Details

sample123.0ms

Algorithm

intervals

Results

48.0ms	247×	body	160	nan
34.0ms	548×	body	80	nan
20.0ms	256×	body	80	valid

simplify89.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

89.0ms

(log (+ x (sqrt (- (* x x) 1))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize14.0ms

Local error

Found 4 expressions with local error:

27.8b	(sqrt (- (* x x) 1))
0.0b	(+ x (sqrt (- (* x x) 1)))
0.0b	(- (* x x) 1)
0.0b	(log (+ x (sqrt (- (* x x) 1))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
5×	`add-exp-log`
4×	`log-prod` `add-cbrt-cube` `insert-posit16` `difference-of-squares`
2×	`log-div` `flip3-+` `flip3--` `sqrt-div` `difference-of-sqr-1` `flip-+` `flip--` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 64

Calls

4 calls:

Slowest

17.0ms	(+ x (sqrt (- (* x x) 1)))
11.0ms	(log (+ x (sqrt (- (* x x) 1))))
8.0ms	(sqrt (- (* x x) 1))
7.0ms	(- (* x x) 1)

series342.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

170.0ms	(log (+ x (sqrt (- (* x x) 1))))
66.0ms	(+ x (sqrt (- (* x x) 1)))
58.0ms	(sqrt (- (* x x) 1))
48.0ms	(- (* x x) 1)

simplify4.1s

Counts

37 → 76

Calls

37 calls:

Slowest

460.0ms	(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
439.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
310.0ms	(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
232.0ms	(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
210.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))

prune469.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.0b	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.0b	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`sqrt-prod`
13×	`*-un-lft-identity`
12×	`sqrt-div`
10×	`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` `insert-posit16` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `difference-of-squares`
1×	`+-commutative` `sum-log` `sqrt-unprod` `difference-of-sqr-1` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

3 → 71

Calls

3 calls:

Slowest

48.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
10.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
5.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

series363.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

192.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
102.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
69.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

simplify4.2s

Counts

59 → 80

Calls

59 calls:

Slowest

403.0ms	(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
398.0ms	(log (+ (pow x 3) (pow (* (sqrt (+ x 1)) (sqrt (- x 1))) 3)))
296.0ms	(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
265.0ms	(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))
233.0ms	(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))))

prune732.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.5b	(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
48×	`sqrt-div`
45×	`sqrt-prod`
31×	`*-un-lft-identity`
30×	`associate-r`
21×	`associate-l`
16×	`frac-times` `pow1` `add-cube-cbrt`
12×	`flip3-+` `flip3--` `flip-+` `flip--` `unswap-sqr`
10×	`add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down`
8×	`cbrt-div` `associate-l/` `associate-r/`
6×	`sqrt-pow1` `pow1/2` `difference-of-squares`
4×	`insert-posit16` `add-log-exp`
3×	`sqrt-unprod` `difference-of-sqr-1` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`
1×	`cbrt-prod` `pow1/3`

Counts

4 → 150

Calls

4 calls:

Slowest

33.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
32.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
29.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
21.0ms	(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))

series528.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

196.0ms	(cbrt (* (sqrt (+ x 1)) (sqrt (- x 1))))
130.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
106.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
95.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify10.6s

Counts

150 → 162

Calls

150 calls:

Slowest

632.0ms	(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
417.0ms	(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
388.0ms	(cbrt (* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3)))))
360.0ms	(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
356.0ms	(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))

prune2.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	16673×	body	80	nan
1.3s	7701×	body	160	nan
745.0ms	8000×	body	80	valid