Details

sample324.0ms

Algorithm

intervals

Results

120.0ms	55×	body	10240	exit
70.0ms	309×	body	80	valid
65.0ms	55×	body	1280	valid
31.0ms	39×	body	640	valid
12.0ms	20×	body	320	valid
4.0ms	10×	body	160	valid

simplify382.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

382.0ms

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize67.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
0.0b	(/ (exp (* x (- -1 eps))) eps)
0.0b	(* x (- -1 eps))
0.0b	(* x (- -1 eps))

rewrite583.0ms

Algorithm

rewrite-expression-head

Rules

4879×	`prod-diff`
3476×	`exp-sum`
2811×	`*-un-lft-identity`
2803×	`add-sqr-sqrt`
2773×	`add-cube-cbrt`
1977×	`associate--r+`
1954×	`times-frac`
1760×	`distribute-rgt-in` `distribute-lft-in`
322×	`sub-neg`
26×	`div-inv`
25×	`associate-/l*`
16×	`add-log-exp`
12×	`distribute-lft-out--`
11×	`difference-of-squares`
10×	`add-cbrt-cube` `associate-r`
9×	`add-exp-log` `distribute-lft-out`
8×	`pow1`
6×	`diff-log` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `fma-neg` `associate-*r/` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sum-log` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate--l+` `associate--r-`

Counts

4 → 2246

Calls

4 calls:

Slowest

274.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
44.0ms	(* x (- -1 eps))
15.0ms	(* x (- -1 eps))
15.0ms	(/ (exp (* x (- -1 eps))) eps)

series303.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
62.0ms	(* x (- -1 eps))
46.0ms	(* x (- -1 eps))
42.0ms	(/ (exp (* x (- -1 eps))) eps)

simplify7.1m

Counts

2309 → 2258

Calls

2309 calls:

Slowest

868.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))
857.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))
841.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))
823.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))
801.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))

prune35.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (/ (exp (* x (- -1 eps))) eps) (/ (exp (* (+ -1 eps) x)) eps))
0.0b	(exp (- (+ (exp (* (+ -1 eps) x)) (exp (* x (- -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (/ (exp (* (+ -1 eps) x)) eps))))
0.0b	(/ (exp (* x (- -1 eps))) eps)
0.0b	(* x (- -1 eps))

rewrite562.0ms

Algorithm

rewrite-expression-head

Rules

1921×	`prod-diff`
1886×	`times-frac`
1664×	`*-un-lft-identity`
1652×	`add-sqr-sqrt`
1586×	`add-cube-cbrt`
1064×	`exp-sum`
517×	`distribute-rgt-in` `distribute-lft-in`
104×	`div-inv`
96×	`sub-neg`
79×	`fma-neg`
27×	`distribute-lft-out--`
25×	`associate-/l*`
22×	`difference-of-squares`
19×	`add-log-exp`
14×	`distribute-lft-out`
8×	`exp-prod` `add-cbrt-cube`
7×	`diff-log` `add-exp-log`
6×	`pow1`
5×	`distribute-rgt-out--` `associate-r` `rem-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-l*`
2×	`sum-log` `flip3--` `associate-*r/` `flip--`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `exp-diff` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `frac-sub` `cbrt-unprod` `sub-div` `associate--r-` `unswap-sqr`

Counts

4 → 1373

Calls

4 calls:

Slowest

428.0ms	(exp (- (+ (exp (* (+ -1 eps) x)) (exp (* x (- -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (/ (exp (* (+ -1 eps) x)) eps))))
48.0ms	(- (/ (exp (* x (- -1 eps))) eps) (/ (exp (* (+ -1 eps) x)) eps))
14.0ms	(* x (- -1 eps))
14.0ms	(/ (exp (* x (- -1 eps))) eps)

series283.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

149.0ms	(exp (- (+ (exp (* (+ -1 eps) x)) (exp (* x (- -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (/ (exp (* (+ -1 eps) x)) eps))))
69.0ms	(- (/ (exp (* x (- -1 eps))) eps) (/ (exp (* (+ -1 eps) x)) eps))
42.0ms	(* x (- -1 eps))
24.0ms	(/ (exp (* x (- -1 eps))) eps)