Details

sample172.0ms

Algorithm

intervals

Results

71.0ms	112×	body	1280	valid
32.0ms	36×	body	80	valid
29.0ms	25×	body	2560	valid
20.0ms	55×	body	640	valid
6.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.9b

localize22.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
3.3b	(sin (+ x eps))

rewrite114.0ms

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:

97.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series92.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (sin (+ x eps)) (sin x))
37.0ms	(sin (+ x eps))

simplify1.0s

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	769
1	202
0	90

prune221.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (cos eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
2.6b	(- (+ (* (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:

10.0ms	(* (sin x) (cos eps))
11.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
9.0ms	(* (cos x) (sin eps))
82.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series412.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin x) (cos eps))
129.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
64.0ms	(* (cos x) (sin eps))
164.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify2.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1942
1	394
0	157

prune736.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 17.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (expm1 (log1p (* (cos x) (sin eps)))))
0.1b	(* (cos x) (sin eps))
0.2b	(log1p (* (cos x) (sin eps)))
2.6b	(- (+ (* (sin x) (cos eps)) (expm1 (log1p (* (cos x) (sin eps))))) (sin x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

8.0ms	(+ (* (sin x) (cos eps)) (expm1 (log1p (* (cos x) (sin eps)))))
9.0ms	(* (cos x) (sin eps))
0.0ms	(log1p (* (cos x) (sin eps)))
62.0ms	(- (+ (* (sin x) (cos eps)) (expm1 (log1p (* (cos x) (sin eps))))) (sin x))

series547.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(+ (* (sin x) (cos eps)) (expm1 (log1p (* (cos x) (sin eps)))))
70.0ms	(* (cos x) (sin eps))
93.0ms	(log1p (* (cos x) (sin eps)))
226.0ms	(- (+ (* (sin x) (cos eps)) (expm1 (log1p (* (cos x) (sin eps))))) (sin x))

simplify2.0s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1736
1	372
0	148

prune669.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 17.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos x))
0.3b	(cbrt (cos x))
0.3b	(cbrt (cos x))
2.6b	(- (+ (* (sin x) (cos eps)) (* (* (cbrt (cos x)) (cbrt (cos x))) (* (cbrt (cos x)) (sin eps)))) (sin x))

rewrite85.0ms

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:

1.0ms	(cbrt (cos x))
1.0ms	(cbrt (cos x))
1.0ms	(cbrt (cos x))
81.0ms	(- (+ (* (sin x) (cos eps)) (* (* (cbrt (cos x)) (cbrt (cos x))) (* (cbrt (cos x)) (sin eps)))) (sin x))

series644.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (cos x))
164.0ms	(cbrt (cos x))
161.0ms	(cbrt (cos x))
180.0ms	(- (+ (* (sin x) (cos eps)) (* (* (cbrt (cos x)) (cbrt (cos x))) (* (cbrt (cos x)) (sin eps)))) (sin x))

simplify1.5s

Counts

81 → 81

Iterations

Iter	Nodes
done	5000
2	1078
1	248
0	106

prune417.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.2b

regimes190.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.3s	3217×	body	1280	valid
1.2s	651×	body	2560	valid
695.0ms	1872×	body	640	valid
213.0ms	784×	body	320	valid
189.0ms	1121×	body	80	valid
51.0ms	355×	body	160	valid