Details

sample180.0ms

Algorithm

intervals

Results

76.0ms	1422×	body	80	nan
25.0ms	376×	body	80	valid
3.0ms	9×	body	640	valid
2.0ms	2×	body	1280	valid
2.0ms	8×	body	320	valid
1.0ms	8×	body	160	valid

simplify399.0ms

Counts

1 → 1

Iterations

Useful iterations: 4 (31.0ms)

Iter	Nodes	Cost
0	17	18
1	30	18
2	58	18
3	112	18
4	286	17
5	973	17
done	5000	17

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.3b	(log (- 1.0 z))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

17.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
13.0ms	(* y (- (log z) t))
13.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
2.0ms	(log (- 1.0 z))

series444.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
72.0ms	(* y (- (log z) t))
186.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
44.0ms	(log (- 1.0 z))

simplify694.0ms

Counts

113 → 113

Iterations

Useful iterations: done (691.0ms)

Iter	Nodes	Cost
0	257	1795
1	633	1715
2	2269	1590
done	5000	1589

prune414.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
0.0b	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
0.1b	(* y (- (log z) t))
0.3b	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

rewrite632.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

411.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
105.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
12.0ms	(* y (- (log z) t))
99.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series590.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
165.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
74.0ms	(* y (- (log z) t))
247.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify781.0ms

Counts

135 → 135

Iterations

Useful iterations: done (771.0ms)

Iter	Nodes	Cost
0	265	3383
1	649	3262
2	2567	3067
done	5000	3066

prune590.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
0.0b	(exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
0.0b	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
6.8b	(* a (pow z 2))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-log-exp`
16×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `exp-prod` `*-un-lft-identity`
9×	`add-exp-log`
8×	`associate-r`
7×	`sum-log`
6×	`add-cbrt-cube`
4×	`pow1` `unpow-prod-down` `rem-exp-log` `unswap-sqr`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-l` `neg-log` `prod-exp`
2×	`+-commutative` `flip3-+` `flip-+` `unpow2` `sqr-pow`
1×	`neg-sub0` `exp-neg` `pow-to-exp` `neg-mul-1` `associate-+r+` `distribute-neg-in` `exp-diff` `exp-sum` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 75

Calls

4 calls:

14.0ms	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
102.0ms	(exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
6.0ms	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
6.0ms	(* a (pow z 2))

series243.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))
47.0ms	(exp (- (+ (* a b) (+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2)))))))
93.0ms	(+ (* 1.0 (* a z)) (* 0.5 (* a (pow z 2))))
33.0ms	(* a (pow z 2))

simplify540.0ms

Counts

87 → 87

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	132	1413
1	350	1327
2	1403	1223
done	5000	1223

prune274.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 z) (exp b))
0.0b	(* (pow (/ z (exp t)) y) (* x (pow (/ (- 1.0 z) (exp b)) a)))
0.2b	(pow (/ z (exp t)) y)
1.7b	(pow (/ (- 1.0 z) (exp b)) a)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
54×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
45×	`unpow-prod-down`
40×	`add-cube-cbrt`
36×	`prod-exp`
22×	`pow-exp`
17×	`associate-l`
12×	`div-exp`
11×	`pow-to-exp` `add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `pow-unpow`
5×	`associate-/l*`
4×	`div-inv` `add-log-exp`
3×	`associate-/r*` `cbrt-unprod` `sqr-pow`
2×	`pow-pow` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `associate-r` `clear-num` `*-commutative` `flip--`

Counts

4 → 148

Calls

4 calls:

8.0ms	(/ (- 1.0 z) (exp b))
40.0ms	(* (pow (/ z (exp t)) y) (* x (pow (/ (- 1.0 z) (exp b)) a)))
4.0ms	(pow (/ z (exp t)) y)
12.0ms	(pow (/ (- 1.0 z) (exp b)) a)

series729.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (- 1.0 z) (exp b))
474.0ms	(* (pow (/ z (exp t)) y) (* x (pow (/ (- 1.0 z) (exp b)) a)))
71.0ms	(pow (/ z (exp t)) y)
157.0ms	(pow (/ (- 1.0 z) (exp b)) a)

simplify854.0ms

Counts

160 → 160

Iterations

Useful iterations: 2 (198.0ms)

Iter	Nodes	Cost
0	284	2460
1	702	2324
2	2251	2180
done	5000	2180

prune522.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes179.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	30
1	32	30
done	32	30

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.2s	40359×	body	80	nan
755.0ms	12297×	body	80	valid
143.0ms	413×	body	640	valid
83.0ms	390×	body	320	valid
58.0ms	80×	body	1280	valid
39.0ms	288×	body	160	valid