Details

sample98.0ms

Algorithm

intervals

Results

29.0ms	227×	body	160	nan
29.0ms	536×	body	80	nan
20.0ms	256×	body	80	valid

simplify2.8s

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize17.0ms

Local error

Found 4 expressions with local error:

30.1b	(sqrt (- (* x x) 1))
0.3b	(log (+ x (sqrt (- (* x x) 1))))
0.0b	(+ x (sqrt (- (* x x) 1)))
0.0b	(- (* x x) 1)

rewrite56.0ms

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)))
13.0ms	(- (* x x) 1)
13.0ms	(sqrt (- (* x x) 1))
12.0ms	(log (+ x (sqrt (- (* x x) 1))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

168.0ms	(log (+ x (sqrt (- (* x x) 1))))
73.0ms	(- (* x x) 1)
60.0ms	(+ x (sqrt (- (* x x) 1)))
51.0ms	(sqrt (- (* x x) 1))

simplify915.0ms

Counts: 76 → 76

prune659.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.2b	(log (- (/ x 1/2) (+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x))))
0.1b	(/ (/ 1/8 x) (* x x))
0.0b	(+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

32×	`times-frac`
25×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`add-cbrt-cube`
13×	`associate-/l*`
7×	`log-prod`
6×	`cbrt-undiv` `div-exp`
5×	`log-div` `add-log-exp`
4×	`pow1`
3×	`frac-sub` `insert-posit16` `div-inv`
2×	`flip3-+` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `flip3--` `rem-log-exp` `log-pow` `flip--` `associate-/l/`

Counts

3 → 83

Calls

3 calls:

Slowest

69.0ms	(log (- (/ x 1/2) (+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x))))
32.0ms	(+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x))
15.0ms	(/ (/ 1/8 x) (* x x))

series327.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

130.0ms	(log (- (/ x 1/2) (+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x))))
127.0ms	(+ (/ (/ 1/8 x) (* x x)) (/ 1/2 x))
70.0ms	(/ (/ 1/8 x) (* x x))

simplify740.0ms

Counts: 92 → 92

prune820.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt x) (sqrt 1/2))
0.5b	(/ (sqrt x) (sqrt 1/2))
0.1b	(/ (/ 1/8 x) (* x x))
0.1b	(/ (/ 1/8 x) (* x x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
88×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
84×	`sqrt-prod`
38×	`associate-/l*`
32×	`add-cbrt-cube` `add-exp-log`
14×	`cbrt-undiv` `associate-/r*` `div-exp`
8×	`div-inv`
4×	`pow1` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`sqrt-undiv` `associate-/l/`

Counts

4 → 218

Calls

4 calls:

Slowest

21.0ms	(/ (/ 1/8 x) (* x x))
20.0ms	(/ (/ 1/8 x) (* x x))
20.0ms	(/ (sqrt x) (sqrt 1/2))
10.0ms	(/ (sqrt x) (sqrt 1/2))

series345.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(/ (sqrt x) (sqrt 1/2))
105.0ms	(/ (sqrt x) (sqrt 1/2))
64.0ms	(/ (/ 1/8 x) (* x x))
51.0ms	(/ (/ 1/8 x) (* x x))

simplify1.9s

Counts: 230 → 230

prune3.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

30.1b	(sqrt (- (* x x) 1))
30.1b	(sqrt (- (* x x) 1))
0.5b	(* (sqrt (+ x (sqrt (- (* x x) 1)))) (sqrt (+ x (sqrt (- (* x x) 1)))))
0.3b	(log (* (sqrt (+ x (sqrt (- (* x x) 1)))) (sqrt (+ x (sqrt (- (* x x) 1))))))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

38×	`sqrt-prod`
37×	`pow1`
30×	`add-sqr-sqrt` `*-un-lft-identity`
28×	`sqrt-div`
18×	`sqrt-pow1` `pow1/2`
14×	`log-pow` `add-cube-cbrt`
12×	`flip3-+` `flip-+`
11×	`swap-sqr`
10×	`pow-prod-up`
9×	`add-exp-log`
8×	`frac-times` `log-div`
7×	`associate-r` `associate-l`
6×	`add-cbrt-cube` `pow-prod-down` `pow-sqr` `distribute-lft-out`
4×	`associate-l/` `associate-r/` `insert-posit16` `add-log-exp` `difference-of-squares` `unswap-sqr`
2×	`pow2` `rem-sqrt-square` `pow-plus` `flip3--` `difference-of-sqr-1` `rem-log-exp` `prod-exp` `flip--`
1×	`log-prod` `rem-square-sqrt` `sqrt-unprod` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

Slowest

128.0ms	(* (sqrt (+ x (sqrt (- (* x x) 1)))) (sqrt (+ x (sqrt (- (* x x) 1)))))
37.0ms	(log (* (sqrt (+ x (sqrt (- (* x x) 1)))) (sqrt (+ x (sqrt (- (* x x) 1))))))
20.0ms	(sqrt (- (* x x) 1))
9.0ms	(sqrt (- (* x x) 1))

series338.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

159.0ms	(log (* (sqrt (+ x (sqrt (- (* x x) 1)))) (sqrt (+ x (sqrt (- (* x x) 1))))))
63.0ms	(sqrt (- (* x x) 1))
62.0ms	(sqrt (- (* x x) 1))
54.0ms	(* (sqrt (+ x (sqrt (- (* x x) 1)))) (sqrt (+ x (sqrt (- (* x x) 1)))))

simplify1.3s

Counts: 146 → 146

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes73.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch4.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.7s	16390×	body	80	nan
1.3s	7858×	body	160	nan
776.0ms	8000×	body	80	valid