Details

sample2.9s

Algorithm

intervals

Results

1.9s	247×	body	5120	exit
763.0ms	3197×	body	80	overflowed
77.0ms	3700×	pre	80	true
31.0ms	249×	body	80	valid
8.0ms	1×	body	5120	valid
2.0ms	1×	body	1280	valid
2.0ms	1×	body	640	valid
1.0ms	4×	body	160	valid

simplify25.0ms

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

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

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
1.0b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
1.0b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
3.9b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg 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:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
39.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
14.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
180.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

simplify114.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	982	5948
1	3157	5704
2	5002	5704

prune296.0ms

Filtered

279 candidates to 79 candidates (71.7%)

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: 0.8b

Counts

280 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.0b	(* 0.5 (* s c_p))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2×	`associate-r` `*-commutative` `add-log-exp`

Counts

2 → 36

Calls

2 calls:

4.0ms	(* 0.5 (* s c_n))
4.0ms	(* 0.5 (* s c_p))

series7.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(* 0.5 (* s c_n))
3.0ms	(* 0.5 (* s c_p))

simplify57.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	153	142
1	595	112
2	2373	112
3	5002	112

prune54.0ms

Filtered

42 candidates to 22 candidates (47.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	41	5	46

Merged error: 0.8b

Counts

46 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
1.0b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
3.9b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))
3.9b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

1102×	`add-exp-log`
624×	`prod-exp`
524×	`pow-exp`
496×	`div-exp`
366×	`pow-to-exp`
36×	`unpow-prod-down`
34×	`*-un-lft-identity`
28×	`add-cbrt-cube`
26×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`cbrt-undiv` `cbrt-unprod`
6×	`pow1` `pow-unpow` `distribute-lft-out`
4×	`associate-/r/` `div-inv` `add-log-exp`
2×	`pow-pow` `frac-2neg` `flip3-+` `clear-num` `associate-/r` `flip-+` `associate-/l` `sqr-pow`

Counts

4 → 438

Calls

4 calls:

7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
42.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))
38.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
14.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
177.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))
182.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

simplify141.0ms

Algorithm

egg-herbie

Counts

450 → 450

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	770	10888
1	2515	10442
2	5001	10442

prune592.0ms

Filtered

450 candidates to 80 candidates (82.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	449	1	450
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	450	5	455

Merged error: 0.8b

Counts

455 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt c_p)
1.0b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
1.1b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) (* (cbrt c_p) (cbrt c_p)))
3.9b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (pow (/ 1.0 (+ 1.0 (exp (neg t)))) (* (cbrt c_p) (cbrt c_p))) (cbrt c_p)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

773×	`add-exp-log`
506×	`pow-exp`
462×	`prod-exp`
345×	`div-exp`
291×	`pow-to-exp`
36×	`unpow-prod-down`
34×	`*-un-lft-identity`
25×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`add-cbrt-cube`
6×	`pow1` `distribute-lft-out`
4×	`cbrt-undiv` `pow-unpow` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`cbrt-prod` `div-inv`
2×	`pow-pow` `flip3-+` `flip-+` `sqr-pow`
1×	`frac-2neg` `pow1/3` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 339

Calls

4 calls:

1.0ms	(cbrt c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) (* (cbrt c_p) (cbrt c_p)))
42.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (pow (/ 1.0 (+ 1.0 (exp (neg t)))) (* (cbrt c_p) (cbrt c_p))) (cbrt c_p)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt c_p)
14.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
41.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) (* (cbrt c_p) (cbrt c_p)))
218.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (pow (/ 1.0 (+ 1.0 (exp (neg t)))) (* (cbrt c_p) (cbrt c_p))) (cbrt c_p)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

simplify138.0ms

Algorithm

egg-herbie

Counts

351 → 351

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	1182	9440
1	3675	9157
2	5001	8649

prune303.0ms

Filtered

351 candidates to 77 candidates (78.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	351	0	351
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	351	5	356

Merged error: 0.8b

Counts

356 → 5

regimes1.0s

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	32
1	52	32

end0.0ms

sample15.2s

Algorithm

intervals

Results

10.2s	1471×	body	5120	exit
3.3s	18459×	body	80	overflowed
440.0ms	21540×	pre	80	true
191.0ms	1553×	body	80	valid
34.0ms	5×	body	5120	valid
27.0ms	11×	body	1280	valid
9.0ms	3×	body	2560	valid
8.0ms	6×	body	640	valid
7.0ms	22×	body	160	valid
3.0ms	6×	body	320	valid
2.0ms	2×	body	320	overflowed
1.0ms	1×	body	640	overflowed
1.0ms	1×	body	160	overflowed

Details

sample2.9s

simplify25.0ms

prune5.0ms

localize21.0ms

rewrite84.0ms

series216.0ms

simplify114.0ms

prune296.0ms

localize8.0ms

rewrite10.0ms

series7.0ms

simplify57.0ms

prune54.0ms

localize27.0ms

rewrite127.0ms

series389.0ms

simplify141.0ms

prune592.0ms

localize29.0ms

rewrite85.0ms

series295.0ms

simplify138.0ms

prune303.0ms

regimes1.0s

bsearch1.0ms

simplify1.0ms

end0.0ms

sample15.2s

Profiling