Details

sample177.0ms

Algorithm

intervals

Results

75.0ms	98×	body	1280	valid
46.0ms	17×	body	2560	valid
27.0ms	66×	body	640	valid
8.0ms	29×	body	320	valid
3.0ms	34×	body	80	valid
2.0ms	12×	body	160	valid

simplify15.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize20.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
4.1b	(sin (+ x eps))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

110.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

series106.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(- (sin (+ x eps)) (sin x))
32.0ms	(sin (+ x eps))

simplify695.0ms

Counts: 30 → 30

prune138.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
3.1b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`add-log-exp`
10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `associate-l`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate--l+` `sin-cos-mult` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

33.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
13.0ms	(* (sin x) (cos eps))
13.0ms	(* (cos x) (sin eps))
107.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series397.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
58.0ms	(* (sin x) (cos eps))
59.0ms	(* (cos x) (sin eps))
174.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify702.0ms

Counts: 76 → 76

prune375.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (- (cos eps) 1))
1.7b	(- (cos eps) 1)

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-r`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `difference-of-squares`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

52.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
23.0ms	(* (cos x) (sin eps))
36.0ms	(* (sin x) (- (cos eps) 1))
20.0ms	(- (cos eps) 1)

series332.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
81.0ms	(* (cos x) (sin eps))
64.0ms	(* (sin x) (- (cos eps) 1))
36.0ms	(- (cos eps) 1)

simplify758.0ms

Counts: 89 → 89

prune466.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (log (exp (- (cos eps) 1))))
1.7b	(- (cos eps) 1)
1.7b	(log (exp (- (cos eps) 1)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`log-pow`
15×	`log-prod`
14×	`exp-prod` `associate-r`
13×	`add-cube-cbrt`
10×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `exp-sum` `add-log-exp` `difference-of-squares`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`sub-neg`
3×	`difference-of-sqr-1` `distribute-lft-out--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 92

Calls

4 calls:

14.0ms	(* (cos x) (sin eps))
103.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
16.0ms	(- (cos eps) 1)
19.0ms	(log (exp (- (cos eps) 1)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (cos x) (sin eps))
65.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
34.0ms	(- (cos eps) 1)
22.0ms	(log (exp (- (cos eps) 1)))

simplify1.6s

Counts: 104 → 104

prune475.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes253.0ms

Accuracy

4.1% (0.3b remaining)

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

bsearch0.0ms

simplify500.0ms

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.2s	3297×	body	1280	valid
1.4s	1868×	body	640	valid
969.0ms	598×	body	2560	valid
263.0ms	799×	body	320	valid
145.0ms	1091×	body	80	valid
63.0ms	347×	body	160	valid