Details

sample37.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
4.0ms	102×	body	80	nan

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
1	8
0	6

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (sqrt (+ 1.0 x)))
0.0b	(sqrt (+ 1.0 x))
0.2b	(/ x (+ 1.0 (sqrt (+ 1.0 x))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

3 → 61

Calls

3 calls:

25.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
12.0ms	(sqrt (+ 1.0 x))
58.0ms	(/ x (+ 1.0 (sqrt (+ 1.0 x))))

series289.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(+ 1.0 (sqrt (+ 1.0 x)))
35.0ms	(sqrt (+ 1.0 x))
203.0ms	(/ x (+ 1.0 (sqrt (+ 1.0 x))))

simplify583.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1500
1	317
0	137

prune297.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(+ 1.0 (pow (sqrt (+ 1.0 x)) 1))
0.2b	(/ x (+ 1.0 (pow (sqrt (+ 1.0 x)) 1)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

3 → 61

Calls

3 calls:

6.0ms	(sqrt (+ 1.0 x))
25.0ms	(+ 1.0 (pow (sqrt (+ 1.0 x)) 1))
55.0ms	(/ x (+ 1.0 (pow (sqrt (+ 1.0 x)) 1)))

series288.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(sqrt (+ 1.0 x))
66.0ms	(+ 1.0 (pow (sqrt (+ 1.0 x)) 1))
184.0ms	(/ x (+ 1.0 (pow (sqrt (+ 1.0 x)) 1)))

simplify648.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	1583
1	330
0	140

prune275.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (+ x 1.0)) 3)
0.2b	(* (pow (sqrt (+ 1.0 x)) 1) (pow (sqrt (+ 1.0 x)) 1))
4.6b	(- (* (pow (sqrt (+ 1.0 x)) 1) (pow (sqrt (+ 1.0 x)) 1)) (* 1.0 (pow (sqrt (+ 1.0 x)) 1)))
6.1b	(/ x (+ (pow (sqrt (+ x 1.0)) 3) (pow 1.0 3)))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

93×	`*-un-lft-identity`
75×	`unpow-prod-down`
63×	`add-sqr-sqrt`
38×	`sqrt-prod`
35×	`add-cube-cbrt`
28×	`distribute-lft-out`
27×	`times-frac`
23×	`cube-prod`
19×	`add-exp-log`
16×	`unswap-sqr`
15×	`swap-sqr`
13×	`sqr-pow`
11×	`associate-r` `associate-l`
9×	`associate-/r*` `add-cbrt-cube` `prod-exp`
7×	`pow-to-exp` `pow-exp`
6×	`pow1` `add-log-exp`
4×	`sum-cubes`
3×	`pow-unpow` `pow-pow` `associate-/l*`
2×	`cube-div` `flip3-+` `sqrt-div` `associate-/r/` `flip-+`
1×	`pow2` `cube-mult` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `distribute-rgt-out--` `pow1/2` `diff-log` `unpow3` `div-exp` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `sqrt-pow2` `flip--` `rem-cube-cbrt`

Counts

4 → 177

Calls

4 calls:

11.0ms	(pow (sqrt (+ x 1.0)) 3)
114.0ms	(* (pow (sqrt (+ 1.0 x)) 1) (pow (sqrt (+ 1.0 x)) 1))
42.0ms	(- (* (pow (sqrt (+ 1.0 x)) 1) (pow (sqrt (+ 1.0 x)) 1)) (* 1.0 (pow (sqrt (+ 1.0 x)) 1)))
96.0ms	(/ x (+ (pow (sqrt (+ x 1.0)) 3) (pow 1.0 3)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(pow (sqrt (+ x 1.0)) 3)
27.0ms	(* (pow (sqrt (+ 1.0 x)) 1) (pow (sqrt (+ 1.0 x)) 1))
82.0ms	(- (* (pow (sqrt (+ 1.0 x)) 1) (pow (sqrt (+ 1.0 x)) 1)) (* 1.0 (pow (sqrt (+ 1.0 x)) 1)))
255.0ms	(/ x (+ (pow (sqrt (+ x 1.0)) 3) (pow 1.0 3)))

simplify2.7s

Counts

189 → 189

Iterations

Iter	Nodes
done	5000
2	4925
1	839
0	283

prune762.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1.0 1.0) (+ 1.0 x)) (- 1.0 (sqrt (+ 1.0 x))))
0.2b	(/ x (/ (- (* 1.0 1.0) (+ 1.0 x)) (- 1.0 (sqrt (+ 1.0 x)))))
4.5b	(- (* 1.0 1.0) (+ 1.0 x))
4.6b	(- 1.0 (sqrt (+ 1.0 x)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-sqr-sqrt`
210×	`times-frac`
135×	`*-un-lft-identity`
91×	`add-cube-cbrt`
76×	`difference-of-squares`
36×	`associate-/r*`
22×	`sqrt-prod` `distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log` `associate-/r/` `add-log-exp`
8×	`flip3--` `flip--`
7×	`associate-/l*`
6×	`div-inv`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`diff-log`
2×	`clear-num` `sub-neg` `frac-2neg` `associate-/l/`
1×	`sum-log` `div-sub` `associate--r+`

Counts

4 → 219

Calls

4 calls:

82.0ms	(/ (- (* 1.0 1.0) (+ 1.0 x)) (- 1.0 (sqrt (+ 1.0 x))))
77.0ms	(/ x (/ (- (* 1.0 1.0) (+ 1.0 x)) (- 1.0 (sqrt (+ 1.0 x)))))
24.0ms	(- (* 1.0 1.0) (+ 1.0 x))
21.0ms	(- 1.0 (sqrt (+ 1.0 x)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(/ (- (* 1.0 1.0) (+ 1.0 x)) (- 1.0 (sqrt (+ 1.0 x))))
98.0ms	(/ x (/ (- (* 1.0 1.0) (+ 1.0 x)) (- 1.0 (sqrt (+ 1.0 x)))))
13.0ms	(- (* 1.0 1.0) (+ 1.0 x))
53.0ms	(- 1.0 (sqrt (+ 1.0 x)))

simplify435.0ms

Counts

231 → 231

Iterations

Iter	Nodes
done	5001
1	930
0	329

prune957.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes56.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	8

end0.0ms

sample800.0ms

Algorithm

intervals

Results

409.0ms	7997×	body	80	valid
122.0ms	2708×	body	80	nan
1.0ms	3×	body	1280	valid