Details

sample32.0ms

Algorithm

intervals

Results

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
3.1b	(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))

rewrite558.0ms

Algorithm

rewrite-expression-head

Rules

1123×	`*-un-lft-identity`
1026×	`times-frac`
953×	`add-sqr-sqrt`
678×	`prod-diff`
610×	`add-cube-cbrt`
236×	`associate--r+`
127×	`difference-of-squares`
116×	`distribute-lft-out--`
106×	`distribute-lft-out`
78×	`associate-/r/`
76×	`div-inv`
34×	`fma-neg`
27×	`flip3-+` `flip-+`
15×	`flip3--` `flip--`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`frac-sub`
4×	`pow1` `expm1-log1p-u` `diff-log` `log1p-expm1-u`
3×	`sub-neg`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`associate--r-`

Counts

4 → 837

Calls

4 calls:

12.0ms	(/ 1.0 (- x 1.0))
13.0ms	(/ 1.0 (+ x 1.0))
70.0ms	(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
349.0ms	(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))

series528.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1.0 (- x 1.0))
46.0ms	(/ 1.0 (+ x 1.0))
73.0ms	(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
358.0ms	(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))

simplify1.8s

Counts

849 → 849

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	871	38837
1	2206	33703
done	5001	27984

prune2.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite552.0ms

Algorithm

rewrite-expression-head

Rules

90×	`associate-*r/`
38×	`flip3--` `flip--`
32×	`frac-sub`
28×	`frac-times`
22×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/l/`
15×	`add-sqr-sqrt`
14×	`associate-*l/`
13×	`*-un-lft-identity`
12×	`associate--l+`
11×	`pow1`
10×	`associate-l` `associate--r+`
9×	`add-cube-cbrt`
8×	`associate-/r/`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`sub-neg` `prod-diff`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `log1p-expm1-u`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `fma-neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`

Counts

4 → 172

Calls

4 calls:

90.0ms	(* (- x 1.0) (- (* 2.0 (+ x 1.0)) (* x 1.0)))
218.0ms	(/ (- (* 1.0 (* x (+ x 1.0))) (* (- x 1.0) (- (* 2.0 (+ x 1.0)) (* x 1.0)))) (* (- x 1.0) (* x (+ x 1.0))))
91.0ms	(* (- x 1.0) (* x (+ x 1.0)))
141.0ms	(- (* 1.0 (* x (+ x 1.0))) (* (- x 1.0) (- (* 2.0 (+ x 1.0)) (* x 1.0))))

series276.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- x 1.0) (- (* 2.0 (+ x 1.0)) (* x 1.0)))
100.0ms	(/ (- (* 1.0 (* x (+ x 1.0))) (* (- x 1.0) (- (* 2.0 (+ x 1.0)) (* x 1.0)))) (* (- x 1.0) (* x (+ x 1.0))))
131.0ms	(* (- x 1.0) (* x (+ x 1.0)))
2.0ms	(- (* 1.0 (* x (+ x 1.0))) (* (- x 1.0) (- (* 2.0 (+ x 1.0)) (* x 1.0))))

simplify700.0ms

Counts

184 → 184

Iterations

Useful iterations: done (688.0ms)

Iter	Nodes	Cost
0	344	5873
1	1274	5479
done	5002	5019

prune929.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite498.0ms

Algorithm

rewrite-expression-head

Rules

78×	`associate-*r/`
38×	`flip3--` `flip--`
32×	`frac-sub`
28×	`frac-times`
26×	`associate-*l/`
22×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
19×	`distribute-rgt-in` `distribute-lft-in`
18×	`associate-/l/`
13×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`associate--l+`
11×	`pow1`
10×	`associate--r+`
9×	`add-cube-cbrt`
8×	`associate-/r/`
7×	`associate-r` `prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
5×	`sub-neg` `prod-diff`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `fma-neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

92.0ms	(* (- x 1.0) (- (* 2.0 (+ x 1.0)) (* x 1.0)))
212.0ms	(/ (- (* 1.0 (* x (+ x 1.0))) (* (- x 1.0) (- (* 2.0 (+ x 1.0)) (* x 1.0)))) (* (* (- x 1.0) x) (+ x 1.0)))
56.0ms	(* (* (- x 1.0) x) (+ x 1.0))
129.0ms	(- (* 1.0 (* x (+ x 1.0))) (* (- x 1.0) (- (* 2.0 (+ x 1.0)) (* x 1.0))))

series728.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (- x 1.0) (- (* 2.0 (+ x 1.0)) (* x 1.0)))
527.0ms	(/ (- (* 1.0 (* x (+ x 1.0))) (* (- x 1.0) (- (* 2.0 (+ x 1.0)) (* x 1.0)))) (* (* (- x 1.0) x) (+ x 1.0)))
141.0ms	(* (* (- x 1.0) x) (+ x 1.0))
2.0ms	(- (* 1.0 (* x (+ x 1.0))) (* (- x 1.0) (- (* 2.0 (+ x 1.0)) (* x 1.0))))

simplify812.0ms

Counts

181 → 181

Iterations

Useful iterations: done (795.0ms)

Iter	Nodes	Cost
0	347	5837
1	1314	5439
done	5002	5079

prune823.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite713.0ms

Algorithm

rewrite-expression-head

Rules

93×	`times-frac`
89×	`*-un-lft-identity`
67×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`unpow-prod-down`
26×	`associate-/r*`
19×	`add-exp-log`
16×	`distribute-lft-out`
12×	`cube-prod` `sqr-pow`
10×	`add-cbrt-cube`
9×	`div-exp` `associate-/l*` `add-log-exp`
8×	`fma-def` `div-inv`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `frac-add` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `sum-log`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `associate-+l+`

Counts

4 → 193

Calls

4 calls:

670.0ms	(+ (+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 3))) (/ 2.0 (pow x 7)))
7.0ms	(/ 2.0 (pow x 5))
8.0ms	(/ 2.0 (pow x 7))
17.0ms	(/ 2.0 (pow x 3))

series293.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 3))) (/ 2.0 (pow x 7)))
61.0ms	(/ 2.0 (pow x 5))
88.0ms	(/ 2.0 (pow x 7))
45.0ms	(/ 2.0 (pow x 3))

simplify1.5s

Counts

205 → 205

Iterations

Useful iterations: 2 (660.0ms)

Iter	Nodes	Cost
0	294	2533
1	659	2232
2	2994	2171
done	5001	2171

prune732.0ms

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

bsearch148.0ms

Steps

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

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	36	75
1	47	75
done	47	75

end0.0ms

sample1.7s

Algorithm

intervals

Results

519.0ms	4208×	body	80	valid
412.0ms	1824×	body	640	valid
265.0ms	925×	body	320	valid
166.0ms	561×	body	1280	valid
110.0ms	485×	body	160	valid