Details

sample109.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
14.0ms	218×	body	80	nan

simplify89.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	19	11
3	21	11
done	21	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite73.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 97

Calls

3 calls:

19.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
33.0ms	(/ (- 1.0 x) (+ 1.0 x))

series155.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
4.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
47.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify2.2s

Counts

106 → 106

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	173	1505
1	372	1422
2	915	1333
3	2329	1320
done	5000	1300

prune387.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

670×	`sqrt-prod`
586×	`*-un-lft-identity`
528×	`times-frac`
514×	`add-sqr-sqrt`
228×	`add-cube-cbrt`
138×	`swap-sqr`
82×	`distribute-lft-out`
74×	`distribute-lft-out--`
62×	`associate-r` `associate-l`
52×	`difference-of-squares`
25×	`unswap-sqr`
20×	`add-exp-log` `add-cbrt-cube`
16×	`sqrt-div` `associate-/l*`
14×	`associate-/r*`
12×	`associate-/r/`
11×	`pow1`
6×	`cbrt-undiv` `sqrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `pow-prod-down` `associate-l/` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 504

Calls

4 calls:

1.0ms	(atan (sqrt (* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
38.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
25.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
239.0ms	(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

series326.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan (sqrt (* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
126.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
138.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
55.0ms	(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

simplify2.3s

Counts

516 → 516

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	316	13994
1	913	11942
2	2745	9995
done	5000	9578

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

37.0ms	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
4.0ms	(cbrt (+ 1.0 x))
4.0ms	(cbrt (+ 1.0 x))
4.0ms	(cbrt (+ 1.0 x))

series616.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
126.0ms	(cbrt (+ 1.0 x))
166.0ms	(cbrt (+ 1.0 x))
154.0ms	(cbrt (+ 1.0 x))

simplify3.0s

Counts

115 → 115

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	143	1535
1	323	1385
2	838	1323
3	2183	1174
done	5000	1140

prune805.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (+ 1.0 x))
0.0b	(cbrt (+ 1.0 x))
0.0b	(cbrt (+ 1.0 x))
0.0b	(* (* (cbrt (pow (sqrt (cbrt (+ 1.0 x))) 4)) (cbrt (pow (sqrt (cbrt (+ 1.0 x))) 4))) (cbrt (pow (sqrt (cbrt (+ 1.0 x))) 4)))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
23×	`pow1`
20×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `associate-r`
13×	`unpow-prod-down`
12×	`add-cube-cbrt` `pow1/3`
9×	`add-exp-log` `sqrt-prod` `pow-prod-up`
6×	`cbrt-div` `pow-plus` `unswap-sqr`
5×	`pow-prod-down` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`flip3-+` `prod-exp` `pow-sqr` `cbrt-unprod` `flip-+`
2×	`pow2` `sqr-pow`
1×	`associate-l` `pow3` `*-commutative`

Counts

4 → 100

Calls

4 calls:

8.0ms	(cbrt (+ 1.0 x))
8.0ms	(cbrt (+ 1.0 x))
7.0ms	(cbrt (+ 1.0 x))
251.0ms	(* (* (cbrt (pow (sqrt (cbrt (+ 1.0 x))) 4)) (cbrt (pow (sqrt (cbrt (+ 1.0 x))) 4))) (cbrt (pow (sqrt (cbrt (+ 1.0 x))) 4)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (+ 1.0 x))
97.0ms	(cbrt (+ 1.0 x))
114.0ms	(cbrt (+ 1.0 x))
195.0ms	(* (* (cbrt (pow (sqrt (cbrt (+ 1.0 x))) 4)) (cbrt (pow (sqrt (cbrt (+ 1.0 x))) 4))) (cbrt (pow (sqrt (cbrt (+ 1.0 x))) 4)))

simplify3.2s

Counts

112 → 112

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	186	2062
1	437	1890
2	1056	1558
3	2497	1220
done	5001	1164

prune868.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	14	23
done	14	23

end0.0ms

sample1.7s

Algorithm

intervals

Results

745.0ms	8000×	body	80	valid
533.0ms	8039×	body	80	nan