Details

sample40.3s

Algorithm

intervals

Results

40.0s	3106×	body	10240	exit
80.0ms	3362×	pre	80	true
23.0ms	247×	body	80	valid
3.0ms	4×	body	640	valid
1.0ms	5×	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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 5.8b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.2b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.7b	(/ (* (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)))

rewrite84.0ms

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:

12.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
38.0ms	(/ (* (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)))

series753.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
65.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
572.0ms	(/ (* (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)))

simplify104.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	976	5948
1	3142	5704
2	5001	5704

prune362.0ms

Filtered

279 candidates to 79 candidates (28.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	277	2	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	278	2	280

Merged error: 0.7b

Counts

280 → 2

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 0.5 (* s c_n))

rewrite5.0ms

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×	`associate-r` `*-commutative` `add-log-exp`

Counts

1 → 18

Calls

1 calls:

4.0ms

(* 0.5 (* s c_n))

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(* 0.5 (* s c_n))

simplify73.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	86	71
1	318	56
2	1232	56
3	3436	56
4	5002	56

prune26.0ms

Filtered

21 candidates to 11 candidates (52.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	21	2	23

Merged error: 0.7b

Counts

23 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.1b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.2b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-exp-log`
88×	`prod-exp`
65×	`div-exp`
55×	`pow-exp`
42×	`pow-to-exp`
23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
18×	`unpow-prod-down` `add-cbrt-cube`
15×	`add-cube-cbrt`
14×	`times-frac`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/`
3×	`pow-unpow` `flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
2×	`associate-r/` `associate-l/` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `flip--` `associate-/l*` `distribute-lft-out--` `unswap-sqr` `sqr-pow`

Counts

4 → 141

Calls

4 calls:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
5.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
38.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series899.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
97.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
688.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify107.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	923	2823
1	4047	2572
2	5002	2572

prune378.0ms

Filtered

153 candidates to 72 candidates (47.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	152	3	155

Merged error: 0.6b

Counts

155 → 3

localize32.0ms

Local error

Found 4 expressions with local error:

1.5b	(sqrt (/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))))
1.5b	(sqrt (/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))))
1.7b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
1.7b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

328×	`add-exp-log`
174×	`prod-exp`
128×	`div-exp`
106×	`pow-exp`
82×	`pow-to-exp`
28×	`add-cbrt-cube`
14×	`sqrt-prod`
8×	`cbrt-undiv` `add-sqr-sqrt` `associate-*l/` `associate-/r/` `cbrt-unprod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`flip3-+` `times-frac` `flip-+` `div-inv` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 178

Calls

4 calls:

33.0ms	(sqrt (/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))))
36.0ms	(sqrt (/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))))
36.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
39.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series3.0s

Counts

4 → 12

Calls

4 calls:

789.0ms	(sqrt (/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))))
778.0ms	(sqrt (/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))))
703.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
707.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify96.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	619	5454
1	2912	4958
2	5001	4958

prune435.0ms

Filtered

190 candidates to 68 candidates (35.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	190	3	193

Merged error: 0.6b

Counts

193 → 3

regimes198.0ms

bsearch3.9s

Steps

Iters	Range		Point
6	-3.4701307512392483e-168	-2.3395287029331725e-169	-9.176994996289448e-169

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	61
1	58	61

end0.0ms

sample1.7m

Algorithm

intervals

Results

1.7m	8060×	body	10240	exit
168.0ms	8704×	pre	80	true
57.0ms	628×	body	80	valid
17.0ms	1×	body	5120	valid
4.0ms	2×	body	1280	valid
3.0ms	4×	body	640	valid
3.0ms	1×	body	2560	valid
2.0ms	8×	body	160	valid

Details

sample40.3s

simplify24.0ms

prune4.0ms

localize24.0ms

rewrite84.0ms

series753.0ms

simplify104.0ms

prune362.0ms

localize8.0ms

rewrite5.0ms

series19.0ms

simplify73.0ms

prune26.0ms

localize27.0ms

rewrite65.0ms

series899.0ms

simplify107.0ms

prune378.0ms

localize32.0ms

rewrite154.0ms

series3.0s

simplify96.0ms

prune435.0ms

regimes198.0ms

bsearch3.9s

simplify2.0ms

end0.0ms

sample1.7m

Profiling