Details

sample47.5s

Algorithm

intervals

Results

46.3s	3078×	body	10240	exit
866.0ms	3334×	pre	80	true
32.0ms	249×	body	80	valid
4.0ms	3×	body	640	valid
1.0ms	3×	body	160	valid
1.0ms	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

localize24.0ms

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)))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

553×	`add-exp-log`
312×	`prod-exp`
262×	`pow-exp`
248×	`div-exp`
183×	`pow-to-exp`
145×	`*-un-lft-identity`
109×	`add-sqr-sqrt`
108×	`prod-diff`
99×	`add-cube-cbrt`
87×	`times-frac`
21×	`distribute-lft-out`
18×	`unpow-prod-down`
16×	`add-cbrt-cube`
14×	`associate-/r/`
8×	`div-inv` `add-log-exp`
7×	`flip3-+` `flip-+`
6×	`fma-neg`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`pow-unpow`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow-pow` `frac-2neg` `clear-num` `associate-/r` `associate-/l` `sqr-pow`

Counts

4 → 371

Calls

4 calls:

40.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
39.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
20.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
172.0ms	(/ (* (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)))

series853.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
56.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
78.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
668.0ms	(/ (* (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

383 → 383

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	570	17315
1	1377	15625
2	3957	13557
done	5000	13545

prune729.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.0b	(fma (log 0.5) c_p (fma 0.5 (* t c_p) 1))
0.3b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
0.4b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

168×	`add-exp-log`
87×	`prod-exp`
84×	`*-un-lft-identity`
65×	`div-exp`
61×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
54×	`prod-diff`
53×	`pow-exp`
50×	`times-frac`
41×	`pow-to-exp`
18×	`add-cbrt-cube`
13×	`distribute-lft-out`
8×	`associate-/r/`
6×	`add-log-exp`
5×	`cbrt-undiv` `associate-/r*` `div-inv`
4×	`pow1` `expm1-log1p-u` `flip3-+` `cbrt-unprod` `flip-+` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--`

Counts

4 → 190

Calls

4 calls:

17.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
0.0ms	(fma (log 0.5) c_p (fma 0.5 (* t c_p) 1))
147.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
47.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))

series944.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
54.0ms	(fma (log 0.5) c_p (fma 0.5 (* t c_p) 1))
807.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
55.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))

simplify1.4s

Counts

202 → 202

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	408	8290
1	992	7513
2	3329	6247
done	5000	5870

prune551.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize42.0ms

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

rewrite391.0ms

Algorithm

rewrite-expression-head

Rules

134×	`*-un-lft-identity`
108×	`prod-diff`
106×	`add-sqr-sqrt`
94×	`add-cube-cbrt`
80×	`times-frac`
18×	`distribute-lft-out`
14×	`sqrt-prod`
12×	`associate-/r/`
8×	`div-inv` `add-log-exp`
6×	`pow1` `flip3-+` `fma-neg` `flip-+`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sqrt-div` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 188

Calls

4 calls:

39.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
40.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
148.0ms	(sqrt (/ (* (pow (/ 1.0 (+ (exp (- s)) 1.0)) c_p) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))) (fma c_p (+ (log 0.5) (* 0.5 t)) 1)))
154.0ms	(sqrt (/ (* (pow (/ 1.0 (+ (exp (- s)) 1.0)) c_p) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))) (fma c_p (+ (log 0.5) (* 0.5 t)) 1)))

series2.1s

Counts

4 → 12

Calls

4 calls:

53.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
53.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
860.0ms	(sqrt (/ (* (pow (/ 1.0 (+ (exp (- s)) 1.0)) c_p) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))) (fma c_p (+ (log 0.5) (* 0.5 t)) 1)))
1.1s	(sqrt (/ (* (pow (/ 1.0 (+ (exp (- s)) 1.0)) c_p) (/ (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))) (fma c_p (+ (log 0.5) (* 0.5 t)) 1)))

simplify1.0s

Counts

200 → 200

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	258	9506
1	571	8378
2	1487	6484
done	5000	5614

prune787.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 0.5 (* s c_n))

rewrite20.0ms

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:

19.0ms

(* 0.5 (* s c_n))

series22.0ms

Counts

1 → 3

Calls

1 calls:

22.0ms

(* 0.5 (* s c_n))

simplify5.6s

Counts

23 → 23

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	37	166
1	87	163
2	300	133
3	1003	133
4	2173	133
5	4443	133
done	5001	133

prune42.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes360.0ms

bsearch4.0s

Steps

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

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	105
1	48	105
done	48	105

end0.0ms

sample44.7s

Algorithm

intervals

Results

44.2s	3441×	body	10240	exit
253.0ms	3721×	pre	80	true
28.0ms	272×	body	80	valid
3.0ms	3×	body	640	valid
1.0ms	3×	body	160	valid
1.0ms	2×	body	320	valid