Details

sample48.8s

Algorithm

intervals

Results

48.4s	3422×	body	10240	exit
116.0ms	3679×	pre	80	true
31.0ms	252×	body	80	valid
5.0ms	3×	body	1280	valid
1.0ms	2×	body	160	valid

simplify614.0ms

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

localize28.0ms

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)))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

556×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
249×	`div-exp`
184×	`pow-to-exp`
36×	`unpow-prod-down` `*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
16×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `distribute-lft-out` `add-log-exp`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod`
3×	`div-inv`
2×	`pow-pow` `flip3-+` `flip-+` `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 → 267

Calls

4 calls:

30.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
21.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
19.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
174.0ms	(/ (* (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)))

series842.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
74.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
74.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
643.0ms	(/ (* (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)))

simplify878.0ms

Counts

279 → 279

Iterations

Useful iterations: 2 (342.0ms)

Iter	Nodes	Cost
0	360	10772
1	844	9979
2	2360	9633
done	5000	9633

prune467.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
2×	`associate-r` `*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

3 → 47

Calls

3 calls:

19.0ms	(+ (* 0.5 (* s c_p)) 1)
15.0ms	(* 0.5 (* s c_n))
15.0ms	(* 0.5 (* s c_p))

series77.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ (* 0.5 (* s c_p)) 1)
20.0ms	(* 0.5 (* s c_n))
20.0ms	(* 0.5 (* s c_p))

simplify2.1s

Counts

56 → 56

Iterations

Useful iterations: 3 (920.0ms)

Iter	Nodes	Cost
0	80	474
1	217	449
2	741	385
3	2776	381
done	5001	381

prune102.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize15.0ms

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)))

rewrite60.0ms

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×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `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 → 58

Calls

4 calls:

24.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
14.0ms	(cbrt (* 0.5 (* s c_n)))
10.0ms	(cbrt (* 0.5 (* s c_n)))
10.0ms	(cbrt (* 0.5 (* s c_n)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
93.0ms	(cbrt (* 0.5 (* s c_n)))
93.0ms	(cbrt (* 0.5 (* s c_n)))
94.0ms	(cbrt (* 0.5 (* s c_n)))

simplify2.4s

Counts

70 → 70

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	86	856
1	204	766
2	517	670
3	1376	586
4	3949	544
done	5000	509

prune187.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.2b	(* (log 0.5) c_p)
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)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-exp-log`
88×	`prod-exp`
65×	`div-exp`
55×	`pow-exp`
42×	`pow-to-exp`
23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
18×	`unpow-prod-down` `add-cbrt-cube`
15×	`add-cube-cbrt`
14×	`times-frac`
8×	`pow1`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `associate-l` `associate-/r/`
3×	`pow-unpow` `associate-r` `distribute-lft-out`
2×	`flip3-+` `associate-*l/` `flip-+` `div-inv` `difference-of-squares`
1×	`sub-neg` `flip3--` `pow-pow` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `log-pow` `-commutative` `flip--` `associate-/l*` `distribute-lft-out--` `unswap-sqr` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

30.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
8.0ms	(* (log 0.5) c_p)
20.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
187.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

53.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
171.0ms	(* (log 0.5) c_p)
74.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
772.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify1.0s

Counts

150 → 150

Iterations

Useful iterations: 2 (404.0ms)

Iter	Nodes	Cost
0	313	5198
1	794	4863
2	2848	4452
done	5000	4452

prune465.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.9b

regimes400.0ms

bsearch4.2s

Steps

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

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	100
1	71	100
done	71	100

end0.0ms

sample5.6m

Algorithm

intervals

Results

5.5m	25783×	body	10240	exit
1.2s	27745×	pre	80	true
219.0ms	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