Details

sample40.7s

Algorithm

intervals

Results

40.5s	3221×	body	10240	exit
76.0ms	3478×	pre	80	true
24.0ms	250×	body	80	valid
1.0ms	1×	body	1280	valid
1.0ms	1×	body	640	valid
1.0ms	4×	body	160	valid
0.0ms	1×	body	320	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: 5.5b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.2b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.4b	(/ (* (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)))

rewrite87.0ms

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:

10.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
8.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
44.0ms	(/ (* (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)))

series936.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
754.0ms	(/ (* (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 (18.0ms)

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

prune379.0ms

Filtered

279 candidates to 79 candidates (28.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	275	4	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	276	4	280

Merged error: 0.3b

Counts

280 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.0b	(* 0.5 (* s c_p))
0.0b	(- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2×	`diff-log` `associate-r` `*-commutative`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 50

Calls

3 calls:

5.0ms	(* 0.5 (* s c_n))
5.0ms	(* 0.5 (* s c_p))
8.0ms	(- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))

series93.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(* 0.5 (* s c_n))
18.0ms	(* 0.5 (* s c_p))
56.0ms	(- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))

simplify138.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	228	292
1	900	254
2	4892	245
3	5001	245

prune89.0ms

Filtered

59 candidates to 34 candidates (57.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	59	4	63

Merged error: 0.3b

Counts

63 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
28.4b	(cbrt (* 0.5 (* s c_n)))
28.4b	(cbrt (* 0.5 (* s c_n)))
28.4b	(cbrt (* 0.5 (* s c_n)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

6.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
4.0ms	(cbrt (* 0.5 (* s c_n)))
4.0ms	(cbrt (* 0.5 (* s c_n)))
4.0ms	(cbrt (* 0.5 (* s c_n)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
89.0ms	(cbrt (* 0.5 (* s c_n)))
89.0ms	(cbrt (* 0.5 (* s c_n)))
89.0ms	(cbrt (* 0.5 (* s c_n)))

simplify92.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	205	441
1	703	390
2	3412	330
3	5001	323

prune179.0ms

Filtered

70 candidates to 56 candidates (80.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	69	5	74

Merged error: 0.3b

Counts

74 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.4b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.5b	(/ (* (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)))

rewrite66.0ms

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:

5.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
10.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
37.0ms	(/ (* (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)))

series922.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
46.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
709.0ms	(/ (* (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 (20.0ms)

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

prune372.0ms

Filtered

153 candidates to 72 candidates (47.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	153	5	158

Merged error: 0.3b

Counts

158 → 5

regimes455.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	15
1	22	15

end0.0ms

sample9.2m

Algorithm

intervals

Results

9.2m	44989×	body	10240	exit
946.0ms	48492×	pre	80	true
306.0ms	3390×	body	80	valid
50.0ms	7×	body	5120	valid
40.0ms	24×	body	1280	valid
20.0ms	7×	body	2560	valid
14.0ms	16×	body	640	valid
11.0ms	41×	body	160	valid
7.0ms	17×	body	320	valid