Details

sample198.0ms

Algorithm

intervals

Results

91.0ms	105×	body	1280	valid
43.0ms	17×	body	2560	valid
32.0ms	59×	body	640	valid
8.0ms	23×	body	320	valid
5.0ms	42×	body	80	valid
2.0ms	10×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (sin (+ x eps)) (sin x))
3.3b	(sin (+ x eps))

rewrite126.0ms

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:

110.0ms	(- (sin (+ x eps)) (sin x))
14.0ms	(sin (+ x eps))

series118.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(- (sin (+ x eps)) (sin x))
37.0ms	(sin (+ x eps))

simplify1.1s

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	769
1	202
0	90

prune256.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (cos eps))
0.1b	(* (cos x) (sin eps))
0.2b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
2.1b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite117.0ms

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))
18.0ms	(* (cos x) (sin eps))
23.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
55.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series448.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin x) (cos eps))
75.0ms	(* (cos x) (sin eps))
125.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
181.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify2.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	1953
1	394
0	157

prune738.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos x))
0.3b	(cbrt (cos x))
0.3b	(cbrt (cos x))
2.1b	(- (+ (* (sin x) (cos eps)) (* (* (cbrt (cos x)) (cbrt (cos x))) (* (cbrt (cos x)) (sin eps)))) (sin x))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`add-cube-cbrt`
9×	`cbrt-prod` `prod-diff` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`fma-neg` `pow1/3`
2×	`diff-log`
1×	`sum-log` `sub-neg` `flip3--` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 69

Calls

4 calls:

2.0ms	(cbrt (cos x))
2.0ms	(cbrt (cos x))
2.0ms	(cbrt (cos x))
89.0ms	(- (+ (* (sin x) (cos eps)) (* (* (cbrt (cos x)) (cbrt (cos x))) (* (cbrt (cos x)) (sin eps)))) (sin x))

series649.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (cos x))
168.0ms	(cbrt (cos x))
171.0ms	(cbrt (cos x))
174.0ms	(- (+ (* (sin x) (cos eps)) (* (* (cbrt (cos x)) (cbrt (cos x))) (* (cbrt (cos x)) (sin eps)))) (sin x))

simplify1.9s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1078
1	248
0	106

prune499.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin eps) (cos x) (- (* (sin x) (cos eps)) (sin x)))
0.1b	(* (sin x) (cos eps))
1.0b	(- (* (sin x) (cos eps)) (sin x))

rewrite22.0ms

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:

0.0ms	(fma (sin eps) (cos x) (- (* (sin x) (cos eps)) (sin x)))
9.0ms	(* (sin x) (cos eps))
11.0ms	(- (* (sin x) (cos eps)) (sin x))

series349.0ms

Counts

3 → 9

Calls

3 calls:

171.0ms	(fma (sin eps) (cos x) (- (* (sin x) (cos eps)) (sin x)))
78.0ms	(* (sin x) (cos eps))
100.0ms	(- (* (sin x) (cos eps)) (sin x))

simplify1.8s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	1150
1	237
0	106

prune409.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes152.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
0	9

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.5s	3248×	body	1280	valid
1.1s	650×	body	2560	valid
991.0ms	1858×	body	640	valid
392.0ms	778×	body	320	valid
108.0ms	1140×	body	80	valid
63.0ms	326×	body	160	valid