Details

sample138.0ms

Algorithm

intervals

Results

49.0ms	249×	body	80	valid
32.0ms	9×	body	1280	valid
5.0ms	6×	body	640	valid
2.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify12.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	21	29
1	73	29
2	452	28
done	5001	28

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
33.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite12.2s

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
33×	`prod-diff`
30×	`add-cube-cbrt`
23×	`cos-sum`
21×	`associate-r`
14×	`exp-sum`
10×	`times-frac`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`pow-unpow` `associate-*r/` `div-inv`
2×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `exp-diff` `pow-exp` `flip-+` `distribute-lft-out--` `sqr-pow`

Counts

4 → 115

Calls

4 calls:

12.0s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))))
79.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.0ms	(* K (+ m n))
46.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

598.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))))
376.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
44.0ms	(* K (+ m n))
75.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify4.2s

Counts

127 → 127

Iterations

Useful iterations: done (4.2s)

Iter	Nodes	Cost
0	380	3715
1	2876	3001
done	5000	2745

prune941.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.7b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`unpow-prod-down` `prod-diff`
10×	`fma-def` `add-log-exp`
5×	`distribute-lft-out` `difference-of-squares`
4×	`pow1` `add-exp-log` `distribute-lft-out--`
3×	`expm1-log1p-u` `pow-unpow` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`times-frac` `diff-log` `sum-log` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `pow-exp` `flip--` `flip-+` `associate--r+`

Counts

3 → 80

Calls

3 calls:

609.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
1.2s	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
83.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series986.0ms

Counts

3 → 9

Calls

3 calls:

280.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) l)
297.0ms	(- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))
408.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.3s

Counts

89 → 89

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	161	2157
1	998	1564
done	5000	1484

prune552.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.7b

localize116.0ms

Local error

Found 4 expressions with local error:

12.9b	(cbrt (/ (* K (+ m n)) 2.0))
12.9b	(cbrt (/ (* K (+ m n)) 2.0))
33.6b	(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))
34.0b	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-div` `pow1/3` `fma-udef` `div-inv`
1×	`cos-sum` `sin-sum`

Counts

4 → 56

Calls

4 calls:

12.0ms	(cbrt (/ (* K (+ m n)) 2.0))
12.0ms	(cbrt (/ (* K (+ m n)) 2.0))
5.0ms	(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))
5.0ms	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))

series2.0s

Counts

4 → 12

Calls

4 calls:

266.0ms	(cbrt (/ (* K (+ m n)) 2.0))
229.0ms	(cbrt (/ (* K (+ m n)) 2.0))
695.0ms	(sin (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))
776.0ms	(cos (fma (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0)) (- M)))

simplify1.5s

Counts

68 → 68

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	132	1600
1	419	1550
done	5000	881

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.5b	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
0.6b	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
33.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`add-cube-cbrt`
23×	`cos-sum`
21×	`prod-diff`
12×	`cbrt-prod`
9×	`times-frac`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-l` `div-inv`
2×	`cube-mult` `unpow3` `associate-*r/` `sqr-pow`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `flip3-+` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `flip-+` `distribute-lft-out` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

40.0ms	(* K (+ m n))
7.0ms	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
12.0ms	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series438.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* K (+ m n))
94.0ms	(cbrt (pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3))
188.0ms	(pow (cos (- (/ (* K (+ m n)) 2.0) M)) 3)
125.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify7.1s

Counts

118 → 118

Iterations

Useful iterations: done (7.1s)

Iter	Nodes	Cost
0	261	2924
1	2222	2108
done	5001	1979

prune665.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.7b

regimes372.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	16	19
1	21	17
done	21	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.9s	8070×	body	80	valid
100.0ms	123×	body	1280	valid
81.0ms	133×	body	640	valid
56.0ms	65×	body	160	valid
47.0ms	102×	body	320	valid
6.0ms	5×	body	2560	valid