Details

sample318.0ms

Algorithm

intervals

Results

102.0ms	60×	body	1280	valid
79.0ms	318×	body	80	valid
68.0ms	53×	body	10240	exit
32.0ms	42×	body	640	valid
9.0ms	18×	body	320	valid
4.0ms	10×	body	160	valid

simplify412.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

412.0ms

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize65.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
0.0b	(* x (+ -1 eps))
0.0b	(* x (+ -1 eps))
0.0b	(* x (- -1 eps))

rewrite583.0ms

Algorithm

rewrite-expression-head

Rules

4789×	`prod-diff`
3388×	`exp-sum`
2725×	`*-un-lft-identity`
2715×	`add-sqr-sqrt`
2685×	`add-cube-cbrt`
1977×	`associate--r+`
1879×	`times-frac`
1707×	`distribute-rgt-in` `distribute-lft-in`
312×	`sub-neg`
25×	`div-inv`
16×	`add-log-exp`
13×	`associate-r`
11×	`distribute-lft-out` `distribute-lft-out--`
10×	`pow1` `add-cbrt-cube` `add-exp-log` `difference-of-squares`
9×	`associate-l`
6×	`diff-log` `associate-*r/`
4×	`expm1-log1p-u` `flip3-+` `flip3--` `fma-neg` `frac-sub` `flip-+` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sum-log`
1×	`associate--l+` `associate--r-`

Counts

4 → 2133

Calls

4 calls:

Slowest

318.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
22.0ms	(* x (- -1 eps))
16.0ms	(* x (+ -1 eps))
13.0ms	(* x (+ -1 eps))

series349.0ms

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)))))
75.0ms	(* x (- -1 eps))
50.0ms	(* x (+ -1 eps))
50.0ms	(* x (+ -1 eps))

simplify6.5m

Counts

2125 → 2145

Calls

2125 calls:

Slowest

917.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
874.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
820.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
812.0ms	(fma 1 (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (* (- (sqrt (/ (exp (* x (- -1 eps))) eps)) (sqrt (exp (* x (- -1 eps))))) (+ (sqrt (/ (exp (* x (- -1 eps))) eps)) (sqrt (exp (* x (- -1 eps))))))))
803.0ms	(fma (- (exp (* x (- -1 eps)))) 1 (* (exp (* x (- -1 eps))) 1))

prune34.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (/ (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	(* (+ -1 eps) x)
0.0b	(* (+ -1 eps) x)

rewrite592.0ms

Algorithm

rewrite-expression-head

Rules

1831×	`prod-diff`
1811×	`times-frac`
1578×	`*-un-lft-identity`
1564×	`add-sqr-sqrt`
1498×	`add-cube-cbrt`
976×	`exp-sum`
462×	`distribute-rgt-in` `distribute-lft-in`
103×	`div-inv`
86×	`sub-neg`
79×	`fma-neg`
26×	`distribute-lft-out--`
21×	`difference-of-squares`
19×	`add-log-exp`
16×	`distribute-lft-out`
8×	`pow1` `exp-prod` `add-cbrt-cube` `associate-l` `add-exp-log`
7×	`diff-log`
6×	`associate-r`
5×	`distribute-rgt-out--` `rem-exp-log`
4×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u`
2×	`sum-log` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`flip3--` `exp-diff` `associate--l+` `frac-sub` `flip--` `sub-div` `associate--r-`

Counts

4 → 1256

Calls

4 calls:

Slowest

454.0ms	(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))
15.0ms	(* (+ -1 eps) x)
14.0ms	(* (+ -1 eps) x)

series256.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

150.0ms	(exp (- (+ (exp (* (+ -1 eps) x)) (exp (* x (- -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (/ (exp (* (+ -1 eps) x)) eps))))
54.0ms	(- (/ (exp (* x (- -1 eps))) eps) (/ (exp (* (+ -1 eps) x)) eps))
27.0ms	(* (+ -1 eps) x)
24.0ms	(* (+ -1 eps) x)