Details

sample1.2m

Algorithm

intervals

Results

1.2m	3196×	body	10240	exit
227.0ms	3452×	pre	80	true
57.0ms	248×	body	80	valid
6.0ms	2×	body	1280	valid
5.0ms	2×	body	640	valid
1.0ms	2×	body	160	valid
1.0ms	2×	body	320	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	744
2	143
1	53
0	22

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.5b

localize117.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(/ (* (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)))
1.9b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

rewrite535.0ms

Algorithm

rewrite-expression-head

Rules

556×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
249×	`div-exp`
184×	`pow-to-exp`
36×	`unpow-prod-down` `*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
16×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `distribute-lft-out` `add-log-exp`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod`
3×	`div-inv`
2×	`pow-pow` `flip3-+` `flip-+` `difference-of-squares` `sqr-pow`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `associate-/r` `flip--` `associate-/l` `distribute-lft-out--`

Counts

4 → 267

Calls

4 calls:

59.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
39.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
347.0ms	(/ (* (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)))
52.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

series1.6s

Counts

4 → 12

Calls

4 calls:

108.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
147.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.2s	(/ (* (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)))
140.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

simplify4.2s

Counts

279 → 279

Iterations

Iter	Nodes
done	5001
2	3161
1	1140
0	360

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (* s c_p))
0.0b	(- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))
0.0b	(* 0.5 (* s c_n))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2×	`diff-log` `associate-r` `*-commutative`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 50

Calls

3 calls:

33.0ms	(* 0.5 (* s c_p))
217.0ms	(- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))
30.0ms	(* 0.5 (* s c_n))

series176.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* 0.5 (* s c_p))
102.0ms	(- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))
36.0ms	(* 0.5 (* s c_n))

simplify5.1s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
3	3215
2	754
1	229
0	86

prune430.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (* s c_p))
0.0b	(* (sqrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))) (sqrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))))
0.0b	(* 0.5 (* s c_n))
0.0b	(* 0.5 (* s c_n))

rewrite936.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1`
27×	`add-sqr-sqrt`
21×	`add-exp-log` `add-cbrt-cube`
18×	`sqrt-prod`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
12×	`sqrt-div` `pow-prod-down`
10×	`prod-exp` `cbrt-unprod`
9×	`associate-r`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`flip3--` `flip--`
5×	`pow-prod-up`
4×	`frac-times` `*-commutative` `add-log-exp` `unswap-sqr`
3×	`pow-sqr`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 111

Calls

4 calls:

29.0ms	(* 0.5 (* s c_p))
829.0ms	(* (sqrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))) (sqrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))))
30.0ms	(* 0.5 (* s c_n))
41.0ms	(* 0.5 (* s c_n))

series236.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* 0.5 (* s c_p))
116.0ms	(* (sqrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))) (sqrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))))
45.0ms	(* 0.5 (* s c_n))
37.0ms	(* 0.5 (* s c_n))

simplify5.7s

Counts

123 → 123

Iterations

Iter	Nodes
done	5013
3	4870
2	998
1	320
0	135

prune951.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize189.0ms

Local error

Found 4 expressions with local error:

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

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`associate-r` `*-commutative` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

36.0ms	(* 0.5 (* s c_n))
35.0ms	(* 0.5 (* s c_n))
39.0ms	(* 0.5 (* s c_n))
36.0ms	(* 0.5 (* s c_n))

series200.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* 0.5 (* s c_n))
44.0ms	(* 0.5 (* s c_n))
55.0ms	(* 0.5 (* s c_n))
53.0ms	(* 0.5 (* s c_n))

simplify12.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
5	4595
4	2096
3	820
2	272
1	86
0	35

prune847.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes2.0s

bsearch2.0ms

simplify24.0ms

Iterations

Iter	Nodes
done	62
1	62
0	47

end0.0ms

sample3.6m

Algorithm

intervals

Results

3.5m	9134×	body	10240	exit
487.0ms	9839×	pre	80	true
203.0ms	684×	body	80	valid
25.0ms	7×	body	1280	valid
23.0ms	2×	body	5120	valid
13.0ms	1×	body	2560	valid
4.0ms	2×	body	640	valid
3.0ms	4×	body	320	valid
3.0ms	5×	body	160	valid