Details

sample2.0s

Algorithm

intervals

Results

1.4s	197×	body	5120	exit
428.0ms	2599×	body	80	overflowed
68.0ms	3052×	pre	80	true
27.0ms	248×	body	80	valid
5.0ms	2×	body	1280	valid
2.0ms	5×	body	160	valid
1.0ms	1×	body	320	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

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

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
3.2b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.7b	(/ (* (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)))

rewrite89.0ms

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:

11.0ms	(- 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)
39.0ms	(/ (* (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)))

series1.0s

Counts

4 → 12

Calls

4 calls:

53.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
74.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
815.0ms	(/ (* (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)))

simplify147.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (26.0ms)

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

prune586.0ms

Filtered

344 candidates to 106 candidates (30.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	342	2	344
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	342	3	345

Merged error: 0.5b

Counts

345 → 3

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:

5.0ms

(* 0.5 (* s c_n))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(* 0.5 (* s c_n))

simplify79.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 1 (5.0ms)

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

prune41.0ms

Filtered

23 candidates to 13 candidates (56.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	22	1	23
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	22	4	26

Merged error: 0.5b

Counts

26 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.1b	(expm1 (log1p (* 0.5 (* s c_n))))
0.2b	(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))
1.0ms	(expm1 (log1p (* 0.5 (* s c_n))))
1.0ms	(log1p (* 0.5 (* s c_n)))

series387.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(* 0.5 (* s c_n))
256.0ms	(expm1 (log1p (* 0.5 (* s c_n))))
112.0ms	(log1p (* 0.5 (* s c_n)))

simplify33.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	265	250
1	1006	219
2	5001	209

prune130.0ms

Filtered

51 candidates to 36 candidates (70.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	51	4	55

Merged error: 0.5b

Counts

55 → 4

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.0b	(/ (* (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)))

rewrite74.0ms

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:

6.0ms	(/ 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)))

series920.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
48.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
77.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
762.0ms	(/ (* (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)))

simplify130.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (26.0ms)

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

prune648.0ms

Filtered

227 candidates to 106 candidates (46.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	227	4	231

Merged error: 0.5b

Counts

231 → 4

regimes470.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	32
1	47	32

end0.0ms

sample37.8s

Algorithm

intervals

Results

25.8s	3955×	body	5120	exit
8.2s	51721×	body	80	overflowed
1.3s	60139×	pre	80	true
450.0ms	4291×	body	80	valid
90.0ms	6×	body	5120	valid
36.0ms	33×	body	640	valid
35.0ms	18×	body	1280	valid
19.0ms	65×	body	160	valid
17.0ms	6×	body	2560	valid
10.0ms	18×	body	320	valid
6.0ms	9×	body	320	overflowed
5.0ms	13×	body	160	overflowed
4.0ms	2×	body	1280	overflowed
2.0ms	2×	body	640	overflowed