Details

sample41.0ms

Algorithm

intervals

Results

21.0ms	263×	body	80	valid
2.0ms	7×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	4×	body	160	valid

simplify832.0ms

Counts

1 → 1

Iterations

Useful iterations: 4 (58.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	94	29
3	205	29
4	470	28
5	1438	28
done	5000	28

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.1b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite3.6s

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
144×	`*-un-lft-identity`
141×	`prod-diff`
130×	`associate-r`
123×	`exp-sum`
72×	`add-cube-cbrt`
66×	`unpow-prod-down`
50×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
46×	`difference-of-squares`
35×	`distribute-lft-out--`
23×	`cos-sum`
20×	`times-frac`
11×	`sqr-pow`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l`
5×	`neg-mul-1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-*r/` `div-inv`
2×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `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` `associate--r-`

Counts

4 → 224

Calls

4 calls:

3.5s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
9.0ms	(* K (+ m n))
31.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
23.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series688.0ms

Counts

4 → 12

Calls

4 calls:

349.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
25.0ms	(* K (+ m n))
260.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.1s

Counts

236 → 236

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	629	9112
1	1191	7956
2	2968	7180
done	5001	7117

prune673.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`add-cube-cbrt` `pow-unpow`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 22

Calls

1 calls:

30.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

series267.0ms

Counts

1 → 3

Calls

1 calls:

267.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify3.6s

Counts

25 → 25

Iterations

Useful iterations: 4 (1.0s)

Iter	Nodes	Cost
0	76	357
1	160	338
2	379	325
3	1101	324
4	4494	316
done	5000	316

prune104.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
32.9b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))
33.0b	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
1.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))
1.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

series427.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
216.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))
211.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- M)))

simplify15.1s

Counts

54 → 54

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	90	826
1	151	770
2	309	696
3	744	476
4	3824	468
done	5001	468

prune410.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
32.8b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
21×	`prod-diff`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `div-inv`
1×	`cos-diff` `sub-neg`

Counts

4 → 72

Calls

4 calls:

0.0ms	(cbrt K)
0.0ms	(cbrt K)
1.0ms	(cbrt K)
52.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series628.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt K)
178.0ms	(cbrt K)
174.0ms	(cbrt K)
101.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify1.1s

Counts

84 → 84

Iterations

Useful iterations: 3 (355.0ms)

Iter	Nodes	Cost
0	202	2442
1	349	2034
2	668	1440
3	2143	963
done	5001	963

prune321.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.7b

regimes191.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 0.9b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	17	20
1	21	18
done	21	18

end0.0ms

sample1.0s

Algorithm

intervals

Results

633.0ms	8116×	body	80	valid
58.0ms	108×	body	1280	valid
47.0ms	141×	body	640	valid
22.0ms	92×	body	320	valid
8.0ms	50×	body	160	valid
2.0ms	3×	body	2560	valid