Details

sample236.0ms

Algorithm

intervals

Results

81.0ms	56×	body	1280	valid
47.0ms	300×	body	80	valid
45.0ms	36×	body	10240	exit
36.0ms	53×	body	640	valid
8.0ms	18×	body	320	valid
1.0ms	5×	body	160	valid

simplify695.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

695.0ms

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (+ (/ (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	(* x (+ -1 eps))

rewrite602.0ms

Algorithm

rewrite-expression-head

Rules

4807×	`prod-diff`
3432×	`exp-sum`
2729×	`*-un-lft-identity`
2717×	`add-sqr-sqrt`
2693×	`add-cube-cbrt`
1977×	`associate--r+`
1879×	`times-frac`
1717×	`distribute-rgt-in` `distribute-lft-in`
314×	`sub-neg`
25×	`div-inv`
20×	`add-log-exp`
10×	`distribute-lft-out` `distribute-lft-out--`
9×	`difference-of-squares`
6×	`pow1` `add-cbrt-cube` `diff-log` `add-exp-log`
4×	`expm1-log1p-u` `fma-neg` `associate-r` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`flip3-+` `flip3--` `associate-l` `flip-+` `flip--`
2×	`exp-prod` `sum-log` `exp-to-pow` `associate-*r/` `rem-exp-log`
1×	`pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `associate--r-` `unswap-sqr`

Counts

4 → 2130

Calls

4 calls:

Slowest

267.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
24.0ms	(* x (+ -1 eps))
14.0ms	(exp (* x (- -1 eps)))
13.0ms	(exp (* x (- -1 eps)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

173.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
48.0ms	(* x (+ -1 eps))
24.0ms	(exp (* x (- -1 eps)))
15.0ms	(exp (* x (- -1 eps)))

simplify7.6m

Counts

2124 → 2142

Calls

2124 calls:

Slowest

1.1s	(- (* (- (* (/ (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))))
918.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
870.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
862.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
855.0ms	(fma (- (exp (* x (- eps)))) (exp (* x -1)) (* (exp (* x (- eps))) (exp (* x -1))))

prune41.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.1b

localize83.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (/ (exp (* (+ -1 eps) x)) eps) (/ (exp (* x (- -1 eps))) eps))
0.2b	(log (exp (+ (+ (exp (* (+ -1 eps) x)) (- (/ (exp (* (+ -1 eps) x)) eps) (/ (exp (* x (- -1 eps))) eps))) (exp (* x (- -1 eps))))))
0.1b	(exp (+ (+ (exp (* (+ -1 eps) x)) (- (/ (exp (* (+ -1 eps) x)) eps) (/ (exp (* x (- -1 eps))) eps))) (exp (* x (- -1 eps)))))
0.0b	(exp (* x (- -1 eps)))

rewrite3.3s

Algorithm

rewrite-expression-head

Rules

1747×	`prod-diff`
1705×	`times-frac`
1452×	`*-un-lft-identity`
1438×	`add-sqr-sqrt`
1426×	`add-cube-cbrt`
882×	`exp-sum`
440×	`distribute-rgt-in` `distribute-lft-in`
95×	`div-inv`
81×	`sub-neg`
18×	`add-log-exp`
13×	`exp-prod` `fma-neg`
10×	`distribute-lft-out`
7×	`log-pow`
6×	`distribute-lft-out--`
5×	`pow1` `sum-log` `rem-exp-log`
4×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`associate-+r-` `exp-diff` `diff-log` `associate-+l-`
1×	`log-div` `flip3--` `exp-to-pow` `distribute-rgt-out--` `rem-log-exp` `frac-sub` `flip--` `sub-div`

Counts

4 → 1146

Calls

4 calls:

Slowest

1.7s	(log (exp (+ (+ (exp (* (+ -1 eps) x)) (- (/ (exp (* (+ -1 eps) x)) eps) (/ (exp (* x (- -1 eps))) eps))) (exp (* x (- -1 eps))))))
1.4s	(exp (+ (+ (exp (* (+ -1 eps) x)) (- (/ (exp (* (+ -1 eps) x)) eps) (/ (exp (* x (- -1 eps))) eps))) (exp (* x (- -1 eps)))))
73.0ms	(- (/ (exp (* (+ -1 eps) x)) eps) (/ (exp (* x (- -1 eps))) eps))
14.0ms	(exp (* x (- -1 eps)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

199.0ms	(exp (+ (+ (exp (* (+ -1 eps) x)) (- (/ (exp (* (+ -1 eps) x)) eps) (/ (exp (* x (- -1 eps))) eps))) (exp (* x (- -1 eps)))))
165.0ms	(log (exp (+ (+ (exp (* (+ -1 eps) x)) (- (/ (exp (* (+ -1 eps) x)) eps) (/ (exp (* x (- -1 eps))) eps))) (exp (* x (- -1 eps))))))
132.0ms	(- (/ (exp (* (+ -1 eps) x)) eps) (/ (exp (* x (- -1 eps))) eps))
15.0ms	(exp (* x (- -1 eps)))