Details

sample268.0ms

Algorithm

intervals

Results

91.0ms	58×	body	10240	exit
59.0ms	58×	body	1280	valid
50.0ms	306×	body	80	valid
29.0ms	42×	body	640	valid
11.0ms	24×	body	320	valid
5.0ms	13×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
5	3061
4	844
3	296
2	120
1	46
0	19

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (- x) (* x eps)))
0.0b	(exp (+ (- x) (* x eps)))
0.0b	(exp (+ (- x) (* x eps)))
3.1b	(- (+ (exp (+ (- x) (* x eps))) (/ (exp (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))

rewrite735.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-log-exp`
19×	`*-un-lft-identity`
12×	`frac-sub`
9×	`add-sqr-sqrt` `exp-prod` `exp-diff` `rem-exp-log`
8×	`diff-log`
7×	`add-cube-cbrt`
6×	`sum-log` `distribute-lft-out--`
5×	`neg-sub0` `associate-+l-`
4×	`pow1` `flip3--` `add-cbrt-cube` `exp-sum` `add-exp-log` `insert-posit16` `flip--`
3×	`sub-neg` `flip3-+` `neg-log` `frac-add` `flip-+`
2×	`distribute-lft-out` `associate--r+`
1×	`associate--l+` `associate--r-` `difference-of-squares`

Counts

4 → 83

Calls

4 calls:

15.0ms	(exp (- (- x) (* x eps)))
16.0ms	(exp (+ (- x) (* x eps)))
31.0ms	(exp (+ (- x) (* x eps)))
671.0ms	(- (+ (exp (+ (- x) (* x eps))) (/ (exp (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(exp (- (- x) (* x eps)))
15.0ms	(exp (+ (- x) (* x eps)))
17.0ms	(exp (+ (- x) (* x eps)))
154.0ms	(- (+ (exp (+ (- x) (* x eps))) (/ (exp (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))

simplify6.1s

Counts

95 → 95

Iterations

Iter	Nodes
3	11631
2	1931
1	478
0	168

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x 2/3) (* x x))
0.3b	(* x 2/3)
5.8b	(+ (- 2 (* x x)) (* (* x 2/3) (* x x)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `associate-l`
3×	`insert-posit16`
2×	`associate-+l+` `sum-log` `*-commutative`
1×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `associate-+l-` `flip-+` `unswap-sqr`

Counts

3 → 58

Calls

3 calls:

22.0ms	(* (* x 2/3) (* x x))
5.0ms	(* x 2/3)
36.0ms	(+ (- 2 (* x x)) (* (* x 2/3) (* x x)))

series143.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (* x 2/3) (* x x))
26.0ms	(* x 2/3)
57.0ms	(+ (- 2 (* x x)) (* (* x 2/3) (* x x)))

simplify3.1s

Counts

67 → 67

Iterations

Iter	Nodes
3	5318
2	896
1	241
0	91

prune622.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x x) (* 2/3 x))
0.3b	(* 2/3 x)
5.8b	(- (* (* x x) (* 2/3 x)) (* x x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`associate-r` `associate-l`
3×	`insert-posit16`
2×	`*-commutative`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `unswap-sqr`

Counts

3 → 55

Calls

3 calls:

28.0ms	(* (* x x) (* 2/3 x))
6.0ms	(* 2/3 x)
36.0ms	(- (* (* x x) (* 2/3 x)) (* x x))

series220.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(* (* x x) (* 2/3 x))
27.0ms	(* 2/3 x)
121.0ms	(- (* (* x x) (* 2/3 x)) (* x x))

simplify4.3s

Counts

64 → 64

Iterations

Iter	Nodes
3	6102
2	858
1	224
0	81

prune505.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite522.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-log-exp`
20×	`*-un-lft-identity`
12×	`frac-sub`
10×	`add-sqr-sqrt`
8×	`exp-diff` `diff-log` `add-cube-cbrt`
6×	`exp-prod` `distribute-lft-out--` `rem-exp-log`
5×	`neg-sub0` `pow1` `add-exp-log` `associate-+l-`
4×	`sum-log` `flip3--` `add-cbrt-cube` `insert-posit16` `flip--`
3×	`pow-unpow` `sub-neg` `unpow-prod-down` `flip3-+` `exp-sum` `frac-add` `flip-+`
2×	`neg-log` `pow-exp` `distribute-lft-out` `associate--r+`
1×	`pow-to-exp` `unpow-prod-up` `e-exp-1` `pow-pow` `associate--l+` `associate--r-` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 88

Calls

4 calls:

19.0ms	(exp (- (- x) (* x eps)))
17.0ms	(exp (+ (- x) (* x eps)))
7.0ms	(pow E (+ (- x) (* x eps)))
477.0ms	(- (+ (exp (+ (- x) (* x eps))) (/ (pow E (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(exp (- (- x) (* x eps)))
24.0ms	(exp (+ (- x) (* x eps)))
36.0ms	(pow E (+ (- x) (* x eps)))
167.0ms	(- (+ (exp (+ (- x) (* x eps))) (/ (pow E (+ (- x) (* x eps))) eps)) (- (/ (exp (- (- x) (* x eps))) eps) (exp (- (- x) (* x eps)))))

simplify924.0ms

Counts

100 → 100

Iterations

Iter	Nodes
2	2084
1	565
0	197

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes111.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.5b

bsearch285.0ms

Steps

Iters	Range		Point
9	9.810191608759935e-05	3826.660001831638	129.10958091941424

simplify10.0ms

Iterations

Iter	Nodes
2	32
1	32
0	26

end0.0ms

sample11.7s

Algorithm

intervals

Results

4.1s	1912×	body	10240	exit
2.5s	10030×	body	80	valid
2.5s	1732×	body	1280	valid
1.6s	1267×	body	640	valid
455.0ms	685×	body	320	valid
106.0ms	290×	body	160	valid