Details

sample44.6s

Algorithm

intervals

Results

44.0s	3254×	body	10240	exit
295.0ms	246×	body	80	valid
146.0ms	3510×	pre	80	true
6.0ms	1×	body	5120	valid
4.0ms	2×	body	1280	valid
3.0ms	1×	body	2560	valid
1.0ms	2×	body	320	valid
1.0ms	3×	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: 6.9b

localize48.0ms

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)))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

1193×	`add-exp-log`
693×	`pow-exp`
684×	`prod-exp`
593×	`div-exp`
345×	`pow-to-exp`
116×	`rec-exp` `1-exp`
47×	`unpow-prod-down`
44×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
29×	`times-frac`
24×	`add-cube-cbrt`
16×	`add-cbrt-cube`
9×	`pow1` `pow-unpow`
7×	`pow-pow`
6×	`distribute-lft-out` `difference-of-squares`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`sqr-pow`
2×	`flip3-+` `flip-+` `pow-flip` `distribute-lft-out--` `inv-pow`
1×	`clear-num` `associate-/r` `frac-2neg` `associate-/l`

Counts

4 → 489

Calls

4 calls:

52.0ms	(pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)
12.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
12.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
133.0ms	(/ (* (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)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)
55.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
56.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
512.0ms	(/ (* (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)))

simplify2.6s

Counts

501 → 501

Iterations

Iter	Nodes
done	5008
2	3660
1	1320
0	469

prune703.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize64.0ms

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)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
47×	`log-prod`
41×	`add-sqr-sqrt`
28×	`times-frac` `add-cube-cbrt`
16×	`add-log-exp`
15×	`add-exp-log`
9×	`pow1` `rem-log-exp` `prod-diff`
7×	`log-pow` `difference-of-squares`
6×	`flip3-+` `flip-+` `distribute-lft-out`
4×	`expm1-log1p-u` `log-div` `sum-log` `add-cbrt-cube` `diff-log` `div-exp` `associate-/r/` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `div-inv` `distribute-lft-out--`
2×	`rec-exp` `sub-neg` `log1p-def` `flip3--` `1-exp` `log-rec` `pow-flip` `flip--` `inv-pow`
1×	`associate--l+` `associate--r+`

Counts

4 → 139

Calls

4 calls:

31.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
6.0ms	(log (/ 1 (+ 1 (exp (- s)))))
6.0ms	(log (/ 1 (+ 1 (exp (- t)))))
57.0ms	(- (+ (* (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)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
53.0ms	(log (/ 1 (+ 1 (exp (- s)))))
56.0ms	(log (/ 1 (+ 1 (exp (- t)))))
298.0ms	(- (+ (* (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)))

simplify1.7s

Counts

151 → 151

Iterations

Iter	Nodes
done	5001
2	2626
1	910
0	362

prune932.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

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)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`log-prod`
21×	`add-cube-cbrt`
20×	`times-frac`
16×	`add-log-exp`
13×	`difference-of-squares`
11×	`add-exp-log`
9×	`prod-diff`
8×	`pow1`
6×	`rem-log-exp`
5×	`log-div` `flip3-+` `log-pow` `flip-+` `distribute-lft-out--`
4×	`expm1-log1p-u` `sum-log` `log1p-def` `add-cbrt-cube` `diff-log` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `fma-neg` `div-inv` `flip--` `distribute-lft-out`
2×	`div-exp` `associate-/r/`
1×	`rec-exp` `1-exp` `log-rec` `associate--l+` `pow-flip` `associate--r+` `inv-pow`

Counts

4 → 129

Calls

4 calls:

32.0ms	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
31.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
6.0ms	(log (/ 1 (+ 1 (exp (- s)))))
55.0ms	(- (+ (* (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)))

series557.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
66.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
56.0ms	(log (/ 1 (+ 1 (exp (- s)))))
367.0ms	(- (+ (* (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

141 → 141

Iterations

Iter	Nodes
done	5001
2	2837
1	893
0	361

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (/ -1 (+ (exp (- t)) 1)))
0.2b	(fma c_n (log1p (/ -1 (+ (exp (- t)) 1))) (* t (* c_p 1/2)))
0.2b	(* (log1p (/ -1 (+ (exp (- s)) 1))) c_n)
8.7b	(- (* (log1p (/ -1 (+ (exp (- s)) 1))) c_n) (fma c_n (log1p (/ -1 (+ (exp (- t)) 1))) (* t (* c_p 1/2))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u`
3×	`associate-r` `associate-l` `prod-diff`
2×	`fma-udef`
1×	`log1p-udef` `sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `flip--` `associate--r+` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

0.0ms	(log1p (/ -1 (+ (exp (- t)) 1)))
0.0ms	(fma c_n (log1p (/ -1 (+ (exp (- t)) 1))) (* t (* c_p 1/2)))
5.0ms	(* (log1p (/ -1 (+ (exp (- s)) 1))) c_n)
8.0ms	(- (* (log1p (/ -1 (+ (exp (- s)) 1))) c_n) (fma c_n (log1p (/ -1 (+ (exp (- t)) 1))) (* t (* c_p 1/2))))

series558.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(log1p (/ -1 (+ (exp (- t)) 1)))
113.0ms	(fma c_n (log1p (/ -1 (+ (exp (- t)) 1))) (* t (* c_p 1/2)))
79.0ms	(* (log1p (/ -1 (+ (exp (- s)) 1))) c_n)
302.0ms	(- (* (log1p (/ -1 (+ (exp (- s)) 1))) c_n) (fma c_n (log1p (/ -1 (+ (exp (- t)) 1))) (* t (* c_p 1/2))))

simplify1.7s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
3	2298
2	779
1	326
0	159

prune471.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes314.0ms

bsearch2.4s

Steps

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

simplify13.0ms

Iterations

Iter	Nodes
done	64
1	64
0	50

end0.0ms

sample8.9m

Algorithm

intervals

Results

8.9m	39729×	body	10240	exit
2.6s	42868×	pre	80	true
568.0ms	3038×	body	80	valid
88.0ms	6×	body	5120	valid
44.0ms	21×	body	1280	valid
30.0ms	8×	body	2560	valid
22.0ms	20×	body	640	valid
15.0ms	36×	body	160	valid
5.0ms	9×	body	320	valid