Details

sample273.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
6.0ms	272×	body	80	nan

simplify15.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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))

rewrite30.0ms

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:

0.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
15.0ms	(/ (- 1.0 x) (+ 1.0 x))

series151.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
96.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
52.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify413.0ms

Counts

106 → 106

Iterations

Useful iterations: done (410.0ms)

Iter	Nodes	Cost
0	173	1505
1	375	1422
2	1119	1333
done	5000	1320

prune240.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b	(/ (- 1.0 x) (+ 1.0 x))
0.0b	(log1p (expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
0.0b	(expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
46×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
25×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `log1p-expm1-u` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `log1p-expm1` `div-exp` `clear-num` `flip--` `expm1-udef`

Counts

4 → 110

Calls

4 calls:

10.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
14.0ms	(/ (- 1.0 x) (+ 1.0 x))
0.0ms	(log1p (expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
0.0ms	(expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
33.0ms	(/ (- 1.0 x) (+ 1.0 x))
120.0ms	(log1p (expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
42.0ms	(expm1 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x)))))

simplify428.0ms

Counts

122 → 122

Iterations

Useful iterations: done (424.0ms)

Iter	Nodes	Cost
0	187	1719
1	394	1604
2	1185	1495
done	5002	1482

prune306.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 x) (+ x 1.0))
0.0b	(expm1 (atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))))
0.0b	(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
0.0b	(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

155×	`*-un-lft-identity`
104×	`sqrt-prod`
103×	`add-sqr-sqrt`
100×	`times-frac`
64×	`cbrt-prod`
61×	`add-cube-cbrt`
58×	`unpow-prod-down` `cube-prod`
26×	`distribute-lft-out`
21×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`flip3-+` `flip-+` `log1p-expm1-u` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `add-log-exp`
3×	`pow-unpow` `pow-pow`
2×	`cube-div` `cube-mult` `sqrt-div` `unpow3` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `expm1-log1p` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-sub` `div-exp` `pow-exp` `clear-num` `sqrt-pow2` `flip--` `rem-cbrt-cube` `expm1-udef` `rem-cube-cbrt`

Counts

4 → 216

Calls

4 calls:

15.0ms	(/ (- 1.0 x) (+ x 1.0))
0.0ms	(expm1 (atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))))
16.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
14.0ms	(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

series369.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0 x) (+ x 1.0))
46.0ms	(expm1 (atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))))
94.0ms	(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
195.0ms	(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

simplify929.0ms

Counts

228 → 228

Iterations

Useful iterations: 2 (221.0ms)

Iter	Nodes	Cost
0	301	4389
1	747	3565
2	2341	3387
done	5000	3387

prune485.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes58.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	13	13
done	13	13

end0.0ms

sample683.0ms

Algorithm

intervals

Results

301.0ms	8000×	body	80	valid
198.0ms	8067×	body	80	nan