Details

sample49.1s

Algorithm

intervals

Results

48.7s	3254×	body	10240	exit
166.0ms	3510×	pre	80	true
74.0ms	246×	body	80	valid
6.0ms	1×	body	5120	valid
5.0ms	2×	body	1280	valid
4.0ms	1×	body	2560	valid
2.0ms	3×	body	160	valid
2.0ms	2×	body	320	valid
1.0ms	1×	body	640	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
3	743
2	143
1	54
0	22

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)
0.7b	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
2.2b	(pow (/ 1 (+ 1 (exp (- t)))) 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)))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

1193×	`add-exp-log`
693×	`pow-exp`
684×	`prod-exp`
593×	`div-exp`
345×	`pow-to-exp`
116×	`rec-exp` `1-exp`
47×	`unpow-prod-down`
44×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
29×	`times-frac`
24×	`add-cube-cbrt`
16×	`add-cbrt-cube`
9×	`pow1` `pow-unpow`
7×	`pow-pow`
6×	`distribute-lft-out` `difference-of-squares`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `insert-posit16` `div-inv` `add-log-exp`
3×	`sqr-pow`
2×	`flip3-+` `flip-+` `pow-flip` `distribute-lft-out--` `inv-pow`
1×	`clear-num` `associate-/r` `frac-2neg` `associate-/l`

Counts

4 → 481

Calls

4 calls:

51.0ms	(pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)
12.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
13.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
134.0ms	(/ (* (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)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)
56.0ms	(pow (/ 1 (+ 1 (exp (- s)))) c_p)
56.0ms	(pow (/ 1 (+ 1 (exp (- t)))) c_p)
513.0ms	(/ (* (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)))

simplify1.7s

Counts

493 → 493

Iterations

Iter	Nodes
done	5016
2	3965
1	1534
0	461

prune684.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
0.7b	(log (/ 1 (+ 1 (exp (- s)))))
2.2b	(log (/ 1 (+ 1 (exp (- t)))))
10.1b	(- (+ (* (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)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

47×	`log-prod`
43×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
28×	`times-frac`
21×	`add-cube-cbrt`
16×	`add-log-exp`
15×	`add-exp-log`
9×	`pow1` `rem-log-exp`
7×	`log-pow` `difference-of-squares`
6×	`flip3-+` `flip-+` `distribute-lft-out`
4×	`log-div` `sum-log` `add-cbrt-cube` `diff-log` `div-exp` `associate-/r/` `frac-sub` `insert-posit16`
3×	`div-inv` `distribute-lft-out--`
2×	`rec-exp` `flip3--` `1-exp` `log-rec` `pow-flip` `flip--` `inv-pow`
1×	`sub-neg` `associate--l+` `associate--r+`

Counts

4 → 117

Calls

4 calls:

26.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
6.0ms	(log (/ 1 (+ 1 (exp (- s)))))
6.0ms	(log (/ 1 (+ 1 (exp (- t)))))
50.0ms	(- (+ (* (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)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
55.0ms	(log (/ 1 (+ 1 (exp (- s)))))
55.0ms	(log (/ 1 (+ 1 (exp (- t)))))
298.0ms	(- (+ (* (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)))

simplify1.7s

Counts

129 → 129

Iterations

Iter	Nodes
done	5004
2	2363
1	812
0	330

prune816.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
0.3b	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
0.7b	(log (/ 1 (+ 1 (exp (- s)))))
10.1b	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (+ (- (log 1/2) (* (* t t) 1/8)) (* t 1/2)) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

40×	`log-prod`
38×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`times-frac`
16×	`add-log-exp`
14×	`add-cube-cbrt`
13×	`difference-of-squares`
11×	`add-exp-log`
8×	`pow1`
6×	`rem-log-exp`
5×	`log-div` `flip3-+` `log-pow` `flip-+` `distribute-lft-out--`
4×	`sum-log` `add-cbrt-cube` `diff-log` `frac-sub` `insert-posit16`
3×	`flip3--` `div-inv` `flip--` `distribute-lft-out`
2×	`div-exp` `associate-/r/`
1×	`rec-exp` `sub-neg` `1-exp` `log-rec` `associate--l+` `pow-flip` `associate--r+` `inv-pow`

