s

Calls

27 calls:

Slowest

428.0ms	(cbrt (- (pow (/ K (/ 2 (+ m n))) 3) (pow M 3)))
363.0ms	(- (exp (* 1/3 (+ (log M) (log -1)))) (+ (* 1/6 (* m (* K (exp (* 1/3 (- (log -1) (* 2 (log M)))))))) (* 1/6 (* K (* n (exp (* 1/3 (- (log -1) (* 2 (log M))))))))))
348.0ms	(cbrt (- (pow (/ K (/ 2 (+ m n))) 3) (pow M 3)))
328.0ms	(cbrt (- (pow (/ K (/ 2 (+ m n))) 3) (pow M 3)))
303.0ms	(exp (* 1/3 (- (log 1/2) (+ (log (/ 1 m)) (log (/ 1 K))))))

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize41.0ms

Local error

Found 4 expressions with local error:

43.0b	(cos (* (* (cbrt (- (/ K (/ 2 (+ m n))) M)) (cbrt (* m (/ K 2)))) (cbrt (- (/ K (/ 2 (+ m n))) M))))
13.7b	(cbrt (- (/ K (/ 2 (+ m n))) M))
13.7b	(cbrt (- (/ K (/ 2 (+ m n))) M))
12.6b	(cbrt (* m (/ K 2)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

7×	`cbrt-prod`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`cbrt-div`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3`
2×	`flip3--` `flip--`
1×	`associate-*r/`

Calls

4 calls:

Slowest

54.0ms	(cos (* (* (cbrt (- (/ K (/ 2 (+ m n))) M)) (cbrt (* m (/ K 2)))) (cbrt (- (/ K (/ 2 (+ m n))) M))))
2.0ms	(cbrt (- (/ K (/ 2 (+ m n))) M))
2.0ms	(cbrt (- (/ K (/ 2 (+ m n))) M))
1.0ms	(cbrt (* m (/ K 2)))

series2.0s

Calls

4 calls:

Slowest

1.4s	(cos (* (* (cbrt (- (/ K (/ 2 (+ m n))) M)) (cbrt (* m (/ K 2)))) (cbrt (- (/ K (/ 2 (+ m n))) M))))
276.0ms	(cbrt (- (/ K (/ 2 (+ m n))) M))
208.0ms	(cbrt (- (/ K (/ 2 (+ m n))) M))
118.0ms	(cbrt (* m (/ K 2)))

simplify4.1s

Calls

24 calls:

Slowest

345.0ms	(cbrt (- (pow (/ K (/ 2 (+ m n))) 3) (pow M 3)))
329.0ms	(- (exp (* 1/3 (+ (log M) (log -1)))) (+ (* 1/6 (* m (* K (exp (* 1/3 (- (log -1) (* 2 (log M)))))))) (* 1/6 (* K (* n (exp (* 1/3 (- (log -1) (* 2 (log M))))))))))
328.0ms	(- (exp (* 1/3 (+ (log M) (log -1)))) (+ (* 1/6 (* m (* K (exp (* 1/3 (- (log -1) (* 2 (log M)))))))) (* 1/6 (* K (* n (exp (* 1/3 (- (log -1) (* 2 (log M))))))))))
320.0ms	(cbrt (- (pow (/ K (/ 2 (+ m n))) 3) (pow M 3)))
260.0ms	(exp (* 1/3 (- (log 1/2) (+ (log (/ 1 m)) (log (/ 1 K))))))

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes393.0ms

Accuracy

0% (0.2b remaining)

Error of 1.5b against oracle of 1.3b and baseline of 1.5b

bsearch5.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.7s	8059×	body	80	valid
221.0ms	123×	body	1280	valid
173.0ms	175×	body	640	valid
85.0ms	118×	body	320	valid
25.0ms	54×	body	160	valid
8.0ms	5×	body	2560	valid