Details

sample376.0ms

Algorithm

intervals

Results

164.0ms	72×	body	10240	exit
75.0ms	58×	body	1280	valid
64.0ms	315×	body	80	valid
29.0ms	32×	body	640	valid
15.0ms	23×	body	320	valid
3.0ms	9×	body	160	valid

simplify269.0ms

Calls

1 calls:

Slowest

268.0ms

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize33.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
0.0b	(exp (* x (- -1 eps)))
0.0b	(exp (* x (- -1 eps)))
0.0b	(exp (* x (+ -1 eps)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

57×	`*-un-lft-identity`
48×	`prod-diff`
35×	`add-sqr-sqrt`
30×	`associate--r+`
26×	`exp-sum`
25×	`add-cube-cbrt`
19×	`add-log-exp`
14×	`sub-neg`
13×	`distribute-rgt-in` `distribute-lft-in`
10×	`distribute-lft-out--`
8×	`distribute-lft-out`
7×	`div-inv`
6×	`diff-log`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `fma-neg` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`exp-prod` `flip3--` `flip--` `rem-exp-log`
2×	`sum-log` `flip3-+` `flip-+`
1×	`associate--l+` `associate--r-`

Calls

4 calls:

Slowest

145.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
4.0ms	(exp (* x (+ -1 eps)))
4.0ms	(exp (* x (- -1 eps)))
3.0ms	(exp (* x (- -1 eps)))

series218.0ms

Calls

4 calls:

Slowest

163.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
23.0ms	(exp (* x (- -1 eps)))
18.0ms	(exp (* x (- -1 eps)))
14.0ms	(exp (* x (+ -1 eps)))

simplify24.1s

Calls

120 calls:

Slowest

673.0ms	(fma (* (cbrt (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps))))) (cbrt (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))))) (cbrt (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps))))) (- (* (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))) (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))))
661.0ms	(- (* (+ (pow (/ (exp (* x (+ -1 eps))) eps) 3) (pow (exp (* x (+ -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 (+ -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)))))) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
499.0ms	(- (* (- (* (/ (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))) eps)) (+ (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))) (* (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))) (* (- (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
489.0ms	(exp (* -1 (* (- 1 eps) x)))
473.0ms	(fma (sqrt (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps))))) (sqrt (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps))))) (- (* (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))) (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))))

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 2 expressions with local error:

6.6b	(fma (* x x) (* 2/3 x) (- 2 (* x x)))
0.3b	(* 2/3 x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`*-commutative` `fma-udef`

Calls

2 calls:

Slowest

0.0ms	(* 2/3 x)
0.0ms	(fma (* x x) (* 2/3 x) (- 2 (* x x)))

series83.0ms

Calls

2 calls:

Slowest

61.0ms	(fma (* x x) (* 2/3 x) (- 2 (* x x)))
22.0ms	(* 2/3 x)

simplify446.0ms

Calls

6 calls:

Slowest

164.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
143.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
127.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
4.0ms	(* 2/3 x)
3.0ms	(* 2/3 x)

prune281.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b