Details

sample60.0ms

Algorithm

intervals

Results

29.0ms	260×	body	80	valid
3.0ms	6×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	2×	body	320	valid

simplify775.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* K (+ m n)) 2.0)
0.0b	(/ (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/r*`
6×	`unpow-prod-down`
5×	`pow1`
4×	`cos-sum` `exp-sum` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`sub-neg` `frac-2neg` `div-sub` `associate-*r/` `clear-num` `div-inv` `associate-/l/` `difference-of-squares`
1×	`cos-diff` `pow-to-exp` `associate-+r-` `pow-pow` `flip3-+` `exp-diff` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `distribute-lft-out--` `sqr-pow`

Counts

4 → 87

Calls

4 calls:

28.0ms	(/ (* K (+ m n)) 2.0)
1.9s	(/ (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
76.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
39.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (* K (+ m n)) 2.0)
567.0ms	(/ (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
368.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
82.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify859.0ms

Counts: 99 → 99

prune643.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(- l (fabs (- m n)))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite659.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`add-log-exp`
6×	`unpow-prod-down`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log`
3×	`pow-unpow` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `associate-+r+` `diff-log` `sum-log` `distribute-lft-out`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3--` `pow-pow` `flip3-+` `times-frac` `pow-exp` `flip--` `flip-+` `sqr-pow`

Counts

3 → 51

Calls

3 calls:

563.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
11.0ms	(- l (fabs (- m n)))
83.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series725.0ms

Counts

3 → 9

Calls

3 calls:

286.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
14.0ms	(- l (fabs (- m n)))
425.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.2s

Counts: 60 → 60

prune366.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.3b	(/ (* K (+ m n)) (sqrt 2.0))
0.4b	(/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0))
33.3b	(cos (- (/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0)) M))

rewrite318.0ms

Algorithm

rewrite-expression-head

Rules

109×	`times-frac`
60×	`sqrt-prod`
58×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
53×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`unpow-prod-down`
5×	`pow1`
4×	`add-log-exp`
3×	`pow-unpow` `associate-/l/`
2×	`cos-sum` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `cbrt-unprod` `difference-of-squares`
1×	`cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `pow-exp` `flip-+` `distribute-lft-out--` `sqr-pow`

Counts

4 → 152

Calls

4 calls:

97.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
16.0ms	(/ (* K (+ m n)) (sqrt 2.0))
40.0ms	(/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0))
157.0ms	(cos (- (/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0)) M))

series1.4s

Counts

4 → 12

Calls

4 calls:

419.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
154.0ms	(/ (* K (+ m n)) (sqrt 2.0))
276.0ms	(/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0))
521.0ms	(cos (- (/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0)) M))

simplify1.1s

Counts: 164 → 164

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0))
0.5b	(cbrt (pow (cos (- (/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0)) M)) 3))
0.6b	(pow (cos (- (/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0)) M)) 3)
33.3b	(cos (- (/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0)) M))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
54×	`sqrt-prod`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
12×	`cbrt-prod`
10×	`associate-/l*`
8×	`div-inv`
6×	`unpow-prod-down` `cube-prod` `associate-/r*`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `cos-sum` `unpow3` `sqr-pow`
1×	`cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `pow-exp` `prod-exp` `clear-num` `rem-cbrt-cube` `cbrt-unprod` `associate-/l/` `rem-cube-cbrt`

Counts

4 → 147

Calls

4 calls:

22.0ms	(/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0))
4.0ms	(cbrt (pow (cos (- (/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0)) M)) 3))
6.0ms	(pow (cos (- (/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0)) M)) 3)
141.0ms	(cos (- (/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0)) M))

series2.2s

Counts

4 → 12

Calls

4 calls:

264.0ms	(/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0))
521.0ms	(cbrt (pow (cos (- (/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0)) M)) 3))
895.0ms	(pow (cos (- (/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0)) M)) 3)
486.0ms	(cos (- (/ (/ (* K (+ m n)) (sqrt 2.0)) (sqrt 2.0)) M))

simplify1.0s

Counts: 159 → 159

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.0b

regimes271.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch0.0ms

simplify546.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.0s	8109×	body	80	valid
157.0ms	140×	body	1280	valid
149.0ms	153×	body	640	valid
39.0ms	90×	body	320	valid
17.0ms	55×	body	160	valid
3.0ms	2×	body	2560	valid