Details

sample46.7s

Algorithm

intervals

Results

46.0s	3124×	body	10240	exit
417.0ms	3380×	pre	80	true
33.0ms	250×	body	80	valid
12.0ms	1×	body	5120	valid
6.0ms	3×	body	1280	valid
4.0ms	1×	body	2560	valid
1.0ms	1×	body	640	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
3	744
2	143
1	53
0	22

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.2b

localize57.0ms

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)
1.2b	(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)))

rewrite206.0ms

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×	`expm1-log1p-u` `cbrt-undiv` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow-pow` `difference-of-squares` `sqr-pow`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `associate-/l` `distribute-lft-out--`

Counts

4 → 332

Calls

4 calls:

31.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
128.0ms	(/ (* (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)))

series782.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
594.0ms	(/ (* (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)))

simplify2.2s

Counts

344 → 344

Iterations

Iter	Nodes
done	5052
2	3918
1	1424
0	477

prune892.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

0.6b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
1.6b	(log (/ 1.0 (+ 1.0 (exp (- t)))))
8.6b	(- (* c_p (log (/ 1.0 (+ 1.0 (exp (- s)))))) (fma c_p (log (/ 1.0 (+ 1.0 (exp (- t))))) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
30.2b	(fma c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* c_p (log (/ 1.0 (+ 1.0 (exp (- s)))))) (fma c_p (log (/ 1.0 (+ 1.0 (exp (- t))))) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

72×	`log-prod`
61×	`*-un-lft-identity`
48×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`associate--l+`
18×	`distribute-rgt-in` `distribute-lft-in`
12×	`distribute-lft-out`
10×	`add-exp-log`
8×	`associate-/r/`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `rem-log-exp` `flip-+` `log1p-expm1-u` `div-inv`
3×	`prod-diff`
2×	`log-div` `div-exp` `log-pow` `fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--` `associate--r+`

Counts

4 → 127

Calls

4 calls:

7.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
7.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
22.0ms	(- (* c_p (log (/ 1.0 (+ 1.0 (exp (- s)))))) (fma c_p (log (/ 1.0 (+ 1.0 (exp (- t))))) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
0.0ms	(fma c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* c_p (log (/ 1.0 (+ 1.0 (exp (- s)))))) (fma c_p (log (/ 1.0 (+ 1.0 (exp (- t))))) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n))))

series760.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
70.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
290.0ms	(- (* c_p (log (/ 1.0 (+ 1.0 (exp (- s)))))) (fma c_p (log (/ 1.0 (+ 1.0 (exp (- t))))) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
330.0ms	(fma c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* c_p (log (/ 1.0 (+ 1.0 (exp (- s)))))) (fma c_p (log (/ 1.0 (+ 1.0 (exp (- t))))) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n))))

simplify2.1s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
3	4710
2	1614
1	725
0	341

prune945.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(* c_p (- s t))
0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.2b	(* (log 0.5) c_n)
40.5b	(fma c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* 0.5 (* c_p (- s t))) (* (log 0.5) c_n)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

85×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
72×	`prod-diff`
63×	`add-cube-cbrt`
37×	`times-frac`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1` `distribute-lft-out`
8×	`add-cbrt-cube` `associate-r` `add-exp-log`
7×	`associate-l`
6×	`associate-/r/` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `flip3-+` `fma-neg` `flip-+` `div-inv` `difference-of-squares`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`diff-log` `log-pow` `fma-udef`

Counts

4 → 151

Calls

4 calls:

18.0ms	(* c_p (- s t))
30.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
6.0ms	(* (log 0.5) c_n)
0.0ms	(fma c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* 0.5 (* c_p (- s t))) (* (log 0.5) c_n)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* c_p (- s t))
51.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
164.0ms	(* (log 0.5) c_n)
185.0ms	(fma c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* 0.5 (* c_p (- s t))) (* (log 0.5) c_n)))

simplify1.3s

Counts

163 → 163

Iterations

Iter	Nodes
done	5001
2	2089
1	814
0	349

prune611.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (log 0.5) c_n))
0.6b	(cbrt (* (log 0.5) c_n))
0.6b	(cbrt (* (log 0.5) c_n))
40.2b	(fma c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* 0.5 (* c_p (- s t))) (* (* (cbrt (* (log 0.5) c_n)) (cbrt (* (log 0.5) c_n))) (cbrt (* (log 0.5) c_n)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3`
1×	`fma-udef`

Counts

4 → 43

Calls

4 calls:

3.0ms	(cbrt (* (log 0.5) c_n))
3.0ms	(cbrt (* (log 0.5) c_n))
3.0ms	(cbrt (* (log 0.5) c_n))
0.0ms	(fma c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* 0.5 (* c_p (- s t))) (* (* (cbrt (* (log 0.5) c_n)) (cbrt (* (log 0.5) c_n))) (cbrt (* (log 0.5) c_n)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

382.0ms	(cbrt (* (log 0.5) c_n))
381.0ms	(cbrt (* (log 0.5) c_n))
379.0ms	(cbrt (* (log 0.5) c_n))
218.0ms	(fma c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* 0.5 (* c_p (- s t))) (* (* (cbrt (* (log 0.5) c_n)) (cbrt (* (log 0.5) c_n))) (cbrt (* (log 0.5) c_n)))))

simplify2.3s

Counts

55 → 55

Iterations

Iter	Nodes
done	5006
4	2398
3	797
2	341
1	165
0	86

prune346.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes174.0ms

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	24
1	24
0	20

end0.0ms

sample4.1m

Algorithm

intervals

Results

4.1m	19517×	body	10240	exit
906.0ms	21006×	pre	80	true
478.0ms	1449×	body	80	valid
27.0ms	14×	body	1280	valid
8.0ms	9×	body	640	valid
8.0ms	2×	body	2560	valid
7.0ms	1×	body	5120	valid
3.0ms	10×	body	160	valid
2.0ms	4×	body	320	valid