Details

sample1.1m

Algorithm

intervals

Results

1.1m	3254×	body	10240	exit
291.0ms	3510×	pre	80	true
71.0ms	246×	body	80	valid
11.0ms	1×	body	5120	valid
5.0ms	1×	body	2560	valid
5.0ms	2×	body	1280	valid
2.0ms	3×	body	160	valid
1.0ms	2×	body	320	valid
1.0ms	1×	body	640	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
3	743
2	143
1	54
0	22

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.9b

localize67.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)
0.7b	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
2.2b	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
3.7b	(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))

rewrite3.0s

Algorithm

rewrite-expression-head

Rules

5829×	`times-frac`
5603×	`add-sqr-sqrt`
5035×	`unpow-prod-down`
3408×	`*-un-lft-identity`
2552×	`associate-l`
1740×	`associate-r` `unswap-sqr`
1416×	`add-cube-cbrt`
1193×	`add-exp-log`
1163×	`sqr-pow`
702×	`difference-of-squares`
693×	`pow-exp`
684×	`prod-exp`
593×	`div-exp`
354×	`distribute-lft-out`
345×	`pow-to-exp`
236×	`associate-/r/` `div-inv`
234×	`distribute-lft-out--`
118×	`flip3-+` `flip-+`
116×	`rec-exp` `1-exp` `*-commutative`
57×	`associate-/r` `associate-/l`
16×	`add-cbrt-cube`
9×	`pow1` `pow-unpow`
7×	`pow-pow`
4×	`cbrt-undiv` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`pow-flip` `inv-pow`
1×	`clear-num` `frac-2neg`

Counts

4 → 3841

Calls

4 calls:

123.0ms	(pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)
32.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
29.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
2.3s	(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))

series895.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)
90.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
78.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
638.0ms	(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))

simplify6.2s

Counts

3853 → 3853

Iterations

Iter	Nodes
done	5000
0	4950

prune21.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
0.7b	(log (/ 1 (+ 1 (exp (- s)))))
2.2b	(log (/ 1 (+ 1 (exp (- t)))))
10.1b	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

311×	`*-un-lft-identity`
240×	`associate-l`
188×	`distribute-lft-out`
129×	`pow1`
127×	`log-pow`
102×	`distribute-lft-out--`
47×	`log-prod`
38×	`add-sqr-sqrt`
28×	`times-frac`
25×	`add-cube-cbrt`
22×	`log-div`
16×	`add-log-exp`
15×	`add-exp-log`
9×	`rem-log-exp`
8×	`associate-/r` `associate-/l`
7×	`difference-of-squares`
6×	`flip3-+` `log-rec` `flip-+`
4×	`clear-num` `sum-log` `add-cbrt-cube` `diff-log` `div-exp` `associate-/r/` `frac-sub` `insert-posit16`
3×	`div-inv`
2×	`+-commutative` `rec-exp` `frac-2neg` `flip3--` `1-exp` `associate--l+` `pow-flip` `flip--` `associate--r+` `inv-pow`
1×	`sub-neg`

Counts

4 → 240

Calls

4 calls:

45.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
24.0ms	(log (/ 1 (+ 1 (exp (- s)))))
25.0ms	(log (/ 1 (+ 1 (exp (- t)))))
951.0ms	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
62.0ms	(log (/ 1 (+ 1 (exp (- s)))))
58.0ms	(log (/ 1 (+ 1 (exp (- t)))))
332.0ms	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

simplify1.8s

Counts

252 → 252

Iterations

Iter	Nodes
done	5000
2	2510
1	852
0	356

prune978.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
0.3b	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
0.7b	(log (/ 1 (+ 1 (exp (- s)))))
10.1b	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (+ (log 1/2) (- (* t 1/2) (* (* t t) 1/8))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

rewrite7.7s

Algorithm

rewrite-expression-head

Rules

2058×	`*-un-lft-identity`
1898×	`associate-l`
1345×	`distribute-lft-out`
854×	`distribute-lft-out--`
672×	`pow1`
669×	`log-pow`
40×	`add-sqr-sqrt` `log-prod`
20×	`times-frac`
16×	`add-cube-cbrt` `add-log-exp`
14×	`log-div`
13×	`difference-of-squares`
11×	`add-exp-log`
6×	`rem-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/r` `sum-log` `add-cbrt-cube` `diff-log` `frac-sub` `insert-posit16` `associate-/l`
3×	`flip3--` `log-rec` `div-inv` `flip--`
2×	`+-commutative` `clear-num` `div-exp` `associate--l+` `associate-/r/` `associate--r+`
1×	`rec-exp` `sub-neg` `frac-2neg` `1-exp` `pow-flip` `inv-pow`

