Details

Time bar (total: 5.1m)

sample52.0s

Algorithm
intervals
Results
51.5s3614×body10240exit
151.0ms3870×pre80true
29.0ms246×body80valid
8.0ms5×body1280valid
1.0ms2×body320valid
1.0ms3×body160valid

simplify517.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02243
15343
214743
384743
done500043

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.5b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.7b
(/ (* (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)))

rewrite280.0ms

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:
39.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
21.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
19.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
175.0ms
(/ (* (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)))

series828.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
72.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
70.0ms
(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
633.0ms
(/ (* (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)))

simplify758.0ms

Counts
344 → 344
Iterations

Useful iterations: done (744.0ms)

IterNodesCost
047114274
1150613193
done500111961

prune722.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.9b
(log (/ 1.0 (+ 1.0 (exp (- t)))))
9.3b
(- (log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n))) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
10.1b
(log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
31×add-exp-log add-sqr-sqrt
29×add-cube-cbrt
24×times-frac
20×log-prod
18×unpow-prod-down
15×rem-log-exp
12×pow1 prod-diff pow-exp prod-exp
8×pow-to-exp
7×log-pow
6×distribute-lft-out
5×div-exp add-log-exp
4×expm1-log1p-u fma-neg associate-/r/ add-cbrt-cube log1p-expm1-u
3×pow-unpow
2×flip3-+ flip-+ div-inv distribute-lft-out--
1×sub-neg log-div flip3-- pow-pow diff-log associate--l+ flip-- fma-udef associate--r+ difference-of-squares sqr-pow
Counts
4 → 125
Calls
4 calls:
20.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
10.0ms
(log (/ 1.0 (+ 1.0 (exp (- t)))))
907.0ms
(- (log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n))) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
92.0ms
(log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)))

series687.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
73.0ms
(log (/ 1.0 (+ 1.0 (exp (- t)))))
335.0ms
(- (log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n))) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
205.0ms
(log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)))

simplify1.0s

Counts
137 → 137
Iterations

Useful iterations: done (1.0s)

IterNodesCost
03035145
17634137
223923781
done50003181

prune666.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)
0.5b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
9.3b
(- (log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n))) (fma (- (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)))
10.1b
(log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity
30×add-exp-log
27×add-sqr-sqrt
23×add-cube-cbrt
18×unpow-prod-down
14×pow1
13×rem-log-exp prod-exp
12×times-frac prod-diff pow-exp
8×pow-to-exp
7×log-pow
6×add-cbrt-cube
5×add-log-exp
4×expm1-log1p-u fma-neg div-exp associate-*l* log1p-expm1-u
3×pow-unpow associate-*r* distribute-lft-out
2×log-prod associate-/r/ distribute-lft-out--
1×sub-neg flip3-- pow-pow flip3-+ diff-log pow-prod-down associate--l+ *-commutative flip-- cbrt-unprod flip-+ fma-udef div-inv associate--r+ difference-of-squares unswap-sqr sqr-pow
Counts
4 → 115
Calls
4 calls:
9.0ms
(* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)
20.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
909.0ms
(- (log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n))) (fma (- (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)))
89.0ms
(log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)))

series944.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)
75.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
529.0ms
(- (log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n))) (fma (- (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)))
206.0ms
(log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)))

simplify1.1s

Counts
127 → 127
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02695711
17034467
223594044
done50003284

prune820.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
6.3b
(+ (log (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)) (fma (log (- 1.0 (/ 1.0 (+ (exp (- s)) 1.0)))) c_n (- (fma (- (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)))))
6.9b
(log (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p))
21.9b
(fma (log (- 1.0 (/ 1.0 (+ (exp (- s)) 1.0)))) c_n (- (fma (- (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))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
54×unpow-prod-down
52×*-un-lft-identity
44×log-prod
36×times-frac
32×add-sqr-sqrt add-cube-cbrt
22×associate-+l+
11×add-exp-log
10×distribute-lft-out
6×associate-/r/
5×pow1 add-log-exp
4×expm1-log1p-u fma-def flip3-+ rem-log-exp pow-exp add-cbrt-cube flip-+ log1p-expm1-u
3×pow-unpow div-inv sqr-pow
2×pow-to-exp div-exp log-pow fma-udef
1×+-commutative associate-+r+ pow-pow sum-log
Counts
4 → 122
Calls
4 calls:
22.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
25.0ms
(+ (log (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)) (fma (log (- 1.0 (/ 1.0 (+ (exp (- s)) 1.0)))) c_n (- (fma (- (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)))))
20.0ms
(log (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p))
0.0ms
(fma (log (- 1.0 (/ 1.0 (+ (exp (- s)) 1.0)))) c_n (- (fma (- (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))))

series1.1s

Counts
4 → 12
Calls
4 calls:
75.0ms
(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
510.0ms
(+ (log (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)) (fma (log (- 1.0 (/ 1.0 (+ (exp (- s)) 1.0)))) c_n (- (fma (- (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)))))
118.0ms
(log (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p))
387.0ms
(fma (log (- 1.0 (/ 1.0 (+ (exp (- s)) 1.0)))) c_n (- (fma (- (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))))

simplify747.0ms

Counts
134 → 134
Iterations

Useful iterations: done (741.0ms)

IterNodesCost
02714304
17234070
221903895
done50023892

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes183.0ms

bsearch18.7s

Steps
ItersRangePoint
8
7.063282869349052e-15
2.9703652465524333e-12
9.060649289903659e-15
10
-5.593212834993475e+18
-42750.626523382765
-746704198.5377269

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
049128
16175
done6175

end0.0ms

sample3.7m

Algorithm
intervals
Results
3.7m17031×body10240exit
626.0ms18375×pre80true
162.0ms1304×body80valid
56.0ms5×body5120valid
21.0ms12×body1280valid
4.0ms2×body2560valid
4.0ms8×body320valid
3.0ms11×body160valid
2.0ms2×body640valid