Details

analyze4.4s (13%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	25%	75%	2
0%	25%	75%	3
0%	25%	75%	4
0%	25%	75%	5
0%	25%	75%	6
0%	25%	75%	7
0%	25%	75%	8
1.6%	23.4%	75%	9
1.6%	23.4%	75%	10
1.6%	23.4%	75%	11
1.6%	23.4%	75%	12
1.6%	23.4%	75%	13
1.6%	23.4%	75%	14

sample5.9s (17.2%)

Algorithm

1×

intervals

Results

3.8s	520×	body	5120	exit
713.0ms	263×	body	1280	overflowed
495.0ms	2315×	body	80	overflowed
379.0ms	269×	body	640	overflowed
106.0ms	127×	body	320	overflowed
103.0ms	3819×	pre	80	true
33.0ms	245×	body	80	valid
32.0ms	68×	body	160	overflowed
10.0ms	4×	body	1280	valid
4.0ms	3×	body	640	valid
1.0ms	4×	body	160	valid
0.0ms	1×	body	80	invalid

simplify57.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5092	43

prune14.0ms (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

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
1.7b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
2.7b	(/ (* (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)))

rewrite88.0ms (0.3%)

Algorithm

1×	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 → 266

Calls

4 calls:

40.0ms	(/ (* (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)))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
10.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)

series225.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (* (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)))
16.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))

simplify82.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5002	9443

prune1.2s (3.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	274	4	278
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	275	4	279

Merged error: 0.1b

Counts

279 → 4

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-r`
4×	`add-sqr-sqrt` `*-un-lft-identity`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`add-cube-cbrt` `sub-neg` `associate-*r/`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-l` `*-commutative` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares`

Counts

1 → 24

Calls

1 calls:

7.0ms

(* (* s 0.5) (- c_p c_n))

series8.0ms (0%)

Counts

1 → 3

Calls

1 calls:

8.0ms

(* (* s 0.5) (- c_p c_n))

simplify41.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5017	220

prune55.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	27	4	31

Merged error: 0.1b

Counts

31 → 4

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
2.0b	(log (/ 1.0 (+ 1.0 (exp (neg t)))))
9.6b	(- (log (/ 1.0 (+ 1.0 (exp (neg s))))) (log (/ 1.0 (+ 1.0 (exp (neg t))))))
9.6b	(- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))))

rewrite63.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`log-prod`
62×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
39×	`times-frac`
30×	`add-cube-cbrt`
24×	`associate--l+` `associate--r+`
13×	`pow1`
11×	`distribute-lft-out--`
9×	`log-pow` `distribute-lft-out`
8×	`difference-of-squares`
7×	`add-exp-log` `log-div`
6×	`associate-/r/` `add-log-exp`
5×	`flip3--` `flip--`
4×	`add-cbrt-cube`
3×	`associate--l-` `sub-neg` `flip3-+` `diff-log` `flip-+` `div-inv` `associate--r-`
2×	`rem-log-exp`
1×	`div-exp`

Counts

4 → 129

Calls

4 calls:

26.0ms	(- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))))
15.0ms	(- (log (/ 1.0 (+ 1.0 (exp (neg s))))) (log (/ 1.0 (+ 1.0 (exp (neg t))))))
10.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
6.0ms	(log (/ 1.0 (+ 1.0 (exp (neg t)))))

series76.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))))
22.0ms	(- (log (/ 1.0 (+ 1.0 (exp (neg s))))) (log (/ 1.0 (+ 1.0 (exp (neg t))))))
15.0ms	(log (/ 1.0 (+ 1.0 (exp (neg t)))))
7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))

simplify61.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5009	2613

prune619.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	142	3	145

Merged error: 0.0b

Counts

145 → 3

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))))
0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
0.3b	(* c_p (- (* 0.5 (- s t)) (* 0.125 (* s s))))
9.6b	(- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))))

rewrite54.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
18×	`log-prod`
11×	`pow1`
10×	`associate--l+`
9×	`add-cube-cbrt` `difference-of-squares`
8×	`sub-neg` `distribute-lft-out--`
7×	`add-exp-log`
6×	`log-div` `flip3--` `add-cbrt-cube` `flip--` `associate--r+` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `log-pow`
4×	`times-frac`
3×	`associate-r` `associate-l`
2×	`associate--l-` `diff-log` `associate-*r/` `associate--r-`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

22.0ms	(- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))))
10.0ms	(* c_p (- (* 0.5 (- s t)) (* 0.125 (* s s))))
10.0ms	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))))
9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))

series72.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))))
18.0ms	(log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))))
16.0ms	(* c_p (- (* 0.5 (- s t)) (* 0.125 (* s s))))
7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))

simplify69.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4912	1903
1	4912	1903

prune304.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	102	2	104

Merged error: 0.0b

Counts

104 → 2

regimes597.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	109	28
1	109	28

end0.0ms (0%)

sample20.0s (58.7%)

Algorithm

1×

intervals

Results

13.1s	1896×	body	5120	exit
2.5s	1007×	body	1280	overflowed
1.7s	8348×	body	80	overflowed
1.2s	905×	body	640	overflowed
352.0ms	448×	body	320	overflowed
317.0ms	13808×	pre	80	true
116.0ms	915×	body	80	valid
114.0ms	256×	body	160	overflowed
27.0ms	12×	body	1280	valid
9.0ms	8×	body	640	valid
5.0ms	1×	body	2560	valid
2.0ms	7×	body	160	valid
2.0ms	3×	body	320	valid
0.0ms	2×	body	80	invalid

Details

analyze4.4s (13%)

sample5.9s (17.2%)

simplify57.0ms (0.2%)

prune14.0ms (0%)

localize23.0ms (0.1%)

rewrite88.0ms (0.3%)

series225.0ms (0.7%)

simplify82.0ms (0.2%)

prune1.2s (3.5%)

localize6.0ms (0%)

rewrite8.0ms (0%)

series8.0ms (0%)

simplify41.0ms (0.1%)

prune55.0ms (0.2%)

localize29.0ms (0.1%)

rewrite63.0ms (0.2%)

series76.0ms (0.2%)

simplify61.0ms (0.2%)

prune619.0ms (1.8%)

localize31.0ms (0.1%)

rewrite54.0ms (0.2%)

series72.0ms (0.2%)

simplify69.0ms (0.2%)

prune304.0ms (0.9%)

regimes597.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample20.0s (58.7%)

Profiling