Details

sample40.7s

Algorithm

intervals

Results

40.3s	3237×	body	10240	exit
98.0ms	3493×	pre	80	true
22.0ms	249×	body	80	valid
2.0ms	6×	body	160	valid
1.0ms	1×	body	640	valid

simplify256.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.2b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
4.7b	(/ (* (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)))

rewrite155.0ms

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:

21.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
90.0ms	(/ (* (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)))

series786.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
66.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
71.0ms	(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)))

simplify1.6s

Counts

344 → 344

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	471	14274
1	1291	13014
2	4162	11668
done	5000	11665

prune623.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.7b

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))

simplify2.7s

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

prune62.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
27.4b	(cbrt (* 0.5 (* s c_n)))
27.4b	(cbrt (* 0.5 (* s c_n)))
27.4b	(cbrt (* 0.5 (* s c_n)))

rewrite20.0ms

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:

7.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
4.0ms	(cbrt (* 0.5 (* s c_n)))
4.0ms	(cbrt (* 0.5 (* s c_n)))
4.0ms	(cbrt (* 0.5 (* s c_n)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
92.0ms	(cbrt (* 0.5 (* s c_n)))
93.0ms	(cbrt (* 0.5 (* s c_n)))
91.0ms	(cbrt (* 0.5 (* s c_n)))

simplify1.4s

Counts

78 → 78

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	90	926
1	214	836
2	686	740
3	2844	656
done	5000	648

prune250.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.0b	(log1p (* 0.5 (* s c_n)))
0.1b	(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:

5.0ms	(* 0.5 (* s c_n))
0.0ms	(log1p (* 0.5 (* s c_n)))
0.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

series372.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(* 0.5 (* s c_n))
111.0ms	(log1p (* 0.5 (* s c_n)))
242.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

simplify1.9s

Counts

51 → 51

Iterations

Useful iterations: 3 (347.0ms)

Iter	Nodes	Cost
0	106	524
1	263	478
2	973	411
3	4664	397
done	5000	397

prune146.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.7b

regimes696.0ms

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	65
1	49	65
done	49	65

end0.0ms

sample9.1m

Algorithm

intervals

Results

9.1m	44127×	body	10240	exit
1.0s	47635×	pre	80	true
289.0ms	3403×	body	80	valid
46.0ms	6×	body	5120	valid
40.0ms	23×	body	1280	valid
21.0ms	6×	body	2560	valid
18.0ms	23×	body	640	valid
9.0ms	38×	body	160	valid
3.0ms	8×	body	320	valid