Details

Time bar (total: 3.4m)

sample40.7s

Algorithm
intervals
Results
40.4s3162×body10240exit
75.0ms3418×pre80true
21.0ms252×body80valid
11.0ms1×body2560valid
2.0ms1×body1280valid
1.0ms1×body640valid
0.0ms1×body160valid

simplify25.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05325
114725
285025
3500125

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.5b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.5b
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.4b
(/ (* (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)))

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:
22.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
10.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
11.0ms
(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)))

series768.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
65.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
70.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
583.0ms
(/ (* (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)))

simplify137.0ms

Algorithm
egg-herbie
Counts
344 → 344
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
012818124
143897090
250017090

prune599.0ms

Filtered
344 candidates to 106 candidates (30.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

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))

series19.0ms

Counts
1 → 3
Calls
1 calls:
19.0ms
(* 0.5 (* s c_n))

simplify72.0ms

Algorithm
egg-herbie
Counts
23 → 23
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
08877
132062
2123462
3343862
4500262

prune53.0ms

Filtered
23 candidates to 13 candidates (56.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

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

series254.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(* 0.5 (* s c_n))
236.0ms
(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

prune93.0ms

Filtered
37 candidates to 25 candidates (67.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.1b
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.5b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.0b
(/ (* (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)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
169×add-exp-log
145×*-un-lft-identity
109×add-sqr-sqrt
108×prod-diff
99×add-cube-cbrt
87×times-frac prod-exp
65×div-exp
55×pow-exp
42×pow-to-exp
21×distribute-lft-out
18×unpow-prod-down
16×add-cbrt-cube
14×associate-/r/
8×div-inv add-log-exp
7×flip3-+ flip-+
6×fma-neg
5×pow1
4×cbrt-undiv expm1-log1p-u cbrt-unprod log1p-expm1-u difference-of-squares
3×pow-unpow
2×sub-neg flip3-- diff-log flip-- distribute-lft-out--
1×pow-pow frac-2neg clear-num associate-/r* associate-/l* sqr-pow
Counts
4 → 254
Calls
4 calls:
23.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
22.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
12.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
85.0ms
(/ (* (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)))

series871.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
46.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
70.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
706.0ms
(/ (* (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)))

simplify78.0ms

Algorithm
egg-herbie
Counts
266 → 266
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
014416977
150025446

prune749.0ms

Filtered
266 candidates to 113 candidates (42.5%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes286.0ms

bsearch5.8s

Steps
ItersRangePoint
8
-3578903.2745927186
-749.8313671573056
-425232.67267408624

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04731
14731

end0.0ms

sample2.6m

Algorithm
intervals
Results
2.6m12570×body10240exit
252.0ms13542×pre80true
76.0ms938×body80valid
25.0ms6×body2560valid
14.0ms7×body1280valid
11.0ms2×body5120valid
3.0ms5×body640valid
2.0ms10×body160valid
1.0ms4×body320valid