Details

sample92.0ms

Algorithm

intervals

Results

41.0ms	96×	body	1280	valid
17.0ms	19×	body	2560	valid
17.0ms	67×	body	640	valid
5.0ms	31×	body	320	valid
2.0ms	33×	body	80	valid
1.0ms	10×	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: 36.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite31.0ms

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:

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

series63.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (sin (+ x eps)) (sin x))
23.0ms	(sin (+ x eps))

simplify1.2s

Counts

46 → 46

Iterations

Useful iterations: 3 (261.0ms)

Iter	Nodes	Cost
0	91	662
1	189	539
2	472	452
3	1618	388
done	5000	388

prune111.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (+ 0 eps) 2)) (cos (/ (+ (+ x eps) x) 2)))
3.5b	(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` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

15.0ms	(+ (+ x eps) x)
13.0ms	(* (sin (/ (+ 0 eps) 2)) (cos (/ (+ (+ x eps) x) 2)))
22.0ms	(cos (/ (+ (+ x eps) x) 2))

series95.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (+ x eps) x)
47.0ms	(* (sin (/ (+ 0 eps) 2)) (cos (/ (+ (+ x eps) x) 2)))
26.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.2s

Counts

60 → 60

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	99	768
1	227	695
2	572	615
3	1507	551
done	5001	550

prune202.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ (+ 0 eps) 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
0.5b	(pow (cos (/ (fma 2 x eps) 2)) 3)
3.5b	(cos (/ (fma 2 x eps) 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
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-l`
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	(* (sin (/ (+ 0 eps) 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
1.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
1.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
2.0ms	(cos (/ (fma 2 x eps) 2))

series144.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin (/ (+ 0 eps) 2)) (cbrt (pow (cos (/ (fma 2 x eps) 2)) 3)))
23.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 3))
45.0ms	(pow (cos (/ (fma 2 x eps) 2)) 3)
27.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.3s

Counts

105 → 105

Iterations

Useful iterations: 3 (739.0ms)

Iter	Nodes	Cost
0	124	1784
1	260	1400
2	755	1252
3	3710	1246
done	5001	1246

prune301.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 2))
0.5b	(cbrt (cos (/ (fma 2 x eps) 2)))
3.5b	(cos (/ (fma 2 x eps) 2))
3.5b	(cos (/ (fma 2 x eps) 2))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down`
2×	`pow1/3`
1×	`unpow2` `sqr-pow`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 2))
1.0ms	(cbrt (cos (/ (fma 2 x eps) 2)))
2.0ms	(cos (/ (fma 2 x eps) 2))
2.0ms	(cos (/ (fma 2 x eps) 2))

series224.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (pow (cos (/ (fma 2 x eps) 2)) 2))
80.0ms	(cbrt (cos (/ (fma 2 x eps) 2)))
27.0ms	(cos (/ (fma 2 x eps) 2))
24.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.3s

Counts

61 → 61

Iterations

Useful iterations: 4 (440.0ms)

Iter	Nodes	Cost
0	74	781
1	145	713
2	311	644
3	628	634
4	2201	618
done	5000	618

prune223.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.3b

regimes129.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 15.1b

bsearch123.0ms

Steps

Iters	Range		Point
8	1.5021325448122442e-13	3.182061564411226e-09	3.1297217212623504e-09
9	-0.04390830018224924	-3.199438276574562e-09	-8.065146023627676e-09

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	53
1	38	38
done	38	38

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	3268×	body	1280	valid
593.0ms	646×	body	2560	valid
487.0ms	1864×	body	640	valid
145.0ms	771×	body	320	valid
63.0ms	1092×	body	80	valid
46.0ms	359×	body	160	valid