Details

sample96.0ms

Algorithm

intervals

Results

44.0ms	45×	body	2560	valid
14.0ms	42×	body	1280	valid
11.0ms	47×	body	640	valid
7.0ms	68×	body	80	valid
6.0ms	34×	body	320	valid
2.0ms	20×	body	160	valid

simplify40.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize13.0ms

Local error

Found 2 expressions with local error:

2.4b	(- 1.0 (cos x))
13.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

6.0ms	(- 1.0 (cos x))
24.0ms	(/ (- 1.0 (cos x)) (* x x))

series125.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- 1.0 (cos x))
98.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.2s

Counts: 48 → 48

prune237.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) x)
0.1b	(/ (/ (- 1.0 (cos x)) x) x)
2.4b	(- 1.0 (cos x))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

33.0ms	(/ (- 1.0 (cos x)) x)
46.0ms	(/ (/ (- 1.0 (cos x)) x) x)
12.0ms	(- 1.0 (cos x))

series156.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (- 1.0 (cos x)) x)
61.0ms	(/ (/ (- 1.0 (cos x)) x) x)
22.0ms	(- 1.0 (cos x))

simplify745.0ms

Counts: 156 → 156

prune377.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
0.3b	(* (cos x) (cos x))
0.5b	(+ 1.0 (cos x))
2.6b	(- (* 1.0 1.0) (* (cos x) (cos x)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
8×	`add-log-exp`
4×	`times-frac` `associate-/l*`
3×	`swap-sqr` `associate-r` `associate-l` `difference-of-squares`
2×	`cbrt-undiv` `sqr-cos` `flip3--` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`+-commutative` `pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `pow-sqr` `cos-mult` `-commutative` `pow-prod-up` `div-inv` `distribute-lft-out` `associate--r+` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

52.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
27.0ms	(* (cos x) (cos x))
12.0ms	(+ 1.0 (cos x))
12.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
29.0ms	(* (cos x) (cos x))
18.0ms	(+ 1.0 (cos x))
46.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify986.0ms

Counts: 93 → 93

prune268.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 (cos x)) (/ (* x (+ 1.0 (cos x))) (- 1.0 (cos x))))
0.5b	(+ 1.0 (cos x))
0.5b	(+ 1.0 (cos x))
2.4b	(- 1.0 (cos x))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

69×	`times-frac`
66×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
14×	`distribute-lft-out`
13×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*` `associate-/r/`
10×	`add-log-exp`
6×	`flip3--` `flip--` `div-inv` `distribute-lft-out--` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-/l*`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `sum-log` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`

Counts

4 → 116

Calls

4 calls:

81.0ms	(/ (+ 1.0 (cos x)) (/ (* x (+ 1.0 (cos x))) (- 1.0 (cos x))))
6.0ms	(+ 1.0 (cos x))
6.0ms	(+ 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series130.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (+ 1.0 (cos x)) (/ (* x (+ 1.0 (cos x))) (- 1.0 (cos x))))
11.0ms	(+ 1.0 (cos x))
16.0ms	(+ 1.0 (cos x))
31.0ms	(- 1.0 (cos x))

simplify1.1s

Counts: 128 → 128

prune365.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes129.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.8b

bsearch131.0ms

Steps

Iters	Range		Point
10	1.5244367550608482e-07	9556.682540875734	0.02733685303105121
9	-1501.2167507114543	-0.006495210018506858	-0.03155884382850993

simplify877.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.8s	1538×	body	2560	valid
638.0ms	1280×	body	1280	valid
529.0ms	1481×	body	640	valid
196.0ms	957×	body	320	valid
139.0ms	2287×	body	80	valid
62.0ms	457×	body	160	valid