Details

sample42.0ms

Algorithm

intervals

Results

12.0ms	61×	body	640	valid
7.0ms	134×	body	80	valid
5.0ms	33×	body	320	valid
4.0ms	16×	body	1280	valid
1.0ms	12×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
10	4810
9	1188
8	437
7	210
6	162
5	135
4	89
3	41
2	31
1	18
0	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize39.0ms

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

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

728×	`*-un-lft-identity`
710×	`times-frac`
526×	`add-sqr-sqrt`
500×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+r+`
94×	`distribute-lft-out`
66×	`div-inv`
60×	`associate-/r/`
29×	`flip3-+` `flip-+`
21×	`fma-def`
18×	`fma-neg`
17×	`distribute-lft-out--`
11×	`add-log-exp` `difference-of-squares`
9×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--`
3×	`frac-add`
2×	`cbrt-undiv` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub`
1×	`+-commutative` `associate-+r-`

Counts

4 → 629

Calls

4 calls:

10.0ms	(/ 1.0 (- x 1.0))
9.0ms	(/ 1.0 (+ x 1.0))
91.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
213.0ms	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1.0 (- x 1.0))
28.0ms	(/ 1.0 (+ x 1.0))
73.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
361.0ms	(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

simplify954.0ms

Counts

641 → 641

Iterations

Iter	Nodes
done	5000
1	1564
0	682

prune3.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.1b	(/ (/ 1.0 (+ 1.0 x)) (- x 1.0))
3.5b	(+ (* (/ (/ 1.0 (+ 1.0 x)) (- x 1.0)) (+ x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
13.5b	(* (/ (/ 1.0 (+ 1.0 x)) (- x 1.0)) (+ x 1.0))

rewrite553.0ms

Algorithm

rewrite-expression-head

Rules

971×	`times-frac`
914×	`*-un-lft-identity`
694×	`add-sqr-sqrt`
599×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+r+`
116×	`distribute-lft-out`
96×	`associate-l`
80×	`associate-/r/`
76×	`div-inv`
47×	`flip3-+` `flip-+`
41×	`difference-of-squares`
40×	`distribute-lft-out--`
18×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*`
15×	`frac-add`
11×	`add-log-exp`
8×	`frac-times` `flip3--` `associate-*r/` `flip--`
6×	`pow1` `cbrt-undiv` `div-exp` `frac-sub`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-r` `associate-*l/` `log1p-expm1-u`
3×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `associate-+l+` `sum-log` `sub-neg` `distribute-lft-in` `diff-log`
1×	`+-commutative` `clear-num` `associate-+r-` `fma-def` `frac-2neg` `pow-prod-down` `*-commutative` `associate-/l/`

Counts

4 → 802

Calls

4 calls:

91.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
40.0ms	(/ (/ 1.0 (+ 1.0 x)) (- x 1.0))
209.0ms	(+ (* (/ (/ 1.0 (+ 1.0 x)) (- x 1.0)) (+ x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
127.0ms	(* (/ (/ 1.0 (+ 1.0 x)) (- x 1.0)) (+ x 1.0))

series565.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
121.0ms	(/ (/ 1.0 (+ 1.0 x)) (- x 1.0))
345.0ms	(+ (* (/ (/ 1.0 (+ 1.0 x)) (- x 1.0)) (+ x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
37.0ms	(* (/ (/ 1.0 (+ 1.0 x)) (- x 1.0)) (+ x 1.0))

simplify2.1s

Counts

814 → 814

Iterations

Iter	Nodes
done	5000
1	3157
0	964

prune3.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- x 1.0) x)
0.1b	(* (* (- x 1.0) x) (+ x 1.0))
0.2b	(- (* x 1.0) (* 2.0 (+ x 1.0)))
30.5b	(fma (- (* x 1.0) (* 2.0 (+ x 1.0))) (- x 1.0) (* (* 1.0 (+ x 1.0)) x))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
10×	`associate-*l/`
7×	`associate-r` `add-cube-cbrt`
6×	`associate-l` `add-log-exp`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`flip3-+` `flip-+`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `-commutative` `associate--r+`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `fma-udef` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

18.0ms	(* (- x 1.0) x)
42.0ms	(* (* (- x 1.0) x) (+ x 1.0))
14.0ms	(- (* x 1.0) (* 2.0 (+ x 1.0)))
1.0ms	(fma (- (* x 1.0) (* 2.0 (+ x 1.0))) (- x 1.0) (* (* 1.0 (+ x 1.0)) x))

series500.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (- x 1.0) x)
130.0ms	(* (* (- x 1.0) x) (+ x 1.0))
63.0ms	(- (* x 1.0) (* 2.0 (+ x 1.0)))
242.0ms	(fma (- (* x 1.0) (* 2.0 (+ x 1.0))) (- x 1.0) (* (* 1.0 (+ x 1.0)) x))

simplify2.4s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	2860
1	435
0	146

prune467.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- x 1.0) x)
0.1b	(* (* (- x 1.0) x) (+ x 1.0))
0.2b	(/ 2.0 (* (* (- x 1.0) x) (+ x 1.0)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 88

Calls

3 calls:

23.0ms	(* (- x 1.0) x)
56.0ms	(* (* (- x 1.0) x) (+ x 1.0))
40.0ms	(/ 2.0 (* (* (- x 1.0) x) (+ x 1.0)))

series310.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(* (- x 1.0) x)
124.0ms	(* (* (- x 1.0) x) (+ x 1.0))
115.0ms	(/ 2.0 (* (* (- x 1.0) x) (+ x 1.0)))

simplify2.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	3321
1	476
0	159

prune453.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

regimes31.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample1.7s

Algorithm

intervals

Results

750.0ms	1849×	body	640	valid
286.0ms	4139×	body	80	valid
217.0ms	979×	body	320	valid
195.0ms	594×	body	1280	valid
80.0ms	441×	body	160	valid