Details

Time bar (total: 10.0m)

sample39.7s

Algorithm
intervals
Results
39.4s3269×body10240exit
80.0ms3525×pre80true
23.0ms248×body80valid
3.0ms4×body640valid
2.0ms1×body1280valid
1.0ms2×body160valid
0.0ms1×body320valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 5.5b

Counts
2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (+ 1.0 (exp (- s))))
0.2b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.7b
(/ (* (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)))

rewrite443.0ms

Algorithm
rewrite-expression-head
Rules
4037×times-frac
3731×add-sqr-sqrt
3436×unpow-prod-down
2200×associate-*l*
2051×*-un-lft-identity
1231×add-cube-cbrt
1200×unswap-sqr
1000×associate-*r*
902×sqr-pow
558×add-exp-log
312×prod-exp
310×distribute-lft-out
264×pow-exp
250×div-exp
206×associate-/r/
200×difference-of-squares
184×pow-to-exp
104×div-inv
103×flip3-+ flip-+
100×*-commutative distribute-lft-out--
53×associate-/r*
52×associate-/l*
18×add-cbrt-cube
6×pow1 pow-unpow
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
2×pow-pow frac-2neg clear-num
Counts
4 → 2789
Calls
4 calls:
5.0ms
(/ 1.0 (+ 1.0 (exp (- s))))
8.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
8.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
116.0ms
(/ (* (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)))

series749.0ms

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

simplify878.0ms

Algorithm
egg-herbie
Counts
2801 → 2801
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
05002117861

prune11.6s

Filtered
2801 candidates to 1889 candidates (67.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New279832801
Fresh000
Picked101
Done000
Total279932802

Merged error: 0.2b

Counts
2802 → 3

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
0.3b
(log (/ 1.0 (+ 1.0 (exp (- s)))))
1.7b
(log (/ 1.0 (+ 1.0 (exp (- t)))))
11.5b
(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
630×*-un-lft-identity
540×associate-*l*
413×distribute-lft-out
277×pow1
273×log-pow
144×prod-diff
101×distribute-lft-out--
57×add-sqr-sqrt
50×add-cube-cbrt
42×log-prod
25×times-frac
22×log-div
16×add-log-exp
12×fma-neg
11×add-exp-log
8×associate-/r* associate-/l*
6×flip3-+ flip-+
5×rem-log-exp
4×expm1-log1p-u diff-log log-rec clear-num sum-log associate-/r/ frac-sub add-cbrt-cube log1p-expm1-u
3×difference-of-squares
2×+-commutative flip3-- frac-2neg div-exp associate--l+ flip-- div-inv associate--r+
1×sub-neg
Counts
4 → 385
Calls
4 calls:
12.0ms
(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
7.0ms
(log (/ 1.0 (+ 1.0 (exp (- s)))))
6.0ms
(log (/ 1.0 (+ 1.0 (exp (- t)))))
49.0ms
(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

series587.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
71.0ms
(log (/ 1.0 (+ 1.0 (exp (- s)))))
72.0ms
(log (/ 1.0 (+ 1.0 (exp (- t)))))
350.0ms
(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

simplify169.0ms

Algorithm
egg-herbie
Counts
397 → 397
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
094816284
1336211850
2500111844

prune742.0ms

Filtered
397 candidates to 113 candidates (28.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New3952397
Fresh112
Picked101
Done000
Total3973400

Merged error: 0.2b

Counts
400 → 3

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)
0.2b
(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
0.3b
(log (/ 1.0 (+ 1.0 (exp (- s)))))
11.5b
(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (fma t 0.5 (- (log 0.5) (* 0.03125 (/ (pow t 2) (pow 0.5 2))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
491×*-un-lft-identity
362×associate-*l*
289×distribute-lft-out
155×pow1
149×log-pow
108×prod-diff
71×distribute-lft-out--
48×add-sqr-sqrt
39×add-cube-cbrt
24×log-prod
16×add-log-exp
13×times-frac
12×log-div fma-neg
10×add-exp-log
6×add-cbrt-cube
5×flip3-+ flip-+
4×expm1-log1p-u diff-log associate-/r* sum-log frac-sub log1p-expm1-u associate-/l*
3×rem-log-exp associate-*r* difference-of-squares
2×+-commutative flip3-- log-rec associate--l+ clear-num associate-/r/ flip-- associate--r+
1×sub-neg frac-2neg div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 298
Calls
4 calls:
7.0ms
(* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)
12.0ms
(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
6.0ms
(log (/ 1.0 (+ 1.0 (exp (- s)))))
40.0ms
(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (fma t 0.5 (- (log 0.5) (* 0.03125 (/ (pow t 2) (pow 0.5 2))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

series737.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)
95.0ms
(log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))))
72.0ms
(log (/ 1.0 (+ 1.0 (exp (- s)))))
444.0ms
(- (+ (* (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n)) (+ (* (fma t 0.5 (- (log 0.5) (* 0.03125 (/ (pow t 2) (pow 0.5 2))))) c_p) (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))

simplify168.0ms

Algorithm
egg-herbie
Counts
310 → 310
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
086513902
131479902
250019895

prune807.0ms

Filtered
310 candidates to 95 candidates (30.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New3091310
Fresh022
Picked011
Done000
Total3094313

Merged error: 0.1b

Counts
313 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (+ (exp (* -1 s)) 1.0))
0.2b
(fma (log (- 1.0 (* 1.0 (/ 1 (+ (exp (- t)) 1.0))))) c_n (* 0.5 (* t c_p)))
0.2b
(log (- 1.0 (* 1.0 (/ 1 (+ (exp (- t)) 1.0)))))
41.8b
(fma (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 s)) 1.0))))) c_n (- (* 0.125 (* (pow t 2) c_p)) (fma (log (- 1.0 (* 1.0 (/ 1 (+ (exp (- t)) 1.0))))) c_n (* 0.5 (* t c_p)))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt *-un-lft-identity
16×add-cube-cbrt
14×times-frac
12×log-prod
9×add-exp-log
6×pow1 add-cbrt-cube
4×expm1-log1p-u associate-/r* log1p-expm1-u distribute-lft-out distribute-lft-out-- add-log-exp difference-of-squares
3×associate-*l* associate-/l* unswap-sqr
2×log-div div-exp associate-/r/ fma-udef
1×cbrt-undiv rec-exp flip3-- distribute-rgt-out-- pow-flip frac-2neg flip3-+ 1-exp rem-log-exp clear-num log-pow *-commutative flip-- flip-+ div-inv inv-pow
Counts
4 → 84
Calls
4 calls:
8.0ms
(/ 1 (+ (exp (* -1 s)) 1.0))
1.0ms
(fma (log (- 1.0 (* 1.0 (/ 1 (+ (exp (- t)) 1.0))))) c_n (* 0.5 (* t c_p)))
24.0ms
(log (- 1.0 (* 1.0 (/ 1 (+ (exp (- t)) 1.0)))))
1.0ms
(fma (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 s)) 1.0))))) c_n (- (* 0.125 (* (pow t 2) c_p)) (fma (log (- 1.0 (* 1.0 (/ 1 (+ (exp (- t)) 1.0))))) c_n (* 0.5 (* t c_p)))))

series542.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(/ 1 (+ (exp (* -1 s)) 1.0))
132.0ms
(fma (log (- 1.0 (* 1.0 (/ 1 (+ (exp (- t)) 1.0))))) c_n (* 0.5 (* t c_p)))
95.0ms
(log (- 1.0 (* 1.0 (/ 1 (+ (exp (- t)) 1.0)))))
292.0ms
(fma (log (- 1.0 (* 1.0 (/ 1 (+ (exp (* -1 s)) 1.0))))) c_n (- (* 0.125 (* (pow t 2) c_p)) (fma (log (- 1.0 (* 1.0 (/ 1 (+ (exp (- t)) 1.0))))) c_n (* 0.5 (* t c_p)))))

simplify45.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04421130
114121005
25001985

prune461.0ms

Filtered
96 candidates to 66 candidates (68.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New95196
Fresh022
Picked101
Done011
Total964100

Merged error: 0.1b

Counts
100 → 4

regimes464.0ms

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04532
14532

end0.0ms

sample9.0m

Algorithm
intervals
Results
9.0m43988×body10240exit
928.0ms47467×pre80true
299.0ms3364×body80valid
61.0ms8×body5120valid
47.0ms25×body1280valid
29.0ms11×body2560valid
22.0ms30×body640valid
8.0ms34×body160valid
2.0ms6×body320valid