Details

sample53.0s

Algorithm

intervals

Results

52.3s	3151×	body	10240	exit
275.0ms	3408×	pre	80	true
66.0ms	247×	body	80	valid
7.0ms	1×	body	2560	valid
3.0ms	3×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
3	744
2	143
1	53
0	22

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.5b

localize91.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
1.0b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.5b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
4.1b	(/ (* (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)))

rewrite374.0ms

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` `insert-posit16`
3×	`div-inv`
2×	`pow-pow` `flip3-+` `flip-+` `difference-of-squares` `sqr-pow`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `associate-/l` `distribute-lft-out--`

Counts

4 → 271

Calls

4 calls:

44.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
28.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
28.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
240.0ms	(/ (* (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)))

series1.5s

Counts

4 → 12

Calls

4 calls:

72.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
113.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
113.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) 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)))

simplify3.4s

Counts

283 → 283

Iterations

Iter	Nodes
done	5019
2	3039
1	1153
0	370

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
2×	`associate-r` `*-commutative` `insert-posit16` `add-log-exp`

Counts

2 → 38

Calls

2 calls:

20.0ms	(* 0.5 (* c_p s))
22.0ms	(* 0.5 (* c_n s))

series53.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(* 0.5 (* c_p s))
26.0ms	(* 0.5 (* c_n s))

simplify6.0s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
4	4040
3	1585
2	515
1	160
0	62

prune319.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize180.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
1.2b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
1.5b	(log (/ 1.0 (+ 1.0 (exp (- t)))))
10.4b	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

42×	`log-prod`
37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
16×	`add-log-exp`
11×	`add-exp-log`
7×	`pow1`
6×	`flip3-+` `flip-+` `distribute-lft-out`
5×	`rem-log-exp`
4×	`log-div` `sum-log` `add-cbrt-cube` `diff-log` `associate-/r/` `frac-sub` `insert-posit16`
3×	`log-pow` `difference-of-squares`
2×	`flip3--` `div-exp` `div-inv` `flip--` `distribute-lft-out--`
1×	`sub-neg` `associate--l+` `associate--r+`

Counts

4 → 102

Calls

4 calls:

43.0ms	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
14.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
14.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
71.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

160.0ms	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
122.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
123.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
695.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

simplify3.1s

Counts

114 → 114

Iterations

Iter	Nodes
done	5002
2	2479
1	827
0	335

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize195.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 0.5 t) (/ 0.5 t))
0.3b	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
1.2b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
10.4b	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (- (+ (* 0.5 t) (log 0.5)) (/ 0.03125 (* (/ 0.5 t) (/ 0.5 t)))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
53×	`times-frac`
51×	`*-un-lft-identity`
41×	`add-cube-cbrt`
24×	`log-prod`
20×	`add-exp-log`
16×	`add-cbrt-cube` `add-log-exp`
13×	`pow1` `swap-sqr` `associate-r` `associate-l`
5×	`flip3-+` `div-exp` `flip-+` `div-inv`
4×	`cbrt-undiv` `sum-log` `diff-log` `prod-exp` `frac-sub` `cbrt-unprod` `insert-posit16` `unswap-sqr`
3×	`log-div` `rem-log-exp` `distribute-lft-out` `difference-of-squares`
2×	`flip3--` `associate-/r/` `log-pow` `flip--` `distribute-lft-out--`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `pow-prod-down` `associate-l/` `associate--l+` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `associate--r+`

Counts

4 → 140

Calls

4 calls:

29.0ms	(* (/ 0.5 t) (/ 0.5 t))
42.0ms	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
14.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
234.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (- (+ (* 0.5 t) (log 0.5)) (/ 0.03125 (* (/ 0.5 t) (/ 0.5 t)))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (/ 0.5 t) (/ 0.5 t))
161.0ms	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
124.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
767.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (- (+ (* 0.5 t) (log 0.5)) (/ 0.03125 (* (/ 0.5 t) (/ 0.5 t)))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

simplify4.4s

Counts

152 → 152

Iterations

Iter	Nodes
done	5000
2	3639
1	1064
0	378

prune1.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes1.3s

bsearch2.0ms

simplify30.0ms

Iterations

Iter	Nodes
done	77
1	77
0	56

end0.0ms

sample7.6m

Algorithm

intervals

Results

7.5m	35434×	body	10240	exit
1.3s	38194×	pre	80	true
572.0ms	2685×	body	80	valid
38.0ms	4×	body	2560	valid
37.0ms	21×	body	1280	valid
16.0ms	3×	body	5120	valid
10.0ms	11×	body	640	valid
6.0ms	23×	body	160	valid
5.0ms	13×	body	320	valid