Details

sample187.0ms

Algorithm

intervals

Results

104.0ms	152×	body	1280	valid
36.0ms	25×	body	2560	valid
23.0ms	52×	body	640	valid
6.0ms	20×	body	320	valid
1.0ms	5×	body	160	valid
0.0ms	2×	body	80	valid

simplify1.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.1b	(cos (+ x eps))

rewrite58.0ms

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:

43.0ms	(- (cos (+ x eps)) (cos x))
12.0ms	(cos (+ x eps))

series143.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(- (cos (+ x eps)) (cos x))
46.0ms	(cos (+ x eps))

simplify106.0ms

Counts: 30 → 30

prune97.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.6b

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))
1.6b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite119.0ms

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:

12.0ms	(* (cos x) (cos eps))
22.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
14.0ms	(* (sin x) (sin eps))
70.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series468.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos x) (cos eps))
117.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
89.0ms	(* (sin x) (sin eps))
206.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify123.0ms

Counts: 82 → 82

prune395.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.4b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
0.3b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.4b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.5b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite565.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`difference-of-squares`
15×	`unpow-prod-down` `cube-prod`
11×	`add-log-exp`
9×	`add-cube-cbrt` `sqr-pow`
8×	`frac-times` `cos-mult` `sin-mult`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`flip3-+` `flip-+`
5×	`flip3--` `flip--` `distribute-lft-out--`
4×	`cube-div` `associate-r` `associate-*l/` `frac-sub` `sub-div`
3×	`pow-unpow` `associate-l`
2×	`sub-neg` `associate-+l+` `diff-log` `associate-*r/` `sum-log` `distribute-lft-out`
1×	`difference-cubes` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `associate-+l-` `pow-pow` `distribute-lft-in` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

270.0ms	(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
75.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
39.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
176.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series1.6s

Counts

4 → 12

Calls

4 calls:

308.0ms	(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
174.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
182.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
984.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify136.0ms

Counts: 124 → 124

prune895.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.3b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.4b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.5b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))
1.6b	(log (exp (- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))))

rewrite503.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
32×	`difference-of-squares`
31×	`*-un-lft-identity`
27×	`unpow-prod-down` `cube-prod`
26×	`log-pow`
25×	`exp-prod`
17×	`sqr-pow`
11×	`add-log-exp`
10×	`distribute-lft-out--`
9×	`add-cube-cbrt`
6×	`pow1`
5×	`add-exp-log` `log-prod` `add-cbrt-cube`
4×	`cube-div`
3×	`sub-neg` `pow-unpow`
2×	`difference-cubes` `associate-+l+` `flip3--` `diff-log` `exp-sum` `sum-log` `cos-mult` `flip--` `sin-mult`
1×	`+-commutative` `cube-mult` `pow-to-exp` `associate-+l-` `log-div` `pow-pow` `flip3-+` `exp-diff` `unpow3` `rem-log-exp` `pow-exp` `frac-sub` `flip-+` `distribute-lft-out` `sub-div` `rem-cube-cbrt`

Counts

4 → 117

Calls

4 calls:

43.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
22.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
148.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))
284.0ms	(log (exp (- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))))

series2.3s

Counts

4 → 12

Calls

4 calls:

171.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
186.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
984.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))
957.0ms	(log (exp (- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))))

simplify100.0ms

Counts: 129 → 129

prune678.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.3b

regimes511.0ms

Accuracy

79.3% (2.0b remaining)

Error of 16.8b against oracle of 14.8b and baseline of 24.6b

bsearch244.0ms

Steps

Iters	Range		Point
10	6.0751252995412134e-09	32504.544960343763	1.7276716505734754e-07
9	-1.0272743538273853e-31	-3.3489748359982436e-41	-9.968609389610828e-32

simplify149.0ms

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.6s	4484×	body	1280	valid
1.1s	644×	body	2560	valid
1.0s	1849×	body	640	valid
209.0ms	693×	body	320	valid
49.0ms	250×	body	160	valid
8.0ms	80×	body	80	valid