Details

sample309.0ms

Algorithm

intervals

Results

117.0ms	61×	body	10240	exit
67.0ms	54×	body	1280	valid
59.0ms	304×	body	80	valid
31.0ms	39×	body	640	valid
11.0ms	19×	body	320	valid
5.0ms	13×	body	160	valid

simplify325.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

325.0ms

(/ (- (* (+ 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: 29.4b

localize35.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (+ (/ (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))

rewrite603.0ms

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

275.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
29.0ms	(* x (- -1 eps))
26.0ms	(* x (+ -1 eps))
25.0ms	(* x (+ -1 eps))

series269.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

145.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
48.0ms	(* x (- -1 eps))
42.0ms	(* x (+ -1 eps))
34.0ms	(* x (+ -1 eps))

simplify9.0m

Counts

2202 → 2145

Calls

2202 calls:

Slowest

877.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (fma (/ (exp (* x (fma (sqrt -1) (sqrt -1) (- (* (cbrt eps) (* (cbrt eps) (cbrt eps))))))) (sqrt eps)) (/ (exp (* x (fma (- (cbrt eps)) (* (cbrt eps) (cbrt eps)) (* (cbrt eps) (* (cbrt eps) (cbrt eps)))))) (sqrt eps)) (- (* (exp (* (fma (- (cbrt eps)) (* (cbrt eps) (cbrt eps)) (* (cbrt eps) (* (cbrt eps) (cbrt eps)))) x)) (exp (* (fma 1 -1 (- (* (cbrt eps) (* (cbrt eps) (cbrt eps))))) x))))))
859.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (fma (/ 1 (sqrt eps)) (/ (exp (* x (- -1 eps))) (sqrt eps)) (- (* (exp (* x (fma (- eps) 1 (* eps 1)))) (exp (* x (fma 1 -1 (- (* eps 1)))))))))
857.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (fma (/ (sqrt (exp (* x (- -1 eps)))) (* (cbrt eps) (cbrt eps))) (/ (sqrt (exp (* x (- -1 eps)))) (cbrt eps)) (- (* (exp (* x (- eps))) (exp (* x -1))))))
824.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (fma (/ (exp (* x (fma (sqrt -1) (sqrt -1) (- (* eps 1))))) (* (cbrt eps) (cbrt eps))) (/ (exp (* x (fma (- eps) 1 (* eps 1)))) (cbrt eps)) (- (* (exp (* x (fma (- eps) 1 (* eps 1)))) (exp (* x (fma (sqrt -1) (sqrt -1) (- (* eps 1)))))))))
807.0ms	(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (fma (/ (exp (* x (fma 1 -1 (- (* eps 1))))) (* (cbrt eps) (cbrt eps))) (/ (exp (* x (fma (- eps) 1 (* eps 1)))) (cbrt eps)) (- (* (exp (* x (fma (- eps) 1 (* eps 1)))) (exp (* x (fma 1 -1 (- (* eps 1)))))))))

prune35.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (/ (exp (* x (- -1 eps))) eps) (/ (exp (- (* x eps) x)) eps))
0.0b	(* x (- -1 eps))
0.0b	(* x (- -1 eps))
0.0b	(* x (- -1 eps))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

4543×	`prod-diff`
4081×	`times-frac`
3142×	`add-sqr-sqrt`
3132×	`*-un-lft-identity`
3118×	`add-cube-cbrt`
3099×	`exp-sum`
990×	`distribute-rgt-in` `distribute-lft-in`
418×	`sub-neg`
110×	`div-inv`
79×	`fma-neg`
15×	`associate-r`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`associate-l`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-*r/` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-out--` `diff-log` `frac-sub` `sub-div`

Counts

4 → 2458

Calls

4 calls:

Slowest

63.0ms	(- (/ (exp (* x (- -1 eps))) eps) (/ (exp (- (* x eps) x)) eps))
17.0ms	(* x (- -1 eps))
14.0ms	(* x (- -1 eps))
14.0ms	(* x (- -1 eps))

series214.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

79.0ms	(- (/ (exp (* x (- -1 eps))) eps) (/ (exp (- (* x eps) x)) eps))
46.0ms	(* x (- -1 eps))
46.0ms	(* x (- -1 eps))
42.0ms	(* x (- -1 eps))