Details

sample66.0ms

Algorithm

intervals

Results

41.0ms	259×	body	80	valid
4.0ms	4×	body	1280	valid
3.0ms	5×	body	640	valid
0.0ms	1×	body	320	valid

simplify967.0ms

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0b	(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))
0.2b	(/ (* (+ m n) K) 2)
35.4b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite357.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

128.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
187.0ms	(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))
18.0ms	(/ (* (+ m n) K) 2)
23.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series344.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
124.0ms	(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))
54.0ms	(/ (* (+ m n) K) 2)
80.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify2.5s

Counts

108 → 108

Iterations

Iter	Nodes
3	8077
2	1863
1	556
0	211

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize56.0ms

Local error

Found 3 expressions with local error:

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

rewrite502.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 98

Calls

3 calls:

88.0ms	(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
180.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
231.0ms	(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))

series476.0ms

Counts

3 → 9

Calls

3 calls:

217.0ms	(+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n))))
115.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
143.0ms	(exp (+ (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)) (- l (fabs (- m n)))))

simplify1.2s

Counts

107 → 107

Iterations

Iter	Nodes
2	3194
1	775
0	217

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
50×	`cbrt-prod`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
14×	`difference-of-squares`
11×	`pow1` `swap-sqr`
9×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
7×	`times-frac`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 107

Calls

4 calls:

134.0ms	(* (cbrt (- (/ (+ m n) 2) M)) (cbrt (- (/ (+ m n) 2) M)))
21.0ms	(cbrt (- (/ (+ m n) 2) M))
22.0ms	(cbrt (- (/ (+ m n) 2) M))
22.0ms	(cbrt (- (/ (+ m n) 2) M))

series1.2s

Counts

4 → 12

Calls

4 calls:

309.0ms	(* (cbrt (- (/ (+ m n) 2) M)) (cbrt (- (/ (+ m n) 2) M)))
296.0ms	(cbrt (- (/ (+ m n) 2) M))
295.0ms	(cbrt (- (/ (+ m n) 2) M))
267.0ms	(cbrt (- (/ (+ m n) 2) M))

simplify2.3s

Counts

119 → 119

Iterations

Iter	Nodes
4	3902
3	1587
2	756
1	322
0	154

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize98.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (+ m n) (sqrt 2)) (/ K (sqrt 2)))
0.4b	(/ (+ m n) (sqrt 2))
0.4b	(/ K (sqrt 2))
35.5b	(cos (- (* (/ (+ m n) (sqrt 2)) (/ K (sqrt 2))) M))

rewrite130.0ms

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-l`
22×	`associate-r`
20×	`add-cbrt-cube` `add-exp-log`
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` `clear-num` `frac-2neg` `associate-/l/`
1×	`cos-diff` `frac-times` `sub-neg` `flip3-+` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+`

Counts

4 → 176

Calls

4 calls:

44.0ms	(* (/ (+ m n) (sqrt 2)) (/ K (sqrt 2)))
24.0ms	(/ (+ m n) (sqrt 2))
8.0ms	(/ K (sqrt 2))
49.0ms	(cos (- (* (/ (+ m n) (sqrt 2)) (/ K (sqrt 2))) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

289.0ms	(* (/ (+ m n) (sqrt 2)) (/ K (sqrt 2)))
132.0ms	(/ (+ m n) (sqrt 2))
104.0ms	(/ K (sqrt 2))
584.0ms	(cos (- (* (/ (+ m n) (sqrt 2)) (/ K (sqrt 2))) M))

simplify4.1s

Counts

188 → 188

Iterations

Iter	Nodes
3	6590
2	1765
1	568
0	219

prune3.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

regimes429.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.0b and baseline of 1.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	23
1	23
0	19

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.7s	8122×	body	80	valid
207.0ms	140×	body	640	valid
159.0ms	104×	body	1280	valid
109.0ms	118×	body	320	valid
26.0ms	57×	body	160	valid
1.0ms	1×	body	2560	valid