Details

sample37.6s

Algorithm

intervals

Results

37.4s	2928×	body	10240	exit
74.0ms	3184×	pre	80	true
22.0ms	250×	body	80	valid
6.0ms	1×	body	5120	valid
2.0ms	2×	body	640	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid

simplify682.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	43
1	53	43
2	147	43
3	728	43
done	5000	43

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
4.2b	(/ (* (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)))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

557×	`add-exp-log`
312×	`prod-exp`
265×	`pow-exp`
249×	`div-exp`
185×	`pow-to-exp`
42×	`unpow-prod-down`
38×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
26×	`times-frac`
24×	`add-cube-cbrt`
16×	`add-cbrt-cube`
9×	`pow-unpow`
7×	`pow1`
6×	`distribute-lft-out`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-inv` `sqr-pow`
2×	`flip3-+` `flip-+` `difference-of-squares`
1×	`frac-2neg` `clear-num` `associate-/r` `associate-/l` `distribute-lft-out--`

Counts

4 → 280

Calls

4 calls:

33.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
11.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
12.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
94.0ms	(/ (* (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)))

series780.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
66.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
66.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
566.0ms	(/ (* (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)))

simplify817.0ms

Counts

292 → 292

Iterations

Useful iterations: 2 (327.0ms)

Iter	Nodes	Cost
0	370	11029
1	990	10220
2	2555	9904
done	5000	9904

prune469.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 0.5 (* s c_n))

rewrite6.0ms

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:

6.0ms

(* 0.5 (* s c_n))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(* 0.5 (* s c_n))

simplify4.6s

Counts

23 → 23

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	37	166
1	88	163
2	286	133
3	901	133
4	1724	133
5	3509	133
done	5000	133

prune45.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

0.0ms	(log1p (* 0.5 (* s c_n)))
6.0ms	(* 0.5 (* s c_n))
0.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

series347.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(log1p (* 0.5 (* s c_n)))
18.0ms	(* 0.5 (* s c_n))
227.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

simplify1.5s

Counts

51 → 51

Iterations

Useful iterations: 3 (592.0ms)

Iter	Nodes	Cost
0	106	524
1	263	478
2	902	411
3	3730	397
done	5000	397

prune140.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

0.0ms	(log1p (* 0.5 (* s c_n)))
0.0ms	(expm1 (log1p (log1p (* 0.5 (* s c_n)))))
6.0ms	(* 0.5 (* s c_n))
0.0ms	(expm1 (expm1 (log1p (log1p (* 0.5 (* s c_n))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

101.0ms	(log1p (* 0.5 (* s c_n)))
321.0ms	(expm1 (log1p (log1p (* 0.5 (* s c_n)))))
18.0ms	(* 0.5 (* s c_n))
626.0ms	(expm1 (expm1 (log1p (log1p (* 0.5 (* s c_n))))))

simplify1.8s

Counts

65 → 65

Iterations

Useful iterations: 3 (660.0ms)

Iter	Nodes	Cost
0	121	755
1	287	650
2	965	563
3	4127	543
done	5000	543

prune177.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

regimes166.0ms

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	19	16
done	19	16

end0.0ms

sample3.7m

Algorithm

intervals

Results

3.6m	18001×	body	10240	exit
392.0ms	19478×	pre	80	true
119.0ms	1431×	body	80	valid
22.0ms	4×	body	2560	valid
13.0ms	8×	body	1280	valid
12.0ms	2×	body	5120	valid
7.0ms	10×	body	640	valid
3.0ms	14×	body	160	valid
3.0ms	8×	body	320	valid