Details

Time bar (total: 7.3m)

sample48.5s

Algorithm
intervals
Results
48.2s3808×body10240exit
83.0ms4064×pre80true
22.0ms247×body80valid
7.0ms3×body1280valid
1.0ms2×body320valid
1.0ms1×body640valid
1.0ms3×body160valid

simplify24.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05325
114725
285025
3500125

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.7b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.9b
(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)))

rewrite148.0ms

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
27×add-sqr-sqrt
26×times-frac
22×add-cube-cbrt
16×add-cbrt-cube
6×pow1 pow-unpow distribute-lft-out add-log-exp
4×cbrt-undiv associate-/r/ cbrt-unprod
3×div-inv
2×pow-pow flip3-+ flip-+ 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 → 267
Calls
4 calls:
16.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
10.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
12.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
92.0ms
(/ (* (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)))

series756.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
69.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
69.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
574.0ms
(/ (* (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)))

simplify274.0ms

Algorithm
egg-herbie
Counts
279 → 279
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
09765948
131425704
250015704

prune426.0ms

Filtered
279 candidates to 79 candidates (28.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.6b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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:
6.0ms
(* 0.5 (* s c_n))
6.0ms
(* 0.5 (* s c_p))

series38.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(* 0.5 (* s c_n))
18.0ms
(* 0.5 (* s c_p))

simplify57.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0153142
1595112
22373112
35002112

prune70.0ms

Filtered
42 candidates to 22 candidates (52.4%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
24.8b
(cbrt (* 0.5 (* s c_n)))
24.8b
(cbrt (* 0.5 (* s c_n)))
24.8b
(cbrt (* 0.5 (* s c_n)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt
9×pow1/3
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×swap-sqr associate-*r* associate-*l* add-cbrt-cube add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 58
Calls
4 calls:
7.0ms
(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
4.0ms
(cbrt (* 0.5 (* s c_n)))
4.0ms
(cbrt (* 0.5 (* s c_n)))
4.0ms
(cbrt (* 0.5 (* s c_n)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
85.0ms
(cbrt (* 0.5 (* s c_n)))
85.0ms
(cbrt (* 0.5 (* s c_n)))
86.0ms
(cbrt (* 0.5 (* s c_n)))

simplify93.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (88.0ms)

IterNodesCost
0205441
1703390
23412330
35001323

prune206.0ms

Filtered
70 candidates to 56 candidates (80.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
0.3b
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.7b
(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)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
170×add-exp-log
87×prod-exp
65×div-exp
56×pow-exp
43×pow-to-exp
25×add-sqr-sqrt *-un-lft-identity
24×unpow-prod-down
16×add-cbrt-cube
15×add-cube-cbrt times-frac
6×pow1 pow-unpow add-log-exp
4×cbrt-undiv associate-/r/ cbrt-unprod difference-of-squares
3×distribute-lft-out
2×pow-pow flip3-+ associate-*l/ flip-+ div-inv distribute-lft-out-- sqr-pow
1×sub-neg flip3-- frac-2neg diff-log clear-num associate-/r* flip-- associate-/l*
Counts
4 → 139
Calls
4 calls:
32.0ms
(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
16.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
10.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
86.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series895.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
45.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
70.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
694.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify106.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
08782899
139992646
250022646

prune427.0ms

Filtered
151 candidates to 71 candidates (47.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.4b

regimes352.0ms

bsearch3.9s

Steps
ItersRangePoint
6
-3.4158361945667567e-79
-5.1113148475473346e-80
-6.3436807628579684e-80

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06352
16352

end0.0ms

sample6.4m

Algorithm
intervals
Results
6.3m31417×body10240exit
618.0ms33809×pre80true
192.0ms2320×body80valid
36.0ms6×body5120valid
33.0ms20×body1280valid
10.0ms13×body640valid
6.0ms3×body2560valid
6.0ms26×body160valid
2.0ms4×body320valid