Details

analyze16.4s

Algorithm

sampling

Space saved by range analysis: 75.048792%

Space saved by search: 75.048792%

Guaranteed chance to sample good point: 6.25%

sample5.4s

Algorithm

intervals

Results

3.4s	488×	body	5120	exit
861.0ms	333×	body	1280	overflowed
429.0ms	2144×	body	80	overflowed
300.0ms	218×	body	640	overflowed
135.0ms	157×	body	320	overflowed
96.0ms	3657×	pre	80	true
31.0ms	249×	body	80	valid
25.0ms	60×	body	160	overflowed
2.0ms	6×	body	160	valid
2.0ms	1×	body	1280	valid
1.0ms	1×	body	640	invalid

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

prune6.0ms

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: 4.8b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (neg t))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
0.7b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
2.9b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

rewrite81.0ms

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×	`cbrt-unprod` `div-inv` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

4 → 285

Calls

4 calls:

5.0ms	(/ 1.0 (+ 1.0 (exp (neg t))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
43.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (+ 1.0 (exp (neg t))))
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
14.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
182.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

simplify101.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	972	6045
1	3266	5797
2	5003	5797

prune321.0ms

Filtered

91 candidates to 297 candidates (-226.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	294	3	297
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	295	3	298

Merged error: 0.5b

Counts

298 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.0b	(* 0.5 (* s c_p))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2×	`associate-r` `*-commutative` `add-log-exp`

Counts

2 → 36

Calls

2 calls:

4.0ms	(* 0.5 (* s c_n))
5.0ms	(* 0.5 (* s c_p))

series7.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(* 0.5 (* s c_n))
3.0ms	(* 0.5 (* s c_p))

simplify54.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	153	142
1	595	112
2	2373	112
3	5002	112

prune50.0ms

Filtered

22 candidates to 42 candidates (-90.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	42	3	45

Merged error: 0.5b

Counts

45 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.1b	(* (* (cbrt 0.5) (cbrt 0.5)) (* (cbrt 0.5) (* s c_p)))
0.3b	(* (cbrt 0.5) (* s c_p))
1.0b	(* (cbrt 0.5) (cbrt 0.5))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

42×	`pow1`
37×	`add-exp-log`
23×	`add-sqr-sqrt` `pow-prod-down` `add-cbrt-cube`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-prod`
16×	`associate-l`
15×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
6×	`pow1/3` `swap-sqr`
4×	`*-commutative` `add-log-exp` `unswap-sqr`
2×	`pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 107

Calls

4 calls:

4.0ms	(* 0.5 (* s c_n))
11.0ms	(* (* (cbrt 0.5) (cbrt 0.5)) (* (cbrt 0.5) (* s c_p)))
5.0ms	(* (cbrt 0.5) (* s c_p))
6.0ms	(* (cbrt 0.5) (cbrt 0.5))

series19.0ms

Counts

4 → 10

Calls

4 calls:

3.0ms	(* 0.5 (* s c_n))
8.0ms	(* (* (cbrt 0.5) (cbrt 0.5)) (* (cbrt 0.5) (* s c_p)))
7.0ms	(* (cbrt 0.5) (* s c_p))
0.0ms	(* (cbrt 0.5) (cbrt 0.5))

simplify47.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	310	620
1	1432	480
2	5001	431

prune146.0ms

Filtered

62 candidates to 117 candidates (-88.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	117	3	120

Merged error: 0.5b

Counts

120 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (neg t))))
0.2b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
1.7b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

173×	`add-exp-log`
88×	`prod-exp`
66×	`div-exp`
55×	`pow-exp`
42×	`pow-to-exp`
38×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
24×	`add-cube-cbrt`
20×	`add-cbrt-cube`
18×	`unpow-prod-down`
7×	`pow1` `distribute-lft-out`
6×	`associate-/r/`
5×	`cbrt-undiv` `associate-/r*` `cbrt-unprod`
4×	`flip3-+` `flip-+` `associate-/l*` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l` `div-inv`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`distribute-rgt-in` `pow-pow` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr` `sqr-pow`

Counts

4 → 159

Calls

4 calls:

5.0ms	(/ 1.0 (+ 1.0 (exp (neg t))))
5.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
36.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (+ 1.0 (exp (neg t))))
11.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
14.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
207.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

simplify106.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	963	2920
1	4334	2665
2	5001	2665

prune297.0ms

Filtered

86 candidates to 171 candidates (-98.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	171	3	174

Merged error: 0.5b

Counts

174 → 3

regimes983.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	11
1	22	11

end0.0ms

analyze15.3s

Algorithm

sampling

Space saved by range analysis: 75.048792%

Space saved by search: 75.048792%

Guaranteed chance to sample good point: 6.25%

sample18.1s

Algorithm

intervals

Results

11.5s	1710×	body	5120	exit
2.7s	975×	body	1280	overflowed
1.5s	7353×	body	80	overflowed
1.1s	802×	body	640	overflowed
367.0ms	464×	body	320	overflowed
287.0ms	12350×	pre	80	true
101.0ms	815×	body	80	valid
86.0ms	199×	body	160	overflowed
17.0ms	8×	body	1280	valid
9.0ms	2×	body	2560	valid
9.0ms	8×	body	640	valid
8.0ms	1×	body	5120	valid
3.0ms	8×	body	160	valid
3.0ms	4×	body	320	valid
1.0ms	1×	body	640	invalid

Details

analyze16.4s

sample5.4s

simplify24.0ms

prune6.0ms

localize21.0ms

rewrite81.0ms

series218.0ms

simplify101.0ms

prune321.0ms

localize7.0ms

rewrite10.0ms

series7.0ms

simplify54.0ms

prune50.0ms

localize11.0ms

rewrite29.0ms

series19.0ms

simplify47.0ms

prune146.0ms

localize27.0ms

rewrite64.0ms

series238.0ms

simplify106.0ms

prune297.0ms

regimes983.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze15.3s

sample18.1s

Profiling