Details

sample214.0ms

Algorithm

intervals

Results

106.0ms	104×	body	1280	valid
35.0ms	21×	body	2560	valid
29.0ms	51×	body	640	valid
11.0ms	28×	body	320	valid
5.0ms	36×	body	80	valid
4.0ms	16×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize70.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
3.8b	(sin (+ x eps))

rewrite232.0ms

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` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

190.0ms	(- (sin (+ x eps)) (sin x))
38.0ms	(sin (+ x eps))

series127.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(- (sin (+ x eps)) (sin x))
50.0ms	(sin (+ x eps))

simplify7.5s

Counts

48 → 48

Iterations

Iter	Nodes
done	5007
4	3899
3	1262
2	462
1	204
0	92

prune482.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize88.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (fma 2 x eps) 2)
0.2b	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
3.6b	(cos (/ (fma 2 x eps) 2))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-cos-mult` `unswap-sqr`

Counts

3 → 62

Calls

3 calls:

23.0ms	(/ (fma 2 x eps) 2)
51.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
9.0ms	(cos (/ (fma 2 x eps) 2))

series239.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (fma 2 x eps) 2)
121.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
44.0ms	(cos (/ (fma 2 x eps) 2))

simplify5.7s

Counts

71 → 71

Iterations

Iter	Nodes
done	5004
3	2153
2	631
1	235
0	117

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize155.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (* 1/2 eps)) (log1p (expm1 (cos (fma 1/2 eps x)))))
0.2b	(log1p (expm1 (cos (fma 1/2 eps x))))
0.4b	(expm1 (cos (fma 1/2 eps x)))
3.6b	(cos (fma 1/2 eps x))

rewrite63.0ms

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` `insert-posit16` `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 → 56

Calls

4 calls:

51.0ms	(* (sin (* 1/2 eps)) (log1p (expm1 (cos (fma 1/2 eps x)))))
1.0ms	(log1p (expm1 (cos (fma 1/2 eps x))))
2.0ms	(expm1 (cos (fma 1/2 eps x)))
7.0ms	(cos (fma 1/2 eps x))

series527.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(* (sin (* 1/2 eps)) (log1p (expm1 (cos (fma 1/2 eps x)))))
114.0ms	(log1p (expm1 (cos (fma 1/2 eps x))))
83.0ms	(expm1 (cos (fma 1/2 eps x)))
49.0ms	(cos (fma 1/2 eps x))

simplify6.5s

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
4	3342
3	1242
2	490
1	195
0	96

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize128.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (* 1/2 eps)) (sin x))
0.2b	(* (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))))

rewrite114.0ms

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` `insert-posit16` `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 → 67

Calls

4 calls:

61.0ms	(* (sin (* 1/2 eps)) (sin x))
42.0ms	(* (sin (* 1/2 eps)) (log1p (expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))))
3.0ms	(log1p (expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))))
3.0ms	(expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

series1.3s

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (sin (* 1/2 eps)) (sin x))
478.0ms	(* (sin (* 1/2 eps)) (log1p (expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))))
394.0ms	(log1p (expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))))
298.0ms	(expm1 (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))

simplify4.6s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	1577
2	583
1	261
0	119

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes539.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.9s	3236×	body	1280	valid
1.7s	1918×	body	640	valid
876.0ms	617×	body	2560	valid
281.0ms	766×	body	320	valid
148.0ms	1090×	body	80	valid
83.0ms	373×	body	160	valid