Details

sample67.0ms

Algorithm

intervals

Results

30.0ms	259×	body	80	valid
3.0ms	4×	body	1280	valid
2.0ms	5×	body	640	valid
1.0ms	1×	body	2560	valid
1.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify733.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (* K (+ m n)) 2.0)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
29.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 53

Calls

3 calls:

14.0ms	(/ (* K (+ m n)) 2.0)
78.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
67.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series562.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (* K (+ m n)) 2.0)
388.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
93.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify700.0ms

Counts: 62 → 62

prune391.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize27.0ms

Local error

Found 1 expressions with local error:

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

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`add-cube-cbrt` `pow-unpow`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 20

Calls

1 calls:

102.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

series398.0ms

Counts

1 → 3

Calls

1 calls:

398.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.3s

Counts: 23 → 23

prune162.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
0.4b	(/ K (sqrt 2.0))
0.5b	(/ (+ m n) (sqrt 2.0))
30.1b	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

rewrite259.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
94×	`add-sqr-sqrt`
90×	`*-un-lft-identity`
64×	`add-cube-cbrt`
54×	`sqrt-prod`
28×	`associate-r`
22×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out`
12×	`associate-/r*`
9×	`unswap-sqr`
7×	`associate-/l*`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`cos-sum` `frac-2neg` `clear-num` `associate-/l/`
1×	`cos-diff` `frac-times` `sub-neg` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 176

Calls

4 calls:

111.0ms	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
13.0ms	(/ K (sqrt 2.0))
34.0ms	(/ (+ m n) (sqrt 2.0))
85.0ms	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

308.0ms	(* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)))
81.0ms	(/ K (sqrt 2.0))
144.0ms	(/ (+ m n) (sqrt 2.0))
542.0ms	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

simplify944.0ms

Counts: 188 → 188

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ m n) (sqrt 2.0))
0.5b	(cbrt (pow (cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M)) 3))
0.6b	(pow (cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M)) 3)
30.1b	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
27×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`times-frac`
15×	`sqrt-prod`
12×	`cbrt-prod`
7×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`unpow-prod-down` `cube-prod` `associate-/r*`
5×	`pow1`
4×	`associate-/l*` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `cos-sum` `unpow3` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 102

Calls

4 calls:

25.0ms	(/ (+ m n) (sqrt 2.0))
7.0ms	(cbrt (pow (cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M)) 3))
10.0ms	(pow (cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M)) 3)
85.0ms	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

series2.0s

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (+ m n) (sqrt 2.0))
448.0ms	(cbrt (pow (cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M)) 3))
908.0ms	(pow (cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M)) 3)
484.0ms	(cos (- (* (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0))) M))

simplify577.0ms

Counts: 114 → 114

prune755.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.9b

regimes214.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify732.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.9s	8092×	body	80	valid
155.0ms	106×	body	1280	valid
88.0ms	149×	body	640	valid
55.0ms	130×	body	320	valid
14.0ms	49×	body	160	valid
3.0ms	3×	body	2560	valid