Details

sample91.0ms

Algorithm

intervals

Results

59.0ms	259×	body	80	valid
6.0ms	6×	body	1280	valid
4.0ms	5×	body	640	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
5	3134
4	819
3	262
2	104
1	51
0	21

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cos (- (* K (/ (+ m n) 2)) M)) (exp (- (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	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
35.2b	(cos (- (* K (/ (+ m n) 2)) M))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`prod-diff`
20×	`add-cube-cbrt`
14×	`associate-r`
11×	`exp-sum`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`cos-sum` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `associate-l`
2×	`fma-udef`
1×	`cos-diff` `flip3--` `exp-diff` `diff-log` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

107.0ms	(* (cos (- (* K (/ (+ m n) 2)) M)) (exp (- (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)
11.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
39.0ms	(cos (- (* K (/ (+ m n) 2)) M))

series962.0ms

Counts

4 → 12

Calls

4 calls:

444.0ms	(* (cos (- (* K (/ (+ m n) 2)) M)) (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))))
228.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
187.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
102.0ms	(cos (- (* K (/ (+ m n) 2)) M))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
3	3401
2	1044
1	442
0	214

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

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` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
5.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))

series422.0ms

Counts

2 → 6

Calls

2 calls:

192.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
230.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))

simplify3.3s

Counts

47 → 47

Iterations

Iter	Nodes
4	6511
3	1493
2	439
1	186
0	88

prune724.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (* (cos (fma K (/ (+ m n) 2) (- (* M 1)))) (cos (fma (- M) 1 (* M 1)))) (* (sin (fma K (/ (+ m n) 2) (- (* M 1)))) (sin (fma (- M) 1 (* M 1))))) (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))))
0.0b	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
35.2b	(cos (fma K (/ (+ m n) 2) (- (* M 1))))
35.2b	(sin (fma K (/ (+ m n) 2) (- (* M 1))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
14×	`associate-r`
11×	`exp-sum`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`exp-diff` `add-exp-log`
4×	`expm1-log1p-u` `frac-times` `associate-*l/` `cos-mult` `insert-posit16` `log1p-expm1-u` `sin-mult`
3×	`flip3--` `fma-neg` `associate-l` `fma-udef` `flip--`
2×	`sub-neg` `frac-sub` `sub-div`
1×	`cos-sum` `sin-sum` `diff-log` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `associate--r+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

100.0ms	(* (- (* (cos (fma K (/ (+ m n) 2) (- (* M 1)))) (cos (fma (- M) 1 (* M 1)))) (* (sin (fma K (/ (+ m n) 2) (- (* M 1)))) (sin (fma (- M) 1 (* M 1))))) (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))))
5.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
2.0ms	(cos (fma K (/ (+ m n) 2) (- (* M 1))))
2.0ms	(sin (fma K (/ (+ m n) 2) (- (* M 1))))

series4.6s

Counts

4 → 12

Calls

4 calls:

4.2s	(* (- (* (cos (fma K (/ (+ m n) 2) (- (* M 1)))) (cos (fma (- M) 1 (* M 1)))) (* (sin (fma K (/ (+ m n) 2) (- (* M 1)))) (sin (fma (- M) 1 (* M 1))))) (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))))
209.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
70.0ms	(cos (fma K (/ (+ m n) 2) (- (* M 1))))
79.0ms	(sin (fma K (/ (+ m n) 2) (- (* M 1))))

simplify2.6s

Counts

105 → 105

Iterations

Iter	Nodes
3	5839
2	1550
1	532
0	236

prune2.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize77.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (* (cos (- (* K (/ (+ m n) 2)) M)) (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))))) (cbrt (* (cos (- (* K (/ (+ m n) 2)) M)) (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))))))
35.2b	(cos (- (* K (/ (+ m n) 2)) M))
35.2b	(cos (- (* K (/ (+ m n) 2)) M))
35.2b	(cos (- (* K (/ (+ m n) 2)) M))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cos-sum`
13×	`add-sqr-sqrt`
11×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`prod-diff`
6×	`pow1/3` `add-exp-log`
5×	`associate-*r/`
4×	`cbrt-prod` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `exp-diff` `swap-sqr` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `sub-neg`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

114.0ms	(* (cbrt (* (cos (- (* K (/ (+ m n) 2)) M)) (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))))) (cbrt (* (cos (- (* K (/ (+ m n) 2)) M)) (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))))))
35.0ms	(cos (- (* K (/ (+ m n) 2)) M))
32.0ms	(cos (- (* K (/ (+ m n) 2)) M))
58.0ms	(cos (- (* K (/ (+ m n) 2)) M))

series1.2s

Counts

4 → 12

Calls

4 calls:

884.0ms	(* (cbrt (* (cos (- (* K (/ (+ m n) 2)) M)) (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))))) (cbrt (* (cos (- (* K (/ (+ m n) 2)) M)) (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))))))
113.0ms	(cos (- (* K (/ (+ m n) 2)) M))
91.0ms	(cos (- (* K (/ (+ m n) 2)) M))
98.0ms	(cos (- (* K (/ (+ m n) 2)) M))

simplify1.3s

Counts

97 → 97

Iterations

Iter	Nodes
3	2268
2	765
1	336
0	159

prune2.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

regimes563.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	19
1	19
0	15

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.7s	8107×	body	80	valid
245.0ms	130×	body	1280	valid
163.0ms	144×	body	640	valid
72.0ms	93×	body	320	valid
20.0ms	44×	body	160	valid
8.0ms	5×	body	2560	valid