Details

sample4.5s

Algorithm

intervals

Results

3.7s	527×	body	5120	exit
509.0ms	2951×	body	80	overflowed
93.0ms	3735×	pre	80	true
28.0ms	250×	body	80	valid
3.0ms	2×	body	1280	valid
1.0ms	1×	body	640	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	320	valid

simplify27.0ms

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 (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: 6.0b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.9b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.2b	(/ (* (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)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

557×	`add-exp-log`
312×	`prod-exp`
265×	`pow-exp`
249×	`div-exp`
185×	`pow-to-exp`
42×	`unpow-prod-down`
38×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
26×	`times-frac`
24×	`add-cube-cbrt`
16×	`add-cbrt-cube`
9×	`pow-unpow`
7×	`pow1`
6×	`distribute-lft-out`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`pow-pow` `div-inv` `sqr-pow`
2×	`flip3-+` `flip-+` `difference-of-squares`
1×	`frac-2neg` `clear-num` `associate-/r` `associate-/l` `distribute-lft-out--`

Counts

4 → 272

Calls

4 calls:

16.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
8.0ms	(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)))

series859.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
73.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
623.0ms	(/ (* (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)))

simplify109.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	980	5999
1	3241	5759
2	5001	5759

prune424.0ms

Filtered

284 candidates to 81 candidates (28.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	281	3	284
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	282	3	285

Merged error: 0b

Counts

285 → 3

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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:

5.0ms	(* 0.5 (* s c_p))
5.0ms	(* 0.5 (* s c_n))

series39.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(* 0.5 (* s c_p))
20.0ms	(* 0.5 (* s c_n))

simplify62.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 1 (6.0ms)

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

prune55.0ms

Filtered

42 candidates to 22 candidates (52.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	42	3	45

Merged error: 0b

Counts

45 → 3

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
0.2b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(/ (* (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)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

172×	`add-exp-log`
88×	`prod-exp`
65×	`div-exp`
56×	`pow-exp`
43×	`pow-to-exp`
25×	`*-un-lft-identity`
24×	`add-sqr-sqrt` `unpow-prod-down`
18×	`add-cbrt-cube`
17×	`add-cube-cbrt`
14×	`times-frac`
8×	`pow1`
6×	`pow-unpow`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/` `add-log-exp`
3×	`flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
2×	`pow-pow` `associate-r/` `associate-l/` `div-inv` `difference-of-squares` `sqr-pow`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l*` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

15.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
6.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
38.0ms	(/ (* (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)))

series1.0s

Counts

4 → 12

Calls

4 calls:

90.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
102.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
74.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
758.0ms	(/ (* (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)))

simplify111.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	929	2874
1	4208	2627
2	5002	2627

prune423.0ms

Filtered

158 candidates to 74 candidates (46.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	158	3	161

Merged error: 0b

Counts

161 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log 0.5) c_n)
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)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (- (+ (* (log 0.5) c_n) 1) (* 0.5 (* t c_n)))))
1.9b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

234×	`add-exp-log`
113×	`prod-exp`
95×	`div-exp`
80×	`pow-exp`
50×	`pow-to-exp`
36×	`unpow-prod-down` `*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
24×	`add-cube-cbrt`
18×	`add-cbrt-cube`
9×	`pow1`
6×	`pow-unpow` `associate-/r/` `distribute-lft-out`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `associate-l` `add-log-exp`
3×	`associate-r` `div-inv`
2×	`pow-pow` `flip3-+` `associate-*r/` `flip-+` `sqr-pow`
1×	`flip3--` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `log-pow` `-commutative` `flip--` `associate-/l*` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

4.0ms	(* (log 0.5) c_n)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
35.0ms	(/ (* (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) (- (+ (* (log 0.5) c_n) 1) (* 0.5 (* t c_n)))))
11.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

series1.4s

Counts

4 → 12

Calls

4 calls:

346.0ms	(* (log 0.5) c_n)
76.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
922.0ms	(/ (* (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) (- (+ (* (log 0.5) c_n) 1) (* 0.5 (* t c_n)))))
74.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

simplify112.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	968	3270
1	3846	3021
2	5002	3021

prune469.0ms

Filtered

181 candidates to 81 candidates (44.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	181	3	184

Merged error: 0b

Counts

184 → 3

regimes284.0ms

bsearch1.5s

Steps

Iters	Range		Point
9	-59.52527005214053	-1.0187921666786291e-07	-1.0357602324729432e-07

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	31
1	52	31

end0.0ms

sample6.4s

Algorithm

intervals

Results

5.3s	763×	body	5120	exit
712.0ms	4272×	body	80	overflowed
128.0ms	5423×	pre	80	true
42.0ms	373×	body	80	valid
12.0ms	6×	body	1280	valid
3.0ms	2×	body	640	overflowed
2.0ms	1×	body	640	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	320	valid
0.0ms	1×	body	160	overflowed