Details

sample117.0ms

Algorithm

intervals

Results

76.0ms	259×	body	80	valid
5.0ms	4×	body	1280	valid
4.0ms	5×	body	640	valid
1.0ms	1×	body	320	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
5	3132
4	821
3	260
2	102
1	51
0	21

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
16×	`associate-r`
13×	`times-frac`
12×	`prod-diff`
11×	`exp-sum`
9×	`add-cbrt-cube` `add-exp-log`
7×	`add-log-exp`
6×	`pow1`
5×	`cos-sum` `exp-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l` `distribute-lft-out`
2×	`sub-neg` `prod-exp` `cbrt-unprod` `unswap-sqr` `rem-exp-log`
1×	`cos-diff` `cbrt-undiv` `exp-diff` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 90

Calls

4 calls:

14.0ms	(* K (/ (+ m n) 2))
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
9.0ms	(exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))
38.0ms	(cos (- (* K (/ (+ m n) 2)) M))

series461.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* K (/ (+ m n) 2))
212.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
124.0ms	(exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))
80.0ms	(cos (- (* K (/ (+ m n) 2)) M))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
3	3716
2	1213
1	486
0	234

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`exp-sum`
8×	`add-log-exp`
5×	`exp-prod`
3×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `fma-neg` `add-exp-log` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `fma-udef` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`
1×	`flip3--` `exp-diff` `flip--` `associate--r+`

Counts

3 → 67

Calls

3 calls:

9.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
19.0ms	(exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))

series892.0ms

Counts

3 → 9

Calls

3 calls:

193.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
190.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
509.0ms	(exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))

simplify730.0ms

Counts

76 → 76

Iterations

Iter	Nodes
3	2209
2	657
1	259
0	124

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize33.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 39

Calls

2 calls:

4.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series394.0ms

Counts

2 → 6

Calls

2 calls:

212.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
182.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

simplify4.5s

Counts

45 → 45

Iterations

Iter	Nodes
4	6050
3	1486
2	435
1	182
0	86

prune560.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize66.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2)
1.0b	(cbrt 2)
1.0b	(cbrt 2)
35.2b	(cos (- (* (* (* (/ (cbrt (+ m n)) (cbrt 2)) (/ (cbrt (+ m n)) (cbrt 2))) K) (/ (cbrt (+ m n)) (cbrt 2))) M))

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`cos-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `prod-diff`
1×	`cos-diff` `sub-neg`

Counts

4 → 54

Calls

4 calls:

1.0ms	(cbrt 2)
1.0ms	(cbrt 2)
1.0ms	(cbrt 2)
346.0ms	(cos (- (* (* (* (/ (cbrt (+ m n)) (cbrt 2)) (/ (cbrt (+ m n)) (cbrt 2))) K) (/ (cbrt (+ m n)) (cbrt 2))) M))

series324.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
324.0ms	(cos (- (* (* (* (/ (cbrt (+ m n)) (cbrt 2)) (/ (cbrt (+ m n)) (cbrt 2))) K) (/ (cbrt (+ m n)) (cbrt 2))) M))

simplify1.6s

Counts

60 → 60

Iterations

Iter	Nodes
5	3949
4	1416
3	608
2	292
1	169
0	100

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.0b

regimes423.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	18
1	18
0	16

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.5s	8122×	body	80	valid
166.0ms	140×	body	640	valid
154.0ms	104×	body	1280	valid
106.0ms	118×	body	320	valid
56.0ms	57×	body	160	valid
1.0ms	1×	body	2560	valid