Details

sample51.6s

Algorithm

intervals

Results

50.7s	3315×	body	10240	exit
456.0ms	3571×	pre	80	true
48.0ms	1×	body	5120	valid
32.0ms	243×	body	80	valid
10.0ms	6×	body	1280	valid
2.0ms	2×	body	640	valid
2.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid

simplify538.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	43
1	53	43
2	147	43
3	847	43
done	5000	43

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 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)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
2.2b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

rewrite268.0ms

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:

31.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
21.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
178.0ms	(/ (* (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)))
20.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

series873.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
76.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
666.0ms	(/ (* (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)))
78.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

simplify1.3s

Counts

279 → 279

Iterations

Useful iterations: 2 (499.0ms)

Iter	Nodes	Cost
0	360	10772
1	1191	10366
2	4396	9633
done	5001	9633

prune471.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.3b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2×	`associate-r` `*-commutative` `add-log-exp`

Counts

2 → 36

Calls

2 calls:

16.0ms	(* 0.5 (* s c_p))
20.0ms	(* 0.5 (* s c_n))

series41.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(* 0.5 (* s c_p))
20.0ms	(* 0.5 (* s c_n))

simplify1.8s

Counts

42 → 42

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	59	308
1	152	302
2	581	242
3	2506	242
done	5001	242

prune78.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
26.2b	(cbrt (* 0.5 (* s c_n)))
26.2b	(cbrt (* 0.5 (* s c_n)))
26.2b	(cbrt (* 0.5 (* s c_n)))

rewrite62.0ms

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:

30.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
10.0ms	(cbrt (* 0.5 (* s c_n)))
10.0ms	(cbrt (* 0.5 (* s c_n)))
10.0ms	(cbrt (* 0.5 (* s c_n)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (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)))

simplify466.0ms

Counts

70 → 70

Iterations

Useful iterations: done (462.0ms)

Iter	Nodes	Cost
0	86	856
1	222	766
2	844	670
done	5000	620

prune246.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 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)
0.7b	(/ (* (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)))

rewrite250.0ms

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:

31.0ms	(- 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)
185.0ms	(/ (* (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:

56.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
181.0ms	(* (log 0.5) c_p)
77.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
793.0ms	(/ (* (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)))

simplify1.5s

Counts

150 → 150

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	313	5198
1	988	4936
2	4701	4525
done	5000	4453

prune482.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.2b

regimes527.0ms

bsearch1.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	79
1	58	79
done	58	79

end0.0ms

sample3.1m

Algorithm

intervals

Results

3.1m	13900×	body	10240	exit
941.0ms	15037×	pre	80	true
400.0ms	1097×	body	80	valid
11.0ms	4×	body	2560	valid
8.0ms	4×	body	1280	valid
7.0ms	1×	body	5120	valid
6.0ms	20×	body	160	valid
5.0ms	6×	body	640	valid
3.0ms	5×	body	320	valid