Details

sample88.0ms

Algorithm

intervals

Results

41.0ms	61×	body	2560	valid
14.0ms	41×	body	1280	valid
11.0ms	46×	body	640	valid
5.0ms	70×	body	80	valid
5.0ms	30×	body	320	valid
1.0ms	8×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

localize11.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1.0 (cos x))
17.8b	(/ (- 1.0 (cos x)) (* x x))

rewrite59.0ms

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:

7.0ms	(- 1.0 (cos x))
50.0ms	(/ (- 1.0 (cos x)) (* x x))

series85.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1.0 (cos x))
64.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify39.0ms

Counts: 48 → 48

prune105.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/720 (pow x 4)) 1/2)
0.3b	(* 1/720 (pow x 4))
0.4b	(* 1/24 (pow x 2))
13.2b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

15.0ms	(+ (* 1/720 (pow x 4)) 1/2)
19.0ms	(* 1/720 (pow x 4))
12.0ms	(* 1/24 (pow x 2))
62.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(+ (* 1/720 (pow x 4)) 1/2)
64.0ms	(* 1/720 (pow x 4))
41.0ms	(* 1/24 (pow x 2))
74.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify154.0ms

Counts: 89 → 89

prune200.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.5b	(- 1.0 (cos x))

rewrite60.0ms

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:

25.0ms	(/ (/ (- 1.0 (cos x)) x) x)
17.0ms	(/ (- 1.0 (cos x)) x)
7.0ms	(- 1.0 (cos x))

series138.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(/ (/ (- 1.0 (cos x)) x) x)
62.0ms	(/ (- 1.0 (cos x)) x)
20.0ms	(- 1.0 (cos x))

simplify55.0ms

Counts: 156 → 156

prune442.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) x)
0.2b	(exp (log (- 1.0 (cos x))))
0.2b	(log (- 1.0 (cos x)))
1.5b	(- 1.0 (cos x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

33.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
7.0ms	(exp (log (- 1.0 (cos x))))
5.0ms	(log (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))

series228.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
23.0ms	(exp (log (- 1.0 (cos x))))
109.0ms	(log (- 1.0 (cos x)))
22.0ms	(- 1.0 (cos x))

simplify77.0ms

Counts: 110 → 110

prune253.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.1b

bsearch118.0ms

Steps

Iters	Range		Point
9	8.845201659255268e-06	4.45864614599283	0.028747241674498873
10	-119.54622503529531	-1.822584514918214e-10	-0.029278016723559293

simplify37.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.9s	1578×	body	2560	valid
673.0ms	1516×	body	640	valid
591.0ms	1246×	body	1280	valid
228.0ms	927×	body	320	valid
219.0ms	2257×	body	80	valid
65.0ms	476×	body	160	valid