Details

sample194.0ms

Algorithm

intervals

Results

114.0ms	103×	body	1280	valid
46.0ms	86×	body	640	valid
11.0ms	37×	body	320	valid
5.0ms	256×	pre	80	true
4.0ms	25×	body	160	valid
0.0ms	5×	body	80	valid

simplify2.0ms

Counts: 1 → 1

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 62.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.8b	(log (- 1.0 x))
6.9b	(log (+ 1.0 x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`times-frac`
15×	`pow1` `add-cube-cbrt`
12×	`log-pow`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-div`
5×	`add-cbrt-cube`
4×	`associate-/r` `associate-/l`
3×	`add-log-exp`
2×	`flip3--` `div-sub` `rem-log-exp` `flip--`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 69

Calls

3 calls:

17.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.0ms	(log (- 1.0 x))
5.0ms	(log (+ 1.0 x))

series751.0ms

Counts

3 → 9

Calls

3 calls:

606.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
58.0ms	(log (- 1.0 x))
87.0ms	(log (+ 1.0 x))

simplify38.0ms

Counts: 78 → 78

prune286.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 59.5b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
6.8b	(log (- 1.0 x))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

92×	`times-frac`
83×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`pow1` `div-exp` `prod-exp` `add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
5×	`log-prod` `log-pow`
4×	`log-div` `associate-/r/` `associate-/l*`
3×	`flip3--` `associate-r/` `associate-l` `associate-/r` `flip--` `add-log-exp`
2×	`cbrt-undiv` `div-sub` `frac-sub` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `flip3-+` `rem-log-exp` `pow-prod-down` `clear-num` `*-commutative` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 163

Calls

3 calls:

105.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
66.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
11.0ms	(log (- 1.0 x))

series357.0ms

Counts

3 → 9

Calls

3 calls:

193.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
81.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
82.0ms	(log (- 1.0 x))

simplify69.0ms

Counts: 172 → 172

prune718.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
158×	`add-sqr-sqrt`
136×	`associate-r`
112×	`unpow-prod-down`
94×	`*-un-lft-identity`
82×	`add-cube-cbrt`
51×	`add-exp-log`
48×	`unpow2` `sqr-pow`
34×	`unswap-sqr`
20×	`prod-exp`
19×	`div-exp`
15×	`add-cbrt-cube`
12×	`pow-to-exp` `pow-exp`
11×	`pow1`
8×	`distribute-lft-out--`
6×	`associate-l` `associate-/l*`
4×	`associate-*r/` `associate-/r/` `log-pow` `cbrt-unprod` `difference-of-squares`
3×	`cbrt-undiv` `associate-/r*` `div-inv` `add-log-exp`
2×	`flip3--` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `associate-/l/`
1×	`frac-2neg` `flip3-+` `div-sub` `clear-num` `flip-+`

Counts

3 → 266

Calls

3 calls:

72.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
64.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
156.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series358.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
74.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
205.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify92.0ms

Counts: 275 → 275

prune883.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(log (exp (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
0.0b	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
0.0b	(exp (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite633.0ms

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
124×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
70×	`add-cube-cbrt`
68×	`associate-r`
56×	`unpow-prod-down`
52×	`exp-prod`
37×	`log-pow`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
20×	`distribute-lft-out--`
17×	`pow1` `unswap-sqr`
12×	`associate-/r/`
11×	`add-cbrt-cube`
10×	`div-exp` `prod-exp` `difference-of-squares`
7×	`associate-*r/`
6×	`pow-to-exp` `pow-exp` `frac-sub` `associate-/l*`
5×	`add-log-exp`
4×	`flip3--` `flip--` `div-inv`
3×	`log-prod` `flip3-+` `div-sub` `associate-l` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `exp-diff` `cbrt-unprod` `associate-/l/`
1×	`log-div` `frac-2neg` `rem-log-exp` `pow-prod-down` `clear-num` `*-commutative` `rem-exp-log`

Counts

4 → 230

Calls

4 calls:

41.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
239.0ms	(log (exp (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
112.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
223.0ms	(exp (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series492.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
126.0ms	(log (exp (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
130.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
178.0ms	(exp (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify87.0ms

Counts: 242 → 242

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

0.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify64.0ms

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.1s	3458×	body	1280	valid
1.9s	2521×	body	640	valid
338.0ms	1204×	body	320	valid
133.0ms	8000×	pre	80	true
99.0ms	615×	body	160	valid
14.0ms	202×	body	80	valid