Details

sample22.0s

Algorithm

intervals

sampling

Space saved by range analysis: 75%

Space saved by search: 86.444092%

Guaranteed chance to sample good point: 11.526339%

Results

3.5s	461×	body	5120	exit
739.0ms	266×	body	1280	overflowed
347.0ms	247×	body	640	overflowed
112.0ms	136×	body	320	overflowed
101.0ms	491×	body	80	overflowed
49.0ms	1916×	pre	80	true
32.0ms	245×	body	80	valid
27.0ms	59×	body	160	overflowed
8.0ms	4×	body	1280	valid
4.0ms	1×	body	2560	valid
3.0ms	2×	body	640	valid
1.0ms	4×	body	160	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

prune5.0ms

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: 6.0b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg 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)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))
2.2b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

556×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
249×	`div-exp`
184×	`pow-to-exp`
36×	`unpow-prod-down` `*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
16×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `distribute-lft-out` `add-log-exp`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod`
3×	`div-inv`
2×	`pow-pow` `flip3-+` `flip-+` `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 → 267

Calls

4 calls:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
37.0ms	(/ (* (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)))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)

series210.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
14.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
175.0ms	(/ (* (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)))
14.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)

simplify105.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	982	5948
1	3157	5704
2	5002	5704

prune286.0ms

Filtered

79 candidates to 279 candidates (-253.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	274	5	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	275	5	280

Merged error: 0.1b

Counts

280 → 5

localize8.0ms

Local error

Found 2 expressions with local error:

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

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_p))
4.0ms	(* 0.5 (* s c_n))

series7.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify56.0ms

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

prune52.0ms

Filtered

22 candidates to 42 candidates (-90.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	42	5	47

Merged error: 0.1b

Counts

47 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
0.4b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
1.0b	(/ (* (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)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-exp-log`
87×	`prod-exp`
65×	`div-exp`
55×	`pow-exp`
42×	`pow-to-exp`
23×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`unpow-prod-down`
16×	`add-cbrt-cube`
15×	`times-frac`
13×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `difference-of-squares`
3×	`pow-unpow` `distribute-lft-out`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-*l/` `flip--` `flip-+` `div-inv` `distribute-lft-out--`
1×	`pow-pow` `frac-2neg` `clear-num` `associate-/r` `associate-/l` `sqr-pow`

Counts

4 → 134

Calls

4 calls:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
6.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
34.0ms	(/ (* (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)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
14.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
201.0ms	(/ (* (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)))

simplify97.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	882	2847
1	3787	2592
2	5001	2592

prune257.0ms

Filtered

69 candidates to 146 candidates (-111.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	146	5	151

Merged error: 0.1b

Counts

151 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
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)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- (+ (* 0.020833333333333336 (pow t 3)) 0.5) (* 0.25 t)) c_n)))
2.2b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

556×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
249×	`div-exp`
184×	`pow-to-exp`
36×	`unpow-prod-down` `*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
16×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `distribute-lft-out` `add-log-exp`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod`
3×	`div-inv`
2×	`pow-pow` `flip3-+` `flip-+` `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 → 267

Calls

4 calls:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
6.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
35.0ms	(/ (* (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 (- (+ (* 0.020833333333333336 (pow t 3)) 0.5) (* 0.25 t)) c_n)))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)

series233.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
14.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
192.0ms	(/ (* (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 (- (+ (* 0.020833333333333336 (pow t 3)) 0.5) (* 0.25 t)) c_n)))
20.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)

simplify111.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	1011	5949
1	3279	5709
2	5002	5709

prune294.0ms

Filtered

80 candidates to 279 candidates (-248.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	279	0	279
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	279	5	284

Merged error: 0.1b

Counts

284 → 5

regimes1.1s

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	32
1	52	32

end0.0ms

sample2.1min

Algorithm

intervals

sampling

Space saved by range analysis: 75%

Space saved by search: 86.444092%

Guaranteed chance to sample good point: 11.526339%

Results

1.3min	11259×	body	5120	exit
15.1s	6074×	body	1280	overflowed
7.3s	5528×	body	640	overflowed
2.4s	2913×	body	320	overflowed
2.2s	11626×	body	80	overflowed
1.1s	44508×	pre	80	true
686.0ms	5612×	body	80	valid
556.0ms	1313×	body	160	overflowed
118.0ms	52×	body	1280	valid
43.0ms	38×	body	640	valid
38.0ms	5×	body	5120	valid
24.0ms	7×	body	2560	valid
19.0ms	57×	body	160	valid
11.0ms	17×	body	320	valid
1.0ms	1×	body	640	invalid
1.0ms	5×	body	80	invalid

Details

sample22.0s

simplify24.0ms

prune5.0ms

localize23.0ms

rewrite282.0ms

series210.0ms

simplify105.0ms

prune286.0ms

localize8.0ms

rewrite10.0ms

series7.0ms

simplify56.0ms

prune52.0ms

localize28.0ms

rewrite67.0ms

series229.0ms

simplify97.0ms

prune257.0ms

localize26.0ms

rewrite74.0ms

series233.0ms

simplify111.0ms

prune294.0ms

regimes1.1s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample2.1min

Profiling