Details

sample193.0ms

Algorithm

intervals

Results

87.0ms	105×	body	1280	valid
28.0ms	59×	body	640	valid
26.0ms	17×	body	2560	valid
25.0ms	23×	body	320	valid
5.0ms	42×	body	80	valid
2.0ms	10×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.4b	(- (sin (+ x eps)) (sin x))
3.3b	(sin (+ x eps))

rewrite104.0ms

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

Counts

2 → 40

Calls

2 calls:

95.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series82.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
36.0ms	(sin (+ x eps))

simplify3.0s

Counts

46 → 46

Iterations

Iter	Nodes
done	5002
4	3880
3	1287
2	445
1	201
0	90

prune259.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
3.1b	(cos (/ (fma 2 x eps) 2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

27.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
5.0ms	(cos (/ (fma 2 x eps) 2))

series112.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
41.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.5s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
4	2892
3	1011
2	353
1	148
0	66

prune267.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (* 1/2 eps)) (expm1 (log1p (cos (fma 1/2 eps x)))))
0.2b	(expm1 (log1p (cos (fma 1/2 eps x))))
0.4b	(log1p (cos (fma 1/2 eps x)))
3.1b	(cos (fma 1/2 eps x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

17.0ms	(* (sin (* 1/2 eps)) (expm1 (log1p (cos (fma 1/2 eps x)))))
0.0ms	(expm1 (log1p (cos (fma 1/2 eps x))))
1.0ms	(log1p (cos (fma 1/2 eps x)))
4.0ms	(cos (fma 1/2 eps x))

series222.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sin (* 1/2 eps)) (expm1 (log1p (cos (fma 1/2 eps x)))))
57.0ms	(expm1 (log1p (cos (fma 1/2 eps x))))
64.0ms	(log1p (cos (fma 1/2 eps x)))
24.0ms	(cos (fma 1/2 eps x))

simplify2.7s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
4	2455
3	924
2	401
1	177
0	89

prune449.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))))
0.2b	(* (sin (* 1/2 eps)) (expm1 (log1p (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))))
0.2b	(* (sin (* 1/2 eps)) (sin x))
0.5b	(log1p (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

0.0ms	(expm1 (log1p (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))))
15.0ms	(* (sin (* 1/2 eps)) (expm1 (log1p (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))))
31.0ms	(* (sin (* 1/2 eps)) (sin x))
1.0ms	(log1p (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

series642.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(expm1 (log1p (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))))
220.0ms	(* (sin (* 1/2 eps)) (expm1 (log1p (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))))
60.0ms	(* (sin (* 1/2 eps)) (sin x))
143.0ms	(log1p (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

simplify2.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	5008
3	1798
2	594
1	240
0	112

prune563.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes240.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	28
1	28
0	21

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.3s	3248×	body	1280	valid
1.0s	650×	body	2560	valid
746.0ms	1858×	body	640	valid
271.0ms	778×	body	320	valid
145.0ms	1140×	body	80	valid
72.0ms	326×	body	160	valid