Details

sample340.0ms

Algorithm

intervals

Results

146.0ms	64×	body	10240	exit
72.0ms	68×	body	1280	valid
52.0ms	312×	body	80	valid
32.0ms	43×	body	640	valid
12.0ms	22×	body	320	valid
4.0ms	12×	body	160	valid

simplify348.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

348.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize39.0ms

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

rewrite480.0ms

Algorithm

rewrite-expression-head

Rules

4771×	`prod-diff`
3396×	`exp-sum`
2719×	`*-un-lft-identity`
2707×	`add-sqr-sqrt`
2681×	`add-cube-cbrt`
1977×	`associate--r+`
1894×	`times-frac`
1700×	`distribute-rgt-in` `distribute-lft-in`
310×	`sub-neg`
26×	`div-inv`
16×	`add-log-exp`
11×	`distribute-lft-out`
10×	`add-cbrt-cube` `distribute-lft-out--`
9×	`add-exp-log` `difference-of-squares`
8×	`pow1` `associate-r`
6×	`diff-log` `associate-l`
5×	`associate-/l*`
4×	`expm1-log1p-u` `flip3-+` `fma-neg` `associate-*r/` `frac-sub` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `flip3--` `flip--`
2×	`sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate--l+` `associate--r-`

Counts

4 → 2124

Calls

4 calls:

Slowest

280.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
17.0ms	(/ (exp (* x (+ -1 eps))) eps)
13.0ms	(* x (+ -1 eps))
13.0ms	(* x (+ -1 eps))

series265.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

160.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
39.0ms	(* x (+ -1 eps))
39.0ms	(* x (+ -1 eps))
27.0ms	(/ (exp (* x (+ -1 eps))) eps)

simplify7.5m

Counts

2127 → 2136

Calls

2127 calls:

Slowest

1.0s	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
898.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
891.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
891.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))
858.0ms	(fma (- (exp (* (- eps) x))) (exp (* -1 x)) (* (exp (* (- eps) x)) (exp (* -1 x))))

prune30.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 2 expressions with local error:

5.6b	(fma (* x (* x x)) 2/3 (- 2 (* x x)))
0.1b	(* x (* x x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
5×	`pow-prod-up`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `fma-udef` `unswap-sqr`

Counts

2 → 38

Calls

2 calls:

Slowest

13.0ms	(* x (* x x))
0.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

series74.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

40.0ms	(* x (* x x))
34.0ms	(fma (* x (* x x)) 2/3 (- 2 (* x x)))

simplify1.1s

Counts

20 → 44

Calls

20 calls:

Slowest

331.0ms	(* (* (* x x) x) (* (* (* x x) (* x x)) (* x x)))
330.0ms	(* (* (* x x) x) (* (* (* x x) x) (* (* x x) x)))
136.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
135.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
132.0ms	(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))

prune270.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize45.0ms

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	(exp (log (- (+ (/ (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))

rewrite498.0ms

Algorithm

rewrite-expression-head

Rules

4771×	`prod-diff`
3396×	`exp-sum`
2723×	`*-un-lft-identity`
2701×	`add-sqr-sqrt`
2673×	`add-cube-cbrt`
1977×	`associate--r+`
1879×	`times-frac`
1696×	`distribute-rgt-in` `distribute-lft-in`
310×	`sub-neg`
25×	`div-inv`
16×	`distribute-lft-out--` `add-log-exp`
13×	`distribute-lft-out`
10×	`difference-of-squares`
9×	`pow1`
8×	`log-prod` `add-cbrt-cube` `associate-r` `add-exp-log` `frac-sub`
6×	`log-div` `flip3-+` `flip3--` `exp-diff` `diff-log` `associate-l` `flip-+` `flip--`
4×	`expm1-log1p-u` `exp-prod` `fma-neg` `associate-*r/` `insert-posit16` `log1p-expm1-u`
2×	`sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`associate--l+` `log-pow` `associate--r-` `rem-exp-log`

Counts

4 → 2115

Calls

4 calls:

Slowest

196.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
117.0ms	(exp (log (- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))))
13.0ms	(* x (+ -1 eps))
13.0ms	(* x (+ -1 eps))

series285.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

121.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
103.0ms	(exp (log (- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))))
30.0ms	(* x (+ -1 eps))
30.0ms	(* x (+ -1 eps))