Details

sample0.0hr

Algorithm

intervals

Results

0.0hr	247×	body	5120	exit
0.0hr	3197×	body	80	overflowed
0.0hr	3700×	pre	80	true
0.0hr	249×	body	80	valid
0.0hr	1×	body	5120	valid
0.0hr	1×	body	1280	valid
0.0hr	1×	body	640	valid
0.0hr	4×	body	160	valid

simplify0.0hr

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0hr)

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

prune0.0hr

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

localize0.0hr

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)))

rewrite0.0hr

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:

0.0hr	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
0.0hr	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
0.0hr	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
0.0hr	(/ (* (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)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
0.0hr	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
0.0hr	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
0.0hr	(/ (* (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)))

simplify0.0hr

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (0.0hr)

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

prune0.0hr

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

localize0.0hr

Local error

Found 2 expressions with local error:

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

rewrite0.0hr

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:

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

series0.0hr

Counts

2 → 6

Calls

2 calls:

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

simplify0.0hr

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 1 (0.0hr)

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

prune0.0hr

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

localize0.0hr

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)))

rewrite0.0hr

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:

0.0hr	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
0.0hr	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
0.0hr	(/ (* (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)))
0.0hr	(/ (* (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)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
0.0hr	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
0.0hr	(/ (* (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)))
0.0hr	(/ (* (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)))

simplify0.0hr

Algorithm

egg-herbie

Counts

450 → 450

Iterations

Useful iterations: 1 (0.0hr)

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

prune0.0hr

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

localize0.0hr

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)))

rewrite0.0hr

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:

0.0hr	(cbrt c_p)
0.0hr	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
0.0hr	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) (* (cbrt c_p) (cbrt c_p)))
0.0hr	(/ (* (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)))

series0.0hr

Counts

4 → 12

Calls

4 calls:

0.0hr	(cbrt c_p)
0.0hr	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
0.0hr	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) (* (cbrt c_p) (cbrt c_p)))
0.0hr	(/ (* (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)))

simplify0.0hr

Algorithm

egg-herbie

Counts

351 → 351

Iterations

Useful iterations: 2 (0.0hr)

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

prune0.0hr

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

regimes0.0hr

bsearch0.0hr

simplify0.0hr

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0hr)

Iter	Nodes	Cost
0	52	32
1	52	32

end0.0hr

sample0.0hr

Algorithm

intervals

Results

0.0hr	1471×	body	5120	exit
0.0hr	18459×	body	80	overflowed
0.0hr	21540×	pre	80	true
0.0hr	1553×	body	80	valid
0.0hr	5×	body	5120	valid
0.0hr	11×	body	1280	valid
0.0hr	3×	body	2560	valid
0.0hr	6×	body	640	valid
0.0hr	22×	body	160	valid
0.0hr	6×	body	320	valid
0.0hr	2×	body	320	overflowed
0.0hr	1×	body	640	overflowed
0.0hr	1×	body	160	overflowed

Details

sample0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

localize0.0hr

rewrite0.0hr

series0.0hr

simplify0.0hr

prune0.0hr

regimes0.0hr

bsearch0.0hr

simplify0.0hr

end0.0hr

sample0.0hr

Profiling