Details

sample353.0ms

Algorithm

intervals

Results

116.0ms	61×	body	1280	valid
85.0ms	61×	body	10240	exit
64.0ms	333×	body	80	valid
35.0ms	39×	body	640	valid
24.0ms	24×	body	320	valid
1.0ms	6×	body	160	valid

simplify373.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

373.0ms

(/ (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))) 2)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize52.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
0.0b	(exp (* x (+ eps -1)))
0.0b	(exp (* x (+ eps -1)))
0.0b	(exp (* x (- -1 eps)))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-log-exp`
16×	`*-un-lft-identity`
8×	`exp-sum`
6×	`add-sqr-sqrt` `diff-log` `distribute-lft-out--`
4×	`distribute-rgt-in` `pow1` `sub-neg` `distribute-lft-in` `add-cbrt-cube` `add-exp-log` `frac-sub` `add-cube-cbrt` `insert-posit16`
3×	`exp-prod` `flip3--` `exp-to-pow` `flip--` `rem-exp-log`
2×	`sum-log` `flip3-+` `flip-+` `distribute-lft-out` `associate--r+`
1×	`associate--l+` `associate--r-` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

Slowest

191.0ms	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
11.0ms	(exp (* x (- -1 eps)))
9.0ms	(exp (* x (+ eps -1)))
9.0ms	(exp (* x (+ eps -1)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

158.0ms	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
24.0ms	(exp (* x (- -1 eps)))
22.0ms	(exp (* x (+ eps -1)))
22.0ms	(exp (* x (+ eps -1)))

simplify9.0s

Counts

51 → 82

Calls

51 calls:

Slowest

733.0ms	(- (* (+ (pow (exp (* x (+ eps -1))) 3) (pow (/ (exp (* x (+ eps -1))) eps) 3)) (+ (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (+ (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))) (* (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))) (* (+ (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (- (* (/ (exp (* x (+ eps -1))) eps) (/ (exp (* x (+ eps -1))) eps)) (* (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)))) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
687.0ms	(- (* (- (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (* (/ (exp (* x (+ eps -1))) eps) (/ (exp (* x (+ eps -1))) eps))) (+ (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (+ (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))) (* (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))) (* (- (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
480.0ms	(- (* (+ (pow (exp (* x (+ eps -1))) 3) (pow (/ (exp (* x (+ eps -1))) eps) 3)) (+ (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))) (* (+ (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (- (* (/ (exp (* x (+ eps -1))) eps) (/ (exp (* x (+ eps -1))) eps)) (* (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)))) (- (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))))))
392.0ms	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
380.0ms	(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

7.6b	(- (- 2 (* x x)) (* (* x (* x x)) -2/3))
0.1b	(* (* x (* x x)) -2/3)
0.1b	(* x (* x x))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1`
17×	`add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `pow-prod-up` `add-cube-cbrt`
4×	`associate-r` `associate-l`
3×	`diff-log` `insert-posit16`
2×	`sub-neg` `associate--l+` `*-commutative`
1×	`associate--l-` `pow2` `pow-plus` `flip3--` `cube-unmult` `pow-sqr` `flip--` `unswap-sqr`

Counts

3 → 64

Calls

3 calls:

Slowest

77.0ms	(* (* x (* x x)) -2/3)
35.0ms	(- (- 2 (* x x)) (* (* x (* x x)) -2/3))
23.0ms	(* x (* x x))

series159.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

60.0ms	(* x (* x x))
60.0ms	(* (* x (* x x)) -2/3)
39.0ms	(- (- 2 (* x x)) (* (* x (* x x)) -2/3))

simplify3.8s

Counts

36 → 73

Calls

36 calls:

Slowest

549.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
474.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
439.0ms	(/ (/ (exp 2) (exp (* x x))) (exp (* (* x (* x x)) -2/3)))
436.0ms	(* (* (* (* x (* x x)) (* x (* x x))) (* x (* x x))) (* (* -2/3 -2/3) -2/3))
256.0ms	(* (* (* (* x x) x) (* (* (* x x) (* x x)) (* x x))) (* (* -2/3 -2/3) -2/3))

prune525.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes71.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 17.0b

bsearch354.0ms

end0.0ms

sample11.5s

Algorithm

intervals

Results

3.2s	1866×	body	10240	exit
2.8s	1728×	body	1280	valid
2.6s	10035×	body	80	valid
1.6s	1238×	body	640	valid
809.0ms	618×	body	320	valid
188.0ms	312×	body	160	valid