Details

sample45.8s

Algorithm

intervals

Results

45.4s	3119×	body	10240	exit
132.0ms	3375×	pre	80	true
48.0ms	241×	body	80	valid
20.0ms	7×	body	1280	valid
6.0ms	1×	body	5120	valid
3.0ms	6×	body	160	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: 7.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (/ 1 (+ 1 (exp (- t)))))
0.2b	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
2.5b	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
4.9b	(/ (* (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)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

1192×	`add-exp-log`
692×	`pow-exp`
684×	`prod-exp`
593×	`div-exp`
344×	`pow-to-exp`
116×	`rec-exp` `1-exp`
103×	`*-un-lft-identity`
76×	`add-sqr-sqrt`
65×	`times-frac` `add-cube-cbrt`
54×	`prod-diff`
36×	`unpow-prod-down`
16×	`add-cbrt-cube`
15×	`distribute-lft-out`
10×	`associate-/r/`
8×	`pow1`
7×	`div-inv`
6×	`pow-unpow` `pow-pow` `add-log-exp` `difference-of-squares`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-undiv` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow-flip` `distribute-lft-out--` `inv-pow` `sqr-pow`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `associate-/l`

Counts

4 → 541

Calls

4 calls:

32.0ms	(- 1 (/ 1 (+ 1 (exp (- t)))))
13.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
13.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
135.0ms	(/ (* (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)))

series643.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- 1 (/ 1 (+ 1 (exp (- t)))))
54.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
55.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
506.0ms	(/ (* (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)))

simplify2.1s

Counts

553 → 553

Iterations

Iter	Nodes
done	5012
2	4056
1	1508
0	555

prune864.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n)
0.2b	(log1p (exp (- s)))
2.7b	(log1p (exp (- t)))
8.2b	(- (- (* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n) (* c_p (log1p (exp (- s))))) (- (* c_n (log1p (/ -1 (+ 1 (exp (- t)))))) (* c_p (log1p (exp (- t))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

7.0ms	(* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n)
0.0ms	(log1p (exp (- s)))
0.0ms	(log1p (exp (- t)))
52.0ms	(- (- (* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n) (* c_p (log1p (exp (- s))))) (- (* c_n (log1p (/ -1 (+ 1 (exp (- t)))))) (* c_p (log1p (exp (- t))))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n)
48.0ms	(log1p (exp (- s)))
49.0ms	(log1p (exp (- t)))
282.0ms	(- (- (* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n) (* c_p (log1p (exp (- s))))) (- (* c_n (log1p (/ -1 (+ 1 (exp (- t)))))) (* c_p (log1p (exp (- t))))))

simplify1.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2278
1	613
0	241

prune628.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c_p (log1p (exp (- s))))
0.2b	(* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n)
0.2b	(log1p (exp (- s)))
8.2b	(- (- (* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n) (* c_p (log1p (exp (- s))))) (- (* c_n (log1p (/ -1 (+ 1 (exp (- t)))))) (* c_p (fma -1/2 t (fma 1/8 (* t t) (log 2))))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`add-log-exp`
15×	`add-cube-cbrt`
11×	`prod-diff`
9×	`pow1`
8×	`add-cbrt-cube` `diff-log` `add-exp-log`
7×	`associate-l`
6×	`associate-r`
5×	`expm1-log1p-u` `flip3--` `flip--`
4×	`frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `associate--l+` `associate--r+`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `log1p-udef` `log1p-expm1` `log-pow` `distribute-lft-out--` `associate--r-` `difference-of-squares`

Counts

4 → 99

Calls

4 calls:

5.0ms	(* c_p (log1p (exp (- s))))
7.0ms	(* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n)
0.0ms	(log1p (exp (- s)))
52.0ms	(- (- (* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n) (* c_p (log1p (exp (- s))))) (- (* c_n (log1p (/ -1 (+ 1 (exp (- t)))))) (* c_p (fma -1/2 t (fma 1/8 (* t t) (log 2))))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* c_p (log1p (exp (- s))))
80.0ms	(* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n)
50.0ms	(log1p (exp (- s)))
362.0ms	(- (- (* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n) (* c_p (log1p (exp (- s))))) (- (* c_n (log1p (/ -1 (+ 1 (exp (- t)))))) (* c_p (fma -1/2 t (fma 1/8 (* t t) (log 2))))))

simplify2.2s

Counts

111 → 111

Iterations

Iter	Nodes
done	5002
2	2310
1	646
0	245

prune806.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c_n (log1p (/ -1 (+ 1 (exp (- t))))))
0.2b	(* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n)
0.4b	(* c_p (fma -1/2 s (fma (* s s) 1/8 (log 2))))
8.2b	(- (- (* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n) (* c_p (fma -1/2 s (fma (* s s) 1/8 (log 2))))) (- (* c_n (log1p (/ -1 (+ 1 (exp (- t)))))) (* c_p (fma -1/2 t (fma 1/8 (* t t) (log 2))))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`add-log-exp`
11×	`pow1` `prod-diff`
10×	`add-cbrt-cube` `associate-l` `add-exp-log`
9×	`associate-r`
8×	`diff-log`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
2×	`fma-udef`
1×	`associate--l-` `distribute-rgt-in` `distribute-lft-in` `log-pow` `distribute-lft-out--` `associate--r-` `difference-of-squares`

Counts

4 → 110

Calls

4 calls:

5.0ms	(* c_n (log1p (/ -1 (+ 1 (exp (- t))))))
7.0ms	(* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n)
5.0ms	(* c_p (fma -1/2 s (fma (* s s) 1/8 (log 2))))
53.0ms	(- (- (* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n) (* c_p (fma -1/2 s (fma (* s s) 1/8 (log 2))))) (- (* c_n (log1p (/ -1 (+ 1 (exp (- t)))))) (* c_p (fma -1/2 t (fma 1/8 (* t t) (log 2))))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* c_n (log1p (/ -1 (+ 1 (exp (- t))))))
80.0ms	(* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n)
72.0ms	(* c_p (fma -1/2 s (fma (* s s) 1/8 (log 2))))
292.0ms	(- (- (* (log (- 1 (/ 1 (+ (exp (- s)) 1)))) c_n) (* c_p (fma -1/2 s (fma (* s s) 1/8 (log 2))))) (- (* c_n (log1p (/ -1 (+ 1 (exp (- t)))))) (* c_p (fma -1/2 t (fma 1/8 (* t t) (log 2))))))

simplify2.1s

Counts

122 → 122

Iterations

Iter	Nodes
done	5004
2	2485
1	701
0	276

prune976.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

regimes197.0ms

bsearch0.0ms

simplify15.0ms

Iterations

Iter	Nodes
done	59
2	59
1	55
0	42

end0.0ms

sample9.0m

Algorithm

intervals

Results

8.9m	40054×	body	10240	exit
2.3s	43230×	pre	80	true
802.0ms	3069×	body	80	valid
65.0ms	8×	body	5120	valid
57.0ms	25×	body	1280	valid
22.0ms	20×	body	640	valid
18.0ms	5×	body	2560	valid
17.0ms	38×	body	160	valid
6.0ms	10×	body	320	valid