Details

Time bar (total: 4.5m)

sample15.8s

Algorithm
intervals
Results
15.2s1617×body10240exit
295.0ms1791×body80overflowed
95.0ms3664×pre80true
38.0ms247×body80valid
4.0ms2×body1280valid
2.0ms2×body640valid
2.0ms4×body160valid
1.0ms1×body320valid

simplify25.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05325
114725
285025
3500125

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ 1.0 (exp (- t))))
0.5b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
0.7b
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
4.2b
(/ (* (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)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
558×add-exp-log
312×prod-exp
264×pow-exp
250×div-exp
184×pow-to-exp
51×*-un-lft-identity
37×times-frac
36×unpow-prod-down
31×add-sqr-sqrt add-cube-cbrt
18×add-cbrt-cube
10×distribute-lft-out
6×pow1 pow-unpow associate-/r/
5×cbrt-undiv associate-/r*
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv associate-/l* add-log-exp
3×flip3-+ flip-+
2×pow-pow frac-2neg clear-num sqr-pow
Counts
4 → 293
Calls
4 calls:
10.0ms
(/ 1.0 (+ 1.0 (exp (- t))))
10.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
10.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
93.0ms
(/ (* (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)))

series801.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ 1.0 (+ 1.0 (exp (- t))))
69.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
75.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
624.0ms
(/ (* (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)))

simplify104.0ms

Algorithm
egg-herbie
Counts
305 → 305
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
09936127
133505877
250025877

prune751.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.3b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(* 0.5 (* s c_n))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 add-exp-log add-cbrt-cube
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
1×expm1-log1p-u associate-*r* *-commutative log1p-expm1-u add-log-exp
Counts
1 → 20
Calls
1 calls:
6.0ms
(* 0.5 (* s c_n))

series20.0ms

Counts
1 → 3
Calls
1 calls:
20.0ms
(* 0.5 (* s c_n))

simplify73.0ms

Algorithm
egg-herbie
Counts
23 → 23
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
08877
132062
2123462
3343862
4500262

prune58.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 0.5 (* s c_n))
0.2b
(expm1 (log1p (* 0.5 (* s c_n))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
3×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*l* pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×expm1-log1p associate-*r* *-commutative expm1-udef
Counts
2 → 31
Calls
2 calls:
5.0ms
(* 0.5 (* s c_n))
0.0ms
(expm1 (log1p (* 0.5 (* s c_n))))

series269.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(* 0.5 (* s c_n))
249.0ms
(expm1 (log1p (* 0.5 (* s c_n))))

simplify52.0ms

Algorithm
egg-herbie
Counts
37 → 37
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0171161
1545137
22039131
35001121

prune103.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.0b
(/ 1.0 (+ 1.0 (exp (- t))))
0.5b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.2b
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
171×add-exp-log
99×*-un-lft-identity
87×prod-exp
70×add-sqr-sqrt
66×div-exp
65×add-cube-cbrt
62×times-frac
55×pow-exp
54×prod-diff
42×pow-to-exp
18×unpow-prod-down add-cbrt-cube
16×distribute-lft-out
10×associate-/r/
6×div-inv add-log-exp
5×pow1 cbrt-undiv flip3-+ associate-/r* flip-+
4×expm1-log1p-u cbrt-unprod log1p-expm1-u associate-/l*
3×pow-unpow fma-neg
2×frac-2neg clear-num difference-of-squares
1×sub-neg flip3-- pow-pow diff-log flip-- distribute-lft-out-- sqr-pow
Counts
4 → 215
Calls
4 calls:
24.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
8.0ms
(/ 1.0 (+ 1.0 (exp (- t))))
10.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
82.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series901.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
32.0ms
(/ 1.0 (+ 1.0 (exp (- t))))
74.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
747.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify128.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
011564971
147873939
250013939

prune716.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.3b

regimes619.0ms

bsearch6.4s

Steps
ItersRangePoint
11
-1.2669587448301954e+23
-5726.9977552392365
-748255414.889585

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04731
14731

end0.0ms

sample4.1m

Algorithm
intervals
Results
3.9m26145×body10240exit
4.5s28535×body80overflowed
1.3s58949×pre80true
624.0ms4145×body80valid
60.0ms29×body1280valid
59.0ms9×body5120valid
33.0ms10×body2560valid
26.0ms23×body640valid
16.0ms41×body160valid
7.0ms12×body320valid