Details

Time bar (total: 3.3m)

sample17.3s

Algorithm
intervals
Results
16.6s1730×body10240exit
324.0ms1878×body80overflowed
111.0ms3865×pre80true
43.0ms248×body80valid
5.0ms2×body1280valid
2.0ms5×body160valid
1.0ms1×body640valid
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

localize21.0ms

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)
1.9b
(pow (/ 1.0 (+ 1.0 (exp (- t)))) 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)))

rewrite142.0ms

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:
8.0ms
(/ 1.0 (+ 1.0 (exp (- t))))
10.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
12.0ms
(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)))

series755.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ 1.0 (+ 1.0 (exp (- t))))
70.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
70.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
589.0ms
(/ (* (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)))

simplify108.0ms

Algorithm
egg-herbie
Counts
305 → 305
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
09936127
133505877
250025877

prune600.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b
(* 0.5 (* s c_n))

rewrite9.0ms

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:
9.0ms
(* 0.5 (* s c_n))

series25.0ms

Counts
1 → 3
Calls
1 calls:
25.0ms
(* 0.5 (* s c_n))

simplify104.0ms

Algorithm
egg-herbie
Counts
23 → 23
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
08877
132062
2123462
3343862
4500262

prune70.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 0.5 (* s c_n))
0.1b
(expm1 (log1p (* 0.5 (* s c_n))))

rewrite10.0ms

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:
9.0ms
(* 0.5 (* s c_n))
0.0ms
(expm1 (log1p (* 0.5 (* s c_n))))

series303.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(* 0.5 (* s c_n))
284.0ms
(expm1 (log1p (* 0.5 (* s c_n))))

simplify46.0ms

Algorithm
egg-herbie
Counts
37 → 37
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0171161
1545137
22039131
35001121

prune90.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize30.0ms

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)
2.5b
(/ (* (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)))

rewrite134.0ms

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:
22.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
8.0ms
(/ 1.0 (+ 1.0 (exp (- t))))
11.0ms
(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)))

series865.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
25.0ms
(/ 1.0 (+ 1.0 (exp (- t))))
71.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
716.0ms
(/ (* (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)))

simplify122.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
011564971
147873939
250013939

prune689.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.6b

regimes192.0ms

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04732
14732

end0.0ms

sample3.0m

Algorithm
intervals
Results
2.8m19286×body10240exit
3.4s21178×body80overflowed
1.0s43675×pre80true
477.0ms3104×body80valid
44.0ms22×body1280valid
39.0ms6×body5120valid
19.0ms19×body640valid
17.0ms42×body160valid
13.0ms5×body2560valid
8.0ms13×body320valid