Details

sample281.0ms

Algorithm

intervals

Results

98.0ms	256×	body	80	valid
24.0ms	231×	body	80	nan

simplify35.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	23
3	23
2	21
1	18
0	9

prune54.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan (sqrt (/ (- 1 x) (+ 1 x))))
0.0b	(sqrt (/ (- 1 x) (+ 1 x)))
0.0b	(/ (- 1 x) (+ 1 x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

79×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
49×	`times-frac`
30×	`sqrt-prod`
26×	`add-cube-cbrt`
18×	`difference-of-squares`
13×	`distribute-lft-out`
9×	`distribute-lft-out--`
6×	`associate-/l*`
5×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`expm1-log1p-u` `insert-posit16` `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 → 109

Calls

3 calls:

1.0ms	(atan (sqrt (/ (- 1 x) (+ 1 x))))
10.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
31.0ms	(/ (- 1 x) (+ 1 x))

series93.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(atan (sqrt (/ (- 1 x) (+ 1 x))))
49.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
40.0ms	(/ (- 1 x) (+ 1 x))

simplify2.5s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
3	2236
2	795
1	360
0	174

prune465.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1 x))
0.0b	(sqrt (/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
0.0b	(/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x)))
0.0b	(/ (- 1 x) (sqrt (+ 1 x)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

1354×	`times-frac`
1252×	`*-un-lft-identity`
1127×	`sqrt-prod`
883×	`add-sqr-sqrt`
522×	`add-cube-cbrt`
226×	`difference-of-squares`
195×	`distribute-lft-out`
113×	`distribute-lft-out--`
54×	`associate-/l*`
39×	`sqrt-div`
36×	`associate-/r/`
19×	`flip3-+` `flip-+`
18×	`div-inv`
14×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
8×	`rem-sqrt-square`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`flip3--` `hypot-1-def` `flip--`

Counts

4 → 871

Calls

4 calls:

5.0ms	(sqrt (+ 1 x))
19.0ms	(sqrt (/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
51.0ms	(/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x)))
33.0ms	(/ (- 1 x) (sqrt (+ 1 x)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(sqrt (+ 1 x))
73.0ms	(sqrt (/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
37.0ms	(/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x)))
105.0ms	(/ (- 1 x) (sqrt (+ 1 x)))

simplify2.2s

Counts

883 → 883

Iterations

Iter	Nodes
done	5032
2	2593
1	1330
0	718

prune2.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- 1 x) (+ 1 x)) (* (/ (- 1 x) (+ 1 x)) (/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x)))))
0.0b	(/ (- 1 x) (sqrt (+ 1 x)))
0.0b	(cbrt (* (/ (- 1 x) (+ 1 x)) (* (/ (- 1 x) (+ 1 x)) (/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x))))))
0.0b	(* (/ (- 1 x) (+ 1 x)) (/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x))))

rewrite364.0ms

Algorithm

rewrite-expression-head

Rules

747×	`times-frac`
698×	`*-un-lft-identity`
535×	`add-sqr-sqrt`
398×	`sqrt-prod`
343×	`associate-r`
285×	`add-cube-cbrt`
130×	`difference-of-squares`
109×	`distribute-lft-out`
92×	`add-cbrt-cube` `add-exp-log`
65×	`distribute-lft-out--`
60×	`associate-l`
35×	`cbrt-undiv` `div-exp`
32×	`prod-exp` `cbrt-unprod`
22×	`associate-/r/`
18×	`sqrt-div`
14×	`unswap-sqr`
11×	`frac-times` `pow1` `flip3-+` `associate-*r/` `flip-+` `div-inv`
7×	`cbrt-div` `associate-/r` `associate-l/`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `associate-/l/`
1×	`cbrt-prod` `clear-num` `frac-2neg` `flip3--` `pow1/3` `div-sub` `flip--`

Counts

4 → 586

Calls

4 calls:

117.0ms	(* (/ (- 1 x) (+ 1 x)) (* (/ (- 1 x) (+ 1 x)) (/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x)))))
27.0ms	(/ (- 1 x) (sqrt (+ 1 x)))
81.0ms	(cbrt (* (/ (- 1 x) (+ 1 x)) (* (/ (- 1 x) (+ 1 x)) (/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x))))))
118.0ms	(* (/ (- 1 x) (+ 1 x)) (/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x))))

series215.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (/ (- 1 x) (+ 1 x)) (* (/ (- 1 x) (+ 1 x)) (/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x)))))
73.0ms	(/ (- 1 x) (sqrt (+ 1 x)))
40.0ms	(cbrt (* (/ (- 1 x) (+ 1 x)) (* (/ (- 1 x) (+ 1 x)) (/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x))))))
45.0ms	(* (/ (- 1 x) (+ 1 x)) (/ (/ (- 1 x) (sqrt (+ 1 x))) (sqrt (+ 1 x))))

simplify2.4s

Counts

598 → 598

Iterations

Iter	Nodes
done	5001
1	2248
0	634

prune2.5s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes23.0ms

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	15
1	15
0	11

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
774.0ms	7614×	body	80	nan