Details

Time bar (total: 3.2m)

sample50.3s

Algorithm
intervals
Results
49.9s3451×body10240exit
234.0ms3708×pre80true
31.0ms248×body80valid
7.0ms2×body2560valid
2.0ms5×body160valid
1.0ms1×body1280valid
1.0ms1×body640valid

simplify621.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02243
15343
214743
383943
done500143

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (- t)))
0.7b
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
1.0b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
3.4b
(/ (* (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)))

rewrite247.0ms

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
25×times-frac
22×add-sqr-sqrt add-cube-cbrt
16×add-cbrt-cube
7×distribute-lft-out
6×pow1 pow-unpow add-log-exp
4×cbrt-undiv associate-/r/ cbrt-unprod
3×flip3-+ flip-+ div-inv
2×pow-pow sqr-pow
1×+-commutative frac-2neg clear-num associate-/r* sum-log associate-/l*
Counts
4 → 264
Calls
4 calls:
9.0ms
(+ 1.0 (exp (- t)))
20.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
22.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
175.0ms
(/ (* (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)))

series811.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(+ 1.0 (exp (- t)))
75.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
75.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
650.0ms
(/ (* (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)))

simplify858.0ms

Counts
276 → 276
Iterations

Useful iterations: 2 (345.0ms)

IterNodesCost
034310620
18089830
222569500
done50009500

prune465.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 0.5 (* s c_n))
0.0b
(* 0.5 (* s c_p))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-exp-log add-cbrt-cube
6×associate-*l* pow-prod-down prod-exp cbrt-unprod
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
2×associate-*r* *-commutative add-log-exp
Counts
2 → 36
Calls
2 calls:
16.0ms
(* 0.5 (* s c_n))
16.0ms
(* 0.5 (* s c_p))

series46.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(* 0.5 (* s c_n))
25.0ms
(* 0.5 (* s c_p))

simplify3.9s

Counts
42 → 42
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
059308
1151302
2560242
31896242
43876242
done5001242

prune74.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (- t)))
0.2b
(* (log 0.5) c_p)
0.9b
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
1.0b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)

rewrite463.0ms

Algorithm
rewrite-expression-head
Rules
171×add-exp-log
88×prod-exp
65×div-exp
55×pow-exp
42×pow-to-exp
23×*-un-lft-identity
18×unpow-prod-down add-cbrt-cube
17×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
8×pow1
6×add-log-exp
5×cbrt-unprod
4×cbrt-undiv associate-*l* associate-/r/ distribute-lft-out
3×pow-unpow flip3-+ associate-*r* flip-+
2×associate-*l/ div-inv
1×+-commutative pow-pow frac-2neg pow-prod-down clear-num associate-/r* sum-log log-pow *-commutative associate-/l* unswap-sqr sqr-pow
Counts
4 → 135
Calls
4 calls:
9.0ms
(+ 1.0 (exp (- t)))
8.0ms
(* (log 0.5) c_p)
419.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
21.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)

series1.1s

Counts
4 → 12
Calls
4 calls:
11.0ms
(+ 1.0 (exp (- t)))
177.0ms
(* (log 0.5) c_p)
789.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
76.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)

simplify1.1s

Counts
147 → 147
Iterations

Useful iterations: 2 (423.0ms)

IterNodesCost
03055046
17824714
228204319
done50024319

prune442.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- (+ (* 1/2 (pow t 2)) 2.0) t))
0.7b
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
1.0b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
3.4b
(/ (* (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 (- (+ (* 1/2 (pow t 2)) 2.0) t))) c_n)))

rewrite395.0ms

Algorithm
rewrite-expression-head
Rules
558×add-exp-log
312×prod-exp
264×pow-exp
250×div-exp
184×pow-to-exp
52×*-un-lft-identity
40×add-sqr-sqrt times-frac
36×unpow-prod-down
32×add-cube-cbrt
18×add-cbrt-cube
6×pow1 pow-unpow associate-/r* associate-/r/ distribute-lft-out
5×cbrt-undiv
4×cbrt-unprod div-inv associate-/l* distribute-lft-out-- add-log-exp difference-of-squares
2×pow-pow frac-2neg flip3-+ clear-num flip-+ sqr-pow
1×flip3-- flip--
Counts
4 → 289
Calls
4 calls:
48.0ms
(/ 1.0 (- (+ (* 1/2 (pow t 2)) 2.0) t))
20.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
20.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
284.0ms
(/ (* (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 (- (+ (* 1/2 (pow t 2)) 2.0) t))) c_n)))

series949.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ 1.0 (- (+ (* 1/2 (pow t 2)) 2.0) t))
76.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
76.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
739.0ms
(/ (* (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 (- (+ (* 1/2 (pow t 2)) 2.0) t))) c_n)))

simplify994.0ms

Counts
301 → 301
Iterations

Useful iterations: 2 (419.0ms)

IterNodesCost
040312005
193011190
2265110798
done500110798

prune680.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes274.0ms

bsearch4.8s

Steps
ItersRangePoint
6
41935.94270129912
293590.332996411
66323.47937865018
6
9.3172751427192e-05
0.0012886725850446681
9.49814226001459e-05

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03569
14957
done4957

end0.0ms

sample2.1m

Algorithm
intervals
Results
2.1m9753×body10240exit
914.0ms10503×pre80true
101.0ms730×body80valid
13.0ms3×body2560valid
8.0ms5×body1280valid
2.0ms9×body160valid
2.0ms3×body640valid