Details

sample150.0ms

Algorithm

intervals

Results

75.0ms	109×	body	1280	valid
27.0ms	63×	body	640	valid
21.0ms	14×	body	2560	valid
7.0ms	23×	body	320	valid
4.0ms	38×	body	80	valid
2.0ms	9×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize27.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sin (+ x eps)) (sin x))
3.0b	(sin (+ x eps))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

37.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series454.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(- (sin (+ x eps)) (sin x))
397.0ms	(sin (+ x eps))

simplify809.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
3	1449
2	381
1	135
0	63

prune141.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
2.9b	(cos (/ (+ x (+ x eps)) 2))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

13.0ms	(+ x (+ x eps))
15.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
25.0ms	(cos (/ (+ x (+ x eps)) 2))

series173.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ x (+ x eps))
101.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
40.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify547.0ms

Counts

49 → 49

Iterations

Iter	Nodes
done	5000
2	993
1	211
0	86

prune288.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ (* 2 x) eps) 2)))
0.3b	(* (log (exp (cos (/ (+ (* 2 x) eps) 2)))) (sin (/ eps 2)))
0.5b	(log (exp (cos (/ (+ (* 2 x) eps) 2))))
2.9b	(cos (/ (+ (* 2 x) eps) 2))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

13.0ms	(exp (cos (/ (+ (* 2 x) eps) 2)))
37.0ms	(* (log (exp (cos (/ (+ (* 2 x) eps) 2)))) (sin (/ eps 2)))
24.0ms	(log (exp (cos (/ (+ (* 2 x) eps) 2))))
25.0ms	(cos (/ (+ (* 2 x) eps) 2))

series237.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(exp (cos (/ (+ (* 2 x) eps) 2)))
90.0ms	(* (log (exp (cos (/ (+ (* 2 x) eps) 2)))) (sin (/ eps 2)))
41.0ms	(log (exp (cos (/ (+ (* 2 x) eps) 2))))
27.0ms	(cos (/ (+ (* 2 x) eps) 2))

simplify1.4s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
3	3134
2	631
1	198
0	95

prune442.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
2.9b	(cos (/ (+ eps (* 2 x)) 2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
13.0ms	(cos (/ (+ eps (* 2 x)) 2))

series530.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt (sin (/ eps 2)))
160.0ms	(cbrt (sin (/ eps 2)))
166.0ms	(cbrt (sin (/ eps 2)))
27.0ms	(cos (/ (+ eps (* 2 x)) 2))

simplify768.0ms

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
3	1132
2	270
1	115
0	59

prune259.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.3b

regimes221.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 14.9b

bsearch172.0ms

Steps

Iters	Range		Point
8	3.3185797753340088e-09	5.09324609688744e-06	6.520854844146571e-09
11	-938.9819325385033	-2.717163482503313e-19	-1.3793080901766334e-08

simplify6.0ms

Iterations

Iter	Nodes
done	39
3	39
2	37
1	35
0	28

end0.0ms

sample6.9s

Algorithm

intervals

Results

3.8s	3263×	body	1280	valid
1.1s	652×	body	2560	valid
1.0s	1858×	body	640	valid
353.0ms	768×	body	320	valid
153.0ms	1089×	body	80	valid
77.0ms	370×	body	160	valid