Details

sample14.8s

Algorithm

intervals

Results

14.1s	1586×	body	10240	exit
399.0ms	1735×	body	80	overflowed
101.0ms	3577×	pre	80	true
54.0ms	247×	body	80	valid
7.0ms	3×	body	1280	valid
6.0ms	1×	body	5120	valid
2.0ms	2×	body	640	valid
1.0ms	2×	body	160	valid
1.0ms	1×	body	320	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: 7.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ 1.0 (exp (- t))))
1.5b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
1.7b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
3.4b	(/ (* (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)))

rewrite136.0ms

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))))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
11.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
89.0ms	(/ (* (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)))

series727.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) 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)))

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

prune532.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

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:

5.0ms

(* 0.5 (* s c_n))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(* 0.5 (* s c_n))

simplify72.0ms

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

prune53.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 3 expressions with local error:

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

series346.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(* 0.5 (* s c_n))
228.0ms	(expm1 (log1p (* 0.5 (* s c_n))))
100.0ms	(log1p (* 0.5 (* s c_n)))

simplify30.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (26.0ms)

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

prune145.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (log1p (* 0.5 (* s c_n))) 3)
0.1b	(expm1 (cbrt (pow (log1p (* 0.5 (* s c_n))) 3)))
0.5b	(log1p (* 0.5 (* s c_n)))
29.0b	(cbrt (pow (log1p (* 0.5 (* s c_n))) 3))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
4×	`add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `log1p-udef` `expm1-log1p` `pow-pow` `pow1/3` `log1p-expm1` `pow-exp` `rem-cbrt-cube` `expm1-udef` `rem-cube-cbrt`

Counts

4 → 70

Calls

4 calls:

1.0ms	(pow (log1p (* 0.5 (* s c_n))) 3)
0.0ms	(expm1 (cbrt (pow (log1p (* 0.5 (* s c_n))) 3)))
0.0ms	(log1p (* 0.5 (* s c_n)))
1.0ms	(cbrt (pow (log1p (* 0.5 (* s c_n))) 3))

series776.0ms

Counts

4 → 12

Calls

4 calls:

347.0ms	(pow (log1p (* 0.5 (* s c_n))) 3)
227.0ms	(expm1 (cbrt (pow (log1p (* 0.5 (* s c_n))) 3)))
99.0ms	(log1p (* 0.5 (* s c_n)))
102.0ms	(cbrt (pow (log1p (* 0.5 (* s c_n))) 3))

simplify91.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	920	914
1	4536	851
2	5001	849

prune286.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

regimes794.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	35
1	56	35

end0.0ms

sample1.5m

Algorithm

intervals

Results

1.4m	9620×	body	10240	exit
2.3s	10552×	body	80	overflowed
550.0ms	21746×	pre	80	true
310.0ms	1518×	body	80	valid
31.0ms	13×	body	1280	valid
23.0ms	3×	body	5120	valid
13.0ms	12×	body	640	valid
10.0ms	22×	body	160	valid
9.0ms	3×	body	2560	valid
2.0ms	3×	body	320	valid