Details

sample39.5s

Algorithm

intervals

Results

39.2s	3269×	body	10240	exit
78.0ms	3525×	pre	80	true
22.0ms	248×	body	80	valid
3.0ms	4×	body	640	valid
2.0ms	1×	body	1280	valid
1.0ms	2×	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

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ 1.0 (exp (- s))))
0.2b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.7b	(/ (* (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)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

558×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
250×	`div-exp`
184×	`pow-to-exp`
51×	`*-un-lft-identity`
37×	`times-frac`
36×	`unpow-prod-down`
31×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-cbrt-cube`
10×	`distribute-lft-out`
6×	`pow1` `pow-unpow` `associate-/r/`
5×	`cbrt-undiv` `associate-/r*`
4×	`cbrt-unprod` `div-inv` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

4 → 285

Calls

4 calls:

5.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
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:

30.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
65.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
587.0ms	(/ (* (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)))

simplify100.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	966	6045
1	3251	5797
2	5003	5797

prune521.0ms

Filtered

297 candidates to 91 candidates (30.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	295	2	297
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	295	3	298

Merged error: 0.7b

Counts

298 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

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

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:

4.0ms	(* 0.5 (* s c_n))
8.0ms	(- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))
5.0ms	(* 0.5 (* s c_p))

series93.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify140.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (28.0ms)

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

prune103.0ms

Filtered

59 candidates to 34 candidates (57.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	57	5	62

Merged error: 0.7b

Counts

62 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))) (cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))) (cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))))
0.3b	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))
0.3b	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))
0.3b	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
23×	`pow1`
14×	`associate-*l/`
13×	`cbrt-prod`
12×	`pow1/3`
11×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `pow-prod-up`
8×	`associate-*r/`
6×	`pow-plus` `associate-r`
5×	`pow-prod-down` `add-cbrt-cube`
4×	`add-log-exp`
3×	`prod-exp` `pow-sqr` `cbrt-unprod`
2×	`pow2` `unswap-sqr`
1×	`associate-l` `pow3` `*-commutative`

Counts

4 → 100

Calls

4 calls:

26.0ms	(* (* (cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))) (cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))) (cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))))
7.0ms	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))
7.0ms	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))
10.0ms	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))

series1.2s

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* (cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))) (cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))) (cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))))
387.0ms	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))
383.0ms	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))
388.0ms	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	345	2764
1	1188	2437
2	5002	2299

prune299.0ms

Filtered

112 candidates to 71 candidates (63.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	1	1	2
Picked	1	0	1
Done	1	1	2
Total	112	5	117

Merged error: 0.7b

Counts

117 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.16666666666666666 (* s c_p))
0.1b	(* 0.16666666666666666 (* s c_n))
0.3b	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))
0.3b	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`cbrt-div` `add-log-exp`
2×	`flip3--` `pow1/3` `associate-r` `*-commutative` `flip--`

Counts

4 → 62

Calls

4 calls:

5.0ms	(* 0.16666666666666666 (* s c_p))
4.0ms	(* 0.16666666666666666 (* s c_n))
10.0ms	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))
7.0ms	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))

series814.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* 0.16666666666666666 (* s c_p))
18.0ms	(* 0.16666666666666666 (* s c_n))
388.0ms	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))
384.0ms	(cbrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	308	600
1	1134	540
2	5001	536

prune217.0ms

Filtered

74 candidates to 52 candidates (70.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	74	5	79

Merged error: 0.7b

Counts

79 → 5

regimes569.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	47
1	65	47

end0.0ms

sample9.3m

Algorithm

intervals

Results

9.2m	45233×	body	10240	exit
1.0s	48801×	pre	80	true
304.0ms	3451×	body	80	valid
61.0ms	8×	body	5120	valid
47.0ms	25×	body	1280	valid
28.0ms	11×	body	2560	valid
24.0ms	30×	body	640	valid
9.0ms	36×	body	160	valid
2.0ms	6×	body	320	valid