Details

sample51.7s

Algorithm

intervals

Results

51.0s	3245×	body	10240	exit
470.0ms	3501×	pre	80	true
70.0ms	246×	body	80	valid
22.0ms	2×	body	5120	valid
6.0ms	1×	body	2560	valid
2.0ms	2×	body	320	valid
2.0ms	4×	body	160	valid
1.0ms	1×	body	640	valid

simplify806.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2041
4	2041
3	743
2	143
1	54
0	22

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (/ 1 (+ 1 (exp (- s)))))
1.0b	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
1.0b	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
3.7b	(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

1192×	`add-exp-log`
692×	`pow-exp`
684×	`prod-exp`
593×	`div-exp`
344×	`pow-to-exp`
116×	`rec-exp` `1-exp`
42×	`*-un-lft-identity`
36×	`unpow-prod-down`
33×	`add-sqr-sqrt`
29×	`times-frac`
22×	`add-cube-cbrt`
16×	`add-cbrt-cube`
8×	`pow1`
6×	`pow-unpow` `pow-pow` `distribute-lft-out` `add-log-exp` `difference-of-squares`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `insert-posit16` `div-inv`
2×	`flip3-+` `flip-+` `pow-flip` `distribute-lft-out--` `inv-pow` `sqr-pow`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `associate-/l`

Counts

4 → 476

Calls

4 calls:

27.0ms	(- 1 (/ 1 (+ 1 (exp (- s)))))
13.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
14.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
140.0ms	(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- 1 (/ 1 (+ 1 (exp (- s)))))
55.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
56.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
517.0ms	(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))

simplify994.0ms

Counts

488 → 488

Iterations

Iter	Nodes
done	2008
2	2008
1	1461
0	451

prune745.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)
1.0b	(log (/ 1 (+ 1 (exp (- t)))))
1.1b	(log (/ 1 (+ 1 (exp (- s)))))
10.0b	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod` `*-un-lft-identity`
26×	`add-sqr-sqrt`
24×	`times-frac`
22×	`add-cube-cbrt`
16×	`add-exp-log` `add-log-exp`
11×	`pow1`
8×	`rem-log-exp`
7×	`log-pow`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
4×	`sum-log` `diff-log` `div-exp` `associate-l` `associate-/r/` `frac-sub` `insert-posit16`
3×	`associate-r`
2×	`log-div` `rec-exp` `1-exp` `log-rec` `div-inv` `pow-flip` `inv-pow`
1×	`sub-neg` `flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

7.0ms	(* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)
6.0ms	(log (/ 1 (+ 1 (exp (- t)))))
6.0ms	(log (/ 1 (+ 1 (exp (- s)))))
49.0ms	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)
56.0ms	(log (/ 1 (+ 1 (exp (- t)))))
56.0ms	(log (/ 1 (+ 1 (exp (- s)))))
301.0ms	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

simplify892.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	2006
2	2006
1	777
0	310

prune816.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c_n (log 1/2))
1.0b	(log (/ 1 (+ 1 (exp (- t)))))
1.1b	(log (/ 1 (+ 1 (exp (- s)))))
10.3b	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (- (* c_n (log 1/2)) (* c_n (+ (* 1/2 t) (* (* t t) 1/8))))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

42×	`log-prod`
38×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`add-log-exp`
24×	`times-frac` `add-cube-cbrt`
16×	`add-exp-log`
11×	`pow1`
8×	`diff-log` `rem-log-exp`
7×	`sum-log` `log-pow`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
4×	`div-exp` `associate-r` `associate-/r/` `frac-sub` `insert-posit16`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
2×	`log-div` `rec-exp` `1-exp` `log-rec` `div-inv` `pow-flip` `inv-pow`
1×	`associate-+r-` `sub-neg` `flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip--` `associate--r+` `distribute-lft-out--` `associate--r-` `difference-of-squares` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

6.0ms	(* c_n (log 1/2))
6.0ms	(log (/ 1 (+ 1 (exp (- t)))))
6.0ms	(log (/ 1 (+ 1 (exp (- s)))))
70.0ms	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (- (* c_n (log 1/2)) (* c_n (+ (* 1/2 t) (* (* t t) 1/8))))))

series652.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* c_n (log 1/2))
57.0ms	(log (/ 1 (+ 1 (exp (- t)))))
54.0ms	(log (/ 1 (+ 1 (exp (- s)))))
366.0ms	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (- (* c_n (log 1/2)) (* c_n (+ (* 1/2 t) (* (* t t) 1/8))))))

simplify932.0ms

Counts

135 → 135

Iterations

Iter	Nodes
done	2001
2	2001
1	807
0	324

prune937.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c_n (log 1/2))
1.0b	(log (/ 1 (+ 1 (exp (- t)))))
1.1b	(log (/ 1 (+ 1 (exp (- s)))))
9.2b	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (* c_n (log 1/2))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

42×	`log-prod`
38×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
24×	`times-frac` `add-cube-cbrt`
16×	`add-exp-log` `add-log-exp`
11×	`pow1`
8×	`rem-log-exp`
7×	`log-pow`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
4×	`sum-log` `diff-log` `div-exp` `associate-r` `associate-/r/` `frac-sub` `insert-posit16`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
2×	`log-div` `rec-exp` `1-exp` `log-rec` `div-inv` `pow-flip` `inv-pow`
1×	`sub-neg` `flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

6.0ms	(* c_n (log 1/2))
7.0ms	(log (/ 1 (+ 1 (exp (- t)))))
6.0ms	(log (/ 1 (+ 1 (exp (- s)))))
53.0ms	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (* c_n (log 1/2))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* c_n (log 1/2))
54.0ms	(log (/ 1 (+ 1 (exp (- t)))))
57.0ms	(log (/ 1 (+ 1 (exp (- s)))))
271.0ms	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (log (/ 1 (+ 1 (exp (- t))))) c_p) (* c_n (log 1/2))))

simplify872.0ms

Counts

132 → 132

Iterations

Iter	Nodes
done	2000
2	2000
1	763
0	310

prune903.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes679.0ms

bsearch4.1s

Steps

Iters	Range		Point
6	2.633462366035074e-13	2.2473089262013714e-12	2.6881255227148673e-13

simplify10.0ms

Iterations

Iter	Nodes
done	63
1	63
0	43

end0.0ms

sample4.4m

Algorithm

intervals

Results

4.3m	19020×	body	10240	exit
993.0ms	20535×	pre	80	true
319.0ms	1460×	body	80	valid
98.0ms	6×	body	5120	valid
20.0ms	6×	body	2560	valid
14.0ms	6×	body	1280	valid
11.0ms	25×	body	160	valid
7.0ms	6×	body	640	valid
4.0ms	6×	body	320	valid