Details

sample46.8s

Algorithm

intervals

Results

46.0s	3138×	body	10240	exit
479.0ms	3395×	pre	80	true
68.0ms	248×	body	80	valid
8.0ms	1×	body	5120	valid
7.0ms	3×	body	1280	valid
2.0ms	5×	body	160	valid

simplify606.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	43
1	53	43
2	147	43
3	839	43
done	5001	43

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
1.9b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.4b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

553×	`add-exp-log`
312×	`prod-exp`
262×	`pow-exp`
248×	`div-exp`
183×	`pow-to-exp`
145×	`*-un-lft-identity`
109×	`add-sqr-sqrt`
108×	`prod-diff`
99×	`add-cube-cbrt`
87×	`times-frac`
21×	`distribute-lft-out`
18×	`unpow-prod-down`
16×	`add-cbrt-cube`
14×	`associate-/r/`
8×	`div-inv` `add-log-exp`
7×	`flip3-+` `flip-+`
6×	`fma-neg`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`pow-unpow`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow-pow` `frac-2neg` `clear-num` `associate-/r` `associate-/l` `sqr-pow`

Counts

4 → 371

Calls

4 calls:

40.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
40.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
20.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
172.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series829.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
49.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
75.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
654.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify1.6s

Counts

383 → 383

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	570	17315
1	1377	15625
2	3960	13557
done	5000	13545

prune700.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 0.5 (* s c_n))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1×	`expm1-log1p-u` `associate-r` `*-commutative` `log1p-expm1-u` `add-log-exp`

Counts

1 → 20

Calls

1 calls:

16.0ms

(* 0.5 (* s c_n))

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

(* 0.5 (* s c_n))

simplify5.9s

Counts

23 → 23

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	37	166
1	87	163
2	300	133
3	1003	133
4	2173	133
5	4443	133
done	5001	133

prune57.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.2b	(expm1 (log1p (* 0.5 (* s c_n))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`expm1-log1p` `associate-r` `*-commutative` `expm1-udef`

Counts

2 → 31

Calls

2 calls:

19.0ms	(* 0.5 (* s c_n))
0.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

series271.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(* 0.5 (* s c_n))
251.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

simplify3.1s

Counts

37 → 37

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	73	344
1	169	311
2	517	261
3	1597	253
4	4166	237
done	5001	236

prune98.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.2b	(exp (log1p (* 0.5 (* s c_n))))
1.0b	(- (exp (log1p (* 0.5 (* s c_n)))) 1)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`add-cube-cbrt`
9×	`prod-diff`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
3×	`expm1-log1p-u` `exp-prod` `fma-neg` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`rem-exp-log` `difference-of-squares`
1×	`sub-neg` `expm1-def` `log1p-udef` `flip3--` `diff-log` `difference-of-sqr-1` `associate-r` `*-commutative` `flip--` `distribute-lft-out--`

Counts

3 → 65

Calls

3 calls:

15.0ms	(* 0.5 (* s c_n))
2.0ms	(exp (log1p (* 0.5 (* s c_n))))
16.0ms	(- (exp (log1p (* 0.5 (* s c_n)))) 1)

series476.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(* 0.5 (* s c_n))
203.0ms	(exp (log1p (* 0.5 (* s c_n))))
253.0ms	(- (exp (log1p (* 0.5 (* s c_n)))) 1)

simplify1.5s

Counts

74 → 74

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	127	1036
1	280	804
2	706	661
3	2271	598
done	5000	538

prune182.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

regimes481.0ms

bsearch1.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	67
1	49	67
done	49	67

end0.0ms

sample8.9m

Algorithm

intervals

Results

8.8m	41661×	body	10240	exit
2.4s	44974×	pre	80	true
1.0s	3200×	body	80	valid
84.0ms	9×	body	5120	valid
42.0ms	23×	body	1280	valid
22.0ms	27×	body	640	valid
11.0ms	41×	body	160	valid
8.0ms	3×	body	2560	valid
6.0ms	9×	body	320	valid