Details

sample89.0ms

Algorithm

intervals

Results

37.0ms	98×	body	1280	valid
20.0ms	24×	body	2560	valid
14.0ms	62×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	33×	body	80	valid
1.0ms	14×	body	160	valid

simplify4.0ms

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: 38.2b

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
5.1b	(sin (+ x eps))

rewrite63.0ms

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:

53.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series64.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify72.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (68.0ms)

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

prune111.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (cos eps))
0.1b	(* (cos x) (sin eps))
4.6b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite98.0ms

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

Counts

4 → 85

Calls

4 calls:

15.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
11.0ms	(* (sin x) (cos eps))
12.0ms	(* (cos x) (sin eps))
58.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series302.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
50.0ms	(* (sin x) (cos eps))
44.0ms	(* (cos x) (sin eps))
120.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify53.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	373	918
1	1424	763
2	5001	741
done	5001	741

prune276.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

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))
2.2b	(- (cos eps) 1)

rewrite24.0ms

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)

series181.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
44.0ms	(* (cos x) (sin eps))
20.0ms	(- (cos eps) 1)

simplify99.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	272	454
1	926	348
2	3454	326
3	5001	304
done	5001	304

prune227.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (cos eps) 1))
0.1b	(* (cos x) (sin eps))
2.2b	(- (cos eps) 1)
2.2b	(log (exp (- (cos eps) 1)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
28×	`add-cube-cbrt`
27×	`prod-diff`
22×	`exp-sum`
14×	`log-prod` `exp-prod`
9×	`add-log-exp`
8×	`log-pow`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `difference-of-sqr-1` `associate-r` `associate-l` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`log-div` `expm1-def` `flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

17.0ms	(exp (- (cos eps) 1))
11.0ms	(* (cos x) (sin eps))
8.0ms	(- (cos eps) 1)
19.0ms	(log (exp (- (cos eps) 1)))

series130.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(exp (- (cos eps) 1))
44.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)
23.0ms	(log (exp (- (cos eps) 1)))

simplify102.0ms

Counts

126 → 126

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	312	784
1	989	541
2	3382	449
3	5002	441
done	5002	441

prune324.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes118.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	9
1	19	9
2	19	9
done	19	9

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	3276×	body	1280	valid
564.0ms	646×	body	2560	valid
447.0ms	1856×	body	640	valid
111.0ms	758×	body	320	valid
58.0ms	1092×	body	80	valid
37.0ms	372×	body	160	valid