Details

sample45.9s

Algorithm

intervals

Results

45.4s	3420×	body	10240	exit
129.0ms	3676×	pre	80	true
30.0ms	248×	body	80	valid
6.0ms	1×	body	2560	valid
5.0ms	2×	body	1280	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	320	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	53	25
1	147	25
2	850	25
3	5001	25

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 6.5b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.5b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) 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)))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

4026×	`times-frac`
3727×	`add-sqr-sqrt`
3436×	`unpow-prod-down`
2200×	`associate-l`
2036×	`*-un-lft-identity`
1222×	`add-cube-cbrt`
1200×	`unswap-sqr`
1000×	`associate-r`
902×	`sqr-pow`
556×	`add-exp-log`
312×	`prod-exp`
306×	`distribute-lft-out`
264×	`pow-exp`
249×	`div-exp`
204×	`associate-/r/`
202×	`difference-of-squares`
184×	`pow-to-exp`
103×	`div-inv`
102×	`flip3-+` `flip-+`
101×	`distribute-lft-out--`
100×	`*-commutative`
49×	`associate-/r` `associate-/l`
16×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `add-log-exp`
4×	`cbrt-undiv` `cbrt-unprod`
2×	`pow-pow`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `flip--`

Counts

4 → 2763

Calls

4 calls:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
12.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
6.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
115.0ms	(/ (* (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)))

series891.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
80.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
80.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
672.0ms	(/ (* (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)))

simplify996.0ms

Algorithm

egg-herbie

Counts

2775 → 2775

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5001	117680

prune11.8s

Filtered

2775 candidates to 1867 candidates (32.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	2772	3	2775
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	2773	3	2776

Merged error: 0.6b

Counts

2776 → 3

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
0.7b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
1.5b	(log (/ 1.0 (+ 1.0 (exp (- t)))))
9.4b	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

305×	`*-un-lft-identity`
240×	`associate-l`
188×	`distribute-lft-out`
127×	`pow1`
123×	`log-pow`
101×	`distribute-lft-out--`
42×	`log-prod`
32×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `times-frac`
22×	`log-div`
16×	`add-log-exp`
11×	`add-exp-log`
8×	`associate-/r` `associate-/l`
6×	`flip3-+` `flip-+`
5×	`rem-log-exp`
4×	`diff-log` `log-rec` `clear-num` `sum-log` `associate-/r/` `frac-sub` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`+-commutative` `flip3--` `frac-2neg` `div-exp` `associate--l+` `flip--` `div-inv` `associate--r+`
1×	`sub-neg`

Counts

4 → 221

Calls

4 calls:

10.0ms	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
6.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
7.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
47.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

series644.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
77.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
77.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
387.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

simplify104.0ms

Algorithm

egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	835	5361
1	2763	5093
2	5001	5092

prune590.0ms

Filtered

233 candidates to 100 candidates (57.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	230	3	233
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	233	3	236

Merged error: 0.1b

Counts

236 → 3

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.3b	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
0.7b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
9.7b	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (- (+ (log 0.5) (* 0.5 t)) (* 0.03125 (/ (pow t 2) (pow 0.5 2)))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

1539×	`*-un-lft-identity`
1284×	`associate-l`
937×	`distribute-lft-out`
672×	`distribute-lft-out--`
468×	`pow1`
464×	`log-pow`
27×	`add-sqr-sqrt`
24×	`log-prod`
18×	`add-log-exp`
15×	`add-cube-cbrt`
14×	`times-frac`
12×	`log-div`
8×	`add-exp-log`
5×	`flip3-+` `diff-log` `flip-+` `difference-of-squares`
4×	`associate-/r` `sum-log` `frac-sub` `add-cbrt-cube` `associate-/l`
3×	`flip3--` `rem-log-exp` `flip--`
2×	`+-commutative` `sub-neg` `log-rec` `associate--l+` `clear-num` `associate-/r/` `associate--r+`
1×	`frac-2neg` `div-exp` `div-inv`

Counts

4 → 466

Calls

4 calls:

10.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
9.0ms	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
7.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
140.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (- (+ (log 0.5) (* 0.5 t)) (* 0.03125 (/ (pow t 2) (pow 0.5 2)))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

series719.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
103.0ms	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
78.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
483.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (- (+ (log 0.5) (* 0.5 t)) (* 0.03125 (/ (pow t 2) (pow 0.5 2)))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

simplify174.0ms

Algorithm

egg-herbie

Counts

478 → 478

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	767	14216
1	2561	13688
2	5003	13687

prune636.0ms

Filtered

478 candidates to 80 candidates (83.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	478	0	478
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	478	3	481

Merged error: 0.1b

Counts

481 → 3

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.7b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
1.5b	(log (/ 1.0 (+ 1.0 (exp (- t)))))
9.4b	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (- (log 0.5) (+ (* 0.5 t) (* 0.03125 (/ (pow t 2) (pow 0.5 2))))) c_n)))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

1525×	`*-un-lft-identity`
1254×	`associate-l`
941×	`distribute-lft-out`
671×	`distribute-lft-out--`
498×	`pow1`
494×	`log-pow`
36×	`log-prod`
31×	`add-sqr-sqrt`
25×	`times-frac`
24×	`add-cube-cbrt`
20×	`log-div`
18×	`add-log-exp`
10×	`add-exp-log`
8×	`associate-/r` `associate-/l`
6×	`flip3-+` `flip-+`
5×	`diff-log`
4×	`rem-log-exp` `log-rec` `clear-num` `sum-log` `associate-/r/` `frac-sub` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `div-exp` `associate--l+` `flip--` `div-inv` `associate--r+`

Counts

4 → 489

Calls

4 calls:

13.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
6.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
6.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
132.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (- (log 0.5) (+ (* 0.5 t) (* 0.03125 (/ (pow t 2) (pow 0.5 2))))) c_n)))

series663.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
76.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
77.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
454.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (- (log 0.5) (+ (* 0.5 t) (* 0.03125 (/ (pow t 2) (pow 0.5 2))))) c_n)))

simplify174.0ms

Algorithm

egg-herbie

Counts

501 → 501

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	822	13949
1	2756	13416
2	5001	13415

prune745.0ms

Filtered

501 candidates to 98 candidates (80.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	501	0	501
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	501	3	504

Merged error: 0.1b

Counts

504 → 3

regimes212.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	33
1	48	33

end0.0ms

sample3.5m

Algorithm

intervals

Results

3.5m	16352×	body	10240	exit
602.0ms	17544×	pre	80	true
120.0ms	1147×	body	80	valid
16.0ms	8×	body	1280	valid
14.0ms	4×	body	2560	valid
12.0ms	2×	body	5120	valid
6.0ms	23×	body	160	valid
3.0ms	3×	body	640	valid
2.0ms	5×	body	320	valid