Details

sample43.5s

Algorithm

intervals

Results

43.3s	3413×	body	10240	exit
80.0ms	3669×	pre	80	true
23.0ms	245×	body	80	valid
6.0ms	1×	body	5120	valid
6.0ms	4×	body	1280	valid
3.0ms	4×	body	640	valid
1.0ms	2×	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: 8.2b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
1.0b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.2b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.9b	(/ (* (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)))

rewrite80.0ms

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:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
40.0ms	(/ (* (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)))

series757.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
574.0ms	(/ (* (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)))

simplify101.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	976	5948
1	3142	5704
2	5001	5704

prune428.0ms

Filtered

279 candidates to 79 candidates (28.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	276	3	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	277	3	280

Merged error: 0.9b

Counts

280 → 3

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

series40.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(* 0.5 (* s c_n))
22.0ms	(* 0.5 (* s c_p))

simplify57.0ms

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

prune75.0ms

Filtered

42 candidates to 22 candidates (52.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	40	5	45

Merged error: 0.9b

Counts

45 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.5b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
1.0b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.7b	(/ (* (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)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-exp-log`
88×	`prod-exp`
65×	`div-exp`
55×	`pow-exp`
42×	`pow-to-exp`
23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
18×	`unpow-prod-down` `add-cbrt-cube`
15×	`add-cube-cbrt`
14×	`times-frac`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/`
3×	`pow-unpow` `flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
2×	`associate-r/` `associate-l/` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `flip--` `associate-/l*` `distribute-lft-out--` `unswap-sqr` `sqr-pow`

Counts

4 → 141

Calls

4 calls:

7.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
10.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
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)))

series911.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
45.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
697.0ms	(/ (* (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)))

simplify104.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	922	2823
1	4079	2572
2	5001	2572

prune444.0ms

Filtered

153 candidates to 72 candidates (47.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	154	4	158

Merged error: 0.9b

Counts

158 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (* (pow (log 0.5) 2) (pow c_p 2)))
0.0b	(* 0.5 (* s c_p))
0.1b	(* (pow (log 0.5) 2) (pow c_p 2))
1.0b	(pow (log 0.5) 2)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
31×	`prod-exp`
28×	`add-sqr-sqrt`
19×	`unpow-prod-down`
16×	`add-cbrt-cube` `unswap-sqr`
15×	`associate-l`
14×	`pow1`
13×	`pow-to-exp` `pow-exp`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`unpow2` `sqr-pow`
10×	`associate-r`
7×	`cbrt-unprod`
5×	`pow-prod-down`
4×	`add-log-exp`
3×	`pow-unpow` `*-commutative`
2×	`log-pow`
1×	`pow-pow`

Counts

4 → 114

Calls

4 calls:

7.0ms	(* 1/2 (* (pow (log 0.5) 2) (pow c_p 2)))
4.0ms	(* 0.5 (* s c_p))
7.0ms	(* (pow (log 0.5) 2) (pow c_p 2))
2.0ms	(pow (log 0.5) 2)

series353.0ms

Counts

4 → 10

Calls

4 calls:

173.0ms	(* 1/2 (* (pow (log 0.5) 2) (pow c_p 2)))
24.0ms	(* 0.5 (* s c_p))
156.0ms	(* (pow (log 0.5) 2) (pow c_p 2))
0.0ms	(pow (log 0.5) 2)

simplify47.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	343	646
1	1473	541
2	5001	535

prune213.0ms

Filtered

124 candidates to 59 candidates (47.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	124	4	128

Merged error: 0.9b

Counts

128 → 4

regimes409.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	87
1	56	87

end0.0ms

sample1.8m

Algorithm

intervals

Results

1.8m	8781×	body	10240	exit
182.0ms	9435×	pre	80	true
56.0ms	634×	body	80	valid
12.0ms	2×	body	5120	valid
8.0ms	5×	body	1280	valid
4.0ms	5×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid