Details

sample132.0ms

Algorithm

intervals

Results

63.0ms	49×	body	2560	valid
41.0ms	91×	body	1280	valid
12.0ms	54×	body	640	valid
5.0ms	32×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	14×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4
done	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
2.5b	(- 1.0 (cos x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ (- 1.0 (cos x)) (sin x))
25.0ms	(- 1.0 (cos x))

simplify32.0ms

Counts

74 → 74

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	292	569
1	965	460
2	5002	460
done	5002	460

prune178.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (- 1.0 (cos x)))
0.1b	(/ (expm1 (log1p (- 1.0 (cos x)))) (sin x))
0.2b	(expm1 (log1p (- 1.0 (cos x))))
2.5b	(- 1.0 (cos x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
9×	`times-frac` `prod-diff`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `log1p-expm1-u`
3×	`fma-neg` `associate-/r` `associate-/l`
2×	`expm1-udef`
1×	`cbrt-undiv` `sub-neg` `log1p-udef` `expm1-log1p` `flip3--` `frac-2neg` `diff-log` `div-sub` `log1p-expm1` `div-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 80

Calls

4 calls:

1.0ms	(log1p (- 1.0 (cos x)))
8.0ms	(/ (expm1 (log1p (- 1.0 (cos x)))) (sin x))
0.0ms	(expm1 (log1p (- 1.0 (cos x))))
7.0ms	(- 1.0 (cos x))

series456.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(log1p (- 1.0 (cos x)))
176.0ms	(/ (expm1 (log1p (- 1.0 (cos x)))) (sin x))
157.0ms	(expm1 (log1p (- 1.0 (cos x))))
20.0ms	(- 1.0 (cos x))

simplify162.0ms

Counts

92 → 92

Iterations

Useful iterations: 3 (155.0ms)

Iter	Nodes	Cost
0	290	669
1	877	520
2	4660	491
3	5001	488
done	5001	488

prune220.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.2b	(/ (cos x) (sin x))
2.5b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

271×	`times-frac`
222×	`add-sqr-sqrt`
218×	`*-un-lft-identity`
210×	`add-cube-cbrt`
169×	`prod-diff`
31×	`div-inv`
13×	`fma-neg`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
5×	`add-log-exp`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

3 → 265

Calls

3 calls:

6.0ms	(/ 1.0 (sin x))
10.0ms	(/ (cos x) (sin x))
44.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series127.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/ 1.0 (sin x))
20.0ms	(/ (cos x) (sin x))
88.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify89.0ms

Counts

274 → 274

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	810	7180
1	2234	5060
2	5001	4434
done	5001	4434

prune370.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
0.4b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
2.3b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

233×	`add-sqr-sqrt`
165×	`*-un-lft-identity`
144×	`prod-diff`
138×	`unpow-prod-down` `cube-prod`
113×	`add-cube-cbrt`
80×	`difference-of-squares`
75×	`times-frac`
66×	`sqr-pow`
26×	`cube-mult` `unpow3`
25×	`associate-/l*` `distribute-lft-out--`
12×	`fma-neg`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 354

Calls

4 calls:

75.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
3.0ms	(pow (cos x) 3)
6.0ms	(+ 1.0 (cos x))
29.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series216.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
29.0ms	(pow (cos x) 3)
17.0ms	(+ 1.0 (cos x))
49.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify151.0ms

Counts

366 → 366

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	828	4951
1	3244	4033
2	5002	3940
done	5002	3940

prune501.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

regimes152.0ms

Accuracy

98.5% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 29.7b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	35
1	34	35
done	34	35

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1569×	body	2560	valid
1.2s	2775×	body	1280	valid
444.0ms	1868×	body	640	valid
147.0ms	943×	body	320	valid
51.0ms	467×	body	160	valid
24.0ms	375×	body	80	valid
11.0ms	3×	body	5120	valid