Details

sample205.0ms

Algorithm

intervals

Results

103.0ms	90×	body	1280	valid
38.0ms	23×	body	2560	valid
27.0ms	53×	body	640	valid
14.0ms	41×	body	320	valid
4.0ms	16×	body	160	valid
3.0ms	33×	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: 36.4b

localize20.0ms

Local error

Found 2 expressions with local error:

3.3b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite72.0ms

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:

62.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series90.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(- (sin (+ x eps)) (sin x))
32.0ms	(sin (+ x eps))

simplify2.9s

Counts

46 → 46

Iterations

Iter	Nodes
done	5002
4	3880
3	1287
2	445
1	201
0	90

prune240.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
3.8b	(cos (/ (fma 2 x eps) 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-cos-mult` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

22.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series102.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
38.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.5s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
4	2892
3	1011
2	353
1	148
0	66

prune268.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (fma 1/2 eps x)) (cos (fma 1/2 eps x))) (cos (fma 1/2 eps x))))
3.8b	(cos (fma 1/2 eps x))
3.8b	(cos (fma 1/2 eps x))
3.8b	(cos (fma 1/2 eps x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`cos-sum` `fma-udef`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 43

Calls

4 calls:

21.0ms	(cbrt (* (* (cos (fma 1/2 eps x)) (cos (fma 1/2 eps x))) (cos (fma 1/2 eps x))))
4.0ms	(cos (fma 1/2 eps x))
4.0ms	(cos (fma 1/2 eps x))
4.0ms	(cos (fma 1/2 eps x))

series107.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(cbrt (* (* (cos (fma 1/2 eps x)) (cos (fma 1/2 eps x))) (cos (fma 1/2 eps x))))
21.0ms	(cos (fma 1/2 eps x))
32.0ms	(cos (fma 1/2 eps x))
21.0ms	(cos (fma 1/2 eps x))

simplify3.3s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
5	3138
4	871
3	304
2	132
1	77
0	49

prune423.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize76.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (cos (fma 1/2 eps x)))
0.5b	(cbrt (* (* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (cos (fma 1/2 eps x))) (cos (fma 1/2 eps x))))
3.8b	(cos (fma 1/2 eps x))
3.8b	(cos (fma 1/2 eps x))

rewrite348.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-*l/`
8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `cbrt-div` `cos-mult` `log1p-expm1-u` `sin-mult` `add-log-exp`
3×	`associate-r` `associate-l`
2×	`cos-sum` `flip3--` `frac-sub` `fma-udef` `flip--` `sub-div`
1×	`cbrt-prod` `pow1/3` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

154.0ms	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (cos (fma 1/2 eps x)))
185.0ms	(cbrt (* (* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (cos (fma 1/2 eps x))) (cos (fma 1/2 eps x))))
4.0ms	(cos (fma 1/2 eps x))
3.0ms	(cos (fma 1/2 eps x))

series551.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (cos (fma 1/2 eps x)))
293.0ms	(cbrt (* (* (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))) (cos (fma 1/2 eps x))) (cos (fma 1/2 eps x))))
34.0ms	(cos (fma 1/2 eps x))
21.0ms	(cos (fma 1/2 eps x))

simplify3.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
3	3016
2	820
1	279
0	115

prune649.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

regimes221.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 13.9b

bsearch55.0ms

Steps

Iters	Range		Point
0	1.711014091985158e-09	1.7501962730858363e-09	1.730605182535497e-09
5	-4.034181863829644e-08	-1.0274293973745148e-08	-1.096393406185499e-08

simplify6.0ms

Iterations

Iter	Nodes
done	35
1	35
0	26

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.8s	3287×	body	1280	valid
823.0ms	1806×	body	640	valid
748.0ms	645×	body	2560	valid
260.0ms	818×	body	320	valid
82.0ms	1102×	body	80	valid
50.0ms	342×	body	160	valid