Details

sample126.0ms

Algorithm

intervals

Results

53.0ms	53×	body	2560	valid
22.0ms	42×	body	1280	valid
18.0ms	53×	body	640	valid
9.0ms	36×	body	320	valid
6.0ms	58×	body	80	valid
2.0ms	14×	body	160	valid

simplify39.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize14.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1.0 (cos x))
15.9b	(/ (- 1.0 (cos x)) (* x x))

rewrite79.0ms

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:

37.0ms	(- 1.0 (cos x))
40.0ms	(/ (- 1.0 (cos x)) (* x x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(- 1.0 (cos x))
80.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify788.0ms

Counts: 48 → 48

prune215.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b	(* 1/720 (pow x 4))
0.4b	(* 1/24 (pow x 2))
10.8b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

14.0ms	(* 1/720 (pow x 4))
16.0ms	(* 1/24 (pow x 2))
78.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series149.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* 1/720 (pow x 4))
42.0ms	(* 1/24 (pow x 2))
58.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify605.0ms

Counts: 75 → 75

prune231.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.2b	(- 1.0 (cos x))

rewrite115.0ms

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:

51.0ms	(/ (/ (- 1.0 (cos x)) x) x)
34.0ms	(/ (- 1.0 (cos x)) x)
13.0ms	(- 1.0 (cos x))

series163.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(/ (/ (- 1.0 (cos x)) x) x)
66.0ms	(/ (- 1.0 (cos x)) x)
38.0ms	(- 1.0 (cos x))

simplify603.0ms

Counts: 156 → 156

prune350.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
0.2b	(* (cos x) (cos x))
0.4b	(+ 1.0 (cos x))
1.4b	(- (* 1.0 1.0) (* (cos x) (cos x)))

rewrite81.0ms

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:

48.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
12.0ms	(* (cos x) (cos x))
9.0ms	(+ 1.0 (cos x))
10.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (- (* 1.0 1.0) (* (cos x) (cos x))) (* x (+ 1.0 (cos x))))
24.0ms	(* (cos x) (cos x))
11.0ms	(+ 1.0 (cos x))
41.0ms	(- (* 1.0 1.0) (* (cos x) (cos x)))

simplify1.0s

Counts: 93 → 93

prune245.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.2b

bsearch88.0ms

Steps

Iters	Range		Point
10	1.3099675947624547e-09	64828.07766974042	0.030474674340301256
9	-1.9338314318659307	-5.99435871131559e-06	-0.02954252618390405

simplify592.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.7s	1631×	body	2560	valid
589.0ms	1461×	body	640	valid
552.0ms	1237×	body	1280	valid
233.0ms	935×	body	320	valid
162.0ms	2256×	body	80	valid
63.0ms	480×	body	160	valid