Details

sample181.0ms

Algorithm

intervals

Results

113.0ms	151×	body	1280	valid
26.0ms	21×	body	2560	valid
16.0ms	46×	body	640	valid
6.0ms	23×	body	320	valid
2.0ms	11×	body	160	valid
0.0ms	4×	body	80	valid

simplify15.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize9.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite37.0ms

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:

22.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

series93.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify1.0s

Counts: 30 → 30

prune159.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.3b	(* (sin x) (sin eps))
2.8b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite113.0ms

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:

20.0ms	(* (cos x) (cos eps))
13.0ms	(+ (* (sin x) (sin eps)) (cos x))
16.0ms	(* (sin x) (sin eps))
60.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (cos x) (cos eps))
81.0ms	(+ (* (sin x) (sin eps)) (cos x))
79.0ms	(* (sin x) (sin eps))
203.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify813.0ms

Counts: 77 → 77

prune444.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.6b

localize63.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.4b	(+ (+ (* (sin x) (sin eps)) (cos x)) (* (cos x) (cos eps)))
0.5b	(pow (* (cos x) (cos eps)) 3)
2.6b	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow1`
19×	`add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down`
15×	`add-sqr-sqrt`
11×	`add-log-exp`
9×	`prod-exp` `cos-mult` `cbrt-unprod`
8×	`difference-of-squares`
7×	`*-un-lft-identity` `sqr-pow`
5×	`cube-div` `add-cube-cbrt`
4×	`pow-sqr` `pow-prod-up`
3×	`unpow-prod-down` `pow-unpow` `flip3-+` `cube-prod` `sum-log` `flip-+`
2×	`pow-pow` `pow-plus` `frac-add` `pow-exp` `frac-sub` `rem-cube-cbrt`
1×	`difference-cubes` `+-commutative` `pow2` `cube-mult` `frac-times` `pow-to-exp` `sub-neg` `associate-+l+` `flip3--` `diff-log` `unpow3` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 99

Calls

4 calls:

68.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
93.0ms	(+ (+ (* (sin x) (sin eps)) (cos x)) (* (cos x) (cos eps)))
18.0ms	(pow (* (cos x) (cos eps)) 3)
84.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

series945.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
141.0ms	(+ (+ (* (sin x) (sin eps)) (cos x)) (* (cos x) (cos eps)))
113.0ms	(pow (* (cos x) (cos eps)) 3)
626.0ms	(- (pow (* (cos x) (cos eps)) 3) (pow (+ (* (sin x) (sin eps)) (cos x)) 3))

simplify1.9s

Counts: 111 → 111

prune739.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 13.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.3b	(* (sin x) (sin eps))
2.8b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
2.8b	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

rewrite173.0ms

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:

25.0ms	(+ (* (sin x) (sin eps)) (cos x))
18.0ms	(* (sin x) (sin eps))
41.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
87.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

series532.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(+ (* (sin x) (sin eps)) (cos x))
63.0ms	(* (sin x) (sin eps))
196.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))
203.0ms	(log (exp (- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))))

simplify2.3s

Counts: 76 → 76

prune391.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 13.5b

regimes446.0ms

Accuracy

83.3% (1.7b remaining)

Error of 16.4b against oracle of 14.7b and baseline of 24.8b

bsearch271.0ms

Steps

Iters	Range		Point
10	5.417009055590288e-16	0.00022617661863457038	1.6042103834021895e-07
9	-2.2652292653064335e-05	-4.677215946277263e-14	-3.9683941879655135e-08

simplify1.6s

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.7s	4380×	body	1280	valid
1.3s	709×	body	2560	valid
828.0ms	1821×	body	640	valid
267.0ms	714×	body	320	valid
112.0ms	275×	body	160	valid
13.0ms	101×	body	80	valid