Details

sample154.0ms

Algorithm

intervals

Results

86.0ms	137×	body	1280	valid
24.0ms	17×	body	2560	valid
21.0ms	63×	body	640	valid
7.0ms	29×	body	320	valid
2.0ms	8×	body	160	valid
0.0ms	2×	body	80	valid

simplify16.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.5b

localize10.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
4.0b	(cos (+ x eps))

rewrite38.0ms

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:

26.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series154.0ms

Counts

2 → 6

Calls

2 calls:

122.0ms	(- (cos (+ x eps)) (cos x))
31.0ms	(cos (+ x eps))

simplify2.3s

Counts: 30 → 30

prune120.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.3b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite152.0ms

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:

15.0ms	(* (cos x) (cos eps))
17.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
12.0ms	(* (sin x) (sin eps))
105.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series426.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (cos x) (cos eps))
116.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
63.0ms	(* (sin x) (sin eps))
180.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify2.1s

Counts: 82 → 82

prune402.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.2b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.3b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite110.0ms

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:

21.0ms	(* (cos eps) (cos x))
25.0ms	(+ (* (sin x) (sin eps)) (cos x))
21.0ms	(* (sin x) (sin eps))
39.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (cos eps) (cos x))
95.0ms	(+ (* (sin x) (sin eps)) (cos x))
56.0ms	(* (sin x) (sin eps))
223.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify2.3s

Counts: 77 → 77

prune438.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.3b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.4b	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

17.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
24.0ms	(* (sin x) (sin eps))
75.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
93.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

series553.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
70.0ms	(* (sin x) (sin eps))
177.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
196.0ms	(log (exp (- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))))

simplify1.8s

Counts: 85 → 85

prune399.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 12.1b

regimes306.0ms

Accuracy

82.6% (1.8b remaining)

Error of 15.8b against oracle of 14.1b and baseline of 24.3b

bsearch122.0ms

Steps

Iters	Range		Point
5	3.7315339822697444e-35	1.0010330982186762e-34	9.786213880671446e-35
7	-0.006495210018506858	-9.497075983896804e-05	-0.00011972221757882519

simplify544.0ms

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.7s	4513×	body	1280	valid
802.0ms	1834×	body	640	valid
783.0ms	598×	body	2560	valid
173.0ms	703×	body	320	valid
77.0ms	269×	body	160	valid
7.0ms	83×	body	80	valid