Details

sample165.0ms

Algorithm

intervals

Results

76.0ms	111×	body	1280	valid
33.0ms	20×	body	2560	valid
23.0ms	56×	body	640	valid
7.0ms	23×	body	320	valid
3.0ms	36×	body	80	valid
2.0ms	10×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune47.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize19.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
2.3b	(sin (+ x eps))

rewrite77.0ms

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:

67.0ms	(- (sin (+ x eps)) (sin x))
8.0ms	(sin (+ x eps))

series93.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(- (sin (+ x eps)) (sin x))
41.0ms	(sin (+ x eps))

simplify1.1s

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	769
1	202
0	90

prune308.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
2.2b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l` `prod-diff`
5×	`associate-+r+`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sin-cos-mult`
2×	`sum-log` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `fma-def` `flip3-+` `fma-neg` `flip-+`

Counts

4 → 82

Calls

4 calls:

20.0ms	(- (* (cos x) (sin eps)) (sin x))
23.0ms	(* (cos x) (sin eps))
18.0ms	(* (sin x) (cos eps))
41.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (* (cos x) (sin eps)) (sin x))
52.0ms	(* (cos x) (sin eps))
58.0ms	(* (sin x) (cos eps))
148.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify2.4s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	2256
1	439
0	161

prune684.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
2.2b	(fma (sin x) (cos eps) (- (* (cos x) (sin eps)) (sin x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `prod-diff` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `flip--` `unswap-sqr`

Counts

3 → 48

Calls

3 calls:

11.0ms	(- (* (cos x) (sin eps)) (sin x))
16.0ms	(* (cos x) (sin eps))
1.0ms	(fma (sin x) (cos eps) (- (* (cos x) (sin eps)) (sin x)))

series287.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(- (* (cos x) (sin eps)) (sin x))
56.0ms	(* (cos x) (sin eps))
160.0ms	(fma (sin x) (cos eps) (- (* (cos x) (sin eps)) (sin x)))

simplify1.4s

Counts

57 → 57

Iterations

Iter	Nodes
done	5001
2	1156
1	256
0	108

prune516.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
2.2b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`add-log-exp`
9×	`prod-diff`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg`
2×	`sum-log` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `fma-def` `flip3-+` `flip3--` `associate--l+` `flip-+` `sin-cos-mult` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 85

Calls

4 calls:

19.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
17.0ms	(* (cos x) (sin eps))
17.0ms	(* (sin x) (cos eps))
75.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series428.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
70.0ms	(* (cos x) (sin eps))
53.0ms	(* (sin x) (cos eps))
156.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify2.8s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1943
1	394
0	157

prune575.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.9b

regimes288.0ms

Accuracy

86% (1.0b remaining)

Error of 15.6b against oracle of 14.6b and baseline of 21.6b

bsearch194.0ms

Steps

Iters	Range		Point
10	2.1214586855945932e-46	8.360833551528579e-33	3.3956626737642713e-46
8	-1.458922800344795e-69	-3.0445147401029157e-72	-1.3983821349997532e-69

simplify5.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.5s	3320×	body	1280	valid
996.0ms	637×	body	2560	valid
851.0ms	1868×	body	640	valid
193.0ms	725×	body	320	valid
100.0ms	1106×	body	80	valid
72.0ms	344×	body	160	valid