Details

sample31.0ms

Algorithm

intervals

Results

9.0ms	67×	body	640	valid
5.0ms	133×	body	80	valid
3.0ms	18×	body	1280	valid
3.0ms	29×	body	320	valid
1.0ms	9×	body	160	valid

simplify1.1s

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	88	15
5	135	15
6	162	15
7	211	15
8	441	15
9	1208	15
done	5000	15

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize19.0ms

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))
3.1b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite595.0ms

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:

26.0ms	(/ 1.0 (- x 1.0))
22.0ms	(/ 1.0 (+ x 1.0))
102.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
435.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ 1.0 (- x 1.0))
46.0ms	(/ 1.0 (+ x 1.0))
79.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
347.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.2s

Counts

126 → 126

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	213	1832
1	516	1716
2	1963	1630
done	5000	1624

prune410.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
0.0b	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
0.0b	(* (* (+ x 1.0) x) (- x 1.0))
15.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite403.0ms

Algorithm

rewrite-expression-head

Rules

90×	`associate-*l/`
36×	`flip3--` `flip--`
32×	`frac-add`
28×	`frac-times`
24×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/l/`
15×	`add-sqr-sqrt`
14×	`associate-*r/`
13×	`*-un-lft-identity`
11×	`pow1`
10×	`associate-r`
9×	`add-cube-cbrt`
8×	`associate-/r/`
7×	`prod-exp` `cbrt-unprod`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-log-exp`
4×	`associate-+l+` `associate-l` `pow-prod-down`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `frac-2neg` `clear-num` `associate-/r*` `sum-log` `div-inv` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

64.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
162.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
93.0ms	(* (* (+ x 1.0) x) (- x 1.0))
63.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series303.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
118.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (* (+ x 1.0) x) (- x 1.0)))
115.0ms	(* (* (+ x 1.0) x) (- x 1.0))
4.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify659.0ms

Counts

156 → 156

Iterations

Useful iterations: done (651.0ms)

Iter	Nodes	Cost
0	292	5330
1	1065	5037
done	5000	4677

prune840.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
0.0b	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (+ x 1.0) (* x (- x 1.0))))
0.0b	(* (+ x 1.0) (* x (- x 1.0)))
15.5b	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite406.0ms

Algorithm

rewrite-expression-head

Rules

78×	`associate-*l/`
36×	`flip3--` `flip--`
32×	`frac-add`
28×	`frac-times`
26×	`associate-*r/`
24×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/l/`
13×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`distribute-rgt-in` `distribute-lft-in`
11×	`pow1`
9×	`add-cube-cbrt`
8×	`sub-neg` `associate-/r/`
7×	`associate-l` `prod-exp` `cbrt-unprod`
6×	`associate-r` `add-log-exp`
4×	`associate-+l+` `pow-prod-down`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`*-commutative`
1×	`+-commutative` `frac-2neg` `clear-num` `associate-/r*` `sum-log` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 147

Calls

4 calls:

59.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
162.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (+ x 1.0) (* x (- x 1.0))))
105.0ms	(* (+ x 1.0) (* x (- x 1.0)))
61.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series324.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
108.0ms	(/ (+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0)) (* (+ x 1.0) (* x (- x 1.0))))
163.0ms	(* (+ x 1.0) (* x (- x 1.0)))
4.0ms	(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify632.0ms

Counts

159 → 159

Iterations

Useful iterations: done (623.0ms)

Iter	Nodes	Cost
0	298	5376
1	1057	5087
done	5001	4727

prune797.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 3)))
0.1b	(/ 2.0 (pow x 5))
0.2b	(/ 2.0 (pow x 7))
0.3b	(/ 2.0 (pow x 3))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
71×	`*-un-lft-identity`
63×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`unpow-prod-down`
26×	`associate-/r*`
19×	`add-exp-log`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`div-inv` `distribute-lft-out`
4×	`pow1` `cube-mult` `unpow3`
3×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`+-commutative` `flip3-+` `frac-add` `sum-log` `flip-+`

Counts

4 → 172

Calls

4 calls:

143.0ms	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 3)))
14.0ms	(/ 2.0 (pow x 5))
8.0ms	(/ 2.0 (pow x 7))
9.0ms	(/ 2.0 (pow x 3))

series482.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(+ (/ 2.0 (pow x 7)) (/ 2.0 (pow x 3)))
60.0ms	(/ 2.0 (pow x 5))
97.0ms	(/ 2.0 (pow x 7))
52.0ms	(/ 2.0 (pow x 3))

simplify1.5s

Counts

184 → 184

Iterations

Useful iterations: 2 (667.0ms)

Iter	Nodes	Cost
0	255	2079
1	536	1812
2	2510	1756
done	5000	1756

prune587.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes59.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 25.2b

bsearch88.0ms

Steps

Iters	Range		Point
8	32715339.804033544	17960083604.66992	33013378.796887353
5	-1333.496421940221	-527.3133570883257	-1313.1390827564153

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	75
1	50	75
done	50	75

end0.0ms

sample1.5s

Algorithm

intervals

Results

677.0ms	1824×	body	640	valid
253.0ms	4208×	body	80	valid
156.0ms	561×	body	1280	valid
151.0ms	925×	body	320	valid
75.0ms	485×	body	160	valid