Details

sample222.0ms

Algorithm

intervals

Results

80.0ms	57×	body	10240	exit
41.0ms	55×	body	1280	valid
33.0ms	326×	body	80	valid
28.0ms	60×	body	640	valid
6.0ms	20×	body	320	valid
1.0ms	8×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	19	29
1	46	29
2	122	29
3	335	27
4	933	27
5	4084	27
done	5000	27

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
2.4b	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite525.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
62×	`add-sqr-sqrt`
46×	`times-frac`
26×	`add-cube-cbrt`
13×	`difference-of-squares`
12×	`distribute-lft-out--`
10×	`add-cbrt-cube` `associate-/l*`
8×	`add-exp-log`
6×	`pow1` `associate-/r*` `distribute-lft-out` `add-log-exp`
5×	`associate-l`
4×	`associate-/l/`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `associate-*l/` `clear-num` `div-inv`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `associate--r-` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

46.0ms	(* (- 1.0 eps) x)
76.0ms	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
66.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
327.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (- 1.0 eps) x)
64.0ms	(/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x)))
70.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
272.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify1.3s

Counts

132 → 132

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	247	2886
1	583	2758
2	1520	2593
done	5000	2552

prune623.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (* x x) (- (* 0.6666666666666667 x) 1.0))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `add-cube-cbrt` `sub-neg` `-un-lft-identity` `distribute-lft-in` `associate-r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `add-log-exp` `unswap-sqr`

Counts

1 → 25

Calls

1 calls:

62.0ms

(* (* x x) (- (* 0.6666666666666667 x) 1.0))

series133.0ms

Counts

1 → 3

Calls

1 calls:

133.0ms

(* (* x x) (- (* 0.6666666666666667 x) 1.0))

simplify1.8s

Counts

28 → 28

Iterations

Useful iterations: 2 (141.0ms)

Iter	Nodes	Cost
0	57	367
1	156	344
2	566	294
3	2178	294
done	5000	294

prune94.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(* (exp (- (* (- 1.0 eps) x))) (+ (/ 1.0 eps) 1.0))
0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
3.4b	(- (* (exp (- (* (- 1.0 eps) x))) (+ (/ 1.0 eps) 1.0)) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
22×	`times-frac`
19×	`add-cube-cbrt`
10×	`add-cbrt-cube`
9×	`difference-of-squares`
8×	`pow1` `add-exp-log` `frac-times` `associate-l` `frac-sub`
7×	`associate-r`
6×	`neg-sub0` `exp-neg` `flip3-+` `exp-diff` `associate-l/` `flip-+` `associate-/l` `add-log-exp`
5×	`distribute-lft-out--`
4×	`associate-*r/`
3×	`flip3--` `associate-/r*` `flip--`
2×	`distribute-rgt-in` `distribute-lft-in` `div-sub` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv` `distribute-lft-out` `associate--r-`

Counts

4 → 116

Calls

4 calls:

28.0ms	(* (- 1.0 eps) x)
80.0ms	(* (exp (- (* (- 1.0 eps) x))) (+ (/ 1.0 eps) 1.0))
67.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
86.0ms	(- (* (exp (- (* (- 1.0 eps) x))) (+ (/ 1.0 eps) 1.0)) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series580.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (- 1.0 eps) x)
85.0ms	(* (exp (- (* (- 1.0 eps) x))) (+ (/ 1.0 eps) 1.0))
72.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
379.0ms	(- (* (exp (- (* (- 1.0 eps) x))) (+ (/ 1.0 eps) 1.0)) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify1.6s

Counts

128 → 128

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	257	2924
1	651	2762
2	2056	2528
done	5000	2479

prune594.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes50.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.3b

bsearch218.0ms

Steps

Iters	Range		Point
9	0.3311692926351245	51141.47312026252	84.47417936124704

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	45
1	40	45
2	42	45
done	42	45

end0.0ms

sample9.2s

Algorithm

intervals

Results

3.2s	1828×	body	10240	exit
2.7s	1778×	body	1280	valid
1.5s	9885×	body	80	valid
799.0ms	1313×	body	640	valid
261.0ms	632×	body	320	valid
67.0ms	297×	body	160	valid