Details

sample134.0ms

Algorithm

intervals

Results

74.0ms	110×	body	1280	valid
23.0ms	22×	body	2560	valid
14.0ms	50×	body	640	valid
6.0ms	28×	body	320	valid
3.0ms	18×	body	160	valid
2.0ms	28×	body	80	valid

simplify4.0ms

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: 40.4b

localize24.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sin (+ x eps)) (sin x))
3.3b	(sin (+ x eps))

rewrite109.0ms

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:

92.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series98.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(- (sin (+ x eps)) (sin x))
34.0ms	(sin (+ x eps))

simplify1.0s

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	769
1	202
0	90

prune283.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (cos eps))
0.1b	(- (* (cos x) (sin eps)) (sin x))
0.2b	(* (cos x) (sin eps))
3.3b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

8.0ms	(* (sin x) (cos eps))
14.0ms	(- (* (cos x) (sin eps)) (sin x))
18.0ms	(* (cos x) (sin eps))
31.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sin x) (cos eps))
110.0ms	(- (* (cos x) (sin eps)) (sin x))
61.0ms	(* (cos x) (sin eps))
162.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify2.3s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	2250
1	439
0	161

prune722.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos eps) (sin x))
0.2b	(fma (cos x) (sin eps) (- (* (cos eps) (sin x)) (sin x)))
1.5b	(- (* (cos eps) (sin x)) (sin x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity`
6×	`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--` `distribute-rgt-out--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `flip--` `unswap-sqr`

Counts

3 → 49

Calls

3 calls:

9.0ms	(* (cos eps) (sin x))
0.0ms	(fma (cos x) (sin eps) (- (* (cos eps) (sin x)) (sin x)))
10.0ms	(- (* (cos eps) (sin x)) (sin x))

series293.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(* (cos eps) (sin x))
142.0ms	(fma (cos x) (sin eps) (- (* (cos eps) (sin x)) (sin x)))
82.0ms	(- (* (cos eps) (sin x)) (sin x))

simplify2.2s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	1336
1	248
0	104

prune474.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 2 expressions with local error:

0.2b	(fma (cos x) (sin eps) (fma (cos eps) (sin x) (- (sin x))))
1.4b	(fma (cos eps) (sin x) (- (sin x)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma (cos x) (sin eps) (fma (cos eps) (sin x) (- (sin x))))
0.0ms	(fma (cos eps) (sin x) (- (sin x)))

series311.0ms

Counts

2 → 6

Calls

2 calls:

215.0ms	(fma (cos x) (sin eps) (fma (cos eps) (sin x) (- (sin x))))
96.0ms	(fma (cos eps) (sin x) (- (sin x)))

simplify1.8s

Counts

26 → 26

Iterations

Iter	Nodes
done	5000
3	1577
2	293
1	80
0	44

prune164.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

regimes282.0ms

Accuracy

0% (0.1b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
0	9

end0.0ms

sample6.8s

Algorithm

intervals

Results

3.5s	3302×	body	1280	valid
1.5s	655×	body	2560	valid
1.2s	1847×	body	640	valid
237.0ms	772×	body	320	valid
105.0ms	1102×	body	80	valid
66.0ms	322×	body	160	valid