Details

sample50.9s

Algorithm

intervals

Results

50.5s	3245×	body	10240	exit
210.0ms	3501×	pre	80	true
51.0ms	246×	body	80	valid
19.0ms	2×	body	5120	valid
6.0ms	1×	body	2560	valid
2.0ms	4×	body	160	valid
2.0ms	1×	body	640	valid
2.0ms	2×	body	320	valid

simplify813.0ms

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

localize45.0ms

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)))

rewrite218.0ms

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`
103×	`*-un-lft-identity`
76×	`add-sqr-sqrt`
65×	`times-frac` `add-cube-cbrt`
54×	`prod-diff`
36×	`unpow-prod-down`
16×	`add-cbrt-cube`
15×	`distribute-lft-out`
10×	`associate-/r/`
8×	`pow1`
7×	`div-inv`
6×	`pow-unpow` `pow-pow` `add-log-exp` `difference-of-squares`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-undiv` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`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 → 541

Calls

4 calls:

34.0ms	(- 1 (/ 1 (+ 1 (exp (- s)))))
13.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
13.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
144.0ms	(/ (* (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)))

series678.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(- 1 (/ 1 (+ 1 (exp (- s)))))
59.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
57.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
533.0ms	(/ (* (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)))

simplify1.0s

Counts

553 → 553

Iterations

Iter	Nodes
done	2000
2	2000
1	1508
0	555

prune1.1s

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)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
36×	`log-prod`
33×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
24×	`times-frac`
16×	`add-exp-log` `add-log-exp`
11×	`pow1`
9×	`prod-diff`
8×	`rem-log-exp`
7×	`log-pow`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
4×	`expm1-log1p-u` `sum-log` `diff-log` `div-exp` `associate-l` `associate-/r/` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `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 → 134

Calls

4 calls:

7.0ms	(* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)
7.0ms	(log (/ 1 (+ 1 (exp (- t)))))
7.0ms	(log (/ 1 (+ 1 (exp (- s)))))
61.0ms	(- (+ (* (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)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)
56.0ms	(log (/ 1 (+ 1 (exp (- t)))))
59.0ms	(log (/ 1 (+ 1 (exp (- s)))))
312.0ms	(- (+ (* (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)))

simplify827.0ms

Counts

146 → 146

Iterations

Iter	Nodes
done	2003
2	2003
1	864
0	342

prune954.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize79.0ms

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 (+ (* 1/8 (* t t)) (* t 1/2))))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
42×	`log-prod`
35×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
25×	`add-log-exp`
24×	`times-frac`
16×	`add-exp-log`
11×	`pow1`
9×	`prod-diff`
8×	`diff-log` `rem-log-exp`
7×	`sum-log` `log-pow`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
4×	`expm1-log1p-u` `div-exp` `associate-r` `associate-/r/` `frac-sub` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `distribute-lft-in` `fma-neg` `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 → 143

Calls

4 calls:

6.0ms	(* c_n (log 1/2))
7.0ms	(log (/ 1 (+ 1 (exp (- t)))))
7.0ms	(log (/ 1 (+ 1 (exp (- s)))))
89.0ms	(- (+ (* (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 (+ (* 1/8 (* t t)) (* t 1/2))))))

series660.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(* c_n (log 1/2))
58.0ms	(log (/ 1 (+ 1 (exp (- t)))))
58.0ms	(log (/ 1 (+ 1 (exp (- s)))))
371.0ms	(- (+ (* (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 (+ (* 1/8 (* t t)) (* t 1/2))))))

simplify752.0ms

Counts

155 → 155

Iterations

Iter	Nodes
done	2001
2	2001
1	896
0	357

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

1.0b	(log1p (exp (- t)))
1.0b	(log1p (exp (- s)))
6.4b	(- (* c_n (log1p (/ -1 (+ 1 (exp (- s)))))) (fma (- (log1p (exp (- t)))) c_p (* c_n (log 1/2))))
31.1b	(fma (- (log1p (exp (- s)))) c_p (- (* c_n (log1p (/ -1 (+ 1 (exp (- s)))))) (fma (- (log1p (exp (- t)))) c_p (* c_n (log 1/2)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`expm1-log1p-u` `add-log-exp`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`prod-diff`
2×	`log1p-udef` `log1p-expm1` `fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--` `associate--r+`

Counts

4 → 55

Calls

4 calls:

0.0ms	(log1p (exp (- t)))
0.0ms	(log1p (exp (- s)))
14.0ms	(- (* c_n (log1p (/ -1 (+ 1 (exp (- s)))))) (fma (- (log1p (exp (- t)))) c_p (* c_n (log 1/2))))
0.0ms	(fma (- (log1p (exp (- s)))) c_p (- (* c_n (log1p (/ -1 (+ 1 (exp (- s)))))) (fma (- (log1p (exp (- t)))) c_p (* c_n (log 1/2)))))

series634.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(log1p (exp (- t)))
49.0ms	(log1p (exp (- s)))
249.0ms	(- (* c_n (log1p (/ -1 (+ 1 (exp (- s)))))) (fma (- (log1p (exp (- t)))) c_p (* c_n (log 1/2))))
282.0ms	(fma (- (log1p (exp (- s)))) c_p (- (* c_n (log1p (/ -1 (+ 1 (exp (- s)))))) (fma (- (log1p (exp (- t)))) c_p (* c_n (log 1/2)))))

simplify709.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	2003
3	2003
2	747
1	299
0	151

prune489.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes708.0ms

bsearch4.1s

Steps

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

simplify8.0ms

Iterations

Iter	Nodes
done	53
1	53
0	40

end0.0ms

sample4.4m

Algorithm

intervals

Results

4.4m	19020×	body	10240	exit
852.0ms	20535×	pre	80	true
349.0ms	1460×	body	80	valid
99.0ms	6×	body	5120	valid
40.0ms	6×	body	2560	valid
13.0ms	6×	body	1280	valid
11.0ms	25×	body	160	valid
7.0ms	6×	body	640	valid
4.0ms	6×	body	320	valid