Details

sample182.0ms

Algorithm

intervals

Results

83.0ms	99×	body	1280	valid
39.0ms	76×	body	640	valid
24.0ms	15×	body	2560	valid
9.0ms	27×	body	320	valid
3.0ms	26×	body	80	valid
3.0ms	13×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize25.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (sin (+ x eps)) (sin x))
3.9b	(sin (+ x eps))

rewrite102.0ms

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` `sin-sum` `add-exp-log` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

86.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series84.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(- (sin (+ x eps)) (sin x))
22.0ms	(sin (+ x eps))

simplify957.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	769
1	202
0	90

prune259.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
2.9b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`add-log-exp`
9×	`prod-diff`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg`
2×	`sum-log` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `fma-def` `flip3-+` `flip3--` `associate--l+` `flip-+` `sin-cos-mult` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

19.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
16.0ms	(* (cos x) (sin eps))
16.0ms	(* (sin x) (cos eps))
77.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series492.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
77.0ms	(* (cos x) (sin eps))
84.0ms	(* (sin x) (cos eps))
201.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify2.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1943
1	394
0	157

prune653.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.6b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
3.0b	(fma (cos eps) (sin x) (- (* (cos x) (sin eps)) (sin x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `prod-diff` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `flip--` `unswap-sqr`

Counts

3 → 48

Calls

3 calls:

20.0ms	(- (* (cos x) (sin eps)) (sin x))
9.0ms	(* (cos x) (sin eps))
0.0ms	(fma (cos eps) (sin x) (- (* (cos x) (sin eps)) (sin x)))

series335.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(- (* (cos x) (sin eps)) (sin x))
59.0ms	(* (cos x) (sin eps))
179.0ms	(fma (cos eps) (sin x) (- (* (cos x) (sin eps)) (sin x)))

simplify1.1s

Counts

57 → 57

Iterations

Iter	Nodes
done	5000
2	1164
1	256
0	109

prune398.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (sin x) (cos eps))
0.2b	(fma (cos x) (sin eps) (- (* (sin x) (cos eps)) (sin x)))
1.0b	(- (* (sin x) (cos eps)) (sin x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `prod-diff` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `sin-cos-mult` `flip--` `unswap-sqr`

Counts

3 → 49

Calls

3 calls:

14.0ms	(* (sin x) (cos eps))
0.0ms	(fma (cos x) (sin eps) (- (* (sin x) (cos eps)) (sin x)))
11.0ms	(- (* (sin x) (cos eps)) (sin x))

series263.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* (sin x) (cos eps))
143.0ms	(fma (cos x) (sin eps) (- (* (sin x) (cos eps)) (sin x)))
64.0ms	(- (* (sin x) (cos eps)) (sin x))

simplify1.5s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	1186
1	241
0	106

prune316.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes278.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.8s	3313×	body	1280	valid
816.0ms	656×	body	2560	valid
728.0ms	1776×	body	640	valid
447.0ms	1118×	body	80	valid
219.0ms	771×	body	320	valid
63.0ms	366×	body	160	valid