Details

sample44.7s

Algorithm

intervals

Results

44.4s	3665×	body	10240	exit
80.0ms	3921×	pre	80	true
22.0ms	251×	body	80	valid
5.0ms	2×	body	2560	valid
0.0ms	1×	body	320	valid
0.0ms	2×	body	160	valid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	25
1	147	25
2	850	25
3	5001	25

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 7.8b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.9b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
4.4b	(/ (* (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)))

rewrite85.0ms

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:

14.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
37.0ms	(/ (* (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)))

series747.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
66.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
568.0ms	(/ (* (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)))

simplify138.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1281	8124
1	4389	7090
2	5001	7090

prune526.0ms

Filtered

344 candidates to 106 candidates (30.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	341	3	344
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	341	4	345

Merged error: 0.5b

Counts

345 → 4

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 0.5 (* s c_n))

rewrite5.0ms

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:

4.0ms

(* 0.5 (* s c_n))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(* 0.5 (* s c_n))

simplify75.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	88	77
1	320	62
2	1234	62
3	3438	62
4	5002	62

prune43.0ms

Filtered

23 candidates to 13 candidates (56.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	21	2	23
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	22	5	27

Merged error: 0.5b

Counts

27 → 5

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.1b	(expm1 (log1p (* 0.5 (* s c_n))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 31

Calls

2 calls:

7.0ms	(* 0.5 (* s c_n))
1.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

series246.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(* 0.5 (* s c_n))
225.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

simplify45.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	171	161
1	545	137
2	2039	131
3	5001	121

prune73.0ms

Filtered

37 candidates to 24 candidates (64.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	37	5	42

Merged error: 0.5b

Counts

42 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.5b	(/ (* (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)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-exp-log`
99×	`*-un-lft-identity`
87×	`prod-exp`
70×	`add-sqr-sqrt`
66×	`div-exp`
65×	`add-cube-cbrt`
62×	`times-frac`
55×	`pow-exp`
54×	`prod-diff`
42×	`pow-to-exp`
18×	`unpow-prod-down` `add-cbrt-cube`
16×	`distribute-lft-out`
10×	`associate-/r/`
6×	`div-inv` `add-log-exp`
5×	`pow1` `cbrt-undiv` `flip3-+` `associate-/r*` `flip-+`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `associate-/l*`
3×	`pow-unpow` `fma-neg`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `pow-pow` `diff-log` `flip--` `distribute-lft-out--` `sqr-pow`

Counts

4 → 215

Calls

4 calls:

5.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
11.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
33.0ms	(/ (* (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)))

series835.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
49.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
64.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
697.0ms	(/ (* (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)))

simplify127.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1156	4971
1	4789	3939
2	5001	3939

prune603.0ms

Filtered

227 candidates to 106 candidates (46.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	227	5	232

Merged error: 0.5b

Counts

232 → 5

regimes541.0ms

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	32
1	47	32

end0.0ms

sample7.0m

Algorithm

intervals

Results

7.0m	34532×	body	10240	exit
695.0ms	37295×	pre	80	true
232.0ms	2694×	body	80	valid
25.0ms	6×	body	2560	valid
24.0ms	15×	body	1280	valid
12.0ms	2×	body	5120	valid
11.0ms	13×	body	640	valid
6.0ms	26×	body	160	valid
3.0ms	7×	body	320	valid