Details

sample130.0ms

Algorithm

intervals

Results

93.0ms	258×	body	80	valid
6.0ms	4×	body	1280	valid
4.0ms	3×	body	640	valid
3.0ms	4×	body	320	valid
1.0ms	2×	body	160	valid

simplify312.0ms

Calls

1 calls:

Slowest

312.0ms

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

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize51.0ms

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

rewrite38.0ms

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

13.0ms	(pow (- (/ (+ m n) 2) M) 2)
12.0ms	(cos (- (/ (* K (+ m n)) 2) M))
10.0ms	(- (/ (* K (+ m n)) 2) M)
2.0ms	(* K (+ m n))

series333.0ms

Calls

4 calls:

Slowest

110.0ms	(pow (- (/ (+ m n) 2) M) 2)
95.0ms	(cos (- (/ (* K (+ m n)) 2) M))
81.0ms	(- (/ (* K (+ m n)) 2) M)
47.0ms	(* K (+ m n))

simplify2.2s

Calls

30 calls:

Slowest

229.0ms	(- (pow M 2) (+ (* m M) (* M n)))
221.0ms	(- (pow M 2) (+ (* m M) (* M n)))
200.0ms	(- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M)
194.0ms	(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))
182.0ms	(- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M)

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

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)

series93.0ms

Calls

1 calls:

Slowest

93.0ms

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

simplify711.0ms

Calls

8 calls:

Slowest

242.0ms	(- (pow M 2) (+ (* m M) (* M n)))
215.0ms	(- (pow M 2) (+ (* m M) (* M n)))
142.0ms	(+ (* 1/2 (* m n)) (+ (* 1/4 (pow m 2)) (* 1/4 (pow n 2))))
51.0ms	(pow (* (cbrt (- (/ (+ m n) 2) M)) (cbrt (- (/ (+ m n) 2) M))) 2)
21.0ms	(- (/ (+ m n) 2) M)

prune323.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize43.0ms

Local error

Found 4 expressions with local error:

31.6b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2) M))
0.5b	(* (cbrt (+ m n)) (cbrt (+ m n)))
0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-div`
12×	`cbrt-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
8×	`flip3-+` `flip-+`
6×	`pow1/3` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cos-sum` `pow-prod-down` `associate-l/` `associate-r/` `pow-prod-up`
1×	`pow2` `cos-diff` `sub-neg` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

21.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2) M))
13.0ms	(* (cbrt (+ m n)) (cbrt (+ m n)))
1.0ms	(cbrt (+ m n))
1.0ms	(cbrt (+ m n))

series815.0ms

Calls

4 calls:

Slowest

222.0ms	(* (cbrt (+ m n)) (cbrt (+ m n)))
219.0ms	(cbrt (+ m n))
212.0ms	(cbrt (+ m n))
162.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2) M))

simplify3.6s

Calls

57 calls:

Slowest

405.0ms	(- (+ (* 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))))
397.0ms	(- (+ (* 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))))
345.0ms	(- (+ (* 2/3 (* m (pow (/ 1 n) 1/3))) (pow n 2/3)) (* 1/9 (* (pow m 2) (pow (/ 1 (pow n 4)) 1/3))))
182.0ms	(* (cbrt (+ (pow m 3) (pow n 3))) (cbrt (- (* m m) (* n n))))
174.0ms	(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))

prune2.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize46.0ms

Local error

Found 4 expressions with local error:

31.5b	(cos (- (/ (* (* K (* (* (cbrt (+ m n)) (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n))))) (cbrt (cbrt (+ m n))))) (cbrt (+ m n))) 2) M))
0.6b	(cbrt (cbrt (+ m n)))
0.6b	(cbrt (cbrt (+ m n)))
0.6b	(cbrt (cbrt (+ m n)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
12×	`cbrt-div`
10×	`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`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Calls

4 calls:

Slowest

10.0ms	(cos (- (/ (* (* K (* (* (cbrt (+ m n)) (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n))))) (cbrt (cbrt (+ m n))))) (cbrt (+ m n))) 2) M))
1.0ms	(cbrt (cbrt (+ m n)))
1.0ms	(cbrt (cbrt (+ m n)))
1.0ms	(cbrt (cbrt (+ m n)))

series1.0s

Calls

4 calls:

Slowest

298.0ms	(cbrt (cbrt (+ m n)))
295.0ms	(cbrt (cbrt (+ m n)))
289.0ms	(cbrt (cbrt (+ m n)))
124.0ms	(cos (- (/ (* (* K (* (* (cbrt (+ m n)) (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n))))) (cbrt (cbrt (+ m n))))) (cbrt (+ m n))) 2) M))

simplify3.2s

Calls

39 calls:

Slowest

478.0ms	(- (+ (* 1/9 (* m (pow (/ 1 (pow n 8)) 1/9))) (pow n 1/9)) (* 4/81 (* (pow m 2) (pow (/ 1 (pow n 17)) 1/9))))
390.0ms	(- (+ (* 1/9 (* m (pow (/ 1 (pow n 8)) 1/9))) (pow n 1/9)) (* 4/81 (* (pow m 2) (pow (/ 1 (pow n 17)) 1/9))))
360.0ms	(- (+ (* 1/9 (* m (pow (/ 1 (pow n 8)) 1/9))) (pow n 1/9)) (* 4/81 (* (pow m 2) (pow (/ 1 (pow n 17)) 1/9))))
276.0ms	(* (cos (/ (* (* K (* (* (cbrt (+ m n)) (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n))))) (cbrt (cbrt (+ m n))))) (cbrt (+ m n))) 2)) (cos M))
258.0ms	(cos (- (+ (* 1/2 (* m K)) (* 1/2 (* K n))) M))

prune2.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

regimes380.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch2.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.9s	8083×	body	80	valid
175.0ms	166×	body	640	valid
150.0ms	103×	body	1280	valid
118.0ms	122×	body	320	valid
59.0ms	38×	body	160	valid
4.0ms	2×	body	2560	valid