Details

sample92.0ms

Algorithm

intervals

Results

48.0ms	145×	body	1280	valid
20.0ms	24×	body	2560	valid
12.0ms	59×	body	640	valid
3.0ms	24×	body	320	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	80	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: 41.0b

localize9.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
4.2b	(cos (+ x eps))

rewrite13.0ms

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

Counts

2 → 40

Calls

2 calls:

7.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

series73.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (cos (+ x eps)) (cos x))
22.0ms	(cos (+ x eps))

simplify1.2s

Counts

46 → 46

Iterations

Useful iterations: 3 (256.0ms)

Iter	Nodes	Cost
0	91	664
1	189	540
2	460	453
3	1565	389
done	5001	389

prune117.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
4.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

41.0ms	(* -2 (* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
15.0ms	(+ (+ x eps) x)
51.0ms	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
21.0ms	(sin (/ (+ (+ x eps) x) 2))

series174.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* -2 (* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
26.0ms	(+ (+ x eps) x)
55.0ms	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
31.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.5s

Counts

84 → 84

Iterations

Useful iterations: 3 (565.0ms)

Iter	Nodes	Cost
0	129	1298
1	300	1154
2	830	995
3	2573	908
done	5001	908

prune279.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
4.4b	(sin (/ (fma 2 x eps) 2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

11.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
2.0ms	(sin (/ (fma 2 x eps) 2))

series95.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
33.0ms	(sin (/ (fma 2 x eps) 2))

simplify4.3s

Counts

35 → 35

Iterations

Useful iterations: 3 (431.0ms)

Iter	Nodes	Cost
0	73	552
1	171	539
2	555	447
3	1678	444
4	3479	444
done	5000	444

prune131.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2))))
0.2b	(log1p (expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))))
0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
4.4b	(sin (/ (fma 2 x eps) 2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `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` `log1p-expm1` `associate-l` `*-commutative` `expm1-udef`

Counts

4 → 51

Calls

4 calls:

0.0ms	(expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2))))
0.0ms	(log1p (expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))))
12.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
2.0ms	(sin (/ (fma 2 x eps) 2))

series307.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2))))
113.0ms	(log1p (expm1 (* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))))
62.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
32.0ms	(sin (/ (fma 2 x eps) 2))

simplify3.6s

Counts

63 → 63

Iterations

Useful iterations: 3 (445.0ms)

Iter	Nodes	Cost
0	98	1072
1	210	1025
2	613	877
3	1856	870
4	3926	870
done	5000	870

prune200.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.2b

regimes228.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.3b

bsearch146.0ms

Steps

Iters	Range		Point
11	2.28145452431431e-18	2231369.5462890854	6.808328837524803e-05
10	-925426.909356872	-1.1036397448000079e-07	-0.0002414674700011765

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	31	53
1	38	51
done	38	51

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	4511×	body	1280	valid
580.0ms	666×	body	2560	valid
363.0ms	1784×	body	640	valid
97.0ms	691×	body	320	valid
25.0ms	259×	body	160	valid
4.0ms	89×	body	80	valid