Details

sample126.0ms

Algorithm

intervals

Results

69.0ms	145×	body	1280	valid
20.0ms	65×	body	640	valid
16.0ms	14×	body	2560	valid
5.0ms	22×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	3×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (cos (+ x eps)) (cos x))
2.9b	(cos (+ x eps))

rewrite35.0ms

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` `cos-sum` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

18.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

series492.0ms

Counts

2 → 6

Calls

2 calls:

456.0ms	(- (cos (+ x eps)) (cos x))
36.0ms	(cos (+ x eps))

simplify778.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	723
1	201
0	91

prune242.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2)))
2.9b	(sin (/ (+ x (+ x eps)) 2))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`sum-log` `fma-def` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

86.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2))))
13.0ms	(+ x (+ x eps))
71.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2)))
24.0ms	(sin (/ (+ x (+ x eps)) 2))

series225.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2))))
27.0ms	(+ x (+ x eps))
60.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2)))
37.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify856.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1224
1	311
0	129

prune626.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

21.0ms	(* (sin (/ (fma x 2 eps) 2)) (* -2 (sin (/ eps 2))))
3.0ms	(sin (/ (fma x 2 eps) 2))

series181.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(* (sin (/ (fma x 2 eps) 2)) (* -2 (sin (/ eps 2))))
35.0ms	(sin (/ (fma x 2 eps) 2))

simplify1.7s

Counts

35 → 35

Iterations

Iter	Nodes
done	5001
3	2026
2	501
1	156
0	67

prune313.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize56.0ms

Local error

Found 4 expressions with local error:

2.9b	(sin (/ (fma x 2 eps) 2))
6.8b	(cbrt (* (sin (/ eps 2)) (sin (/ (fma x 2 eps) 2))))
6.8b	(cbrt (* (sin (/ eps 2)) (sin (/ (fma x 2 eps) 2))))
6.8b	(cbrt (* (sin (/ eps 2)) (sin (/ (fma x 2 eps) 2))))

rewrite33.0ms

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×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`

Counts

4 → 45

Calls

4 calls:

3.0ms	(sin (/ (fma x 2 eps) 2))
9.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (fma x 2 eps) 2))))
10.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (fma x 2 eps) 2))))
10.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (fma x 2 eps) 2))))

series611.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sin (/ (fma x 2 eps) 2))
205.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (fma x 2 eps) 2))))
167.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (fma x 2 eps) 2))))
202.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (fma x 2 eps) 2))))

simplify697.0ms

Counts

57 → 57

Iterations

Iter	Nodes
done	5000
3	978
2	299
1	132
0	67

prune474.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.3b

regimes519.0ms

Accuracy

96.1% (0.6b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.0b

bsearch168.0ms

Steps

Iters	Range		Point
9	6968.3439428623215	12923530959.442633	7051.556907543755
8	-72632609.50044116	-1138.2876542095912	-1170.229056579155

simplify9.0ms

Iterations

Iter	Nodes
done	37
2	37
1	36
0	30

end0.0ms

sample6.4s

Algorithm

intervals

Results

4.0s	4460×	body	1280	valid
1.1s	652×	body	2560	valid
717.0ms	1851×	body	640	valid
266.0ms	693×	body	320	valid
56.0ms	291×	body	160	valid
5.0ms	53×	body	80	valid