Details

sample43.0s

Algorithm

intervals

Results

42.8s	3350×	body	10240	exit
77.0ms	3606×	pre	80	true
23.0ms	245×	body	80	valid
8.0ms	2×	body	2560	valid
3.0ms	3×	body	640	valid
2.0ms	1×	body	1280	valid
1.0ms	5×	body	160	valid

simplify25.0ms

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: 5.0b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.2b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.2b	(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)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

2.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
2.0ms	(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)))

series763.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
580.0ms	(/ (* (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)))

simplify86.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	803	3203
1	3333	3161
2	5001	3161

prune613.0ms

Filtered

110 candidates to 104 candidates (94.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	3	111

Merged error: 0.5b

Counts

111 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
1.2b	(log (/ 1.0 (+ 1.0 (exp (- t)))))
8.9b	(- (* (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)))
32.3b	(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))))

series791.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
71.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
347.0ms	(- (* (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)))
302.0ms	(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))))

simplify66.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (60.0ms)

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

prune178.0ms

Filtered

34 candidates to 28 candidates (82.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	34	3	37

Merged error: 0b

Counts

37 → 3

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)
0.3b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
39.2b	(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))))

series398.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
150.0ms	(* (log 0.5) c_p)
71.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
146.0ms	(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

prune83.0ms

Filtered

26 candidates to 18 candidates (69.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	26	3	29

Merged error: 0b

Counts

29 → 3

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Merged error: 0b

Counts

3 → 3

regimes380.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	13
1	28	13
2	28	13

end0.0ms

sample4.1m

Algorithm

intervals

Results

4.1m	19866×	body	10240	exit
402.0ms	21460×	pre	80	true
139.0ms	1543×	body	80	valid
18.0ms	3×	body	5120	valid
16.0ms	8×	body	1280	valid
11.0ms	3×	body	2560	valid
7.0ms	9×	body	640	valid
6.0ms	22×	body	160	valid
2.0ms	6×	body	320	valid