Details

sample93.0ms

Algorithm

intervals

Results

39.0ms	93×	body	1280	valid
21.0ms	24×	body	2560	valid
15.0ms	60×	body	640	valid
4.0ms	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

localize8.0ms

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

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

5.0ms	(sin (+ x eps))
25.0ms	(- (sin (+ x eps)) (sin x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(sin (+ x eps))
41.0ms	(- (sin (+ x eps)) (sin x))

simplify1.9s

Counts

30 → 30

Iterations

Useful iterations: 4 (422.0ms)

Iter	Nodes	Cost
0	64	309
1	134	295
2	299	281
3	851	275
4	2902	271
done	5000	271

prune68.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 40

Calls

3 calls:

13.0ms	(+ (+ x eps) x)
8.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
20.0ms	(cos (/ (+ (+ x eps) x) 2))

series115.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(+ (+ x eps) x)
70.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
22.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.1s

Counts

49 → 49

Iterations

Useful iterations: 3 (424.0ms)

Iter	Nodes	Cost
0	86	633
1	206	621
2	564	541
3	1914	529
done	5000	529

prune131.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ (+ x eps) x) 2)))
0.2b	(* (log (exp (cos (/ (+ (+ x eps) x) 2)))) (sin (/ eps 2)))
0.5b	(log (exp (cos (/ (+ (+ x eps) x) 2))))
2.0b	(cos (/ (+ (+ x eps) x) 2))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`log-prod` `associate-r`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 55

Calls

4 calls:

18.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
41.0ms	(* (log (exp (cos (/ (+ (+ x eps) x) 2)))) (sin (/ eps 2)))
39.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
20.0ms	(cos (/ (+ (+ x eps) x) 2))

series151.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
64.0ms	(* (log (exp (cos (/ (+ (+ x eps) x) 2)))) (sin (/ eps 2)))
22.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
24.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify909.0ms

Counts

67 → 67

Iterations

Useful iterations: 3 (197.0ms)

Iter	Nodes	Cost
0	97	1017
1	201	917
2	507	801
3	1671	793
done	5000	793

prune192.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

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×	`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 → 85

Calls

4 calls:

14.0ms	(* (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)) (sin (/ eps 2)))
2.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
2.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
23.0ms	(cos (/ (+ (+ x eps) x) 2))

series184.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)) (sin (/ eps 2)))
23.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
57.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
32.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify511.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	114	1726
1	259	1448
2	941	1306
done	5001	1306

prune231.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.5b

regimes111.0ms

Accuracy

99.5% (0.1b remaining)

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

bsearch83.0ms

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: 0 (1.0ms)

Iter	Nodes	Cost
0	27	51
1	35	51
done	35	51

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3253×	body	1280	valid
602.0ms	649×	body	2560	valid
466.0ms	1841×	body	640	valid
128.0ms	779×	body	320	valid
62.0ms	1072×	body	80	valid
46.0ms	406×	body	160	valid