Details

sample95.0ms

Algorithm

intervals

Results

48.0ms	133×	body	1280	valid
19.0ms	22×	body	2560	valid
14.0ms	67×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	2×	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: 37.5b

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
4.0b	(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))

series68.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify1.2s

Counts

46 → 46

Iterations

Useful iterations: 3 (250.0ms)

Iter	Nodes	Cost
0	91	664
1	198	540
2	533	453
3	2210	389
done	5000	389

prune107.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

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))

rewrite135.0ms

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:

43.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
15.0ms	(+ (+ x eps) x)
53.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
21.0ms	(sin (/ (+ (+ x eps) x) 2))

series169.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* -2 (* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
24.0ms	(+ (+ x eps) x)
53.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
31.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify3.5s

Counts

84 → 84

Iterations

Useful iterations: 3 (455.0ms)

Iter	Nodes	Cost
0	129	1298
1	303	1154
2	971	995
3	4339	908
done	5000	908

prune438.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (* -2 (sin (* 1/2 eps))) (sin (/ (+ (+ x eps) x) 2)))
4.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`fma-def` `distribute-lft-out`
3×	`expm1-log1p-u` `associate-r` `pow-prod-down` `prod-exp` `sum-log` `cbrt-unprod` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

3 → 50

Calls

3 calls:

15.0ms	(+ (+ x eps) x)
42.0ms	(* (* -2 (sin (* 1/2 eps))) (sin (/ (+ (+ x eps) x) 2)))
21.0ms	(sin (/ (+ (+ x eps) x) 2))

series114.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(+ (+ x eps) x)
64.0ms	(* (* -2 (sin (* 1/2 eps))) (sin (/ (+ (+ x eps) x) 2)))
28.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.1s

Counts

59 → 59

Iterations

Useful iterations: 3 (396.0ms)

Iter	Nodes	Cost
0	97	751
1	253	723
2	828	615
3	3532	559
done	5000	559

prune177.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ eps 0) 2)))
0.6b	(cbrt (sin (/ (+ eps 0) 2)))
0.6b	(cbrt (sin (/ eps 2)))
4.1b	(sin (* (fma 2 x eps) 1/2))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`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×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

3.0ms	(cbrt (sin (/ (+ eps 0) 2)))
3.0ms	(cbrt (sin (/ (+ eps 0) 2)))
1.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(sin (* (fma 2 x eps) 1/2))

series354.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (sin (/ (+ eps 0) 2)))
106.0ms	(cbrt (sin (/ (+ eps 0) 2)))
106.0ms	(cbrt (sin (/ eps 2)))
33.0ms	(sin (* (fma 2 x eps) 1/2))

simplify696.0ms

Counts

60 → 60

Iterations

Useful iterations: 3 (142.0ms)

Iter	Nodes	Cost
0	78	670
1	135	585
2	302	541
3	1182	501
done	5000	501

prune268.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.3b

regimes147.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.2b

bsearch114.0ms

Steps

Iters	Range		Point
8	9.143643357499823e-08	5.968040026638966e-05	2.684800803254601e-05
9	-4030.930838101798	-2.879878352494296e-05	-4.402851865399074e-05

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	50
1	36	50
done	36	50

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4457×	body	1280	valid
591.0ms	686×	body	2560	valid
401.0ms	1837×	body	640	valid
96.0ms	656×	body	320	valid
33.0ms	292×	body	160	valid
4.0ms	72×	body	80	valid