Details

sample43.0ms

Algorithm

intervals

Results

12.0ms	56×	body	640	valid
7.0ms	134×	body	80	valid
5.0ms	36×	body	320	valid
3.0ms	14×	body	1280	valid
2.0ms	16×	body	160	valid

simplify150.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	198
9	198
8	170
7	103
6	83
5	72
4	60
3	41
2	31
1	18
0	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize40.0ms

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))
3.2b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite590.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `frac-sub`
1×	`+-commutative` `associate-+l-`

Counts

4 → 618

Calls

4 calls:

15.0ms	(/ 1.0 (+ x 1.0))
21.0ms	(/ 1.0 (- x 1.0))
88.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
412.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1.0 (+ x 1.0))
51.0ms	(/ 1.0 (- x 1.0))
81.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
341.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.9s

Counts

630 → 630

Iterations

Iter	Nodes
done	5001
2	3147
1	1189
0	501

prune3.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
2.0b	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
14.1b	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

17.0ms	(/ 1.0 (- x 1.0))
12.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
73.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
28.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

series686.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1.0 (- x 1.0))
48.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
478.0ms	(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
112.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

simplify2.8s

Counts

120 → 120

Iterations

Iter	Nodes
done	5004
2	2384
1	594
0	210

prune702.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(* (/ 1 (+ x 1.0)) (- 1.0 (/ (+ x 1.0) (/ x 2.0))))
0.0b	(- 1.0 (/ (+ x 1.0) (/ x 2.0)))
2.9b	(+ (* (/ 1 (+ x 1.0)) (- 1.0 (/ (+ x 1.0) (/ x 2.0)))) (/ 1.0 (- x 1.0)))

rewrite681.0ms

Algorithm

rewrite-expression-head

Rules

1355×	`times-frac`
1348×	`*-un-lft-identity`
972×	`add-sqr-sqrt`
939×	`add-cube-cbrt`
855×	`prod-diff`
346×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
198×	`distribute-lft-out`
77×	`div-inv`
19×	`associate-/r/`
18×	`associate-l`
15×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`associate-r`
6×	`pow1` `flip3--` `flip--` `distribute-lft-out--`
5×	`associate-/r*` `sub-neg` `frac-add`
4×	`expm1-log1p-u` `frac-times` `prod-exp` `associate-*r/` `log1p-expm1-u`
3×	`fma-neg` `div-exp` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `associate-*l/` `cbrt-unprod` `flip-+`
1×	`+-commutative` `rec-exp` `clear-num` `sum-log` `fma-def` `frac-2neg` `diff-log` `1-exp` `pow-prod-down` `*-commutative`

Counts

4 → 992

Calls

4 calls:

9.0ms	(/ 1.0 (- x 1.0))
252.0ms	(* (/ 1 (+ x 1.0)) (- 1.0 (/ (+ x 1.0) (/ x 2.0))))
78.0ms	(- 1.0 (/ (+ x 1.0) (/ x 2.0)))
172.0ms	(+ (* (/ 1 (+ x 1.0)) (- 1.0 (/ (+ x 1.0) (/ x 2.0)))) (/ 1.0 (- x 1.0)))

series636.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1.0 (- x 1.0))
75.0ms	(* (/ 1 (+ x 1.0)) (- 1.0 (/ (+ x 1.0) (/ x 2.0))))
79.0ms	(- 1.0 (/ (+ x 1.0) (/ x 2.0)))
439.0ms	(+ (* (/ 1 (+ x 1.0)) (- 1.0 (/ (+ x 1.0) (/ x 2.0)))) (/ 1.0 (- x 1.0)))

simplify3.5s

Counts

1004 → 1004

Iterations

Iter	Nodes
done	5001
1	3455
0	1103

prune6.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.1b	(* (- (* x x) (* 1.0 1.0)) x)
3.1b	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (- (* x x) (* 1.0 1.0)) x))
28.6b	(fma (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (- (* x x) (* 1.0 1.0)) x)) (- x 1.0) (/ 1.0 (- x 1.0)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `associate-l` `associate-*l/` `log1p-expm1-u` `flip--`
3×	`times-frac` `associate-r` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `pow-prod-down` `-commutative` `fma-udef` `div-inv` `difference-of-squares` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

9.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
22.0ms	(* (- (* x x) (* 1.0 1.0)) x)
24.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (- (* x x) (* 1.0 1.0)) x))
0.0ms	(fma (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (- (* x x) (* 1.0 1.0)) x)) (- x 1.0) (/ 1.0 (- x 1.0)))

series847.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* 1.0 x) (* (+ x 1.0) 2.0))
123.0ms	(* (- (* x x) (* 1.0 1.0)) x)
137.0ms	(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (- (* x x) (* 1.0 1.0)) x))
542.0ms	(fma (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (- (* x x) (* 1.0 1.0)) x)) (- x 1.0) (/ 1.0 (- x 1.0)))

simplify2.7s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	2182
1	449
0	159

prune514.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

99.6% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 10.1b

bsearch153.0ms

Steps

Iters	Range		Point
9	44.35744796693956	12146952.384825662	111.63759388748683
10	-733100.9210806559	-4.034181863829644e-08	-132.12574632089513

simplify12.0ms

Iterations

Iter	Nodes
done	40
1	40
0	30

end0.0ms

sample1.9s

Algorithm

intervals

Results

707.0ms	4129×	body	80	valid
414.0ms	1832×	body	640	valid
312.0ms	577×	body	1280	valid
262.0ms	976×	body	320	valid
54.0ms	486×	body	160	valid