Details

sample49.6s

Algorithm

intervals

Results

49.0s	3422×	body	10240	exit
256.0ms	3679×	pre	80	true
30.0ms	252×	body	80	valid
6.0ms	3×	body	1280	valid
1.0ms	2×	body	160	valid

simplify606.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	43
1	53	43
2	147	43
3	839	43
done	5001	43

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.9b	(/ (* (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)))

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

556×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
249×	`div-exp`
184×	`pow-to-exp`
97×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
62×	`times-frac`
54×	`prod-diff`
36×	`unpow-prod-down`
16×	`add-cbrt-cube`
15×	`distribute-lft-out`
10×	`associate-/r/`
6×	`pow1` `pow-unpow` `div-inv` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow-pow` `difference-of-squares` `sqr-pow`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `associate-/r` `flip--` `associate-/l` `distribute-lft-out--`

Counts

4 → 332

Calls

4 calls:

42.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
20.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
22.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
175.0ms	(/ (* (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)))

series858.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
75.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
75.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
656.0ms	(/ (* (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)))

simplify1.4s

Counts

344 → 344

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	471	14274
1	1137	13014
2	3191	11812
done	5000	11521

prune566.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.5 (* s c_p) 1)
0.0b	(* 0.5 (* s c_n))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`associate-r` `*-commutative` `fma-udef`

Counts

2 → 30

Calls

2 calls:

0.0ms	(fma 0.5 (* s c_p) 1)
16.0ms	(* 0.5 (* s c_n))

series60.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(fma 0.5 (* s c_p) 1)
21.0ms	(* 0.5 (* s c_n))

simplify2.8s

Counts

36 → 36

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	52	276
1	109	270
2	352	227
3	1191	227
4	2885	227
done	5000	227

prune86.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
23.1b	(cbrt (* 0.5 (* s c_n)))
23.1b	(cbrt (* 0.5 (* s c_n)))
23.1b	(cbrt (* 0.5 (* s c_n)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

27.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
15.0ms	(cbrt (* 0.5 (* s c_n)))
11.0ms	(cbrt (* 0.5 (* s c_n)))
11.0ms	(cbrt (* 0.5 (* s c_n)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
97.0ms	(cbrt (* 0.5 (* s c_n)))
97.0ms	(cbrt (* 0.5 (* s c_n)))
97.0ms	(cbrt (* 0.5 (* s c_n)))

simplify2.3s

Counts

78 → 78

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	90	926
1	211	836
2	546	740
3	1447	648
4	4040	606
done	5000	573

prune226.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-exp-log`
145×	`*-un-lft-identity`
109×	`add-sqr-sqrt`
108×	`prod-diff`
99×	`add-cube-cbrt`
87×	`times-frac` `prod-exp`
65×	`div-exp`
55×	`pow-exp`
42×	`pow-to-exp`
21×	`distribute-lft-out`
18×	`unpow-prod-down`
16×	`add-cbrt-cube`
14×	`associate-/r/`
8×	`div-inv` `add-log-exp`
7×	`flip3-+` `flip-+`
6×	`fma-neg`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`pow-unpow`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow-pow` `frac-2neg` `clear-num` `associate-/r` `associate-/l` `sqr-pow`

Counts

4 → 254

Calls

4 calls:

42.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
42.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
20.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
155.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series987.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
54.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
73.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
806.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify1.6s

Counts

266 → 266

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	550	11940
1	1359	10677
2	4218	8567
done	5000	8555

prune863.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.9b

regimes437.0ms

bsearch4.4s

Steps

Iters	Range		Point
3	929.2230967103569	1152.9458673759273	1133.0396377537263
5	5.584792604326362e-120	1.2147547225272793e-119	5.6408403315168225e-120

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	95
1	59	95
done	59	95

end0.0ms

sample5.6m

Algorithm

intervals

Results

5.6m	25783×	body	10240	exit
2.0s	27745×	pre	80	true
252.0ms	1893×	body	80	valid
56.0ms	6×	body	5120	valid
20.0ms	11×	body	1280	valid
15.0ms	17×	body	640	valid
10.0ms	4×	body	2560	valid
6.0ms	21×	body	160	valid
4.0ms	10×	body	320	valid