Details

Time bar (total: 5.2m)

sample44.3s

Algorithm
intervals
Results
44.1s3485×body10240exit
75.0ms3741×pre80true
21.0ms248×body80valid
3.0ms1×body2560valid
1.0ms5×body160valid
1.0ms2×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 (+ 1.0 (exp (- s)))))
0.5b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.0b
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.9b
(/ (* (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)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
556×add-exp-log
312×prod-exp
264×pow-exp
249×div-exp
184×pow-to-exp
97×*-un-lft-identity
70×add-sqr-sqrt
65×add-cube-cbrt
62×times-frac
54×prod-diff
36×unpow-prod-down
16×add-cbrt-cube
15×distribute-lft-out
10×associate-/r/
6×pow1 pow-unpow div-inv add-log-exp
5×flip3-+ flip-+
4×cbrt-undiv expm1-log1p-u cbrt-unprod log1p-expm1-u
3×fma-neg
2×pow-pow difference-of-squares sqr-pow
1×sub-neg flip3-- frac-2neg diff-log clear-num associate-/r* flip-- associate-/l* distribute-lft-out--
Counts
4 → 332
Calls
4 calls:
24.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
11.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
10.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
95.0ms
(/ (* (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)))

series770.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
70.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
69.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
584.0ms
(/ (* (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)))

simplify132.0ms

Algorithm
egg-herbie
Counts
344 → 344
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
012818124
143807090
250017090

prune624.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

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))

series22.0ms

Counts
1 → 3
Calls
1 calls:
22.0ms
(* 0.5 (* s c_n))

simplify71.0ms

Algorithm
egg-herbie
Counts
23 → 23
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
08877
132062
2123462
3343862
4500262

prune51.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

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:
6.0ms
(* 0.5 (* s c_n))
0.0ms
(expm1 (log1p (* 0.5 (* s c_n))))

series256.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(* 0.5 (* s c_n))
237.0ms
(expm1 (log1p (* 0.5 (* s c_n))))

simplify44.0ms

Algorithm
egg-herbie
Counts
37 → 37
Iterations

Useful iterations: 3 (41.0ms)

IterNodesCost
0171161
1545137
22039131
35001121

prune96.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ 1.0 (exp (- s))))
0.0b
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.5b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.5b
(/ (* (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)))

rewrite136.0ms

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:
8.0ms
(/ 1.0 (+ 1.0 (exp (- s))))
22.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
11.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
84.0ms
(/ (* (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)))

series859.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ 1.0 (+ 1.0 (exp (- s))))
46.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
70.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
713.0ms
(/ (* (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)))

simplify116.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
010874971
145983939
250013939

prune715.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes496.0ms

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04732
14732

end0.0ms

sample4.4m

Algorithm
intervals
Results
4.4m21497×body10240exit
438.0ms23205×pre80true
137.0ms1660×body80valid
59.0ms7×body5120valid
15.0ms8×body1280valid
5.0ms18×body160valid
4.0ms5×body640valid
3.0ms9×body320valid
2.0ms1×body2560valid