Details

sample23.0ms

Algorithm

intervals

Results

7.0ms	69×	body	640	valid
4.0ms	137×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	11×	body	1280	valid
1.0ms	18×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	31	7
2	43	7
3	57	7
4	73	7
5	92	7
6	126	7
7	158	7
8	207	7
9	209	7
10	209	7
done	209	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
1.9b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

10.0ms	(/ 1.0 (+ x 1.0))
10.0ms	(/ 1.0 (- x 1.0))
57.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
266.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 1.0 (+ x 1.0))
31.0ms	(/ 1.0 (- x 1.0))
40.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
206.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify46.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	496	865
1	1681	827
2	5001	816
done	5001	816

prune245.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ x 1.0)))
0.1b	(sqrt (/ 1.0 (+ x 1.0)))
0.2b	(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
8.8b	(+ (- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

134×	`sqrt-prod`
116×	`*-un-lft-identity`
94×	`add-sqr-sqrt`
92×	`times-frac`
60×	`add-cube-cbrt`
29×	`swap-sqr`
25×	`distribute-lft-out`
21×	`pow1` `associate-r` `associate-l`
12×	`associate-/r/`
10×	`sqrt-pow1` `pow1/2` `sqrt-div`
9×	`add-log-exp` `unswap-sqr`
7×	`flip3-+` `flip-+`
6×	`add-exp-log` `add-cbrt-cube` `div-inv`
5×	`frac-add` `pow-prod-up`
4×	`rem-sqrt-square`
3×	`pow-prod-down` `pow-sqr` `frac-sub`
2×	`frac-times` `associate-+l+` `associate-r/` `associate-l/` `sum-log`
1×	`+-commutative` `pow2` `associate-+l-` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 189

Calls

4 calls:

10.0ms	(sqrt (/ 1.0 (+ x 1.0)))
10.0ms	(sqrt (/ 1.0 (+ x 1.0)))
58.0ms	(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
185.0ms	(+ (- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (/ 1.0 (+ x 1.0)))
89.0ms	(sqrt (/ 1.0 (+ x 1.0)))
76.0ms	(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
139.0ms	(+ (- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify84.0ms

Counts

201 → 201

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	601	1683
1	2878	1525
2	5002	1483
done	5002	1483

prune433.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
16.3b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

48×	`associate-*l/`
21×	`flip3--` `flip--`
17×	`add-sqr-sqrt`
16×	`frac-times` `frac-add`
15×	`*-un-lft-identity`
13×	`pow1` `add-exp-log` `flip3-+` `associate-r` `add-cbrt-cube` `flip-+`
9×	`add-cube-cbrt`
8×	`associate-r/` `associate-l*`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`associate-+l+`
3×	`*-commutative`
2×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

4 → 116

Calls

4 calls:

20.0ms	(* (+ x 1.0) x)
39.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
43.0ms	(* (* (+ x 1.0) x) (- x 1.0))
31.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series185.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (+ x 1.0) x)
38.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
99.0ms	(* (* (+ x 1.0) x) (- x 1.0))
2.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify127.0ms

Counts

128 → 128

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	805	1580
1	4760	1496
2	5001	1496
done	5001	1496

prune338.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log` `add-cbrt-cube`
18×	`associate-*l/`
12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`pow1`
8×	`frac-times` `add-cube-cbrt` `associate-r` `associate-/r/`
7×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
6×	`flip3--` `flip--`
5×	`associate-l`
4×	`associate-*r/` `pow-prod-down`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

19.0ms	(* (+ x 1.0) x)
34.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
44.0ms	(* (* (+ x 1.0) x) (- x 1.0))

series231.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* (+ x 1.0) x)
89.0ms	(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))
100.0ms	(* (* (+ x 1.0) x) (- x 1.0))

simplify58.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	430	600
1	2216	516
2	5001	515
done	5001	515

prune153.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5
done	10	5

end0.0ms

sample624.0ms

Algorithm

intervals

Results

199.0ms	1870×	body	640	valid
123.0ms	4106×	body	80	valid
77.0ms	983×	body	320	valid
77.0ms	561×	body	1280	valid
26.0ms	483×	body	160	valid