Details

sample147.0ms

Algorithm

intervals

Results

76.0ms	137×	body	1280	valid
26.0ms	21×	body	2560	valid
19.0ms	55×	body	640	valid
6.0ms	24×	body	320	valid
3.0ms	17×	body	160	valid
0.0ms	2×	body	80	valid

simplify3.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.1b

localize42.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (cos (+ x eps)) (cos x))
4.3b	(cos (+ x eps))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

16.0ms	(- (cos (+ x eps)) (cos x))
11.0ms	(cos (+ x eps))

series104.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (cos (+ x eps)) (cos x))
18.0ms	(cos (+ x eps))

simplify105.0ms

Counts: 30 → 30

prune109.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.8b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

13.0ms	(* (cos x) (cos eps))
13.0ms	(+ (* (sin x) (sin eps)) (cos x))
13.0ms	(* (sin x) (sin eps))
40.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos x) (cos eps))
72.0ms	(+ (* (sin x) (sin eps)) (cos x))
66.0ms	(* (sin x) (sin eps))
199.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify164.0ms

Counts: 77 → 77

prune367.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
0.3b	(log (exp (+ (* (sin x) (sin eps)) (cos x))))
8.8b	(- (* (cos x) (cos eps)) (log (exp (+ (* (sin x) (sin eps)) (cos x)))))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`log-prod`
7×	`pow1` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`log-pow` `associate--r+`
3×	`exp-prod` `associate-r` `associate-l`
2×	`exp-sum`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

24.0ms	(+ (* (sin x) (sin eps)) (cos x))
24.0ms	(* (sin x) (sin eps))
47.0ms	(log (exp (+ (* (sin x) (sin eps)) (cos x))))
65.0ms	(- (* (cos x) (cos eps)) (log (exp (+ (* (sin x) (sin eps)) (cos x)))))

series433.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (* (sin x) (sin eps)) (cos x))
52.0ms	(* (sin x) (sin eps))
95.0ms	(log (exp (+ (* (sin x) (sin eps)) (cos x))))
216.0ms	(- (* (cos x) (cos eps)) (log (exp (+ (* (sin x) (sin eps)) (cos x)))))

simplify90.0ms

Counts: 74 → 74

prune389.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.9b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.6b	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))
2.8b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

27.0ms	(+ (* (sin x) (sin eps)) (cos x))
28.0ms	(* (sin x) (sin eps))
100.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))
66.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (* (sin x) (sin eps)) (cos x))
84.0ms	(* (sin x) (sin eps))
197.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))
171.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify114.0ms

Counts: 76 → 76

prune376.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 13.9b

regimes370.0ms

Accuracy

83.6% (1.6b remaining)

Error of 16.6b against oracle of 15.0b and baseline of 24.6b

bsearch257.0ms

Steps

Iters	Range		Point
10	8.879694756015093e-10	208.71590408624647	5.093598697252222e-08
10	-0.00045950116694092144	-7.210541768011361e-14	-1.1761155027807802e-08

simplify122.0ms

end0.0ms

sample6.8s

Algorithm

intervals

Results

3.9s	4407×	body	1280	valid
1.1s	674×	body	2560	valid
1.1s	1844×	body	640	valid
239.0ms	673×	body	320	valid
52.0ms	306×	body	160	valid
9.0ms	96×	body	80	valid