Details

sample180.0ms

Algorithm

intervals

Results

87.0ms	110×	body	1280	valid
37.0ms	22×	body	2560	valid
26.0ms	50×	body	640	valid
9.0ms	28×	body	320	valid
4.0ms	18×	body	160	valid
3.0ms	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

localize39.0ms

Local error

Found 2 expressions with local error:

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

rewrite59.0ms

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:

51.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (sin (+ x eps)) (sin x))
27.0ms	(sin (+ x eps))

simplify3.3s

Counts

46 → 46

Iterations

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

prune205.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
2.9b	(cos (/ (fma 2 x eps) 2))

rewrite17.0ms

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:

14.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series97.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
27.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.2s

Counts

36 → 36

Iterations

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

prune331.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize30.0ms

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))))
2.9b	(cos (fma 1/2 eps x))
2.9b	(cos (fma 1/2 eps x))
2.9b	(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:

28.0ms	(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))
2.0ms	(cos (fma 1/2 eps x))
2.0ms	(cos (fma 1/2 eps x))

series125.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(cbrt (* (* (cos (fma 1/2 eps x)) (cos (fma 1/2 eps x))) (cos (fma 1/2 eps x))))
28.0ms	(cos (fma 1/2 eps x))
21.0ms	(cos (fma 1/2 eps x))
39.0ms	(cos (fma 1/2 eps x))

simplify3.4s

Counts

55 → 55

Iterations

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

prune476.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.3b

localize79.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos (fma 1/2 eps x)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
0.5b	(cbrt (* (* (cos (fma 1/2 eps x)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))) (cos (fma 1/2 eps x))))
2.9b	(cos (fma 1/2 eps x))
2.9b	(cos (fma 1/2 eps x))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

94.0ms	(* (cos (fma 1/2 eps x)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
137.0ms	(cbrt (* (* (cos (fma 1/2 eps x)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))) (cos (fma 1/2 eps x))))
2.0ms	(cos (fma 1/2 eps x))
2.0ms	(cos (fma 1/2 eps x))

series502.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(* (cos (fma 1/2 eps x)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
274.0ms	(cbrt (* (* (cos (fma 1/2 eps x)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))) (cos (fma 1/2 eps x))))
24.0ms	(cos (fma 1/2 eps x))
30.0ms	(cos (fma 1/2 eps x))

simplify2.7s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
3	3345
2	930
1	319
0	129

prune705.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

regimes343.0ms

Accuracy

97.4% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 14.9b

bsearch245.0ms

Steps

Iters	Range		Point
10	2.765405219724019e-10	1875.4132169206714	9.294677533277006e-09
9	-245180560723.46045	-1212215.9807367995	-1230266.9135965805

simplify9.0ms

Iterations

Iter	Nodes
done	34
1	34
0	25

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.6s	3302×	body	1280	valid
1.5s	655×	body	2560	valid
1.2s	1847×	body	640	valid
232.0ms	772×	body	320	valid
86.0ms	1102×	body	80	valid
54.0ms	322×	body	160	valid