Details

sample87.0ms

Algorithm

intervals

Results

15.0ms	273×	body	80	nan
15.0ms	256×	body	80	valid

simplify39.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
24×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

3 → 91

Calls

3 calls:

82.0ms	(/ (- 1.0 x) (+ 1.0 x))
59.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series192.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (- 1.0 x) (+ 1.0 x))
126.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
20.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify2.1s

Counts: 100 → 100

prune401.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3)))
0.0b	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
0.0b	(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
0.0b	(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

176×	`*-un-lft-identity`
124×	`add-sqr-sqrt`
122×	`cbrt-prod` `times-frac`
80×	`unpow-prod-down` `cube-prod`
68×	`add-cube-cbrt`
61×	`sqrt-prod`
30×	`distribute-lft-out`
24×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r/`
7×	`add-exp-log` `rem-sqrt-square` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+` `div-inv`
4×	`add-log-exp` `sqr-pow`
3×	`cube-div` `cube-mult` `pow-unpow` `unpow3`
2×	`cbrt-div` `sqrt-pow1` `pow1/3` `pow-exp` `rem-cube-cbrt`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `pow1/2` `sqrt-div` `div-exp` `rem-cbrt-cube`

Counts

4 → 226

Calls

4 calls:

79.0ms	(sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3)))
1.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
21.0ms	(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
22.0ms	(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

series290.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3)))
3.0ms	(atan (sqrt (cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))))
36.0ms	(cbrt (pow (/ (- 1.0 x) (+ 1.0 x)) 3))
113.0ms	(pow (/ (- 1.0 x) (+ 1.0 x)) 3)

simplify1.2s

Counts: 238 → 238

prune567.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ x 1.0))
0.0b	(atan (sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x)))))
0.0b	(/ (- (pow 1.0 3) (pow x 3)) (* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x)))
0.0b	(* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
32×	`difference-of-squares`
25×	`times-frac` `associate-/l*`
24×	`unpow-prod-down` `cube-prod`
16×	`sqr-pow`
13×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
10×	`add-cube-cbrt` `distribute-lft-out--`
8×	`pow1` `frac-times` `associate-r` `associate-/r/`
6×	`associate-r/` `associate-l*`
4×	`associate-*l/` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
2×	`difference-cubes` `cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `pow-prod-down` `*-commutative` `associate-/l/` `distribute-lft-out` `unswap-sqr`
1×	`flip3--` `frac-2neg` `div-sub` `clear-num` `associate-/r*` `flip--` `div-inv`

Counts

4 → 135

Calls

4 calls:

22.0ms	(* x (+ x 1.0))
1.0ms	(atan (sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x)))))
138.0ms	(/ (- (pow 1.0 3) (pow x 3)) (* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x)))
103.0ms	(* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x))

series248.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* x (+ x 1.0))
13.0ms	(atan (sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x)))))
111.0ms	(/ (- (pow 1.0 3) (pow x 3)) (* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x)))
57.0ms	(* (+ (* x (+ x 1.0)) (* 1.0 1.0)) (+ 1.0 x))

simplify1.9s

Counts: 147 → 147

prune695.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0s

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
472.0ms	7966×	body	80	nan