Details

sample50.6s

Algorithm

intervals

Results

49.8s	3254×	body	10240	exit
532.0ms	3510×	pre	80	true
54.0ms	246×	body	80	valid
6.0ms	1×	body	5120	valid
6.0ms	2×	body	1280	valid
3.0ms	1×	body	2560	valid
2.0ms	3×	body	160	valid
2.0ms	2×	body	320	valid
1.0ms	1×	body	640	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.9b

localize51.0ms

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)))

rewrite2.6s

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×	`expm1-log1p-u` `cbrt-undiv` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-flip` `inv-pow`
1×	`clear-num` `frac-2neg`

Counts

4 → 3849

Calls

4 calls:

83.0ms	(pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)
26.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
27.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
1.8s	(/ (* (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)))

series724.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)
57.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
59.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
540.0ms	(/ (* (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)))

simplify4.7s

Counts

3861 → 3861

Iterations

Iter	Nodes
done	5000
0	4958

prune23.1s

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)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

636×	`*-un-lft-identity`
540×	`associate-l`
413×	`distribute-lft-out`
279×	`pow1`
277×	`log-pow`
144×	`prod-diff`
102×	`distribute-lft-out--`
63×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
47×	`log-prod`
28×	`times-frac`
22×	`log-div`
16×	`add-log-exp`
15×	`add-exp-log`
12×	`fma-neg`
9×	`rem-log-exp`
8×	`associate-/r` `associate-/l`
7×	`difference-of-squares`
6×	`flip3-+` `log-rec` `flip-+`
4×	`expm1-log1p-u` `clear-num` `sum-log` `add-cbrt-cube` `diff-log` `div-exp` `associate-/r/` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`div-inv`
2×	`+-commutative` `rec-exp` `sub-neg` `frac-2neg` `log1p-def` `flip3--` `1-exp` `associate--l+` `pow-flip` `flip--` `associate--r+` `inv-pow`

Counts

4 → 406

Calls

4 calls:

52.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
24.0ms	(log (/ 1 (+ 1 (exp (- s)))))
24.0ms	(log (/ 1 (+ 1 (exp (- t)))))
1.1s	(- (+ (* (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)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
61.0ms	(log (/ 1 (+ 1 (exp (- s)))))
57.0ms	(log (/ 1 (+ 1 (exp (- t)))))
323.0ms	(- (+ (* (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)))

simplify2.0s

Counts

418 → 418

Iterations

Iter	Nodes
done	5001
2	2784
1	948
0	388

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize80.0ms

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)) (+ (* (fma (* t t) -1/8 (fma 1/2 t (log 1/2))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

504×	`*-un-lft-identity`
358×	`associate-l`
289×	`distribute-lft-out`
154×	`pow1`
151×	`log-pow`
108×	`prod-diff`
74×	`distribute-lft-out--`
62×	`add-sqr-sqrt`
40×	`log-prod`
38×	`add-cube-cbrt`
20×	`times-frac`
16×	`add-log-exp`
14×	`log-div`
13×	`difference-of-squares`
12×	`fma-neg`
11×	`add-exp-log`
6×	`rem-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-/r` `sum-log` `log1p-def` `add-cbrt-cube` `diff-log` `frac-sub` `insert-posit16` `log1p-expm1-u` `associate-/l`
3×	`sub-neg` `flip3--` `log-rec` `div-inv` `flip--`
2×	`+-commutative` `clear-num` `div-exp` `associate--l+` `associate-/r/` `associate--r+`
1×	`rec-exp` `frac-2neg` `1-exp` `pow-flip` `inv-pow`

Counts

4 → 319

Calls

4 calls:

52.0ms	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
52.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
24.0ms	(log (/ 1 (+ 1 (exp (- s)))))
934.0ms	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (fma (* t t) -1/8 (fma 1/2 t (log 1/2))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

series599.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
71.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
62.0ms	(log (/ 1 (+ 1 (exp (- s)))))
395.0ms	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (fma (* t t) -1/8 (fma 1/2 t (log 1/2))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

simplify2.1s

Counts

331 → 331

Iterations

Iter	Nodes
done	5001
2	2923
1	918
0	377

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.5b	(* c_n (log1p (/ -1 (+ (exp (- t)) 1))))
0.7b	(log1p (exp (- s)))
7.8b	(- (fma c_n (log1p (/ -1 (+ (exp (- s)) 1))) (- (* (- c_p) (log1p (exp (- s)))) (* c_n (log1p (/ -1 (+ (exp (- t)) 1)))))) (* (fma (* t t) -1/8 (fma 1/2 t (log 1/2))) c_p))
23.6b	(fma c_n (log1p (/ -1 (+ (exp (- s)) 1))) (- (* (- c_p) (log1p (exp (- s)))) (* c_n (log1p (/ -1 (+ (exp (- t)) 1))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`prod-diff`
32×	`*-un-lft-identity`
28×	`add-cube-cbrt`
13×	`associate-l`
12×	`associate-r`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`expm1-log1p-u` `unswap-sqr`
4×	`*-commutative` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`fma-udef` `distribute-lft-out--` `difference-of-squares`
1×	`log1p-udef` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `associate--l+` `log1p-expm1` `cbrt-unprod` `flip--`

Counts

4 → 103

Calls

4 calls:

7.0ms	(* c_n (log1p (/ -1 (+ (exp (- t)) 1))))
0.0ms	(log1p (exp (- s)))
16.0ms	(- (fma c_n (log1p (/ -1 (+ (exp (- s)) 1))) (- (* (- c_p) (log1p (exp (- s)))) (* c_n (log1p (/ -1 (+ (exp (- t)) 1)))))) (* (fma (* t t) -1/8 (fma 1/2 t (log 1/2))) c_p))
0.0ms	(fma c_n (log1p (/ -1 (+ (exp (- s)) 1))) (- (* (- c_p) (log1p (exp (- s)))) (* c_n (log1p (/ -1 (+ (exp (- t)) 1))))))

series766.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* c_n (log1p (/ -1 (+ (exp (- t)) 1))))
51.0ms	(log1p (exp (- s)))
402.0ms	(- (fma c_n (log1p (/ -1 (+ (exp (- s)) 1))) (- (* (- c_p) (log1p (exp (- s)))) (* c_n (log1p (/ -1 (+ (exp (- t)) 1)))))) (* (fma (* t t) -1/8 (fma 1/2 t (log 1/2))) c_p))
243.0ms	(fma c_n (log1p (/ -1 (+ (exp (- s)) 1))) (- (* (- c_p) (log1p (exp (- s)))) (* c_n (log1p (/ -1 (+ (exp (- t)) 1))))))

simplify1.6s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	1571
1	599
0	263

prune939.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes378.0ms

bsearch2.8s

Steps

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

simplify12.0ms

Iterations

Iter	Nodes
done	63
1	63
0	50

end0.0ms

sample8.3m

Algorithm

intervals

Results

8.3m	36825×	body	10240	exit
2.0s	39719×	pre	80	true
633.0ms	2801×	body	80	valid
112.0ms	6×	body	5120	valid
40.0ms	19×	body	1280	valid
26.0ms	7×	body	2560	valid
21.0ms	18×	body	640	valid
15.0ms	34×	body	160	valid
5.0ms	8×	body	320	valid