Details

sample2.1s

Algorithm

intervals

Results

1.4s	203×	body	5120	exit
455.0ms	2552×	body	80	overflowed
72.0ms	3012×	pre	80	true
28.0ms	249×	body	80	valid
7.0ms	1×	body	5120	valid
5.0ms	1×	body	1280	valid
2.0ms	5×	body	160	valid
1.0ms	1×	body	640	overflowed

simplify27.0ms

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: 5.8b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.3b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.2b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.9b	(/ (* (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)))

rewrite94.0ms

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)))))
8.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
40.0ms	(/ (* (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)))

series861.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
73.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
76.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
658.0ms	(/ (* (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)))

simplify150.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (26.0ms)

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

prune589.0ms

Filtered

344 candidates to 106 candidates (30.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	341	3	344
Fresh	0	0	0
Picked	1	0	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))

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

(* 0.5 (* s c_n))

simplify81.0ms

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

prune46.0ms

Filtered

23 candidates to 13 candidates (56.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	1	23
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
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)))

series400.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* 0.5 (* s c_n))
260.0ms	(expm1 (log1p (* 0.5 (* s c_n))))
116.0ms	(log1p (* 0.5 (* s c_n)))

simplify34.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (29.0ms)

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

prune133.0ms

Filtered

51 candidates to 36 candidates (70.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	2	2
Picked	1	0	1
Done	1	0	1
Total	51	4	55

Merged error: 0.5b

Counts

55 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (log1p (* 0.5 (* s c_n)))) (cbrt (log1p (* 0.5 (* s c_n)))))
26.9b	(cbrt (log1p (* 0.5 (* s c_n))))
26.9b	(cbrt (log1p (* 0.5 (* s c_n))))
26.9b	(cbrt (log1p (* 0.5 (* s c_n))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt (log1p (* 0.5 (* s c_n)))) (cbrt (log1p (* 0.5 (* s c_n)))))
1.0ms	(cbrt (log1p (* 0.5 (* s c_n))))
1.0ms	(cbrt (log1p (* 0.5 (* s c_n))))
1.0ms	(cbrt (log1p (* 0.5 (* s c_n))))

series2.7s

Counts

4 → 12

Calls

4 calls:

1.4s	(* (cbrt (log1p (* 0.5 (* s c_n)))) (cbrt (log1p (* 0.5 (* s c_n)))))
440.0ms	(cbrt (log1p (* 0.5 (* s c_n))))
434.0ms	(cbrt (log1p (* 0.5 (* s c_n))))
435.0ms	(cbrt (log1p (* 0.5 (* s c_n))))

simplify99.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	828	1670
1	3976	1529
2	5001	1511

prune396.0ms

Filtered

93 candidates to 79 candidates (84.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	93	4	97

Merged error: 0.5b

Counts

97 → 4

regimes335.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	20
1	23	20

end0.0ms

sample19.0s

Algorithm

intervals

Results

12.7s	1914×	body	5120	exit
4.3s	25548×	body	80	overflowed
667.0ms	29664×	pre	80	true
232.0ms	2135×	body	80	valid
32.0ms	15×	body	1280	valid
26.0ms	7×	body	2560	valid
24.0ms	2×	body	5120	valid
9.0ms	9×	body	640	valid
6.0ms	18×	body	160	valid
5.0ms	4×	body	640	overflowed
4.0ms	8×	body	320	valid
1.0ms	3×	body	160	overflowed
1.0ms	1×	body	320	overflowed