Details

sample4.5s

Algorithm

intervals

Results

3.8s	527×	body	5120	exit
521.0ms	2951×	body	80	overflowed
90.0ms	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

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 6.0b

Counts

2 → 1

localize23.0ms

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)))

rewrite86.0ms

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` `expm1-log1p-u` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `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 → 280

Calls

4 calls:

10.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
43.0ms	(/ (* (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)))

series847.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
75.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
76.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
604.0ms	(/ (* (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)))

simplify119.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	1007	6085
1	3337	5843
2	5002	5843

prune451.0ms

Filtered

292 candidates to 89 candidates (30.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	289	3	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	290	3	293

Merged error: 0b

Counts

293 → 3

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 0.5 (* s c_n))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1×	`expm1-log1p-u` `associate-r` `*-commutative` `log1p-expm1-u` `add-log-exp`

Counts

1 → 20

Calls

1 calls:

5.0ms

(* 0.5 (* s c_n))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(* 0.5 (* s c_n))

simplify79.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	88	77
1	320	62
2	1234	62
3	3438	62
4	5002	62

prune42.0ms

Filtered

23 candidates to 13 candidates (56.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	23	3	26

Merged error: 0b

Counts

26 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (log 0.5) c_p (fma 0.5 (* t c_p) 1))
0.2b	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
87×	`prod-exp`
65×	`div-exp`
56×	`pow-exp`
43×	`pow-to-exp`
24×	`unpow-prod-down`
23×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
15×	`add-cube-cbrt`
14×	`times-frac`
6×	`pow1` `pow-unpow`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out`
2×	`pow-pow` `associate-/r/` `div-inv` `difference-of-squares` `sqr-pow`
1×	`frac-2neg` `flip3-+` `clear-num` `associate-/r` `flip-+` `fma-udef` `associate-/l` `distribute-lft-out--`

Counts

4 → 138

Calls

4 calls:

1.0ms	(fma (log 0.5) c_p (fma 0.5 (* t c_p) 1))
10.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
36.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series943.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(fma (log 0.5) c_p (fma 0.5 (* t c_p) 1))
88.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
73.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
732.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify96.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	789	2745
1	3315	2507
2	5001	2503

prune427.0ms

Filtered

150 candidates to 72 candidates (48.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	150	3	153

Merged error: 0b

Counts

153 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
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) (fma c_n (log 0.5) (- 1 (* 0.5 (* t c_n))))))
1.9b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

232×	`add-exp-log`
112×	`prod-exp`
97×	`*-un-lft-identity`
95×	`div-exp`
80×	`pow-exp`
70×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
62×	`times-frac`
54×	`prod-diff`
50×	`pow-to-exp`
36×	`unpow-prod-down`
16×	`add-cbrt-cube`
15×	`distribute-lft-out`
10×	`associate-/r/`
6×	`pow1` `pow-unpow` `div-inv` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow-pow` `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 → 228

Calls

4 calls:

11.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
33.0ms	(/ (* (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) (fma c_n (log 0.5) (- 1 (* 0.5 (* t c_n))))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

series1.1s

Counts

4 → 12

Calls

4 calls:

52.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
74.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
870.0ms	(/ (* (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) (fma c_n (log 0.5) (- 1 (* 0.5 (* t c_n))))))
78.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

simplify132.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1235	5382
1	4699	4346
2	5001	4346

prune632.0ms

Filtered

240 candidates to 106 candidates (44.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	240	3	243

Merged error: 0b

Counts

243 → 3

regimes293.0ms

bsearch1.7s

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	45	29
1	45	29

end0.0ms

sample6.2s

Algorithm

intervals

Results

5.2s	763×	body	5120	exit
710.0ms	4272×	body	80	overflowed
123.0ms	5423×	pre	80	true
39.0ms	373×	body	80	valid
11.0ms	6×	body	1280	valid
3.0ms	2×	body	640	overflowed
1.0ms	1×	body	640	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	320	valid
0.0ms	1×	body	160	overflowed