Details

Time bar (total: 50.2s)

sample37.2s

Algorithm
intervals
Results
36.9s2993×body10240exit
71.0ms3249×pre80true
23.0ms245×body80valid
5.0ms3×body1280valid
2.0ms3×body640valid
2.0ms1×body2560valid
1.0ms4×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 7.0b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.7b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.0b
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
4.9b
(/ (* (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)))

rewrite86.0ms

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:
11.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
7.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
7.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
40.0ms
(/ (* (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)))

series742.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
67.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
67.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
561.0ms
(/ (* (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)))

simplify133.0ms

Algorithm
egg-herbie
Counts
344 → 344
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
012818124
143897090
250017090

prune534.0ms

Filtered
344 candidates to 106 candidates (30.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New3413344
Fresh000
Picked101
Done000
Total3423345

Merged error: 1.0b

Counts
345 → 3

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(* 0.5 (* s c_n))

rewrite5.0ms

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:
5.0ms
(* 0.5 (* s c_n))

series18.0ms

Counts
1 → 3
Calls
1 calls:
18.0ms
(* 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

prune47.0ms

Filtered
23 candidates to 13 candidates (56.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New21223
Fresh022
Picked011
Done000
Total21526

Merged error: 1.0b

Counts
26 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
24.1b
(cbrt (* 0.5 (* s c_n)))
24.1b
(cbrt (* 0.5 (* s c_n)))
24.1b
(cbrt (* 0.5 (* s c_n)))

rewrite17.0ms

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×expm1-log1p-u swap-sqr associate-*r* associate-*l* add-cbrt-cube log1p-expm1-u 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 → 66
Calls
4 calls:
5.0ms
(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
3.0ms
(cbrt (* 0.5 (* s c_n)))
3.0ms
(cbrt (* 0.5 (* s c_n)))
4.0ms
(cbrt (* 0.5 (* s c_n)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
89.0ms
(cbrt (* 0.5 (* s c_n)))
88.0ms
(cbrt (* 0.5 (* s c_n)))
87.0ms
(cbrt (* 0.5 (* s c_n)))

simplify96.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (90.0ms)

IterNodesCost
0212478
1738427
23536370
35002365

prune223.0ms

Filtered
78 candidates to 64 candidates (82.1%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New76278
Fresh033
Picked101
Done101
Total78583

Merged error: 1.0b

Counts
83 → 5

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))
1.0ms
(expm1 (log1p (* 0.5 (* s c_n))))

series251.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(* 0.5 (* s c_n))
233.0ms
(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

prune68.0ms

Filtered
37 candidates to 25 candidates (67.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New37037
Fresh044
Picked011
Done000
Total37542

Merged error: 1.0b

Counts
42 → 5

regimes434.0ms

bsearch9.8s

Steps
ItersRangePoint
8
2.703590242943542
1558.1114502043392
1062.9423532569451
6
1.0761465663171227e-129
5.690793995257063e-129
1.0901247291415457e-129