Details

sample37.2s

Algorithm

intervals

Results

37.0s	2928×	body	10240	exit
66.0ms	3184×	pre	80	true
21.0ms	250×	body	80	valid
6.0ms	1×	body	5120	valid
1.0ms	2×	body	640	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid

simplify839.0ms

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

localize24.0ms

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)))

rewrite167.0ms

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` `associate-/r/` `cbrt-unprod` `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 → 272

Calls

4 calls:

34.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
11.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
93.0ms	(/ (* (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)))

series782.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(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)
569.0ms	(/ (* (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)))

simplify753.0ms

Counts

284 → 284

Iterations

Useful iterations: 2 (302.0ms)

Iter	Nodes	Cost
0	362	10877
1	970	10075
2	2488	9755
done	5000	9755

prune416.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 36

Calls

2 calls:

5.0ms	(* 0.5 (* s c_p))
6.0ms	(* 0.5 (* s c_n))

series36.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(* 0.5 (* s c_p))
18.0ms	(* 0.5 (* s c_n))

simplify3.8s

Counts

42 → 42

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	59	308
1	153	302
2	532	242
3	1748	242
4	3682	242
done	5001	242

prune69.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
0.2b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.0b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ 1 (* c_p (+ (log 0.5) (* 0.5 t)))) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

172×	`add-exp-log`
88×	`prod-exp`
65×	`div-exp`
56×	`pow-exp`
43×	`pow-to-exp`
25×	`*-un-lft-identity`
24×	`add-sqr-sqrt` `unpow-prod-down`
18×	`add-cbrt-cube`
17×	`add-cube-cbrt`
14×	`times-frac`
8×	`pow1`
6×	`pow-unpow`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/` `add-log-exp`
3×	`flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
2×	`pow-pow` `associate-r/` `associate-l/` `div-inv` `difference-of-squares` `sqr-pow`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l*` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

32.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
8.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
83.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ 1 (* c_p (+ (log 0.5) (* 0.5 t)))) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series920.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
92.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
66.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
680.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ 1 (* c_p (+ (log 0.5) (* 0.5 t)))) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify925.0ms

Counts

158 → 158

Iterations

Useful iterations: done (920.0ms)

Iter	Nodes	Cost
0	332	5288
1	916	4929
2	3058	4547
done	5001	4546

prune428.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (* s c_p))
0.2b	(* (pow (log 0.5) 2) (pow c_p 2))
1.0b	(pow (log 0.5) 2)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`add-exp-log`
19×	`unpow-prod-down`
16×	`unswap-sqr`
12×	`associate-l` `prod-exp`
11×	`pow1` `unpow2` `sqr-pow`
10×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r`
7×	`pow-to-exp` `pow-exp`
4×	`pow-prod-down` `cbrt-unprod`
3×	`pow-unpow` `add-log-exp`
2×	`log-pow` `*-commutative`
1×	`pow-pow`

Counts

3 → 89

Calls

3 calls:

5.0ms	(* 0.5 (* s c_p))
9.0ms	(* (pow (log 0.5) 2) (pow c_p 2))
1.0ms	(pow (log 0.5) 2)

series165.0ms

Counts

3 → 7

Calls

3 calls:

18.0ms	(* 0.5 (* s c_p))
147.0ms	(* (pow (log 0.5) 2) (pow c_p 2))
0.0ms	(pow (log 0.5) 2)

simplify2.0s

Counts

96 → 96

Iterations

Useful iterations: 3 (922.0ms)

Iter	Nodes	Cost
0	124	974
1	279	851
2	1017	682
3	3549	674
done	5000	674

prune167.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.7b

regimes173.0ms

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	18	13
done	18	13

end0.0ms

sample3.7m

Algorithm

intervals

Results

3.6m	18001×	body	10240	exit
355.0ms	19478×	pre	80	true
116.0ms	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