Details

sample757.0ms

Algorithm

intervals

Results

460.0ms	410×	body	80	valid
142.0ms	1266×	body	80	nan
7.0ms	12×	body	640	valid
3.0ms	7×	body	320	valid
2.0ms	9×	body	160	valid
1.0ms	1×	body	1280	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 4 (52.0ms)

Iter	Nodes	Cost
0	17	18
1	30	18
2	58	18
3	127	18
4	311	17
5	1010	17
done	5000	17

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
0.2b	(* y (- (log z) t))
0.5b	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
4.6b	(log (- 1.0 z))

rewrite145.0ms

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:

48.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
54.0ms	(* y (- (log z) t))
35.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
5.0ms	(log (- 1.0 z))

series646.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))
106.0ms	(* y (- (log z) t))
252.0ms	(+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b)))
77.0ms	(log (- 1.0 z))

simplify1.3s

Counts

113 → 113

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	257	1795
1	631	1715
2	1998	1590
done	5000	1562

prune654.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

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

rewrite1.6s

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:

1.1s	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
252.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
35.0ms	(* y (- (log z) t))
245.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

series911.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))
260.0ms	(exp (+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b))))
107.0ms	(* y (- (log z) t))
362.0ms	(+ (* y (- (log z) t)) (* a (- (- (log 1.0) (+ (* 1/2 (/ (pow z 2) (pow 1.0 2))) (* 1.0 z))) b)))

simplify1.3s

Counts

135 → 135

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	265	3383
1	646	3262
2	2088	3069
done	5000	2993

prune884.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow 1.0 a) (exp (+ (* 1/2 (/ (* a (pow z 2)) (pow 1.0 2))) (+ (* a b) (+ (* t y) (* 1.0 (* a z)))))))
0.0b	(+ (* t y) (* 1.0 (* a z)))
0.4b	(+ (* a b) (+ (* t y) (* 1.0 (* a z))))
7.6b	(* a (pow z 2))

rewrite468.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`times-frac`
25×	`add-cube-cbrt` `*-un-lft-identity`
19×	`unpow-prod-down`
11×	`add-exp-log` `add-log-exp`
8×	`associate-r` `exp-sum` `add-cbrt-cube`
7×	`associate-/l*` `sqr-pow`
4×	`pow1` `associate-/r*` `sum-log` `unswap-sqr`
3×	`div-exp` `associate-l` `prod-exp`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `flip-+` `unpow2`
1×	`cbrt-undiv` `associate-+r+` `frac-2neg` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 104

Calls

4 calls:

395.0ms	(/ (pow 1.0 a) (exp (+ (* 1/2 (/ (* a (pow z 2)) (pow 1.0 2))) (+ (* a b) (+ (* t y) (* 1.0 (* a z)))))))
10.0ms	(+ (* t y) (* 1.0 (* a z)))
30.0ms	(+ (* a b) (+ (* t y) (* 1.0 (* a z))))
26.0ms	(* a (pow z 2))

series558.0ms

Counts

4 → 12

Calls

4 calls:

391.0ms	(/ (pow 1.0 a) (exp (+ (* 1/2 (/ (* a (pow z 2)) (pow 1.0 2))) (+ (* a b) (+ (* t y) (* 1.0 (* a z)))))))
62.0ms	(+ (* t y) (* 1.0 (* a z)))
67.0ms	(+ (* a b) (+ (* t y) (* 1.0 (* a z))))
38.0ms	(* a (pow z 2))

simplify1.3s

Counts

116 → 116

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	210	3339
1	483	3248
2	1688	3069
done	5000	2876

prune809.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log z) t)
0.0b	(* x (exp (+ (* (- (log z) t) y) (* a (log 1.0)))))
0.0b	(exp (+ (* (- (log z) t) y) (* a (log 1.0))))
0.2b	(* (- (log z) t) y)

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
10×	`pow1` `add-cube-cbrt`
9×	`associate-l`
8×	`add-cbrt-cube` `add-log-exp`
7×	`add-exp-log` `associate-r`
4×	`distribute-lft-out--`
3×	`log-prod` `exp-prod` `associate--l+`
2×	`flip3--` `exp-sum` `pow-prod-down` `associate-l/` `prod-exp` `log-pow` `-commutative` `flip--` `cbrt-unprod` `rem-exp-log` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `diff-log` `sum-log`

Counts

4 → 73

Calls

4 calls:

12.0ms	(- (log z) t)
188.0ms	(* x (exp (+ (* (- (log z) t) y) (* a (log 1.0)))))
84.0ms	(exp (+ (* (- (log z) t) y) (* a (log 1.0))))
48.0ms	(* (- (log z) t) y)

series540.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (log z) t)
216.0ms	(* x (exp (+ (* (- (log z) t) y) (* a (log 1.0)))))
145.0ms	(exp (+ (* (- (log z) t) y) (* a (log 1.0))))
104.0ms	(* (- (log z) t) y)

simplify2.1s

Counts

85 → 85

Iterations

Useful iterations: 3 (831.0ms)

Iter	Nodes	Cost
0	136	1012
1	288	986
2	749	797
3	3010	774
done	5000	774

prune463.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes302.0ms

Accuracy

73% (3.3b remaining)

Error of 3.3b against oracle of 0.0b and baseline of 12.2b

bsearch681.0ms

Steps

Iters	Range		Point
9	7.848534304038427e+105	4.2958803122934513e+111	1.0795444971458526e+106
9	-6422736.341078997	-1.077122854642652	-2.303180600045709

simplify13.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	41	72
1	59	59
done	59	59

end0.0ms

sample14.5s

Algorithm

intervals

Results

7.5s	41350×	body	80	nan
1.7s	12411×	body	80	valid
350.0ms	394×	body	640	valid
149.0ms	407×	body	320	valid
90.0ms	82×	body	1280	valid
70.0ms	282×	body	160	valid