Details

sample166.0ms

Algorithm

intervals

Results

98.0ms	147×	body	1280	valid
27.0ms	20×	body	2560	valid
18.0ms	55×	body	640	valid
4.0ms	17×	body	320	valid
1.0ms	10×	body	160	valid
1.0ms	7×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize24.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
2.4b	(cos (+ x eps))

rewrite69.0ms

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

Counts

2 → 40

Calls

2 calls:

52.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

series87.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(- (cos (+ x eps)) (cos x))
30.0ms	(cos (+ x eps))

simplify798.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
2	723
1	201
0	91

prune314.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(/ (+ x (+ x eps)) 2)
0.3b	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2)))
2.4b	(sin (/ (+ x (+ x eps)) 2))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `sum-log` `fma-def` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

17.0ms	(+ x (+ x eps))
71.0ms	(/ (+ x (+ x eps)) 2)
92.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2)))
44.0ms	(sin (/ (+ x (+ x eps)) 2))

series220.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ x (+ x eps))
57.0ms	(/ (+ x (+ x eps)) 2)
84.0ms	(* (sin (/ (+ eps 0) 2)) (sin (/ (+ x (+ x eps)) 2)))
42.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify898.0ms

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	1294
1	323
0	142

prune745.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (sin (/ (fma 2 x eps) 2)))
0.3b	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
2.5b	(sin (/ (fma 2 x eps) 2))

rewrite33.0ms

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×	`log1p-udef` `expm1-log1p` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `expm1-udef` `unswap-sqr`

Counts

4 → 51

Calls

4 calls:

0.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
0.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
26.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
6.0ms	(sin (/ (fma 2 x eps) 2))

series442.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
104.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
207.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
53.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.7s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
3	3231
2	610
1	186
0	91

prune549.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize77.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (fma 2 x eps) 2)))
2.5b	(sin (/ (fma 2 x eps) 2))
2.5b	(sin (/ (fma 2 x eps) 2))
2.5b	(sin (/ (fma 2 x eps) 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

3.0ms	(cbrt (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))
6.0ms	(sin (/ (fma 2 x eps) 2))
6.0ms	(sin (/ (fma 2 x eps) 2))

series318.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (sin (/ (fma 2 x eps) 2)))
41.0ms	(sin (/ (fma 2 x eps) 2))
62.0ms	(sin (/ (fma 2 x eps) 2))
56.0ms	(sin (/ (fma 2 x eps) 2))

simplify1.2s

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
3	1055
2	294
1	115
0	58

prune460.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.2b

regimes429.0ms

Accuracy

96.9% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.3b

bsearch193.0ms

Steps

Iters	Range		Point
10	7.42116589675916e-09	160.65039477392645	0.00014597753908590782
9	-3322970397.4786234	-6367.3348759504115	-6443.306290177518

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.0s	4435×	body	1280	valid
1.0s	637×	body	2560	valid
865.0ms	1874×	body	640	valid
284.0ms	665×	body	320	valid
123.0ms	307×	body	160	valid
8.0ms	82×	body	80	valid