Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	63×	body	640	valid
4.0ms	123×	body	80	valid
3.0ms	36×	body	320	valid
2.0ms	17×	body	1280	valid
1.0ms	17×	body	160	valid

simplify143.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	18	15
2	31	15
3	41	15
4	50	15
5	55	15
6	64	15
7	82	15
8	99	15
9	109	15
done	109	15

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize18.0ms

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))
3.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite559.0ms

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:

21.0ms	(/ 1.0 (- x 1.0))
11.0ms	(/ 1.0 (+ x 1.0))
95.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
423.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (- x 1.0))
29.0ms	(/ 1.0 (+ x 1.0))
60.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
269.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.6s

Counts

126 → 126

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	213	1832
1	498	1716
2	1314	1630
3	3767	1608
done	5000	1608

prune374.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ 1.0 (- x 1.0)))
0.4b	(cbrt (/ 1.0 (- x 1.0)))
0.4b	(cbrt (/ 1.0 (- x 1.0)))
21.7b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))

rewrite424.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
49×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
39×	`cbrt-div`
31×	`add-cube-cbrt`
21×	`frac-add`
15×	`frac-times` `associate-*l/`
10×	`flip3--` `flip--`
9×	`associate-*r/` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`frac-sub`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `div-inv`
2×	`associate-+l+` `sum-log`
1×	`+-commutative` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `flip-+`

Counts

4 → 126

Calls

4 calls:

12.0ms	(cbrt (/ 1.0 (- x 1.0)))
11.0ms	(cbrt (/ 1.0 (- x 1.0)))
12.0ms	(cbrt (/ 1.0 (- x 1.0)))
377.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))

series963.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt (/ 1.0 (- x 1.0)))
191.0ms	(cbrt (/ 1.0 (- x 1.0)))
209.0ms	(cbrt (/ 1.0 (- x 1.0)))
367.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))

simplify1.2s

Counts

138 → 138

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	268	3804
1	637	3640
2	1751	3151
done	5001	2984

prune605.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.2b	(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
8.5b	(+ (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)) 1.0)
13.2b	(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)) 1.0)) (* (- x 1.0) (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))))

rewrite662.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
13×	`flip3-+` `flip-+`
12×	`frac-times`
11×	`associate-/r/` `associate-/l/`
10×	`add-log-exp`
9×	`times-frac`
8×	`frac-add` `distribute-lft-out`
5×	`associate-r/` `associate-l/`
4×	`pow1` `cbrt-undiv` `add-sqr-sqrt` `add-cube-cbrt` `associate-+l+` `flip3--` `div-exp` `prod-exp` `flip--` `cbrt-unprod`
3×	`+-commutative` `sum-log`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`frac-2neg` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 88

Calls

4 calls:

66.0ms	(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
67.0ms	(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
170.0ms	(+ (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)) 1.0)
356.0ms	(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)) 1.0)) (* (- x 1.0) (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))))

series678.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
48.0ms	(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
157.0ms	(+ (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)) 1.0)
421.0ms	(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)) 1.0)) (* (- x 1.0) (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))))

simplify1.7s

Counts

100 → 100

Iterations

Useful iterations: 2 (675.0ms)

Iter	Nodes	Cost
0	182	3288
1	677	3235
2	3525	2721
done	5000	2721

prune373.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x 1.0) x)
0.0b	(* (+ x 1.0) x)
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
18.8b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

40.0ms	(* (+ x 1.0) x)
40.0ms	(* (+ x 1.0) x)
56.0ms	(* (* (+ x 1.0) x) (- x 1.0))
45.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series270.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (+ x 1.0) x)
71.0ms	(* (+ x 1.0) x)
151.0ms	(* (* (+ x 1.0) x) (- x 1.0))
3.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify2.7s

Counts

117 → 117

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	211	2807
1	747	2643
2	3759	2497
done	5001	2497

prune444.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 25.9b

bsearch161.0ms

Steps

Iters	Range		Point
9	110.15968793260775	1173724448.4928873	642.4163412587075
9	-3484513403575543.0	-66911392.43097515	-136532428.3902713

simplify10.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	31	73
1	44	57
done	44	57

end0.0ms

sample978.0ms

Algorithm

intervals

Results

307.0ms	1881×	body	640	valid
183.0ms	4156×	body	80	valid
128.0ms	553×	body	1280	valid
118.0ms	935×	body	320	valid
44.0ms	476×	body	160	valid