Details

analyze4.7s

Algorithm

sampling

Space saved by range analysis: 0.438596%

Space saved by search: 0.438596%

Guaranteed chance to sample good point: 40.155029%

sample51.0ms

Algorithm

intervals

Results

29.0ms

256×

body

valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	17
1	120	17
2	311	17
3	677	17
4	1422	17
5	2726	17
6	5001	17

prune7.0ms

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: 0.0b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT)
0.0b	(+ 1.0 (exp (/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT)))
0.0b	(/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)
0.0b	(exp (/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

277×	`*-un-lft-identity`
135×	`times-frac`
105×	`add-sqr-sqrt`
84×	`distribute-lft-out--`
77×	`add-cube-cbrt`
61×	`distribute-rgt-neg-in`
58×	`exp-prod`
49×	`distribute-lft-neg-in` `distribute-lft-out`
27×	`associate-/l*`
14×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `add-log-exp`
6×	`associate-/r*`
5×	`div-sub`
4×	`pow1` `associate-/l/`
3×	`neg-sub0` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `distribute-frac-neg` `div-exp` `clear-num` `flip-+` `distribute-neg-frac`
1×	`+-commutative` `exp-neg` `associate-+r-` `flip3--` `exp-diff` `unsub-neg` `sum-log` `flip--` `rem-exp-log`

Counts

4 → 227

Calls

4 calls:

15.0ms	(/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT)
13.0ms	(+ 1.0 (exp (/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT)))
16.0ms	(/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)
15.0ms	(exp (/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT))

series80.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT)
24.0ms	(+ 1.0 (exp (/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT)))
19.0ms	(/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)
22.0ms	(exp (/ (neg (- (- (- Ec Vef) EDonor) mu)) KbT))

simplify57.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	559	1864
1	1972	1780
2	5001	1768

prune213.0ms

Filtered

140 candidates to 239 candidates (-70.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	239	1	240

Merged error: 0.0b

Counts

240 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)))
0.0b	(/ 1 (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT)))
0.0b	(/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)
0.0b	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

176×	`*-un-lft-identity`
78×	`times-frac`
60×	`add-sqr-sqrt`
50×	`exp-prod`
49×	`distribute-lft-out`
48×	`add-cube-cbrt`
36×	`distribute-lft-out--`
26×	`pow-flip`
12×	`distribute-rgt-neg-in` `associate-/l*`
8×	`add-cbrt-cube`
7×	`add-exp-log` `add-log-exp`
6×	`associate-/r*` `difference-of-squares`
5×	`pow1` `div-sub`
4×	`div-inv`
3×	`div-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `exp-diff` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-sub0` `associate-+r-` `rec-exp` `1-exp` `unsub-neg` `sum-log` `associate-/r/` `rem-exp-log` `inv-pow`

Counts

4 → 159

Calls

4 calls:

12.0ms	(+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)))
15.0ms	(/ 1 (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT)))
13.0ms	(/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)
11.0ms	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))

series96.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)))
32.0ms	(/ 1 (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT)))
15.0ms	(/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)
25.0ms	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))

simplify48.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	485	1298
1	1696	1189
2	5001	1165

prune159.0ms

Filtered

99 candidates to 171 candidates (-72.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	170	2	172

Merged error: 0.0b

Counts

172 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))) (cbrt (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))))
0.0b	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))
0.0b	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))
0.0b	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

126×	`*-un-lft-identity`
75×	`exp-prod`
71×	`add-sqr-sqrt`
63×	`times-frac`
54×	`distribute-lft-out--`
45×	`add-cube-cbrt`
16×	`cbrt-prod`
11×	`pow1`
9×	`difference-of-squares`
7×	`exp-diff` `div-sub` `add-log-exp`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`cbrt-div` `add-cbrt-cube` `unswap-sqr`
3×	`div-inv` `rem-exp-log`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 145

Calls

4 calls:

26.0ms	(* (cbrt (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))) (cbrt (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))))
12.0ms	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))
12.0ms	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))
12.0ms	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))

series141.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (cbrt (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))) (cbrt (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))))
27.0ms	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))
23.0ms	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))
24.0ms	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))

simplify89.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	226	1303
1	819	1194
2	3376	1099
3	5001	1085

prune173.0ms

Filtered

101 candidates to 157 candidates (-55.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	158	1	159

Merged error: 0.0b

Counts

159 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT)))
0.0b	(/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)
0.0b	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))
0.0b	(pow (exp 2) (/ (- (- (- Ec Vef) EDonor) mu) KbT))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

170×	`*-un-lft-identity`
69×	`times-frac`
55×	`add-sqr-sqrt`
48×	`distribute-lft-out`
43×	`add-cube-cbrt`
36×	`distribute-lft-out--`
28×	`exp-prod`
25×	`pow-unpow`
12×	`distribute-rgt-neg-in`
9×	`associate-/l*`
6×	`add-exp-log` `div-sub` `add-cbrt-cube` `difference-of-squares`
5×	`pow1` `add-log-exp`
4×	`unpow-prod-down` `pow-pow`
3×	`cbrt-prod` `associate-/r*` `div-inv`
2×	`exp-diff` `associate-/l/`
1×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `associate-+r-` `cbrt-div` `frac-2neg` `flip3-+` `pow1/3` `div-exp` `unsub-neg` `pow-exp` `clear-num` `flip-+` `exp-lft-sqr` `rem-exp-log` `pow-sub` `sqr-pow`

Counts

4 → 146

Calls

4 calls:

12.0ms	(cbrt (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT)))
13.0ms	(/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)
13.0ms	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))
12.0ms	(pow (exp 2) (/ (- (- (- Ec Vef) EDonor) mu) KbT))

series102.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(cbrt (exp (/ (- (- (- Ec Vef) EDonor) mu) KbT)))
15.0ms	(/ (+ (+ (+ Ev Vef) EAccept) (neg mu)) KbT)
25.0ms	(exp (/ (- (- (- Ec Vef) EDonor) mu) KbT))
28.0ms	(pow (exp 2) (/ (- (- (- Ec Vef) EDonor) mu) KbT))

simplify48.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	483	1165
1	1853	1074
2	5002	1060

prune230.0ms

Filtered

97 candidates to 158 candidates (-62.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	1	159

Merged error: 0.0b

Counts

159 → 1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	29
1	46	29

end0.0ms

analyze4.6s

Algorithm

sampling

Space saved by range analysis: 0.438596%

Space saved by search: 0.438596%

Guaranteed chance to sample good point: 40.155029%

sample1.4s

Algorithm

intervals

Results

995.0ms	7999×	body	80	valid
1.0ms	1×	body	2560	valid

Details

analyze4.7s

sample51.0ms

simplify42.0ms

prune7.0ms

localize23.0ms

rewrite71.0ms

series80.0ms

simplify57.0ms

prune213.0ms

localize25.0ms

rewrite59.0ms

series96.0ms

simplify48.0ms

prune159.0ms

localize29.0ms

rewrite69.0ms

series141.0ms

simplify89.0ms

prune173.0ms

localize32.0ms

rewrite57.0ms

series102.0ms

simplify48.0ms

prune230.0ms

simplify2.0ms

end0.0ms

analyze4.6s

sample1.4s

Profiling