Details

sample144.0ms

Algorithm

intervals

Results

66.0ms	110×	body	1280	valid
31.0ms	25×	body	2560	valid
18.0ms	46×	body	640	valid
7.0ms	26×	body	320	valid
3.0ms	38×	body	80	valid
2.0ms	11×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize28.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (sin (+ x eps)) (sin x))
3.7b	(sin (+ x eps))

rewrite93.0ms

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:

77.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series115.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(- (sin (+ x eps)) (sin x))
43.0ms	(sin (+ x eps))

simplify3.2s

Counts

46 → 46

Iterations

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

prune243.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
3.7b	(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)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series134.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
46.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.0s

Counts

36 → 36

Iterations

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

prune287.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (* 1/2 eps)) (log1p (expm1 (cos (fma 1/2 eps x)))))
0.3b	(log1p (expm1 (cos (fma 1/2 eps x))))
0.5b	(expm1 (cos (fma 1/2 eps x)))
3.7b	(cos (fma 1/2 eps x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`log1p-expm1-u`
4×	`expm1-log1p-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:

26.0ms	(* (sin (* 1/2 eps)) (log1p (expm1 (cos (fma 1/2 eps x)))))
0.0ms	(log1p (expm1 (cos (fma 1/2 eps x))))
1.0ms	(expm1 (cos (fma 1/2 eps x)))
4.0ms	(cos (fma 1/2 eps x))

series296.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (sin (* 1/2 eps)) (log1p (expm1 (cos (fma 1/2 eps x)))))
77.0ms	(log1p (expm1 (cos (fma 1/2 eps x))))
68.0ms	(expm1 (cos (fma 1/2 eps x)))
23.0ms	(cos (fma 1/2 eps x))

simplify3.4s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
4	3032
3	1131
2	456
1	192
0	92

prune358.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (* 1/2 eps)) (sin x))
0.3b	(* (sin (* 1/2 eps)) (log1p (expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))))
0.3b	(log1p (expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))))
0.4b	(expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

rewrite34.0ms

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×	`log1p-expm1-u`
4×	`expm1-log1p-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:

18.0ms	(* (sin (* 1/2 eps)) (sin x))
13.0ms	(* (sin (* 1/2 eps)) (log1p (expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))))
0.0ms	(log1p (expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))))
0.0ms	(expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

series613.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sin (* 1/2 eps)) (sin x))
187.0ms	(* (sin (* 1/2 eps)) (log1p (expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))))
173.0ms	(log1p (expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))))
177.0ms	(expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

simplify1.9s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	1805
2	600
1	257
0	115

prune489.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes237.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.2s	3309×	body	1280	valid
981.0ms	671×	body	2560	valid
808.0ms	1805×	body	640	valid
207.0ms	794×	body	320	valid
127.0ms	1079×	body	80	valid
56.0ms	342×	body	160	valid