Details

sample92.0ms

Algorithm

intervals

Results

35.0ms	87×	body	1280	valid
22.0ms	24×	body	2560	valid
18.0ms	77×	body	640	valid
4.0ms	28×	body	320	valid
1.0ms	30×	body	80	valid
1.0ms	10×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite59.0ms

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:

49.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series62.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify74.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	192	386
1	538	285
2	2616	275
3	5002	220
done	5002	220

prune117.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.2b

localize15.0ms

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))
2.6b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

13.0ms	(- (* (cos x) (sin eps)) (sin x))
11.0ms	(* (cos x) (sin eps))
11.0ms	(* (sin x) (cos eps))
34.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (* (cos x) (sin eps)) (sin x))
47.0ms	(* (cos x) (sin eps))
47.0ms	(* (sin x) (cos eps))
121.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify52.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	414	729
1	1617	662
2	5002	648
done	5002	648

prune299.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
2.7b	(- (cos eps) 1)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-exp-log`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `associate-l` `log1p-expm1-u`
2×	`difference-of-squares`
1×	`sub-neg` `expm1-def` `flip3--` `diff-log` `difference-of-sqr-1` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

0.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
11.0ms	(* (cos x) (sin eps))
8.0ms	(- (cos eps) 1)

series184.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
46.0ms	(* (cos x) (sin eps))
24.0ms	(- (cos eps) 1)

simplify99.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	276	442
1	932	347
2	3460	325
3	5001	303
done	5001	303

prune231.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(expm1 (log1p (* (cos x) (sin eps))))
0.3b	(log1p (* (cos x) (sin eps)))
2.7b	(- (cos eps) 1)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-exp-log`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u`
3×	`fma-neg` `associate-r` `associate-l`
2×	`difference-of-squares`
1×	`sub-neg` `expm1-def` `log1p-udef` `expm1-log1p` `flip3--` `diff-log` `difference-of-sqr-1` `log1p-expm1` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `expm1-udef` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

13.0ms	(* (cos x) (sin eps))
0.0ms	(expm1 (log1p (* (cos x) (sin eps))))
0.0ms	(log1p (* (cos x) (sin eps)))
9.0ms	(- (cos eps) 1)

series231.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos x) (sin eps))
83.0ms	(expm1 (log1p (* (cos x) (sin eps))))
77.0ms	(log1p (* (cos x) (sin eps)))
20.0ms	(- (cos eps) 1)

simplify90.0ms

Counts

85 → 85

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	271	460
1	877	364
2	3022	339
3	5001	317
done	5001	317

prune241.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes133.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	15	9
done	15	9

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3355×	body	1280	valid
588.0ms	646×	body	2560	valid
431.0ms	1810×	body	640	valid
116.0ms	747×	body	320	valid
60.0ms	1099×	body	80	valid
35.0ms	343×	body	160	valid