Details

sample43.6s

Algorithm

intervals

Results

43.3s	3342×	body	10240	exit
80.0ms	3599×	pre	80	true
34.0ms	1×	body	5120	valid
22.0ms	242×	body	80	valid
13.0ms	7×	body	1280	valid
2.0ms	3×	body	640	valid
1.0ms	4×	body	160	valid

simplify24.0ms

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

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: 7.5b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.8b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.9b	(/ (* (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)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

558×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
250×	`div-exp`
184×	`pow-to-exp`
51×	`*-un-lft-identity`
37×	`times-frac`
36×	`unpow-prod-down`
31×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-cbrt-cube`
10×	`distribute-lft-out`
6×	`pow1` `pow-unpow` `associate-/r/`
5×	`cbrt-undiv` `associate-/r*`
4×	`cbrt-unprod` `div-inv` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

4 → 285

Calls

4 calls:

5.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
37.0ms	(/ (* (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)))

series759.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
71.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
588.0ms	(/ (* (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)))

simplify103.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	966	6045
1	3251	5797
2	5003	5797

prune511.0ms

Filtered

297 candidates to 91 candidates (30.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	293	4	297
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	294	4	298

Merged error: 0.6b

Counts

298 → 4

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.2b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.8b	(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)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

173×	`add-exp-log`
88×	`prod-exp`
66×	`div-exp`
55×	`pow-exp`
42×	`pow-to-exp`
38×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
24×	`add-cube-cbrt`
20×	`add-cbrt-cube`
18×	`unpow-prod-down`
7×	`pow1` `distribute-lft-out`
6×	`associate-/r/`
5×	`cbrt-undiv` `associate-/r*` `cbrt-unprod`
4×	`flip3-+` `flip-+` `associate-/l*` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l` `div-inv`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`distribute-rgt-in` `pow-pow` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr` `sqr-pow`

Counts

4 → 159

Calls

4 calls:

5.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
5.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
34.0ms	(/ (* (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)))

series1.1s

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
95.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
876.0ms	(/ (* (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

171 → 171

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	965	2920
1	4351	2665
2	5001	2665

prune510.0ms

Filtered

171 candidates to 86 candidates (50.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	171	4	175

Merged error: 0.6b

Counts

175 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.020833333333333336 (pow t 3))
0.2b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.8b	(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 (- (+ (* 0.25 t) 0.5) (* 0.020833333333333336 (pow t 3)))) c_n)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-exp-log`
91×	`prod-exp`
65×	`div-exp`
56×	`pow-exp`
43×	`pow-to-exp`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
22×	`unpow-prod-down`
20×	`add-cbrt-cube`
19×	`add-cube-cbrt`
15×	`associate-r`
13×	`times-frac`
7×	`pow1`
6×	`associate-l` `cbrt-unprod`
5×	`unswap-sqr`
4×	`cbrt-undiv` `cube-prod` `associate-/r/` `add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+` `distribute-lft-out` `sqr-pow`
2×	`associate-r/` `associate-l/` `*-commutative` `div-inv`
1×	`distribute-rgt-in` `cube-mult` `pow-pow` `frac-2neg` `distribute-lft-in` `unpow3` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 157

Calls

4 calls:

6.0ms	(* 0.020833333333333336 (pow t 3))
5.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
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)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (- (+ (* 0.25 t) 0.5) (* 0.020833333333333336 (pow t 3)))) c_n)))

series976.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* 0.020833333333333336 (pow t 3))
97.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
770.0ms	(/ (* (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 (- (+ (* 0.25 t) 0.5) (* 0.020833333333333336 (pow t 3)))) c_n)))

simplify114.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	960	2856
1	4442	2596
2	5002	2596

prune520.0ms

Filtered

169 candidates to 79 candidates (46.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	169	4	173

Merged error: 0.6b

Counts

173 → 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))

series38.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify58.0ms

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

prune59.0ms

Filtered

42 candidates to 22 candidates (52.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	42	4	46

Merged error: 0.6b

Counts

46 → 4

regimes337.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	59
1	71	59

end0.0ms

sample2.7m

Algorithm

intervals

Results

2.7m	13408×	body	10240	exit
290.0ms	14456×	pre	80	true
89.0ms	1011×	body	80	valid
54.0ms	3×	body	5120	valid
18.0ms	11×	body	1280	valid
5.0ms	2×	body	2560	valid
4.0ms	5×	body	640	valid
3.0ms	13×	body	160	valid
1.0ms	3×	body	320	valid