Details

sample37.9s

Algorithm

intervals

Results

37.6s	2928×	body	10240	exit
81.0ms	3184×	pre	80	true
22.0ms	250×	body	80	valid
6.0ms	1×	body	5120	valid
1.0ms	2×	body	640	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid

simplify254.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	43
1	53	43
2	147	43
3	735	43
done	5000	43

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
4.2b	(/ (* (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)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

557×	`add-exp-log`
312×	`prod-exp`
265×	`pow-exp`
249×	`div-exp`
185×	`pow-to-exp`
42×	`unpow-prod-down`
38×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
26×	`times-frac`
24×	`add-cube-cbrt`
16×	`add-cbrt-cube`
9×	`pow-unpow`
7×	`pow1`
6×	`distribute-lft-out`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-inv` `sqr-pow`
2×	`flip3-+` `flip-+` `difference-of-squares`
1×	`frac-2neg` `clear-num` `associate-/r` `associate-/l` `distribute-lft-out--`

Counts

4 → 280

Calls

4 calls:

34.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
11.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
95.0ms	(/ (* (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)))

series823.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
66.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
72.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
597.0ms	(/ (* (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)))

simplify1.2s

Counts

292 → 292

Iterations

Useful iterations: 2 (350.0ms)

Iter	Nodes	Cost
0	370	11029
1	1013	10220
2	3190	9884
done	5000	9884

prune514.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 0.5 (* s c_n))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 20

Calls

1 calls:

6.0ms

(* 0.5 (* s c_n))

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(* 0.5 (* s c_n))

simplify2.6s

Counts

23 → 23

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	37	166
1	88	163
2	288	133
3	928	133
4	1938	133
5	3809	133
done	5001	133

prune228.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(log1p (* 0.5 (* s c_n)))
0.0b	(* 0.5 (* s c_n))
0.0b	(expm1 (log1p (* 0.5 (* s c_n))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

0.0ms	(log1p (* 0.5 (* s c_n)))
6.0ms	(* 0.5 (* s c_n))
0.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

series361.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(log1p (* 0.5 (* s c_n)))
22.0ms	(* 0.5 (* s c_n))
235.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

simplify1.9s

Counts

51 → 51

Iterations

Useful iterations: 3 (344.0ms)

Iter	Nodes	Cost
0	106	524
1	263	478
2	972	411
3	4655	397
done	5000	397

prune149.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (log1p (* 0.5 (* s c_n)))) (cbrt (log1p (* 0.5 (* s c_n)))))
27.7b	(cbrt (log1p (* 0.5 (* s c_n))))
27.7b	(cbrt (log1p (* 0.5 (* s c_n))))
27.7b	(cbrt (log1p (* 0.5 (* s c_n))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt (log1p (* 0.5 (* s c_n)))) (cbrt (log1p (* 0.5 (* s c_n)))))
0.0ms	(cbrt (log1p (* 0.5 (* s c_n))))
0.0ms	(cbrt (log1p (* 0.5 (* s c_n))))
1.0ms	(cbrt (log1p (* 0.5 (* s c_n))))

series2.5s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (cbrt (log1p (* 0.5 (* s c_n)))) (cbrt (log1p (* 0.5 (* s c_n)))))
404.0ms	(cbrt (log1p (* 0.5 (* s c_n))))
399.0ms	(cbrt (log1p (* 0.5 (* s c_n))))
395.0ms	(cbrt (log1p (* 0.5 (* s c_n))))

simplify959.0ms

Counts

93 → 93

Iterations

Useful iterations: done (955.0ms)

Iter	Nodes	Cost
0	270	2980
1	830	2743
2	3861	2442
done	5000	2441

prune406.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

regimes194.0ms

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	23	31
done	23	31

end0.0ms

sample3.7m

Algorithm

intervals

Results

3.7m	18001×	body	10240	exit
433.0ms	19478×	pre	80	true
123.0ms	1431×	body	80	valid
22.0ms	4×	body	2560	valid
13.0ms	8×	body	1280	valid
12.0ms	2×	body	5120	valid
7.0ms	10×	body	640	valid
3.0ms	8×	body	320	valid
3.0ms	14×	body	160	valid