Details

sample240.0ms

Algorithm

intervals

Results

117.0ms	1375×	body	80	nan
30.0ms	418×	body	80	valid
5.0ms	13×	body	640	valid
5.0ms	12×	body	320	valid
3.0ms	3×	body	1280	valid
2.0ms	11×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1299
4	353
3	127
2	58
1	30
0	17

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.2b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.1b	(log (- 1.0 z))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`associate--l+`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`associate-+r+` `add-cube-cbrt`
10×	`associate-+l+` `associate-*r/`
9×	`pow1`
7×	`sub-neg` `flip3--` `add-exp-log` `flip--` `distribute-lft-out--` `add-log-exp`
6×	`add-cbrt-cube` `associate-r`
5×	`difference-of-squares`
4×	`frac-add`
3×	`associate-l` `log-pow`
2×	`log-div`
1×	`+-commutative` `sum-log` `flip3-+` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

10.0ms	(- (log z) t)
36.0ms	(* y (- (log z) t))
32.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
6.0ms	(log (- 1.0 z))

series509.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- (log z) t)
99.0ms	(* y (- (log z) t))
259.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
60.0ms	(log (- 1.0 z))

simplify1.4s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
2	2201
1	617
0	241

prune852.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (- (log z) t))
0.2b	(* (/ 1.0 z) (/ 1.0 z))
0.5b	(/ 1/2 (* (/ 1.0 z) (/ 1.0 z)))
0.5b	(+ (* y (- (log z) t)) (* a (- (- (- (log 1.0) (* 1.0 z)) (/ 1/2 (* (/ 1.0 z) (/ 1.0 z)))) b)))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
43×	`times-frac`
42×	`associate--l+` `add-cube-cbrt`
36×	`add-cbrt-cube` `add-exp-log`
19×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
18×	`associate-+r+` `log-prod`
16×	`associate-l`
14×	`pow1`
13×	`cbrt-undiv` `swap-sqr` `div-exp`
12×	`associate-*r/`
10×	`associate-+l+` `sub-neg`
9×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`flip3--` `div-inv` `flip--` `unswap-sqr`
4×	`frac-add`
3×	`associate-/r/` `associate-/l*`
2×	`frac-times` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out--`
1×	`pow2` `+-commutative` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `flip3-+` `pow-plus` `pow-sqr` `log-pow` `pow-prod-up` `flip-+` `difference-of-squares`

Counts

4 → 173

Calls

4 calls:

23.0ms	(* y (- (log z) t))
18.0ms	(* (/ 1.0 z) (/ 1.0 z))
11.0ms	(/ 1/2 (* (/ 1.0 z) (/ 1.0 z)))
138.0ms	(+ (* y (- (log z) t)) (* a (- (- (- (log 1.0) (* 1.0 z)) (/ 1/2 (* (/ 1.0 z) (/ 1.0 z)))) b)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* y (- (log z) t))
28.0ms	(* (/ 1.0 z) (/ 1.0 z))
37.0ms	(/ 1/2 (* (/ 1.0 z) (/ 1.0 z)))
258.0ms	(+ (* y (- (log z) t)) (* a (- (- (- (log 1.0) (* 1.0 z)) (/ 1/2 (* (/ 1.0 z) (/ 1.0 z)))) b)))

simplify970.0ms

Counts

185 → 185

Iterations

Iter	Nodes
done	5000
1	1002
0	329

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (- (+ (* (* z a) 1.0) (+ (* b a) (* (* z (* z 0.5)) a)))))
0.0b	(+ (* (* z a) 1.0) (+ (* b a) (* (* z (* z 0.5)) a)))
6.2b	(* (* z (* z 0.5)) a)

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-log-exp`
12×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`exp-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`sum-log` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`rem-exp-log`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-r` `neg-log`
1×	`neg-sub0` `exp-neg` `+-commutative` `associate-+r+` `distribute-neg-in` `neg-mul-1` `flip3-+` `exp-diff` `associate-l` `exp-sum` `*-commutative` `flip-+`

Counts

3 → 58

Calls

3 calls:

182.0ms	(exp (- (+ (* (* z a) 1.0) (+ (* b a) (* (* z (* z 0.5)) a)))))
27.0ms	(+ (* (* z a) 1.0) (+ (* b a) (* (* z (* z 0.5)) a)))
61.0ms	(* (* z (* z 0.5)) a)

series148.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(exp (- (+ (* (* z a) 1.0) (+ (* b a) (* (* z (* z 0.5)) a)))))
54.0ms	(+ (* (* z a) 1.0) (+ (* b a) (* (* z (* z 0.5)) a)))
24.0ms	(* (* z (* z 0.5)) a)

simplify1.9s

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
2	2014
1	342
0	124

prune339.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* a (+ b (* z (* z 0.5)))) (* (* 1.0 a) z)))
0.0b	(/ 1 (exp (+ (* a (+ b (* z (* z 0.5)))) (* (* 1.0 a) z))))
0.0b	(+ (* a (+ b (* z (* z 0.5)))) (* (* 1.0 a) z))
0.0b	(* a (+ b (* z (* z 0.5))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
9×	`add-log-exp`
8×	`add-cbrt-cube`
7×	`pow1` `add-exp-log`
6×	`exp-prod`
5×	`exp-sum`
4×	`associate-/r*` `pow-flip`
3×	`associate-r` `associate-l` `associate-/l*`
2×	`distribute-rgt-in` `associate-+l+` `sum-log` `distribute-lft-in` `flip3-+` `div-exp` `associate-*r/` `flip-+` `rem-exp-log`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `clear-num` `frac-2neg` `1-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

38.0ms	(exp (+ (* a (+ b (* z (* z 0.5)))) (* (* 1.0 a) z)))
61.0ms	(/ 1 (exp (+ (* a (+ b (* z (* z 0.5)))) (* (* 1.0 a) z))))
21.0ms	(+ (* a (+ b (* z (* z 0.5)))) (* (* 1.0 a) z))
14.0ms	(* a (+ b (* z (* z 0.5))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(exp (+ (* a (+ b (* z (* z 0.5)))) (* (* 1.0 a) z)))
73.0ms	(/ 1 (exp (+ (* a (+ b (* z (* z 0.5)))) (* (* 1.0 a) z))))
71.0ms	(+ (* a (+ b (* z (* z 0.5)))) (* (* 1.0 a) z))
83.0ms	(* a (+ b (* z (* z 0.5))))

simplify1.4s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1909
1	393
0	143

prune634.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes374.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	28
1	28
0	23

end0.0ms

sample10.5s

Algorithm

intervals

Results

5.6s	41321×	body	80	nan
1.8s	12560×	body	80	valid
189.0ms	370×	body	640	valid
139.0ms	430×	body	320	valid
86.0ms	260×	body	160	valid
81.0ms	82×	body	1280	valid