Details

sample43.6s

Algorithm

intervals

Results

43.3s	3342×	body	10240	exit
79.0ms	3599×	pre	80	true
34.0ms	1×	body	5120	valid
24.0ms	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

localize21.0ms

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)))

rewrite26.0ms

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))))
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)))

series748.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 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)
581.0ms	(/ (* (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

111 → 111

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	763	3186
1	3182	3166
2	5001	3166

prune636.0ms

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

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p)
0.7b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
2.7b	(log (/ 1.0 (+ 1.0 (exp (- t)))))
10.9b	(- (+ (* (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)))

rewrite20.0ms

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)))

series599.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p)
72.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
68.0ms	(log (/ 1.0 (+ 1.0 (exp (- t)))))
356.0ms	(- (+ (* (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)))

simplify53.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (13.0ms)

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

prune260.0ms

Filtered

40 candidates to 35 candidates (87.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	40	5	45

Merged error: 0.1b

Counts

45 → 5

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)
0.7b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
10.9b	(- (+ (* (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)))

series690.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p)
73.0ms	(* (- (+ (log 0.5) (* 0.5 t)) (* 0.03125 (/ (pow t 2) (pow 0.5 2)))) c_p)
68.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
445.0ms	(- (+ (* (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)))

simplify79.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (66.0ms)

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

prune397.0ms

Filtered

52 candidates to 44 candidates (84.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	53	4	57

Merged error: 0b

Counts

57 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow t 2) c_p)
0.1b	(* c_n (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 s)) 1.0))))))
0.2b	(* c_n (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 t)) 1.0))))))
8.6b	(- (+ (* 0.125 (* (pow t 2) c_p)) (* c_n (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 s)) 1.0))))))) (+ (* 0.5 (* t c_p)) (* c_n (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 t)) 1.0))))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

4×	`flip3-+` `frac-sub` `flip-+`
3×	`*-commutative`
2×	`+-commutative` `associate-l` `associate--l+` `associate--r+`
1×	`sub-neg` `flip3--` `flip--` `unpow2` `sqr-pow`

Counts

4 → 17

Calls

4 calls:

3.0ms	(* (pow t 2) c_p)
3.0ms	(* c_n (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 s)) 1.0))))))
3.0ms	(* c_n (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 t)) 1.0))))))
14.0ms	(- (+ (* 0.125 (* (pow t 2) c_p)) (* c_n (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 s)) 1.0))))))) (+ (* 0.5 (* t c_p)) (* c_n (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 t)) 1.0))))))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (pow t 2) c_p)
94.0ms	(* c_n (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 s)) 1.0))))))
90.0ms	(* c_n (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 t)) 1.0))))))
148.0ms	(- (+ (* 0.125 (* (pow t 2) c_p)) (* c_n (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 s)) 1.0))))))) (+ (* 0.5 (* t c_p)) (* c_n (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 t)) 1.0))))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	369	880
1	1617	841
2	5002	786

prune140.0ms

Filtered

29 candidates to 20 candidates (69.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	29	4	33

Merged error: 0b

Counts

33 → 4

regimes256.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	33
1	48	33

end0.0ms

sample2.7m

Algorithm

intervals

Results

2.7m	13408×	body	10240	exit
303.0ms	14456×	pre	80	true
96.0ms	1011×	body	80	valid
55.0ms	3×	body	5120	valid
19.0ms	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