Details

sample42.6s

Algorithm

intervals

Results

42.4s	3350×	body	10240	exit
77.0ms	3606×	pre	80	true
21.0ms	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

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: 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)))

rewrite24.0ms

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)))

series909.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
723.0ms	(/ (* (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)))

simplify84.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	787	3208
1	3263	3186
2	5002	3186

prune596.0ms

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

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p)
0.3b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
1.2b	(log (/ 1.0 (+ 1.0 (exp (- t)))))
12.1b	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

6×	`log-div` `log-prod` `flip3-+` `flip-+`
5×	`clear-num`
4×	`associate-/r/` `frac-sub`
3×	`log-rec`
2×	`+-commutative` `frac-2neg` `associate--l+` `div-inv` `associate--r+`
1×	`distribute-lft-neg-out` `sub-neg` `flip3--` `*-commutative` `flip--`

Counts

4 → 28

Calls

4 calls:

3.0ms	(* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p)
3.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
3.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
9.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

series593.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p)
71.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
72.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
350.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

simplify52.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	557	1184
1	1966	1143
2	5002	1143

prune237.0ms

Filtered

40 candidates to 35 candidates (87.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	41	2	43

Merged error: 0.5b

Counts

43 → 2

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p)
0.2b	(* (- (+ (log 0.5) (* 0.5 t)) (* 0.03125 (/ (pow t 2) (pow 0.5 2)))) c_p)
0.3b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
12.1b	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (- (+ (log 0.5) (* 0.5 t)) (* 0.03125 (/ (pow t 2) (pow 0.5 2)))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

20×	`frac-sub`
18×	`associate-*l/`
14×	`associate-*r/`
13×	`flip3-+` `flip-+`
7×	`clear-num`
4×	`associate-/r` `associate-/l` `unpow2` `sqr-pow`
3×	`log-div` `log-prod` `frac-2neg`
2×	`+-commutative` `flip3--` `log-rec` `associate--l+` `associate-/r/` `un-div-inv` `*-commutative` `flip--` `associate--r+`
1×	`distribute-lft-neg-out` `sub-neg` `div-inv`

Counts

4 → 40

Calls

4 calls:

3.0ms	(* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p)
9.0ms	(* (- (+ (log 0.5) (* 0.5 t)) (* 0.03125 (/ (pow t 2) (pow 0.5 2)))) c_p)
3.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
16.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (- (+ (log 0.5) (* 0.5 t)) (* 0.03125 (/ (pow t 2) (pow 0.5 2)))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

series694.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p)
69.0ms	(* (- (+ (log 0.5) (* 0.5 t)) (* 0.03125 (/ (pow t 2) (pow 0.5 2)))) c_p)
73.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
448.0ms	(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (- (+ (log 0.5) (* 0.5 t)) (* 0.03125 (/ (pow t 2) (pow 0.5 2)))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

simplify78.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	777	1570
1	2979	1533
2	5002	1531

prune385.0ms

Filtered

52 candidates to 43 candidates (82.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	52	2	54

Merged error: 0.5b

Counts

54 → 2

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

2 alts after pruning (0 fresh and 2 done)

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

Merged error: 0.5b

Counts

2 → 2

regimes150.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	33
1	48	33

end0.0ms

sample4.2m

Algorithm

intervals

Results

4.1m	19866×	body	10240	exit
409.0ms	21460×	pre	80	true
134.0ms	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