Counts

4 → 607

Calls

4 calls:

45.0ms	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
44.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
25.0ms	(log (/ 1 (+ 1 (exp (- s)))))
7.5s	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (+ (log 1/2) (- (* t 1/2) (* (* t t) 1/8))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

series607.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
72.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
63.0ms	(log (/ 1 (+ 1 (exp (- s)))))
405.0ms	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (+ (log 1/2) (- (* t 1/2) (* (* t t) 1/8))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

simplify1.9s

Counts

619 → 619

Iterations

Iter	Nodes
done	5000
2	2449
1	820
0	346

prune879.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (- 1 (/ 1 (+ (exp (- t)) 1)))) c_n)
0.3b	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
0.3b	(log (- 1 (/ 1 (+ (exp (- t)) 1))))
8.7b	(+ (- (- (* 1/8 (* t (* t c_p))) (* t (* c_p 1/2))) (* (log (- 1 (/ 1 (+ (exp (- t)) 1)))) c_n)) (* c_n (log (- 1 (/ 1 (+ 1 (exp (- s))))))))

rewrite8.2s

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
64×	`associate-l`
62×	`distribute-lft-out--`
56×	`add-sqr-sqrt`
44×	`log-prod`
32×	`distribute-lft-out`
24×	`difference-of-squares`
22×	`associate-+r+`
19×	`pow1`
16×	`times-frac`
13×	`log-pow` `add-log-exp`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-cube-cbrt`
8×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`log-div` `associate-+l+` `insert-posit16` `div-inv`
3×	`sum-log` `diff-log` `associate-r`
2×	`sub-neg` `flip3--` `rem-log-exp` `associate--l+` `associate-+l-` `flip--`
1×	`associate--l-` `+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 140

Calls

4 calls:

9.0ms	(* (log (- 1 (/ 1 (+ (exp (- t)) 1)))) c_n)
44.0ms	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
67.0ms	(log (- 1 (/ 1 (+ (exp (- t)) 1))))
8.1s	(+ (- (- (* 1/8 (* t (* t c_p))) (* t (* c_p 1/2))) (* (log (- 1 (/ 1 (+ (exp (- t)) 1)))) c_n)) (* c_n (log (- 1 (/ 1 (+ 1 (exp (- s))))))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (log (- 1 (/ 1 (+ (exp (- t)) 1)))) c_n)
72.0ms	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
71.0ms	(log (- 1 (/ 1 (+ (exp (- t)) 1))))
137.0ms	(+ (- (- (* 1/8 (* t (* t c_p))) (* t (* c_p 1/2))) (* (log (- 1 (/ 1 (+ (exp (- t)) 1)))) c_n)) (* c_n (log (- 1 (/ 1 (+ 1 (exp (- s))))))))

simplify2.6s

Counts

152 → 152

Iterations

Iter	Nodes
done	5001
3	4937
2	1552
1	623
0	286

prune736.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes666.0ms

bsearch2.6s

Steps

Iters	Range		Point
5	2.138597944988289e-25	8.405593532113127e-25	2.202640187188369e-25

simplify14.0ms

Iterations

Iter	Nodes
done	68
1	68
0	51

end0.0ms

sample7.8m

Algorithm

intervals

Results

7.7m	34546×	body	10240	exit
2.4s	37248×	pre	80	true
577.0ms	2616×	body	80	valid
90.0ms	6×	body	5120	valid
38.0ms	17×	body	1280	valid
26.0ms	7×	body	2560	valid
19.0ms	16×	body	640	valid
14.0ms	31×	body	160	valid
5.0ms	8×	body	320	valid