Details

sample111.0ms

Algorithm

intervals

Results

73.0ms	260×	body	80	valid
6.0ms	3×	body	1280	valid
5.0ms	4×	body	640	valid
2.0ms	2×	body	320	valid
1.0ms	1×	body	160	valid

simplify990.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	2910
4	776
3	248
2	100
1	51
0	21

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ m n) K)
0.0b	(/ (* (+ m n) K) 2)
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
36.0b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

30.0ms	(* (+ m n) K)
25.0ms	(/ (* (+ m n) K) 2)
248.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
32.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series247.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (+ m n) K)
31.0ms	(/ (* (+ m n) K) 2)
90.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
96.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify4.5s

Counts

118 → 118

Iterations

Iter	Nodes
3	7224
2	1778
1	523
0	199

prune913.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite325.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`flip3--` `flip--`
23×	`*-un-lft-identity`
16×	`frac-add`
12×	`frac-times`
10×	`pow1` `add-log-exp`
9×	`difference-of-squares`
8×	`swap-sqr`
7×	`add-cube-cbrt` `distribute-lft-out--`
6×	`sub-neg` `associate-r` `associate-l` `associate-l/` `associate-r/`
5×	`add-cbrt-cube` `add-exp-log`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `times-frac`
3×	`insert-posit16`
2×	`associate-+r+` `sum-log` `diff-log`
1×	`pow2` `+-commutative` `associate-+r-` `flip3-+` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 100

Calls

3 calls:

12.0ms	(- l (fabs (- m n)))
98.0ms	(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
211.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

series294.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(- l (fabs (- m n)))
191.0ms	(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
90.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify1.1s

Counts

109 → 109

Iterations

Iter	Nodes
2	2952
1	719
0	204

prune762.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* (+ m n) K) 2) M)))
36.0b	(cos (- (/ (* (+ m n) K) 2) M))
36.0b	(cos (- (/ (* (+ m n) K) 2) M))
36.0b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 45

Calls

4 calls:

3.0ms	(cbrt (cos (- (/ (* (+ m n) K) 2) M)))
27.0ms	(cos (- (/ (* (+ m n) K) 2) M))
27.0ms	(cos (- (/ (* (+ m n) K) 2) M))
38.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series473.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(cbrt (cos (- (/ (* (+ m n) K) 2) M)))
71.0ms	(cos (- (/ (* (+ m n) K) 2) M))
103.0ms	(cos (- (/ (* (+ m n) K) 2) M))
86.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify2.8s

Counts

57 → 57

Iterations

Iter	Nodes
7	4516
6	1404
5	563
4	284
3	166
2	115
1	81
0	50

prune606.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.0b

localize67.0ms

Local error

Found 4 expressions with local error:

16.6b	(cbrt (* (+ m n) K))
16.6b	(cbrt (* (+ m n) K))
16.6b	(cbrt (* (+ m n) K))
35.8b	(cos (- (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2) M))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

12.0ms	(cbrt (* (+ m n) K))
11.0ms	(cbrt (* (+ m n) K))
10.0ms	(cbrt (* (+ m n) K))
67.0ms	(cos (- (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2) M))

series508.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (* (+ m n) K))
154.0ms	(cbrt (* (+ m n) K))
120.0ms	(cbrt (* (+ m n) K))
75.0ms	(cos (- (/ (* (* (cbrt (* (+ m n) K)) (cbrt (* (+ m n) K))) (cbrt (* (+ m n) K))) 2) M))

simplify982.0ms

Counts

59 → 59

Iterations

Iter	Nodes
4	2138
3	929
2	442
1	222
0	105

prune616.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.0b

regimes608.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	18
1	18
0	16

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.8s	8088×	body	80	valid
272.0ms	122×	body	1280	valid
173.0ms	139×	body	640	valid
87.0ms	117×	body	320	valid
25.0ms	52×	body	160	valid
2.0ms	1×	body	2560	valid