Details

sample111.0ms

Algorithm

intervals

Results

59.0ms	144×	body	1280	valid
19.0ms	20×	body	2560	valid
15.0ms	58×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	4×	body	80	valid

simplify3.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.6b	(cos (+ x eps))

rewrite52.0ms

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:

42.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series81.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

simplify105.0ms

Counts: 30 → 30

prune86.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.6b

localize19.0ms

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))
2.4b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite72.0ms

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:

10.0ms	(* (cos x) (cos eps))
12.0ms	(+ (* (sin x) (sin eps)) (cos x))
13.0ms	(* (sin x) (sin eps))
35.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos x) (cos eps))
59.0ms	(+ (* (sin x) (sin eps)) (cos x))
51.0ms	(* (sin x) (sin eps))
143.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify41.0ms

Counts: 77 → 77

prune254.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.2b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite110.0ms

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`
4×	`diff-log`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

11.0ms	(* (cos x) (cos eps))
17.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
16.0ms	(* (sin x) (sin eps))
64.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series336.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos x) (cos eps))
93.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
51.0ms	(* (sin x) (sin eps))
143.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify111.0ms

Counts: 82 → 82

prune254.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))
0.2b	(* (sin x) (sin eps))
2.4b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
2.5b	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

77.0ms	(exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))
12.0ms	(* (sin x) (sin eps))
28.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
56.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x))))
49.0ms	(* (sin x) (sin eps))
147.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
142.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

simplify123.0ms

Counts: 81 → 81

prune230.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 15.4b

regimes198.0ms

Accuracy

79.9% (1.9b remaining)

Error of 16.8b against oracle of 15.0b and baseline of 24.4b

bsearch107.0ms

Steps

Iters	Range		Point
9	5.155942382976535e-09	0.001020768799921521	1.0758141977209933e-06
3	-3.0251795372243202e-22	-2.2992823799250236e-22	-2.9798109648931143e-22

simplify1.0ms

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.9s	4405×	body	1280	valid
757.0ms	663×	body	2560	valid
537.0ms	1886×	body	640	valid
171.0ms	700×	body	320	valid
104.0ms	248×	body	160	valid
6.0ms	98×	body	80	valid