Details

sample97.0ms

Algorithm

intervals

Results

47.0ms	117×	body	1280	valid
21.0ms	24×	body	2560	valid
12.0ms	52×	body	640	valid
4.0ms	27×	body	320	valid
1.0ms	29×	body	80	valid
1.0ms	7×	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: 39.0b

localize9.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (sin (+ x eps)) (sin x))
2.2b	(sin (+ x eps))

rewrite67.0ms

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:

56.0ms	(- (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))
19.0ms	(sin (+ x eps))

simplify75.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (71.0ms)

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

prune115.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.8b

localize15.0ms

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))
3.2b	(- (+ (* (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))
11.0ms	(* (cos x) (sin eps))
59.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series304.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
45.0ms	(* (sin x) (cos eps))
46.0ms	(* (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 (42.0ms)

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

prune277.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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))
1.9b	(- (cos eps) 1)

rewrite22.0ms

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)

series185.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
47.0ms	(* (cos x) (sin eps))
23.0ms	(- (cos eps) 1)

simplify98.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (93.0ms)

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

prune226.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (- (cos eps) 1))
1.9b	(- (cos eps) 1)

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
45×	`*-un-lft-identity` `prod-diff`
39×	`add-cube-cbrt`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`associate-r`
9×	`add-exp-log`
8×	`pow1` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`fma-neg`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `expm1-def` `fma-def` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 135

Calls

4 calls:

26.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
11.0ms	(* (cos x) (sin eps))
32.0ms	(* (sin x) (- (cos eps) 1))
8.0ms	(- (cos eps) 1)

series235.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
49.0ms	(* (cos x) (sin eps))
48.0ms	(* (sin x) (- (cos eps) 1))
21.0ms	(- (cos eps) 1)

simplify53.0ms

Counts

147 → 147

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	446	1178
1	1727	907
2	5001	882
done	5001	882

prune394.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes105.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	17
1	36	17
2	36	17
done	36	17

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3395×	body	1280	valid
567.0ms	627×	body	2560	valid
432.0ms	1811×	body	640	valid
135.0ms	789×	body	320	valid
53.0ms	1058×	body	80	valid
33.0ms	320×	body	160	valid