Details

sample156.0ms

Algorithm

intervals

Results

76.0ms	106×	body	1280	valid
20.0ms	28×	body	320	valid
20.0ms	52×	body	640	valid
16.0ms	11×	body	2560	valid
4.0ms	44×	body	80	valid
3.0ms	15×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize9.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sin (+ x eps)) (sin x))
3.7b	(sin (+ x eps))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sin-sum` `add-cbrt-cube` `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:

94.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series95.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify843.0ms

Counts

46 → 46

Iterations

Useful iterations: done (841.0ms)

Iter	Nodes	Cost
0	91	662
1	203	542
2	771	452
done	5000	388

prune138.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
3.6b	(cos (/ (+ (+ x eps) x) 2))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`fma-def` `distribute-lft-out`
3×	`expm1-log1p-u` `associate-r` `associate-l` `sum-log` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

39.0ms	(+ (+ x eps) x)
34.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
54.0ms	(cos (/ (+ (+ x eps) x) 2))

series141.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (+ x eps) x)
69.0ms	(* (sin (/ (+ eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
31.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify950.0ms

Counts

60 → 60

Iterations

Useful iterations: done (948.0ms)

Iter	Nodes	Cost
0	99	768
1	240	695
2	1026	617
done	5000	596

prune314.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (cos (/ (+ (+ x eps) x) 2))))
0.2b	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (cos (/ (+ (+ x eps) x) 2)))))
0.4b	(log1p (cos (/ (+ (+ x eps) x) 2)))
3.6b	(cos (/ (+ (+ x eps) x) 2))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

1.0ms	(expm1 (log1p (cos (/ (+ (+ x eps) x) 2))))
33.0ms	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (cos (/ (+ (+ x eps) x) 2)))))
0.0ms	(log1p (cos (/ (+ (+ x eps) x) 2)))
66.0ms	(cos (/ (+ (+ x eps) x) 2))

series326.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(expm1 (log1p (cos (/ (+ (+ x eps) x) 2))))
126.0ms	(* (sin (/ (+ eps 0) 2)) (expm1 (log1p (cos (/ (+ (+ x eps) x) 2)))))
84.0ms	(log1p (cos (/ (+ (+ x eps) x) 2)))
47.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.0s

Counts

63 → 63

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	94	969
1	204	821
2	671	713
3	3288	693
done	5000	639

prune248.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.3b	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.5b	(expm1 (cos (/ (fma 2 x eps) 2)))
3.6b	(cos (/ (fma 2 x eps) 2))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

33.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
1.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series266.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (sin (/ (+ eps 0) 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
64.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
61.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
27.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.5s

Counts

63 → 63

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	95	903
1	206	763
2	669	669
3	3425	661
done	5000	642

prune303.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

regimes158.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 15.0b

bsearch209.0ms

Steps

Iters	Range		Point
10	5.105604430862771e-28	2.9767731294600714e-09	2.9200806353561473e-09
11	-3.317152845340719e+16	-2.9526231381329305e-09	-1.0387684299316812e-08

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	52
1	37	37
2	38	37
done	38	37

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.7s	3365×	body	1280	valid
1.3s	648×	body	2560	valid
877.0ms	1771×	body	640	valid
634.0ms	773×	body	320	valid
90.0ms	1095×	body	80	valid
57.0ms	348×	body	160	valid