Details

sample103.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
10.0ms	245×	body	80	nan

simplify16.0ms

Counts

1 → 1

Iterations

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

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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))

rewrite52.0ms

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))))
19.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
22.0ms	(/ (- 1.0 x) (+ 1.0 x))

series188.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
95.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
88.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify1.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1484
1	370
0	168

prune489.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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))))

rewrite78.0ms

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))
39.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ x 1.0)))
12.0ms	(sqrt (+ x 1.0))
15.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ x 1.0))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (- 1.0 x))
124.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ x 1.0)))
45.0ms	(sqrt (+ x 1.0))
3.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ x 1.0))))

simplify758.0ms

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

localize17.0ms

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))

rewrite53.0ms

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)))
7.0ms	(atan (/ (sqrt (- (* 1.0 1.0) (* x x))) (+ 1.0 x)))
34.0ms	(/ (sqrt (- (* 1.0 1.0) (* x x))) (+ 1.0 x))

series273.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(sqrt (- (* 1.0 1.0) (* x x)))
8.0ms	(atan (/ (sqrt (- (* 1.0 1.0) (* x x))) (+ 1.0 x)))
155.0ms	(/ (sqrt (- (* 1.0 1.0) (* x x))) (+ 1.0 x))

simplify1.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1723
1	396
0	170

prune448.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

227×	`sqrt-prod`
153×	`*-un-lft-identity`
146×	`cbrt-prod`
133×	`add-sqr-sqrt`
110×	`times-frac`
89×	`add-cube-cbrt`
22×	`sqrt-div`
20×	`distribute-lft-out`
18×	`cbrt-div`
14×	`swap-sqr`
11×	`pow1` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
10×	`associate-/r` `associate-r` `associate-l*`
9×	`flip3-+` `flip-+` `unswap-sqr`
8×	`pow1/3` `add-exp-log`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `associate-r/` `associate-/r/` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `frac-2neg` `pow-plus` `flip3--` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `flip--`

Counts

4 → 258

Calls

4 calls:

4.0ms	(cbrt (sqrt (+ 1.0 x)))
5.0ms	(cbrt (sqrt (+ 1.0 x)))
53.0ms	(/ (sqrt (sqrt (- 1.0 x))) (cbrt (sqrt (+ 1.0 x))))
44.0ms	(* (cbrt (sqrt (+ 1.0 x))) (cbrt (sqrt (+ 1.0 x))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(cbrt (sqrt (+ 1.0 x)))
131.0ms	(cbrt (sqrt (+ 1.0 x)))
338.0ms	(/ (sqrt (sqrt (- 1.0 x))) (cbrt (sqrt (+ 1.0 x))))
132.0ms	(* (cbrt (sqrt (+ 1.0 x))) (cbrt (sqrt (+ 1.0 x))))

simplify1.5s

Counts

270 → 270

Iterations

Iter	Nodes
done	5000
2	2903
1	763
0	381

prune1.6s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	11

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
497.0ms	8043×	body	80	nan