Details

sample73.0ms

Algorithm

intervals

Results

23.0ms	536×	body	80	nan
17.0ms	267×	body	160	nan
10.0ms	256×	body	80	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.2b	(log (+ x (sqrt (- (* x x) 1.0))))
28.8b	(sqrt (- (* x x) 1.0))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod` `sqrt-prod`
3×	`add-cbrt-cube`
2×	`log-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `flip--` `difference-of-squares`

Counts

3 → 43

Calls

3 calls:

44.0ms	(+ x (sqrt (- (* x x) 1.0)))
31.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
13.0ms	(sqrt (- (* x x) 1.0))

series402.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(+ x (sqrt (- (* x x) 1.0)))
267.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
52.0ms	(sqrt (- (* x x) 1.0))

simplify62.0ms

Counts: 52 → 52

prune186.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`*-un-lft-identity` `sqrt-div`
9×	`associate-r`
8×	`pow1` `add-cube-cbrt`
7×	`associate-l`
6×	`add-exp-log`
5×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`log-prod` `flip3--` `pow-prod-down` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `difference-of-squares`
1×	`+-commutative` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 67

Calls

3 calls:

8.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
6.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
85.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series766.0ms

Counts

3 → 9

Calls

3 calls:

185.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
372.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
209.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify44.0ms

Counts: 76 → 76

prune326.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)))
0.2b	(+ (log 2) (- (log x) (+ (* 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4))) (/ (* 1/4 1.0) (pow x 2)))))
0.3b	(/ (pow (sqrt 1.0) 4) (pow x 4))
0.8b	(/ (* 1/4 1.0) (pow x 2))

rewrite405.0ms

Algorithm

rewrite-expression-head

Rules

169×	`unpow-prod-down`
160×	`times-frac`
130×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
99×	`add-cube-cbrt`
74×	`associate-r`
52×	`add-exp-log`
48×	`sqrt-prod`
45×	`sqr-pow`
24×	`div-exp`
16×	`add-cbrt-cube`
15×	`associate-/r*`
14×	`pow-to-exp` `pow-exp`
13×	`prod-exp` `unswap-sqr`
11×	`pow1` `associate-/l*`
8×	`add-log-exp`
6×	`log-prod` `distribute-lft-out`
5×	`associate-+r+` `log-pow`
4×	`cbrt-undiv` `sum-log` `distribute-lft-out--`
3×	`associate-+l+` `associate-l` `associate--l+` `cbrt-unprod` `div-inv`
2×	`frac-2neg` `diff-log` `clear-num` `unpow2`
1×	`+-commutative` `associate-+r-` `sub-neg` `flip3-+` `associate-r/` `pow-prod-down` `-commutative` `flip-+`

Counts

4 → 282

Calls

4 calls:

57.0ms	(* 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)))
292.0ms	(+ (log 2) (- (log x) (+ (* 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4))) (/ (* 1/4 1.0) (pow x 2)))))
20.0ms	(/ (pow (sqrt 1.0) 4) (pow x 4))
14.0ms	(/ (* 1/4 1.0) (pow x 2))

series568.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)))
232.0ms	(+ (log 2) (- (log x) (+ (* 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4))) (/ (* 1/4 1.0) (pow x 2)))))
127.0ms	(/ (pow (sqrt 1.0) 4) (pow x 4))
36.0ms	(/ (* 1/4 1.0) (pow x 2))

simplify79.0ms

Counts: 294 → 294

prune979.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes79.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.3s	15996×	body	80	nan
759.0ms	7560×	body	160	nan
481.0ms	8000×	body	80	valid