Details

sample89.0ms

Algorithm

intervals

Results

37.0ms	93×	body	1280	valid
21.0ms	24×	body	2560	valid
14.0ms	60×	body	640	valid
3.0ms	22×	body	320	valid
2.0ms	39×	body	80	valid
2.0ms	18×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize12.0ms

Local error

Found 2 expressions with local error:

1.8b	(sin (+ x eps))
2.5b	(- (sin (+ x eps)) (sin x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sin-sum` `add-cbrt-cube` `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:

4.0ms	(sin (+ x eps))
25.0ms	(- (sin (+ x eps)) (sin x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(sin (+ x eps))
40.0ms	(- (sin (+ x eps)) (sin x))

simplify866.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (223.0ms)

Iter	Nodes	Cost
0	91	662
1	189	539
2	470	452
3	1618	388
done	5000	388

prune110.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ (- eps 0) 2)))
2.0b	(cos (/ (+ (+ x eps) x) 2))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 50

Calls

3 calls:

18.0ms	(+ (+ x eps) x)
12.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ (- eps 0) 2)))
21.0ms	(cos (/ (+ (+ x eps) x) 2))

series111.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (+ x eps) x)
66.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ (- eps 0) 2)))
23.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.4s

Counts

59 → 59

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	94	741
1	221	671
2	573	589
3	1493	529
done	5000	526

prune198.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (expm1 (log1p (cos (/ (fma x 2 eps) 2)))) (sin (/ (- eps 0) 2)))
0.2b	(expm1 (log1p (cos (/ (fma x 2 eps) 2))))
0.4b	(log1p (cos (/ (fma x 2 eps) 2)))
2.0b	(cos (/ (fma x 2 eps) 2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

16.0ms	(* (expm1 (log1p (cos (/ (fma x 2 eps) 2)))) (sin (/ (- eps 0) 2)))
0.0ms	(expm1 (log1p (cos (/ (fma x 2 eps) 2))))
0.0ms	(log1p (cos (/ (fma x 2 eps) 2)))
2.0ms	(cos (/ (fma x 2 eps) 2))

series220.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (expm1 (log1p (cos (/ (fma x 2 eps) 2)))) (sin (/ (- eps 0) 2)))
52.0ms	(expm1 (log1p (cos (/ (fma x 2 eps) 2))))
48.0ms	(log1p (cos (/ (fma x 2 eps) 2)))
23.0ms	(cos (/ (fma x 2 eps) 2))

simplify1.4s

Counts

63 → 63

Iterations

Useful iterations: 4 (612.0ms)

Iter	Nodes	Cost
0	90	900
1	176	763
2	413	687
3	924	681
4	2109	652
done	5001	652

prune218.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (pow (cos (/ (fma x 2 eps) 2)) 3)) (sin (/ (- eps 0) 2)))
0.5b	(cbrt (pow (cos (/ (fma x 2 eps) 2)) 3))
0.5b	(pow (cos (/ (fma x 2 eps) 2)) 3)
2.0b	(cos (/ (fma x 2 eps) 2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-r`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 93

Calls

4 calls:

19.0ms	(* (cbrt (pow (cos (/ (fma x 2 eps) 2)) 3)) (sin (/ (- eps 0) 2)))
2.0ms	(cbrt (pow (cos (/ (fma x 2 eps) 2)) 3))
1.0ms	(pow (cos (/ (fma x 2 eps) 2)) 3)
2.0ms	(cos (/ (fma x 2 eps) 2))

series166.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (cbrt (pow (cos (/ (fma x 2 eps) 2)) 3)) (sin (/ (- eps 0) 2)))
23.0ms	(cbrt (pow (cos (/ (fma x 2 eps) 2)) 3))
49.0ms	(pow (cos (/ (fma x 2 eps) 2)) 3)
24.0ms	(cos (/ (fma x 2 eps) 2))

simplify3.5s

Counts

105 → 105

Iterations

Useful iterations: 3 (935.0ms)

Iter	Nodes	Cost
0	121	1777
1	257	1402
2	778	1274
3	4553	1268
done	5000	1268

prune280.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.5b

regimes117.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.2b

bsearch80.0ms

Steps

Iters	Range		Point
7	6.841021425788069e-10	8.116859208030337e-08	7.436477518387171e-09
6	-2.8343233054530806e-08	-2.2450763006537216e-09	-6.6823151206119754e-09

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	53
1	37	51
done	37	51

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3253×	body	1280	valid
590.0ms	649×	body	2560	valid
458.0ms	1841×	body	640	valid
129.0ms	779×	body	320	valid
60.0ms	1072×	body	80	valid
43.0ms	406×	body	160	valid