Details

sample24.0ms

Algorithm

intervals

Results

8.0ms	77×	body	640	valid
3.0ms	122×	body	80	valid
3.0ms	21×	body	1280	valid
2.0ms	23×	body	320	valid
1.0ms	13×	body	160	valid

simplify74.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	15
1	18	15
2	31	15
3	41	15
4	52	15
5	59	15
6	68	15
7	86	15
8	107	15
9	117	15
done	117	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.5b

localize9.0ms

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))
1.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

725×	`*-un-lft-identity`
703×	`times-frac`
524×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
468×	`prod-diff`
236×	`associate-+l+`
95×	`distribute-lft-out`
65×	`div-inv`
58×	`associate-/r/`
29×	`flip3-+` `flip-+`
18×	`fma-neg`
17×	`distribute-lft-out--`
12×	`difference-of-squares`
11×	`add-log-exp`
10×	`fma-def`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

5.0ms	(/ 1.0 (+ x 1.0))
6.0ms	(/ 1.0 (- x 1.0))
52.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
231.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ x 1.0))
31.0ms	(/ 1.0 (- x 1.0))
42.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
223.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.2s

Counts

630 → 630

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	502	19834
1	1100	17345
2	2903	12902
done	5001	12778

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (cbrt 1.0) (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (+ x 1.0))) (/ 2.0 x))
1.2b	(+ (- (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
57×	`times-frac`
54×	`add-sqr-sqrt`
46×	`add-cube-cbrt`
26×	`prod-diff`
15×	`cbrt-prod` `associate-+l+`
11×	`add-log-exp`
9×	`associate-/r` `associate-/l`
8×	`add-exp-log` `distribute-lft-out`
7×	`add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `div-inv` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `fma-def` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `associate-*r/` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+`
1×	`+-commutative` `associate-+l-` `fma-neg`

Counts

4 → 155

Calls

4 calls:

6.0ms	(/ (cbrt 1.0) (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
20.0ms	(- (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (+ x 1.0))) (/ 2.0 x))
147.0ms	(+ (- (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (cbrt 1.0) (+ x 1.0))
28.0ms	(/ 1.0 (- x 1.0))
71.0ms	(- (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (+ x 1.0))) (/ 2.0 x))
257.0ms	(+ (- (* (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (+ x 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.0s

Counts

167 → 167

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	349	3324
1	824	3047
2	2545	2468
done	5000	2464

prune413.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(* (+ x 1.0) x)
0.7b	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
15.6b	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
21×	`times-frac`
20×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
9×	`fma-def`
6×	`pow1` `associate-l/` `associate-/r` `associate-/r/` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `associate-l` `flip-+` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`flip3--` `frac-2neg` `div-sub` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `associate-+l-` `pow-prod-down` `frac-add` `sum-log` `*-commutative` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

5.0ms	(/ 1.0 (- x 1.0))
10.0ms	(* (+ x 1.0) x)
41.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
10.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

series426.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ 1.0 (- x 1.0))
45.0ms	(* (+ x 1.0) x)
284.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
68.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

simplify1.0s

Counts

127 → 127

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	210	1869
1	560	1760
2	1881	1371
done	5000	1365

prune258.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b	(/ 1 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
1.0b	(fma (/ 1 (+ x 1.0)) (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) x) (/ 1.0 (- x 1.0)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
27×	`times-frac`
23×	`add-cube-cbrt`
10×	`add-exp-log`
9×	`associate-/r*`
8×	`add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
3×	`div-exp`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `flip--` `div-inv`
1×	`sub-neg` `rec-exp` `pow-flip` `flip3-+` `fma-neg` `diff-log` `1-exp` `prod-diff` `flip-+` `fma-udef` `inv-pow`

Counts

4 → 104

Calls

4 calls:

3.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
8.0ms	(/ 1 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
0.0ms	(fma (/ 1 (+ x 1.0)) (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) x) (/ 1.0 (- x 1.0)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
22.0ms	(/ 1 (+ x 1.0))
28.0ms	(/ 1.0 (- x 1.0))
295.0ms	(fma (/ 1 (+ x 1.0)) (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) x) (/ 1.0 (- x 1.0)))

simplify2.0s

Counts

116 → 116

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	201	1450
1	454	1335
2	1222	1203
3	3828	1178
done	5001	1176

prune241.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes27.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 9.5b

bsearch100.0ms

Steps

Iters	Range		Point
11	0.08347146558812443	3.320253512051989e+22	120.64077220743235
7	-1162.6651869185068	-5.7596417613087905	-115.11631650208354

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	64
1	40	48
done	40	48

end0.0ms

sample571.0ms

Algorithm

intervals

Results

192.0ms	1883×	body	640	valid
111.0ms	4149×	body	80	valid
78.0ms	970×	body	320	valid
72.0ms	568×	body	1280	valid
27.0ms	433×	body	160	valid