Details

sample45.6s

Algorithm

intervals

Results

45.2s	3078×	body	10240	exit
112.0ms	3334×	pre	80	true
32.0ms	249×	body	80	valid
3.0ms	3×	body	640	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid

simplify601.0ms

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: 5.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.4b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
1.5b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.2b	(/ (* (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)))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

553×	`add-exp-log`
312×	`prod-exp`
262×	`pow-exp`
248×	`div-exp`
183×	`pow-to-exp`
23×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`unpow-prod-down`
16×	`add-cbrt-cube`
15×	`times-frac`
13×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `cbrt-unprod` `difference-of-squares`
3×	`pow-unpow` `distribute-lft-out`
2×	`sub-neg` `flip3--` `diff-log` `associate-/r/` `flip--` `div-inv` `distribute-lft-out--`
1×	`pow-pow` `frac-2neg` `flip3-+` `clear-num` `associate-/r` `flip-+` `associate-/l` `sqr-pow`

Counts

4 → 249

Calls

4 calls:

32.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
30.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
21.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
171.0ms	(/ (* (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)))

series834.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
52.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
75.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
657.0ms	(/ (* (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)))

simplify789.0ms

Counts

261 → 261

Iterations

Useful iterations: 2 (311.0ms)

Iter	Nodes	Cost
0	329	10459
1	771	9693
2	2216	9337
done	5000	9337

prune410.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.3b	(/ (* (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)))
0.3b	(* (log 0.5) c_p)
0.4b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

18.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
184.0ms	(/ (* (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)))
8.0ms	(* (log 0.5) c_p)
37.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
809.0ms	(/ (* (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)))
182.0ms	(* (log 0.5) c_p)
54.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))

simplify961.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (377.0ms)

Iter	Nodes	Cost
0	299	5040
1	745	4721
2	2792	4159
done	5000	4159

prune469.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.4b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
1.7b	(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
1.7b	(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))

rewrite5.7s

Algorithm

rewrite-expression-head

Rules

52468×	`times-frac`
30560×	`add-sqr-sqrt`
28238×	`unpow-prod-down`
25190×	`*-un-lft-identity`
15806×	`add-cube-cbrt`
14510×	`sqrt-prod`
5784×	`difference-of-squares`
3570×	`sqr-pow`
2892×	`distribute-lft-out--`
1800×	`distribute-lft-out`
1622×	`associate-/r/`
822×	`div-inv`
800×	`flip3-+` `flip-+`
98×	`rem-sqrt-square`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
2×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `flip--`

Counts

4 → 14658

Calls

4 calls:

30.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
31.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
1.4s	(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
1.1s	(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))

series4.4s

Counts

4 → 12

Calls

4 calls:

50.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
54.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
2.1s	(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))
2.1s	(sqrt (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n) (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (+ 1 (* c_p (+ (log 0.5) (* 0.5 t))))))))

simplify6.2s

Counts

14670 → 14670

Iterations

Useful iterations: 0 (2.0s)

Iter	Nodes	Cost
0	18749	1436016
done	18749	1436016

prune2.2m

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite37.0ms

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:

21.0ms	(* 0.5 (* s c_n))
16.0ms	(* 0.5 (* s c_p))

series42.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(* 0.5 (* s c_n))
21.0ms	(* 0.5 (* s c_p))

simplify3.8s

Counts

42 → 42

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	59	308
1	151	302
2	560	242
3	1896	242
4	3876	242
done	5001	242

prune63.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes339.0ms

bsearch4.0s

Steps

Iters	Range		Point
6	-7.215218833396148e-165	-1.4476561172262608e-165	-1.5858411174365545e-165

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	108
1	52	108
done	52	108

end0.0ms

sample44.6s

Algorithm

intervals

Results

44.3s	3441×	body	10240	exit
72.0ms	3721×	pre	80	true
29.0ms	272×	body	80	valid
3.0ms	3×	body	640	valid
1.0ms	3×	body	160	valid
1.0ms	2×	body	320	valid