Details

sample113.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
13.0ms	245×	body	80	nan

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
3	21
2	19
1	16
0	9

prune64.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite72.0ms

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-cbrt-cube` `add-exp-log` `associate-/l*`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `div-exp` `flip--`

Counts

3 → 97

Calls

3 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
25.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
42.0ms	(/ (- 1.0 x) (+ 1.0 x))

series210.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
139.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
64.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify1.2s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1484
1	370
0	168

prune551.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
78×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
56×	`times-frac`
40×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`sqrt-div` `associate-/l*`
7×	`associate-/r*`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `clear-num` `frac-2neg` `div-exp` `hypot-def` `div-inv`

Counts

4 → 137

Calls

4 calls:

8.0ms	(sqrt (- 1.0 x))
31.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ x 1.0)))
12.0ms	(sqrt (+ x 1.0))
14.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ x 1.0))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (- 1.0 x))
125.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ x 1.0)))
46.0ms	(sqrt (+ x 1.0))
3.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ x 1.0))))

simplify702.0ms

Counts

149 → 149

Iterations

Iter	Nodes
done	5000
2	1244
1	368
0	196

prune649.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
28×	`times-frac`
24×	`sqrt-prod`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`associate-/l*`
6×	`difference-of-squares`
5×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `associate-/r*` `sqrt-div`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `flip-+` `div-inv`

Counts

3 → 84

Calls

3 calls:

9.0ms	(sqrt (- (* 1.0 1.0) (* x x)))
8.0ms	(atan (/ (sqrt (- (* 1.0 1.0) (* x x))) (+ 1.0 x)))
30.0ms	(/ (sqrt (- (* 1.0 1.0) (* x x))) (+ 1.0 x))

series203.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(sqrt (- (* 1.0 1.0) (* x x)))
7.0ms	(atan (/ (sqrt (- (* 1.0 1.0) (* x x))) (+ 1.0 x)))
109.0ms	(/ (sqrt (- (* 1.0 1.0) (* x x))) (+ 1.0 x))

simplify1.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1723
1	396
0	170

prune415.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (sqrt (+ 1.0 x)))
0.0b	(cbrt (sqrt (+ 1.0 x)))
0.0b	(* (* (cbrt (sqrt (+ 1.0 x))) (cbrt (sqrt (+ 1.0 x)))) (cbrt (sqrt (+ 1.0 x))))
0.0b	(* (cbrt (sqrt (+ 1.0 x))) (cbrt (sqrt (+ 1.0 x))))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

71×	`cbrt-prod`
70×	`cbrt-div` `sqrt-div`
48×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
41×	`sqrt-prod`
35×	`flip3-+` `flip-+`
32×	`frac-times`
30×	`pow1`
23×	`add-cube-cbrt`
20×	`associate-r`
17×	`pow1/3`
16×	`associate-*l/`
14×	`swap-sqr`
12×	`unswap-sqr`
11×	`associate-l` `add-exp-log` `pow-prod-up`
10×	`associate-*r/`
9×	`distribute-lft-out`
7×	`pow-plus` `pow-prod-down`
5×	`add-cbrt-cube` `pow-sqr`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow2`
2×	`*-commutative`
1×	`pow3`

Counts

4 → 177

Calls

4 calls:

7.0ms	(cbrt (sqrt (+ 1.0 x)))
9.0ms	(cbrt (sqrt (+ 1.0 x)))
90.0ms	(* (* (cbrt (sqrt (+ 1.0 x))) (cbrt (sqrt (+ 1.0 x)))) (cbrt (sqrt (+ 1.0 x))))
36.0ms	(* (cbrt (sqrt (+ 1.0 x))) (cbrt (sqrt (+ 1.0 x))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (sqrt (+ 1.0 x)))
119.0ms	(cbrt (sqrt (+ 1.0 x)))
54.0ms	(* (* (cbrt (sqrt (+ 1.0 x))) (cbrt (sqrt (+ 1.0 x)))) (cbrt (sqrt (+ 1.0 x))))
116.0ms	(* (cbrt (sqrt (+ 1.0 x))) (cbrt (sqrt (+ 1.0 x))))

simplify4.9s

Counts

189 → 189

Iterations

Iter	Nodes
done	5000
2	4015
1	633
0	254

prune1.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes53.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	13
1	13
0	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
637.0ms	8043×	body	80	nan