Details

sample267.0ms

Algorithm

intervals

Results

143.0ms	153×	body	1280	valid
54.0ms	49×	body	640	valid
42.0ms	20×	body	2560	valid
10.0ms	23×	body	320	valid
3.0ms	10×	body	160	valid
0.0ms	1×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize13.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite63.0ms

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:

56.0ms	(- (cos (+ x eps)) (cos x))
6.0ms	(cos (+ x eps))

series109.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(- (cos (+ x eps)) (cos x))
33.0ms	(cos (+ x eps))

simplify2.0s

Counts

46 → 46

Iterations

Iter	Nodes
4	2973
3	1076
2	407
1	198
0	91

prune368.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

38.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
25.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
5.0ms	(sin (/ (fma 2 x eps) 2))

series273.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
101.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
61.0ms	(sin (/ (fma 2 x eps) 2))

simplify4.3s

Counts

60 → 60

Iterations

Iter	Nodes
4	5515
3	1749
2	590
1	219
0	99

prune729.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

47.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series165.0ms

Counts

2 → 6

Calls

2 calls:

112.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
53.0ms	(sin (/ (fma 2 x eps) 2))

simplify3.9s

Counts

35 → 35

Iterations

Iter	Nodes
4	4883
3	1649
2	481
1	169
0	71

prune456.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (sin (/ (fma 2 x eps) 2)))
0.3b	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
0.3b	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

1.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
0.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
32.0ms	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
3.0ms	(sin (/ (fma 2 x eps) 2))

series305.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
64.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
122.0ms	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
51.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.5s

Counts

63 → 63

Iterations

Iter	Nodes
4	3443
3	1544
2	552
1	217
0	96

prune710.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.4b

regimes242.0ms

Accuracy

97.5% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.9b

bsearch191.0ms

Steps

Iters	Range		Point
9	2.856347663939308e-08	0.9676876931049737	0.0001353150742087212
8	-1.3860482868045466e-05	-3.3361098338481354e-09	-7.94700459656321e-06

simplify9.0ms

Iterations

Iter	Nodes
2	31
1	31
0	27

end0.0ms

sample8.6s

Algorithm

intervals

Results

5.1s	4466×	body	1280	valid
1.7s	1878×	body	640	valid
1.2s	624×	body	2560	valid
286.0ms	669×	body	320	valid
67.0ms	266×	body	160	valid
14.0ms	97×	body	80	valid