Counts

4 → 105

Calls

4 calls:

26.0ms	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
26.0ms	(log (- 1 (/ 1 (+ 1 (exp (- t))))))
6.0ms	(log (/ 1 (+ 1 (exp (- s)))))
82.0ms	(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (+ (- (log 1/2) (* (* t t) 1/8)) (* t 1/2)) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

series548.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(log (- 1 (/ 1 (+ 1 (exp (- s))))))
64.0ms	(log (- 1 (/ 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 1/2) (* (* t t) 1/8)) (* t 1/2)) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- t)))))) c_n)))

simplify2.0s

Counts

117 → 117

Iterations

Iter	Nodes
done	5003
2	2366
1	794
0	330

prune856.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c_n (log (- 1 (/ 1 (+ (exp (- t)) 1)))))
0.3b	(log (- 1 (/ 1 (+ (exp (- s)) 1))))
0.3b	(log (- 1 (/ 1 (+ (exp (- t)) 1))))
8.7b	(- (+ (* c_n (log (- 1 (/ 1 (+ (exp (- s)) 1))))) (- (* (* (* 1/8 t) t) c_p) (* (* 1/2 t) c_p))) (* c_n (log (- 1 (/ 1 (+ (exp (- t)) 1))))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
66×	`log-prod`
60×	`*-un-lft-identity`
36×	`difference-of-squares`
24×	`times-frac`
22×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
13×	`add-log-exp`
12×	`add-cube-cbrt` `distribute-lft-out--`
9×	`pow1`
8×	`add-exp-log`
6×	`add-cbrt-cube` `div-inv`
4×	`log-div` `diff-log` `associate-r` `insert-posit16`
3×	`flip3--` `associate-l` `log-pow` `flip--`
2×	`sum-log` `rem-log-exp`
1×	`associate--l-` `associate-+r-` `sub-neg` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 127

Calls

4 calls:

82.0ms	(* c_n (log (- 1 (/ 1 (+ (exp (- t)) 1)))))
39.0ms	(log (- 1 (/ 1 (+ (exp (- s)) 1))))
39.0ms	(log (- 1 (/ 1 (+ (exp (- t)) 1))))
876.0ms	(- (+ (* c_n (log (- 1 (/ 1 (+ (exp (- s)) 1))))) (- (* (* (* 1/8 t) t) c_p) (* (* 1/2 t) c_p))) (* c_n (log (- 1 (/ 1 (+ (exp (- t)) 1))))))

series401.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* c_n (log (- 1 (/ 1 (+ (exp (- t)) 1)))))
62.0ms	(log (- 1 (/ 1 (+ (exp (- s)) 1))))
64.0ms	(log (- 1 (/ 1 (+ (exp (- t)) 1))))
210.0ms	(- (+ (* c_n (log (- 1 (/ 1 (+ (exp (- s)) 1))))) (- (* (* (* 1/8 t) t) c_p) (* (* 1/2 t) c_p))) (* c_n (log (- 1 (/ 1 (+ (exp (- t)) 1))))))

simplify1.6s

Counts

139 → 139

Iterations

Iter	Nodes
done	5004
2	1578
1	627
0	289

prune807.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes389.0ms

bsearch2.5s

Steps

Iters	Range		Point
5	2.138597944988289e-25	8.405593532113127e-25	2.202640187188369e-25

simplify13.0ms

Iterations

Iter	Nodes
done	71
1	71
0	55

end0.0ms

sample8.9m

Algorithm

intervals

Results

8.8m	39084×	body	10240	exit
2.8s	42170×	pre	80	true
634.0ms	2987×	body	80	valid
89.0ms	6×	body	5120	valid
46.0ms	21×	body	1280	valid
31.0ms	8×	body	2560	valid
24.0ms	20×	body	640	valid
16.0ms	35×	body	160	valid
5.0ms	8×	body	320	valid