Details

sample241.0ms

Algorithm

intervals

Results

79.0ms	58×	body	10240	exit
49.0ms	51×	body	1280	valid
43.0ms	316×	body	80	valid
22.0ms	38×	body	640	valid
9.0ms	24×	body	320	valid
3.0ms	8×	body	160	valid

simplify646.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(exp (* (- 1.0 eps) x))
0.0b	(exp (* (+ 1.0 eps) x))
2.7b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite540.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
94×	`times-frac`
81×	`add-sqr-sqrt`
26×	`distribute-lft-out--`
25×	`add-cube-cbrt`
17×	`difference-of-squares`
14×	`add-log-exp`
6×	`add-cbrt-cube` `distribute-lft-out` `associate-/l*`
5×	`add-exp-log`
4×	`pow1` `exp-to-pow`
3×	`div-sub` `associate-/r*` `div-inv`
2×	`exp-prod` `flip3--` `diff-log` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `distribute-rgt-out--` `frac-2neg` `div-exp` `clear-num` `sum-log` `frac-sub` `sub-div` `associate--r-`

Counts

4 → 105

Calls

4 calls:

50.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
11.0ms	(exp (* (- 1.0 eps) x))
7.0ms	(exp (* (+ 1.0 eps) x))
465.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series425.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
35.0ms	(exp (* (- 1.0 eps) x))
36.0ms	(exp (* (+ 1.0 eps) x))
303.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify603.0ms

Counts: 117 → 117

prune512.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 1 expressions with local error:

0.0b	(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-l`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-r` `prod-exp` `add-cbrt-cube`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/` `unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `flip3--` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

69.0ms

(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

series132.0ms

Counts

1 → 3

Calls

1 calls:

132.0ms

(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

simplify2.3s

Counts: 36 → 36

prune116.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite577.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
60×	`times-frac`
45×	`*-un-lft-identity`
18×	`add-log-exp`
12×	`difference-of-squares`
10×	`add-cube-cbrt` `distribute-lft-out--`
6×	`exp-to-pow`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`exp-prod` `rem-exp-log` `distribute-lft-out`
2×	`diff-log` `sum-log` `div-inv`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `frac-sub` `flip--` `sub-div`

Counts

4 → 70

Calls

4 calls:

9.0ms	(exp (* (- 1.0 eps) x))
7.0ms	(exp (* (+ 1.0 eps) x))
7.0ms	(exp (* (+ 1.0 eps) x))
550.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))) 2.0))

series254.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(exp (* (- 1.0 eps) x))
24.0ms	(exp (* (+ 1.0 eps) x))
34.0ms	(exp (* (+ 1.0 eps) x))
164.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))) 2.0))

simplify1.3s

Counts: 82 → 82

prune425.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (- 1.0 eps)))
0.0b	(exp (* x (+ eps 1.0)))
0.0b	(exp (* (+ 1.0 eps) x))
2.2b	(- (/ (/ 0.5 eps) (exp (* x (+ eps 1.0)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps)))))

rewrite476.0ms

Algorithm

rewrite-expression-head

Rules

62×	`times-frac`
54×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`distribute-lft-out--`
14×	`add-log-exp`
9×	`difference-of-squares`
6×	`exp-sum`
4×	`pow1` `add-exp-log` `exp-to-pow` `add-cbrt-cube` `div-inv`
3×	`distribute-rgt-in` `sub-neg` `exp-prod` `distribute-lft-in` `rem-exp-log`
1×	`flip3--` `diff-log` `sum-log` `frac-sub` `flip--`

Counts

4 → 74

Calls

4 calls:

13.0ms	(exp (* x (- 1.0 eps)))
10.0ms	(exp (* x (+ eps 1.0)))
12.0ms	(exp (* (+ 1.0 eps) x))
437.0ms	(- (/ (/ 0.5 eps) (exp (* x (+ eps 1.0)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps)))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(exp (* x (- 1.0 eps)))
13.0ms	(exp (* x (+ eps 1.0)))
24.0ms	(exp (* (+ 1.0 eps) x))
153.0ms	(- (/ (/ 0.5 eps) (exp (* x (+ eps 1.0)))) (/ (/ 0.5 eps) (exp (* x (- 1.0 eps)))))

simplify1.3s

Counts: 86 → 86

prune429.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes81.0ms

Accuracy

0% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 1.0b

bsearch0.0ms

simplify751.0ms

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.7s	1961×	body	10240	exit
1.8s	9950×	body	80	valid
1.5s	1715×	body	1280	valid
733.0ms	1276×	body	640	valid
642.0ms	629×	body	320	valid
64.0ms	324×	body	160	valid