Details

sample43.6s

Algorithm

intervals

Results

43.2s	3342×	body	10240	exit
77.0ms	3599×	pre	80	true
34.0ms	1×	body	5120	valid
23.0ms	242×	body	80	valid
14.0ms	7×	body	1280	valid
3.0ms	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

localize23.0ms

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)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

74×	`sqr-pow`
72×	`associate-l`
64×	`times-frac`
60×	`unpow-prod-down`
42×	`associate-/r/`
22×	`div-inv`
21×	`flip3-+` `flip-+`
18×	`associate-r` `*-commutative` `unswap-sqr`
8×	`associate-/r` `associate-/l`
6×	`pow-to-exp`
2×	`frac-2neg` `prod-exp` `clear-num`
1×	`div-exp`

Counts

4 → 99

Calls

4 calls:

3.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
3.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
12.0ms	(/ (* (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)))

series738.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
577.0ms	(/ (* (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)))

simplify82.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	776	3181
1	3241	3142
2	5001	3142

prune635.0ms

Filtered

111 candidates to 107 candidates (96.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	5	112

Merged error: 0.1b

Counts

112 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
2.7b	(log (/ 1.0 (+ 1.0 (exp (- t)))))
9.8b	(- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
25.9b	(fma c_p (log (/ 1.0 (+ 1.0 (exp (- s))))) (- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`log-div` `log-prod`
4×	`clear-num` `associate-/r/`
2×	`frac-2neg` `flip3-+` `fma-neg` `log-rec` `flip-+` `fma-udef` `div-inv`
1×	`sub-neg` `flip3--` `*-commutative` `flip--` `associate--r+`

Counts

4 → 22

Calls

4 calls:

3.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
3.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
4.0ms	(- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
1.0ms	(fma c_p (log (/ 1.0 (+ 1.0 (exp (- s))))) (- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n))))

series799.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
72.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
349.0ms	(- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
306.0ms	(fma c_p (log (/ 1.0 (+ 1.0 (exp (- s))))) (- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n))))

simplify67.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	386	483
1	951	472
2	3291	467
3	5001	466

prune195.0ms

Filtered

34 candidates to 28 candidates (82.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	34	5	39

Merged error: 0.1b

Counts

39 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- s))))
0.2b	(* (log 0.5) c_p)
0.7b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
35.3b	(fma c_p (log (/ 1.0 (+ 1.0 (exp (- s))))) (fma (* c_n 0.5) (- t s) (- (* (log 0.5) c_p))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`associate-/r/`
3×	`log-div` `log-prod` `clear-num`
2×	`frac-2neg` `flip3-+` `flip-+` `div-inv`
1×	`log-rec` `*-commutative` `fma-udef`

Counts

4 → 14

Calls

4 calls:

3.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
2.0ms	(* (log 0.5) c_p)
3.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
1.0ms	(fma c_p (log (/ 1.0 (+ 1.0 (exp (- s))))) (fma (* c_n 0.5) (- t s) (- (* (log 0.5) c_p))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
156.0ms	(* (log 0.5) c_p)
67.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
148.0ms	(fma c_p (log (/ 1.0 (+ 1.0 (exp (- s))))) (fma (* c_n 0.5) (- t s) (- (* (log 0.5) c_p))))

simplify37.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	182	159
1	438	154
2	1350	154
3	5001	152

prune106.0ms

Filtered

26 candidates to 19 candidates (73.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	26	5	31

Merged error: 0.1b

Counts

31 → 5

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)
2.7b	(log (/ 1.0 (+ 1.0 (exp (- t)))))
9.8b	(- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
25.9b	(fma c_p (fma s 0.5 (- (log 0.5) (* 0.03125 (/ (pow s 2) (pow 0.5 2))))) (- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

3×	`log-div` `log-prod`
2×	`fma-neg` `clear-num` `associate-/r/` `*-commutative` `fma-udef`
1×	`sub-neg` `flip3--` `frac-2neg` `flip3-+` `log-rec` `flip--` `flip-+` `div-inv` `associate--r+`

Counts

4 → 16

Calls

4 calls:

2.0ms	(* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)
3.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
4.0ms	(- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
1.0ms	(fma c_p (fma s 0.5 (- (log 0.5) (* 0.03125 (/ (pow s 2) (pow 0.5 2))))) (- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n))))

series812.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)
73.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
350.0ms	(- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
265.0ms	(fma c_p (fma s 0.5 (- (log 0.5) (* 0.03125 (/ (pow s 2) (pow 0.5 2))))) (- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n))))

simplify241.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (236.0ms)

Iter	Nodes	Cost
0	355	416
1	895	405
2	3101	400
3	5002	397

prune156.0ms

Filtered

28 candidates to 21 candidates (75.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	25	3	28
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	29	4	33

Merged error: 0.1b

Counts

33 → 4

regimes266.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample2.7m

Algorithm

intervals

Results

2.7m	13408×	body	10240	exit
283.0ms	14456×	pre	80	true
90.0ms	1011×	body	80	valid
55.0ms	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