Details

sample322.0ms

Algorithm

intervals

Results

113.0ms	58×	body	10240	exit
65.0ms	54×	body	1280	valid
60.0ms	312×	body	80	valid
43.0ms	47×	body	640	valid
13.0ms	21×	body	320	valid
3.0ms	8×	body	160	valid

simplify1.7s

Counts: 1 → 1

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize46.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (+ (/ (/ 1/2 (exp (- x (* x eps)))) eps) (/ 1/2 (exp (- x (* x eps))))) (- (/ (/ 1/2 (exp (+ x (* x eps)))) eps) (/ 1/2 (exp (+ x (* x eps))))))
0.0b	(/ 1/2 (exp (+ x (* x eps))))
0.0b	(/ 1/2 (exp (+ x (* x eps))))
0.0b	(+ x (* x eps))

rewrite684.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
28×	`times-frac`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
18×	`add-log-exp`
12×	`frac-sub`
8×	`associate-/r*` `add-cbrt-cube` `exp-sum` `distribute-lft-out--`
6×	`diff-log` `add-exp-log` `associate-/l*`
4×	`pow1` `flip3-+` `flip3--` `flip-+` `insert-posit16` `flip--`
3×	`sum-log` `frac-add` `distribute-lft-out`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `div-exp` `div-inv` `associate--r+`
1×	`+-commutative` `associate--l+` `associate--r-` `difference-of-squares`

Counts

4 → 111

Calls

4 calls:

Slowest

651.0ms	(- (+ (/ (/ 1/2 (exp (- x (* x eps)))) eps) (/ 1/2 (exp (- x (* x eps))))) (- (/ (/ 1/2 (exp (+ x (* x eps)))) eps) (/ 1/2 (exp (+ x (* x eps))))))
13.0ms	(/ 1/2 (exp (+ x (* x eps))))
12.0ms	(/ 1/2 (exp (+ x (* x eps))))
5.0ms	(+ x (* x eps))

series335.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

207.0ms	(- (+ (/ (/ 1/2 (exp (- x (* x eps)))) eps) (/ 1/2 (exp (- x (* x eps))))) (- (/ (/ 1/2 (exp (+ x (* x eps)))) eps) (/ 1/2 (exp (+ x (* x eps))))))
55.0ms	(+ x (* x eps))
38.0ms	(/ 1/2 (exp (+ x (* x eps))))
35.0ms	(/ 1/2 (exp (+ x (* x eps))))

simplify1.4s

Counts: 123 → 123

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 3 expressions with local error:

6.6b	(+ (- 1 (* 1/2 (* x x))) (* (* 1/3 x) (* x x)))
0.3b	(* 1/3 x)
0.1b	(* (* 1/3 x) (* x x))

rewrite104.0ms

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:

Slowest

45.0ms	(+ (- 1 (* 1/2 (* x x))) (* (* 1/3 x) (* x x)))
43.0ms	(* (* 1/3 x) (* x x))
15.0ms	(* 1/3 x)

series149.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

71.0ms	(* (* 1/3 x) (* x x))
54.0ms	(+ (- 1 (* 1/2 (* x x))) (* (* 1/3 x) (* x x)))
24.0ms	(* 1/3 x)

simplify1.3s

Counts: 67 → 67

prune607.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 2 expressions with local error:

0.3b	(* 1/3 x)
0.1b	(* (* x x) (- 1/2 (* 1/3 x)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`associate-r`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-r/` `-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

2 → 45

Calls

2 calls:

Slowest

46.0ms	(* (* x x) (- 1/2 (* 1/3 x)))
10.0ms	(* 1/3 x)

series164.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

136.0ms	(* (* x x) (- 1/2 (* 1/3 x)))
28.0ms	(* 1/3 x)

simplify813.0ms

Counts: 51 → 51

prune488.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/3 x)
0.1b	(* (* x x) (- 1/2 (* 1/3 x)))
0.0b	(log (/ E (exp (* (* x x) (- 1/2 (* 1/3 x))))))
0.0b	(/ E (exp (* (* x x) (- 1/2 (* 1/3 x)))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac`
33×	`add-sqr-sqrt`
30×	`*-un-lft-identity` `add-cube-cbrt`
28×	`exp-sum`
25×	`log-prod`
16×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
14×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`pow1`
7×	`associate-/r*`
6×	`associate-r`
4×	`div-exp` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`rem-log-exp` `associate-/l*`
2×	`e-exp-1` `associate-r/` `-commutative` `div-inv` `unswap-sqr`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3--` `log-pow` `flip--`

Counts

4 → 128

Calls

4 calls:

Slowest

36.0ms	(* (* x x) (- 1/2 (* 1/3 x)))
22.0ms	(/ E (exp (* (* x x) (- 1/2 (* 1/3 x)))))
9.0ms	(log (/ E (exp (* (* x x) (- 1/2 (* 1/3 x))))))
5.0ms	(* 1/3 x)

series306.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

135.0ms	(log (/ E (exp (* (* x x) (- 1/2 (* 1/3 x))))))
92.0ms	(* (* x x) (- 1/2 (* 1/3 x)))
55.0ms	(/ E (exp (* (* x x) (- 1/2 (* 1/3 x)))))
24.0ms	(* 1/3 x)

simplify1.6s

Counts: 140 → 140

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes85.0ms

Accuracy

97% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.6b

bsearch254.0ms

end0.0ms

sample11.9s

Algorithm

intervals

Results

3.5s	1940×	body	10240	exit
3.1s	10072×	body	80	valid
2.7s	1765×	body	1280	valid
1.2s	1280×	body	640	valid
868.0ms	610×	body	320	valid
116.0ms	306×	body	160	valid