Details

sample104.0ms

Algorithm

intervals

Results

45.0ms	53×	body	2560	valid
18.0ms	41×	body	1280	valid
12.0ms	39×	body	640	valid
8.0ms	34×	body	320	valid
7.0ms	76×	body	80	valid
2.0ms	13×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize7.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1.0 (cos x))
14.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite50.0ms

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))
41.0ms	(/ (- 1.0 (cos x)) (* x x))

series89.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(- 1.0 (cos x))
60.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify52.0ms

Counts: 48 → 48

prune149.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(* 1/24 (pow x 2))
0.3b	(* 1/720 (pow x 4))
13.2b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite115.0ms

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:

18.0ms	(* 1/24 (pow x 2))
21.0ms	(* 1/720 (pow x 4))
73.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series113.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* 1/24 (pow x 2))
41.0ms	(* 1/720 (pow x 4))
46.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify127.0ms

Counts: 75 → 75

prune194.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- 1.0 (cos x))) x)
0.1b	(/ (sqrt (- 1.0 (cos x))) x)
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
40×	`sqrt-prod`
38×	`add-cube-cbrt`
16×	`associate-/l*`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r*`
4×	`pow1` `flip3--` `sqrt-div` `flip--` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 126

Calls

4 calls:

19.0ms	(/ (sqrt (- 1.0 (cos x))) x)
16.0ms	(/ (sqrt (- 1.0 (cos x))) x)
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series255.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (sqrt (- 1.0 (cos x))) x)
96.0ms	(/ (sqrt (- 1.0 (cos x))) x)
19.0ms	(- 1.0 (cos x))
20.0ms	(- 1.0 (cos x))

simplify63.0ms

Counts: 138 → 138

prune427.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(log (exp (- 1.0 (cos x))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

47.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
9.0ms	(- 1.0 (cos x))
9.0ms	(- 1.0 (cos x))
22.0ms	(log (exp (- 1.0 (cos x))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
27.0ms	(- 1.0 (cos x))
32.0ms	(- 1.0 (cos x))
26.0ms	(log (exp (- 1.0 (cos x))))

simplify51.0ms

Counts: 123 → 123

prune400.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 31.9b

bsearch103.0ms

Steps

Iters	Range		Point
10	1.5265582717444966e-05	421651.551737869	0.034460236947598206
9	-3616.0534617336225	-0.01082959410075795	-0.02818960784412063

simplify159.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.8s	1611×	body	2560	valid
456.0ms	1243×	body	1280	valid
449.0ms	1474×	body	640	valid
155.0ms	902×	body	320	valid
127.0ms	2277×	body	80	valid
58.0ms	493×	body	160	valid