Details

Time bar (total: 3.5m)

sample48.1s

Algorithm
intervals
Results
47.7s3117×body10240exit
180.0ms3373×pre80true
34.0ms252×body80valid
2.0ms1×body1280valid
1.0ms2×body160valid
1.0ms1×body320valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0221425
1531425
21431425
37441425
done50021425

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.7b
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
0.7b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b
(/ (* (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)))

rewrite211.0ms

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×clear-num associate-/r* sub-neg frac-2neg flip3-- diff-log flip-- associate-/l* distribute-lft-out--
Counts
4 → 267
Calls
4 calls:
25.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
16.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
16.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
138.0ms
(/ (* (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)))

series821.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
72.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
74.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
623.0ms
(/ (* (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)))

simplify4.7s

Counts
279 → 279
Iterations

Useful iterations: 2 (2.4s)

IterNodesCost
0366301591
11139251055
23033249793
done5008249793

prune679.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

1.0b
(log (/ 1.0 (+ 1.0 (exp (- t)))))
1.2b
(log (/ 1.0 (+ 1.0 (exp (- s)))))
9.7b
(- (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- t)))))) (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))))))
10.5b
(+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- t)))))) (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
96×log-prod
72×*-un-lft-identity
60×add-sqr-sqrt
52×times-frac
40×add-cube-cbrt
36×associate-+l+
30×distribute-rgt-in distribute-lft-in
24×associate--l+
18×add-log-exp
14×associate-+r+
12×distribute-lft-out
10×add-exp-log
8×associate-/r/ difference-of-squares
6×pow1
5×sum-log flip3-+ flip-+
4×add-cbrt-cube diff-log rem-log-exp div-inv distribute-lft-out--
2×log-div sub-neg div-exp log-pow
1×+-commutative associate-+r- flip3-- flip-- associate--r+
Counts
4 → 148
Calls
4 calls:
8.0ms
(log (/ 1.0 (+ 1.0 (exp (- t)))))
8.0ms
(log (/ 1.0 (+ 1.0 (exp (- s)))))
60.0ms
(- (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- t)))))) (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))))))
96.0ms
(+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- t)))))) (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))))))

series783.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(log (/ 1.0 (+ 1.0 (exp (- t)))))
74.0ms
(log (/ 1.0 (+ 1.0 (exp (- s)))))
304.0ms
(- (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- t)))))) (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))))))
332.0ms
(+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- t)))))) (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))))))

simplify3.2s

Counts
160 → 160
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0386124878
1878120722
22139119676
done5001116592

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* c_p (log (/ 1.0 (+ 1.0 (exp (- s))))))
0.3b
(* c_p (log 0.5))
1.2b
(log (/ 1.0 (+ 1.0 (exp (- s)))))
8.0b
(+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* (* 0.5 c_n) (- t s)) (* c_p (log 0.5))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
96×log-prod
80×*-un-lft-identity
60×times-frac
54×add-sqr-sqrt
50×add-cube-cbrt
41×distribute-rgt-in distribute-lft-in
36×associate-+l+
15×distribute-lft-out
11×pow1 add-exp-log
10×associate-/r/
9×add-log-exp
8×add-cbrt-cube associate-*r*
6×associate-+r+ flip3-+ associate-*l* flip-+
5×div-inv
4×associate--l+
3×sub-neg log-pow
2×sum-log rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×+-commutative log-div associate-+r- diff-log div-exp
Counts
4 → 164
Calls
4 calls:
22.0ms
(* c_p (log (/ 1.0 (+ 1.0 (exp (- s))))))
7.0ms
(* c_p (log 0.5))
8.0ms
(log (/ 1.0 (+ 1.0 (exp (- s)))))
58.0ms
(+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* (* 0.5 c_n) (- t s)) (* c_p (log 0.5))))

series473.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* c_p (log (/ 1.0 (+ 1.0 (exp (- s))))))
165.0ms
(* c_p (log 0.5))
74.0ms
(log (/ 1.0 (+ 1.0 (exp (- s)))))
160.0ms
(+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- s)))))) (- (* (* 0.5 c_n) (- t s)) (* c_p (log 0.5))))

simplify2.7s

Counts
176 → 176
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
029091614
163587358
2149386673
3469984673
done504484673

prune941.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize108.0ms

Local error

Found 4 expressions with local error:

0.7b
(* c_p (+ (* 0.5 s) (- (log 0.5) (* (* (/ s 0.5) (/ s 0.5)) 0.03125))))
1.0b
(log (/ 1.0 (+ 1.0 (exp (- t)))))
9.7b
(- (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- t)))))) (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))))))
10.5b
(+ (* c_p (+ (* 0.5 s) (- (log 0.5) (* (* (/ s 0.5) (/ s 0.5)) 0.03125)))) (- (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- t)))))) (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))))))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
42×log-prod
40×add-sqr-sqrt
32×*-un-lft-identity
24×associate--l+
18×add-cube-cbrt add-log-exp
16×times-frac
14×distribute-rgt-in associate-+r+ distribute-lft-in
9×add-exp-log
8×difference-of-squares
7×pow1
6×add-cbrt-cube associate-*r/
5×sum-log flip3-+ flip-+
4×diff-log frac-add distribute-lft-out--
3×flip3-- associate-*r* associate-*l* flip-- distribute-lft-out
2×associate-+l+ sub-neg rem-log-exp associate-/r/
1×+-commutative log-div associate-+r- div-exp pow-prod-down prod-exp log-pow *-commutative cbrt-unprod div-inv associate--r+ unswap-sqr
Counts
4 → 111
Calls
4 calls:
44.0ms
(* c_p (+ (* 0.5 s) (- (log 0.5) (* (* (/ s 0.5) (/ s 0.5)) 0.03125))))
8.0ms
(log (/ 1.0 (+ 1.0 (exp (- t)))))
60.0ms
(- (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- t)))))) (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))))))
93.0ms
(+ (* c_p (+ (* 0.5 s) (- (log 0.5) (* (* (/ s 0.5) (/ s 0.5)) 0.03125)))) (- (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- t)))))) (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))))))

series749.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* c_p (+ (* 0.5 s) (- (log 0.5) (* (* (/ s 0.5) (/ s 0.5)) 0.03125))))
74.0ms
(log (/ 1.0 (+ 1.0 (exp (- t)))))
305.0ms
(- (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- t)))))) (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))))))
284.0ms
(+ (* c_p (+ (* 0.5 s) (- (log 0.5) (* (* (/ s 0.5) (/ s 0.5)) 0.03125)))) (- (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (+ (* c_p (log (/ 1.0 (+ 1.0 (exp (- t)))))) (* c_n (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))))))

simplify3.9s

Counts
123 → 123
Iterations

Useful iterations: done (3.8s)

IterNodesCost
0335103127
188297863
2329296776
done500396612

prune983.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes542.0ms

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
020686
126686
done26686

end0.0ms

sample2.2m

Algorithm
intervals
Results
2.2m10584×body10240exit
381.0ms11412×pre80true
114.0ms808×body80valid
7.0ms2×body2560valid
5.0ms1×body5120valid
3.0ms2×body1280valid
2.0ms9×body160valid
2.0ms3×body640valid
1.0ms3×body320valid