Details

sample40.2s

Algorithm

intervals

Results

39.9s	3188×	body	10240	exit
75.0ms	3446×	pre	80	true
21.0ms	247×	body	80	valid
6.0ms	1×	body	5120	valid
4.0ms	2×	body	1280	valid
3.0ms	1×	body	2560	valid
2.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	640	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.2b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.5b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
4.2b	(/ (* (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)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

558×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
250×	`div-exp`
184×	`pow-to-exp`
51×	`*-un-lft-identity`
37×	`times-frac`
36×	`unpow-prod-down`
31×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-cbrt-cube`
10×	`distribute-lft-out`
6×	`pow1` `pow-unpow` `associate-/r/`
5×	`cbrt-undiv` `associate-/r*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

4 → 293

Calls

4 calls:

8.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
12.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
11.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
95.0ms	(/ (* (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)))

series754.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
71.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
588.0ms	(/ (* (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)))

simplify106.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	993	6127
1	3350	5877
2	5002	5877

prune549.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize7.0ms

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:

6.0ms

(* 0.5 (* s c_n))

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(* 0.5 (* s c_n))

simplify71.0ms

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

prune51.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.2b	(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:

6.0ms	(* 0.5 (* s c_n))
0.0ms	(expm1 (log1p (* 0.5 (* s c_n))))
0.0ms	(log1p (* 0.5 (* s c_n)))

series364.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(* 0.5 (* s c_n))
238.0ms	(expm1 (log1p (* 0.5 (* s c_n))))
107.0ms	(log1p (* 0.5 (* s c_n)))

simplify29.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (26.0ms)

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

prune141.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.0b	(expm1 (log1p (log1p (* 0.5 (* s c_n)))))
0.2b	(expm1 (expm1 (log1p (log1p (* 0.5 (* s c_n))))))
0.2b	(log1p (* 0.5 (* s c_n)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

6.0ms	(* 0.5 (* s c_n))
0.0ms	(expm1 (log1p (log1p (* 0.5 (* s c_n)))))
0.0ms	(expm1 (expm1 (log1p (log1p (* 0.5 (* s c_n))))))
0.0ms	(log1p (* 0.5 (* s c_n)))

series1.2s

Counts

4 → 12

Calls

4 calls:

21.0ms	(* 0.5 (* s c_n))
316.0ms	(expm1 (log1p (log1p (* 0.5 (* s c_n)))))
807.0ms	(expm1 (expm1 (log1p (log1p (* 0.5 (* s c_n))))))
103.0ms	(log1p (* 0.5 (* s c_n)))

simplify32.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	289	343
1	1079	304
2	5001	296

prune187.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.0b

regimes292.0ms

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	34
1	49	34

end0.0ms

sample6.1m

Algorithm

intervals

Results

6.1m	29561×	body	10240	exit
605.0ms	31815×	pre	80	true
179.0ms	2176×	body	80	valid
83.0ms	7×	body	5120	valid
28.0ms	16×	body	1280	valid
14.0ms	19×	body	640	valid
7.0ms	3×	body	2560	valid
6.0ms	25×	body	160	valid
3.0ms	8×	body	320	valid